NASASP-135

METEOR ORBITS

AND DUST

THE PROCEEDINGS OF A SYMPOSIUM

SMITHSONIAN

CONTRIBUTIONS

ASTROPHYSICS

Volume 11

Cambridge, Mass.

August 9-13, 1965

Sponsored by

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

SMITHSONIAN INSTITUTION

NASASP-135

SCA VOL II

METEOR ORBITS

AND DUST

THE PROCEEDINGS OF A SYMPOSIUM

Edited by

Gerald S. Hawkins

Smithsonian Astrophysical Observatory

Results of a symposium held August 9-13, 1965, at

Cambridge, Mass., and sponsored by the Smithsonian

Institution and the National Aeronautics and Space

Administration. This Publication is Volume 11 of

Smithsonian Contributions to Astrophysics.

Scientific and Technical Information Division

OFFICE OF TECHNOLOGY UTILIZATION 1967

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Washington, D.C.
Preface

The Proceedings of the Symposium on Meteor Orbit* and Dust is published

simultaneously as a NASA Special Publication (SP-135) and as Volume 11

of the Smithsonian Contributions to Astrophysics. This single publication

thus serves in a dual capacity to satisfy the requirements of both agencies

for the published record of this international meeting.

The NASA Special Publications series, begun in 1962, makes available

information derived from or of value to NASA activities, and includes such

publications as conference proceedings, monographs, data compilations,

handbooks, Bourcebooks, and special bibliographies.

The Smithsonian Contributions to Astrophysics series was inaugurated in

1956 to provide a proper communication for the results of research conducted

at the Astrophysical Observatory of the Smithsonian Institution. Its

purpose is the "increase and diffusion of knowledge" in the field of astrophysics, with particular emphasis on the problems of the sun, the earth, and

the solar system. Its pages are open to a limited number of papers by other

investigators with whom the Observatory has common interests.

Additional information concerning this and other NASA scientific and

technical publications can be obtained from the Scientific and Technical

Information Division, National Aeronautics and Space Administration,

Washington, D.C. 20546. Additional information concerning the publications of the Astrophysical Observatory can be secured from the Publications

Department, Smithsonian Institution Astrophysical Observatory, 60 Garden

Street, Cambridge, Mass. 02138.

Cambridge, Mass. FRED L. WHIPPLE, Director,

Astrophysical Observatory,

Smithsonian Institution

For Sale by the Superintendent of Documents,

U.S. Government Printing Office, Washington, D.C. 20402

Price $2.50 (paper cover)

LUrmy ef Congress CataUg Card Ntombtr 67-40003
Contents

Session 1 P^,,

1. Selected results from precision-reduced Super-Schmidt meteors 1

L. G. Jacchia, F. Verniani, and R. E. Briggs

2. Relation of meteor orbits to the orbits of comets and asteroids 9

L. Kresak

3. Classification of meteor orbits Z. Ceplecha 35

4. Comments on CepUcha's paper "Classification of meteor orbits" 61

F. Verniani

Abstract of Ceplecha's reply to Verniani's comments 64

Further comments by F. Verniani 65

5. Orbits of bright photographic meteors 67

P. B. Babadzhanov and E. N. Kramer

6. Inferences from photographic meteors C. C. Dal ton 81

7. Equipment for the observations of meteor trails J. Delcourt 91

8. Meteor photography with an image orthicon system 95

G. T. Hicks, G. G. Barton, Jr., and W. J. Dambeck

9. Some characteristics of the major meteor showers P. M. Millman 105

10. Research on orbits of minor meteor streams A. K. Terentjeva 109

11. On two problems of sporadic meteor activity J. Stohl 115

12. Remark on a cosmic-probe investigation of meteor showers with 119

retrograde motion V. Guth

Session 2

13. Incidence of meteors on the earth derived from radio observations 121

W. G. Elford

14. Radar observations of meteor deceleration J. V. Evans 133

15. Radar meteor echoes P. M. Millman 151

16. Structure of the major Northern-Hemisphere meteor streams 157

L. M. G. Poole

17. Luminosity function of sporadic meteors and extrapolation of the

influx rate to the micrometeorUe region B.-A. Lindblad 171

18. Duration distribution of radio echoes obtained from underdense

shower meteor trains L. M. G. Poole 181

19. Radar studies of meteors 183

B. L. Kashcheyev and V. N. Lebedinets

20. Further data concerning the 1963 anomalous increase in radar

meteor rates B. A. Mclntosh 201

m
I V CONTENTS

Session 3 P«**

21. Zodiacal light as an indicator of the nature of the interplanetary

matter—past, present, and prospective results J. L. Weinberg 203

22. Conditions of encounter between dust and the planets 213

C. W. McCracken

23. The brightness of the zodiacal light at the ecliptic pole 225

F. E. Roach

24. Interplanetary dust-particle flux measurements between 1.0 and 227

1.56 a. u.from Mariner 4 cosmic-dust experiment (asbstract)

W. M. Alexander, O. E. Berg, C. W. McCracken, L. Secretan,

and J. L. Boon

25. A new solar-terrestrial effect C. Hoffmeister 229

Session 4

26. Rocket and satellite studies of meteoric dust T. N. Nazarova 231

27. Recent NASA meteoroid penetration results from satellites 239

C. T. D'Aiutolo, W. H. Kinard, and R. J. Naumann

28. Some penetration and charge-detection techniques 253

R. C. Jennison

29. Direct measurements of the mass distribution and time variations 259

in the flux of small dust particles

C. W. McCracken, W. M. Alexander, and M. Dubin

30. Physical parameters of cosmic dust obtained from rocket collections 271

O. E. Berg and L. Secretan

31. Electron diffraction control studies of Venus Flytrap particles 285

N. N. Greenman and C. B. Gilpin

32. Aerosol samples obtained from 9- to 12-km altitude 293

C. E. Melton

33. Measured velocities of interplanetary dust particles from OOO-l 301

C. S. Nilsson and W. M. Alexander

34. Measurements of interplanetary dust-particle flux from Explorer 307

16 CdS and wire grid dust-particle detectors L. Secretan

35. Dust dynamics in the magnetosphere and interplanetary space 317

S. F. Singer

36. Extraterrestrial dust concentrations in the upper atmosphere 323

R. K. Soberman

37. Photographs of particles from an Aerobee rocket at 130- to 204-km 333

altitude

R. Tousey, M. J. Koomen, R. E. McCullough, and R. T. Seal

Session 5

38. Vertical distribution of dust in the stratosphere 345

J. M. Rosen and E. P. Ney

39. Meteoric dust in the stratosphere determined by optical scattering 349

techniques G. Newkirk, Jr.

40. Dynamics of orbiting dust particles (abstract) 359

I. I. Shapiro, D. A. Lautman, and G. Colombo

41. Concentration of magnetic dust in the stratosphere T. Grjebine 361
CONTENTS

Session 5—Continued Page

42. Role oj meteoric dust in the lower ionosphere (abstract) 365

R. Parthasarathy and D. B. Rai

43. Injrared optical characteristics oj ice spheres W. M. Irvine 367

Session 6

44. Evidence jor extraterrestrial particles in polar ice 373

E. L. Fireman

45. On chemical compositions oj interiors oj possibly cosmic 381

particles and the problem oj origin oj naturally occurring ironrich spherules P. W. Hodge and F. W. Wright

46. Recovery of magnetic spherules jrom sedimentary rocks 389

T. A. Mutch and J. T. Parr

47. Fusion crust oj iron meteorites and mesosiderites and produc- 391

tion of cosmic spherules A. El Goresy and H. Fechtig

48. Some studies oj separated jractions of low accumulation-rate dust 399

D. Tilles

PROCEEDINGS OF THE SYMPOSIUM

ON

METEOR ORBITS AND DUST

Selected Results from Precision-Reduced

Super-Schmidt Meteors

L. G. JACCHIA,1 F. VERNIANI,2 and R. E. BRIGGS3

Introduction

We recently completed a general analysis of

the atmospheric trajectories of 413 precisely

reduced Super-Schmidt photographic meteors

(Jacchia, Verniani, and Briggs, 1965). We

studied the dependence of heights, lengths,

decelerations, and magnitudes on such basic

parameters as velocity, angle of incidence, and

mass, as well as on derived parameters such as

the ablation coefficient and the fragmentation

index; the latter were in turn related to the

other geometrical and physical characteristics,

including the phenomena of wake and terminal

blending. The results of the analysis are

mainly concerned with physical characteristics

of meteors; in this paper we shall limit ourselves

to only a few points related to problems of

orbits and distribution, namely, physical differences dependent on the type of orbit, peculiarities of individual showers, and the mass

scale for photographic meteors.

Systematic differences between groups of

meteors

Systematic differences in some physical characteristics between meteors in short-period

and long-period orbits were first pointed out

by Jacchia (1958, 1963). He found that the

beginning heights of meteors with aphelion

distances greater than 7 a.u. were higher than

the corresponding heights of meteors with

aphelion distances smaller than 7 a.u. All

meteors were, of course, reduced to the same

brightness.

• Smithsonian Astrophysical Observatory and Harvard College Observatory, Cambridge, Massachusetts.

'Smithsonian Astrophysical Observatory and Harvard College Observatory; on leave from Centra Nationals per la Fisica dell'Atmosfera

c la Meteorologia del C.N.R., Rome, Italy.

* Smithsonian Astrophysical Observatory, Cambridge, Massachusetts.

The present general analysis has confirmed

the effect found by Jacchia: meteors with

aphelion distance smaller than 6 a.u. appear

1.8 km lower than meteors in long-period orbits,

reduced to the same velocity, mass, and zenith

angle. The maximum light and end heights

are correspondingly lower (fig. 1). This effect

is related to the different densities that we find

for the two groups: on the average, meteors in

short-period orbits appear to be about 1.4

times as dense as meteors in long-period orbits.

In addition, for short-period meteors, the

density increases as the aphelion distance

decreases (fig. 2). These systematic differences

-100

- TO

FIGURE I.—Heights of the standard meteor when the mass

is varied. Means for mass groups; all Super-Schmidt

meteors, divided into two groups according to aphelion

distance Q\ HB = beginning height; HML = height of maximum light; Hg = end height; p = atmospheric density (according to the U.S. Standard Atmosphere, 1962); a.u. = astronomical unit. The standard meteor has a velocity of 30

km/sec, a zenith angle ZR such that log cos ZR = —0. 2, log

<r= —11.20, and x=0 . 25. The ablation coefficient and

the fragmentation index are a and x, respectively.

1
SYMPOSIUM ON METEOR ORBITS AND DUST

0.0

"-0.I5 -

2 3 4 5

• £*

. w

. \

6 7

Q (ou)

IO 100

Qlau.)

4-

8 9

b •

-

10 II i

ooo

•

2

/ "

If' •

n • •

JM,J

T h

|~t1—t

 (j—-j—,j

t-

«r ftX

of i r

«• M

• i

* * *

f r

i

FIGURE 2.—The quantity log p.,—log pm as a function of the

aphelion distance Q, in natural values (top) and logarithms

(bottom); pM = meteor density in g/cm*; log p . mean

logarithmic value of the density of all meteors.

in density could be ascribed to the different

conditions in which the meteoroids were formed

and to different resistance to destroying agents.

Most of the meteors in short orbits may have

originated in short-period comets that by now

are completely evaporated; those that came

from the inner core of Whipple's icy conglomerate should be denser because of the greater

pressure to which they were subjected. Meteoroids with a loose structure are probably

destroyed faster by collisions, erosion, and

thermal effects.

Peculiarities of individual showers

Table 1 and figure 3 give a synoptic survey of

the physical characteristics of those of our

Super-Schmidt meteors that belong to major

showers. The exceptional character of the

Draconids shows up in all diagrams. The

Geminids are 4 times as dense as the average

meteor, i.e., about 1 g/cm3, but they crumble

just as easily as any ordinary meteor. They

have, in fact, a normal fragmentation index and

normal blending; moreover, their heights are

close to the average. The S Aquarids are

crumbly and have large fragmentation and

blending indices; they appear 3 km lower than

the average meteor with the same velocity and

mass. The Southern Taurids have great tensile strength, as is shown by their fragmentation index equal to about zero and by the

FIGURE 3.—Physical characteristics of individual meteor

showers arranged in order of increasing velocity. A'// M

is the deviation of the height //,.j from the mean curve

corresponding to sporadic meteors taking into account the

aphelion distance Q. The height //.••, is the height of the

point where the absolute photographic magnitude of the

brightening meteor reaches the value+ 2. 5; pm = meteor

density in g/cm1. The other parameters in the graphs are

the logarithm of the ablation coefficient a. the fragmentation index x. >nd the blending index Ii. The standard

deviations of the mean value of B for Southern Taurids

(18 meteors) and a Hydrids (3 meteors) are equal to zero.

absence of terminal blending. Rather surprisingly, they are not denser than the average.

Mass scale for photographic meteors

MAGNITUDES AND MASSES.—The statistical analysis of the photographic magnitudes of our

Super-Schmidt meteors has yielded the following relationship between magnitude, velocity,

mass, and zenith angle of meteors in cgs units:

Mpm=55.34-8.75 log p.-2.25 log m.

— 1.5 log cos ZR.

We have adopted the luminous efficiency derived by Verniani (1964), r,= 1.0 X 10~"P, where

the velocity v is expressed in cm/sec and the

intensity is expressed in zero magnitude units.

From our results, the color index of a zero magnitude meteor is — 1T86. Therefore the initial

mass of a zero visual magnitude meteor with a

velocity of 40 km/sec and a zenith angle of 50°

is 0.76 g. This mass depends strongly on velocity and on zenith angle, as is shown in table 2.

FRAGMENTATION.—It has often been repeated

in meteor literature that the abrupt increase in
PRECISION-REDUCED SUPER-SCHMIDT METEOR RESULTS—JACCHIA ET AL.

brightness occurring in some photographic meteors—the so-called abrupt-beginning meteors—

occurs at a point in the trajectory corresponding

to a constant value of pol, where p is the

atmospheric density. The point of abrupt

beginning clearly marks the breakup of the

meteor body. We used our material to see

whether or not we could confirm such results.

Our Super-Schmidt material includes 26 meteors with an abrupt beginning, or about 6 percent of the total number. McCrosky (1955)

estimates that 13 percent of all Super-Schmidt

meteors belong to this category; the smaller

percentage in our material is probably due

partly to selection (many of the abrupt-beginning meteors are of too short duration to yield

a good deceleration, which was the primary

goal of our selection) and partly to a more

stringent rule for classification. Even among

our 26 meteors some have a less abrupt beginning than others; for 12 of them the rise is

almost instantaneous.

If we take the atmospheric density pAB corresponding to the abrupt beginning of all 26

meteors and put PABVL — const, we find by

least squares that l£=3.6±0.3. Using only

the 12 ultra-abrupt meteors, we obtain K=

3.0 ±0.5. Taking the density pB corresponding

to the beginning heights of all Super-Schmidt

meteors and putting pBv1 = const, we find

K=S.0±0.1.

We see then that fragile meteors tend to

break up at a point corresponding to a constant

value of pva rather than of pel, and that the

power of Po, is not too different from that found

from the beginning points of ordinary meteors.

Abrupt meteors do, however, begin 4 km lower,

on the average, than ordinary meteors, probably because, were it not for the breakup, we

would not have photographed them.

The pvl= const relation would suggest heat

transfer rather than pressure as the trigger for

the breakup of meteors. This could be the

case if we have to deal with a body so porous

that air molecules will penetrate deep inside to

do their heating and melting, thus destroying

the precarious cohesion of the body as a wholeIn larger meteors the penetration of air molecules will be relatively smaller because of the

shielding by the outer layers; this could explain

why no meteors with abrupt beginnings are

found among small-camera meteors. This

process of flaking-off of large meteors and complete breakup of small meteors was already

described by Jacchia (1955) in his first paper on

fragmentation.

Cometary and asteroidal meteors

Since several major showers are associated

with comets and since the heights, decelerations, and other physical characteristics of

shower meteors, taken in their totality, do not

differ from those of most sporadic meteors, we

must conclude that the overwhelming majority

of the photographic meteors are of cometary

origin. A search for meteors of asteroidal

origin has led to the conclusion that only 1 of

our 413 meteors has all the requisites to qualify

as an asteroidal meteor, in spite of the fact that

the criteria employed for the selection of our

meteors favor long, bright meteors. Individual

meteor densities computed from decelerations

generally have little meaning because of the

scatter introduced by diversity in shape and

fragmentation, by atmospheric variations, and

by intrinsic deceleration errors. It is noteworthy, however, that 82 percent of the computed densities fall within a factor of 4 of the

mean density—which, according to our calculations, is 0.26 g/cm3—and that for only 14

meteors the computed density is larger than 2

g/cm3. Even these 14, however, with the exception of the one mentioned above, are normal

in other respects, such as heights and fragmentation, or have dubious decelerations or belong

to cometary showers. The lone candidate for

membership in the asteroidal group yields a

density of 4 or 5 g/cm3. While the objections

to individual densities stand, we think this

value is more reliable than the average in view

of the exceptionally long trajectory of the

meteor and the consistency of the decelerations.

The common occurrence of fragmentation,

the behavior of abrupt-beginning meteors, the

low density of nearly all meteors, and, in addition, the fact that most meteors are associated

in streams and associations further confirm

Whipple's theory of comets and of meteor origin.
TABLK 1.—Physical characteristics of individual meteor showers

Showers

(km/sec)

cos ZK M, (km) (km) IIUL (km) (km) D(sec) « 0 0

AH meteors

Sporadic meteorsShower meteors

Abrupt-beginning

meteors

Short, flare-like

meteors

Individual Showers:

Quadrant idsVirgin ids

Lyrids

i; Aquarids

S Aquarids

a Capricorn idsSouthern i Aquarids

Northern t Aquarids

Perse ids

K Cygnids

Draconids

Or ion ids

Southern Taurids

Northern TauridsLeonids

a HydridsGeminids

35. 3±0. 833. 7±1. 0

39. 3±1 . 228. 8±3. 1

36. 8±4. 2

43. l±0. 230. 8±3. 7

48. 8±1. 1

66.8

42. 5±0. 3

25. 6±0. 4

34. 4±1. 0

35. 9±1. 7

60. 2±0. 2

23. 2±0. 4

20. 2±0. 1

68. 0±0. 4

29. 9±0. 4

31. l±0. 5

71.7

59. 2±0. 6

36. 2±0. 1

0.67 ±0.010.66 ±0.010.69 ±0.02

0. 67 ±0. 040. 78±O. 04

0.61 ±0.050. 73 ±0. 02

0. 93 ±0.05

0.42

0. 58 ±0. 03

0.69 ±0.030. 54±0. 04

0. 70 ±0. 080. 52 ±0. 08

0. 68 ±0. 13

0. 61 ±0. 060. 60 ±0. 08

0.73 ±0.03

0.84 ±0.07

0.89

0.84 ±0.02

0. 86±0. 04

+ 0. 0±0. 1

+ 0. l±0. 1

- 0 . 2±0. 1

- 0 . l±0. 2

- 0 . 8±0. 2

+ 0. 2±0. 3- 0 . 2±0. 3

- 1 . 0±0. 3

-0. 7

- 0 . l±0. 3

4-0. 7±0.2

+ 0. 5±0. 4

+ 0. 6±0. 9

- 1 . 4±0. 4+ 0. 8±0. 3

+ 0. l±0. 0

- 1 . l±0. 3

+ 0. 5±0. 3

- 0 . 8±0. 5

-3. 3

- 0 . 7±0. 1

- 0 . 8±0. 3

100. 0±0. 4

98. 8±0. 6

102. 9 ±0.6

92. 5±2. 1

94.3±2. 7

102. 8 ±0.7

96. 0±5. 4

107. l±0. 9

115. 6

99. 8±1. 197. 8±0. 8

96.3±1. 999. 1 ± 1. 5

114. 1±1. 1

99. 2±0. 8

103. 6 ±0.2117. 0±<X5

100. 8±0.5103. 3± 1.0

127.8

111. 7±0. 3

100. 4±0. 3

99. 6±0.59&2±0. 6

103. 0±0. 7

92. 4±2. 3

94 4±2. 8

103. 1±(X7

96. 0±3. 4

107. 9±0.7

119. 6

99. 8±1. 2

96. 9±0. 8

95.7±1. 79&8±1. 4

U4.8±l. 1

97. 1 ± 1. 1

102. 6±0.2119. 6± 1.0

99. 6±0. 6

103. 0±l. 2

125.9

113. 6 ±1.6

101. 3±0. 5

89. 8±0. 489. l±0. 591. 5±0. 7

87. 6± 1. 7

89. 7±2.0

95. 7 ± 1. 5

83.7±0-897. 3±2. 6

102. 1

93.0±0.7

89. 6±1. 1

90.2±l. 189. 9±3. 999. 0± 1. 58R 9±2. 3

96-7±0.4

105. 9± 1.7

87. 9±0. 9

83.2±1. 3

89. 1

92. 9±0. 4

» : . «; • l :.

85. 1 ±0.484.5±0. 5

86. 5±0. 781. 5±1. 4

85.2±1. 9

90. 6±1. 677. 7±1. 187. 6±2. 5

99.7

88.4±0. 886.0±l. 3

86. 5±1. 1

84.7±4 1

94. 3±1. 8

85.5±2. 0

91. 0±0. 49ft3±l. 7

82. 2±0. 9

79. 5±1. 4

87.2

88. 8±1. 8

80. Oil. 8

0. 76 ±0.02

0.80 ±0.03

0.67 ±0.030. 62±0. 04

0. 32 ± 0. 02

0.48 ±0.03

0.89 ±0.420. 43 ±0. 07

0. 58

0. 49±0. 06

0.70 ±0.08

0. 58±0. 120. 57±0. 020. 67 ±0. 10

0. 94±0. 08

1. 22 ±0. 12

0.47 ±0.05

0.91 ±0.05

0. 97 ±0. 16

0.64

0. 46±0. 02

0. 64±0. 04

-0.42 ±0.02 *- 0 . 44±0. 03 S- 0 . 36±0. 05 |

o

- 0 . 50±0. 07 W

O

-0. 52±0. 10 I

-0. 58±0. 09 >

-0.31 ±0.31 a

-0. 18±0. 14 o

- 0 . 20 g

-0. 59±0. 11 H-0. 67±0. 12

-0. 73±0. 12-0. 63±0. 24

+ 0. 16±0. 20

-0. 65±0. 05

-0. 29±0. 03-0. 14±0. 10

-0. 45±0. 10

+ 0. 00±0. 22

+ 0.72

-0. 29±0. 08

-0. 18 ±0. 13
All meteors

Sporadic meteors

Shower meteors

Abrupt-be ginning

meteors

Short, flare-like

meteors

Individual Showers:

Quadrant ids

Virginids

Lyrids

tj Aquarids5 Aquarids

a Capricornids

Southern t AquaridsNorthern i AquaridsPerse ids

K Cygnids

Draconids

Orion ids

Southern Taurids

Northern TauridsLeonids

a HydridsGeminids

(g)

0. 80±0. 11

0. 96 ±0. 16

0. 42 ±0.070. 65 ±0. 12

0.32 ±0.090. 08 ±0. 02

0. 59 ±0.47

0. 13 ±0. 04

0.04

0. 09 ±0. 03

0. 53 ±0. 24

0. ll±0. 020. 11 ±0. 04

0. 27 ±0. 13

0.39 ±0.06

2. 00±0. 13

0.06 ±0.02

0. 48 ±0. 13

1. 01 ±0. 32

0.29

0.05 ±0.01

0. 76 ±0. 28

log a

(cm-1 sec1)

-11 . 19±0. 01

-11 . 16±0. 01

-11 . 25±0. 02

-11 . 04±0. 06

-11 . 18±0. 12

-11 . 48±0. 09-11 . 19±0. 06

-11 . 17±0. 17

-11.01

-11 . 40±0. 05

-11 . 09±0. 08-11 . 27±0. 12-11 . 48±0. 25

-11 . 26±0. 06

-11 . 07±0. 08

[-14. 88 ±0.79]

-11 . 20±0. 11

-11 . 31 ±0.03-11 . 36±0. 06

-10. 99

-11 . 46±0. 06-11 . 23±0. 07

X

0.27 ±0.01

0. 27 ± 0. 02

0. 27 ± 0. 03

0. 25 ±0. 05

0.27 ±0.06

0. 44±0. 110. 15 ±0.03

0.08 ±0.09

0. 09

0. 52 ±0.08

0.38 ±0.07

0. 18 ±0. 09

0. 10 ±0.26

0. 28 ±0. 10

0. 11 ±0.09

1.89 ±0.57

0. 46 ±0. 06

0.04 ±0.05

0.03 ±0.07

0.37

0.04 ±0.040.21 ±0.05

A lOg Pcrr

(g/cm»)

0. 00±0. 010. 00±0. 02

0. 00±0. 02

- 0 . 18±0. 08

0. 15±0. 120. 03 ±0.08

- 0 . 36±0. 12

- 0 . 10±0. 09

-0.21

0.03 ±0.04

0. 15 ±0.03

- 0 . 05±0. 06

- 0 . 24±0. 28

- 0 . 03±0. 05

0. 15±0. 06

4. 61 ±0.85

0. 14 ±0.08

- 0 . 00±0. 03- 0 . 06±0. 07

-0.23

- 0 . 10±0. 12

- 0 . 39±0. 06

W

0.74 ±0.050. 77±O. 06

0. 67±0. 08

0. 59 ±0. 13

0.83 ±0.30

0. 40 ±0. 19

1. 15±1. 15

0. 43 ±0. 30

0.0

0. 21 ±0. 12

0.74 ±0.270.33 ±0.210. 50 ±0. 50

0.96 ±0.35

1. 00±0. 20

0. 00±0. 00

0.34 ±0.25

0. 14 ±0.08

0.72 ±0.43

4.0

0. 33 ±0. 33

1.48 ±0.26

B

0.51 ±0.05

0.47 ±0.050. 63±0. 08

1.35 ±0.24

0.57 ±0.23

0. 80±0. 11

0.25 ±0.25

0. 50±0. 50

0.0

1.55 ±0.27

1. 00±0. 34

0.83 ±0.540. 50±0. 500.03 ±0.030. 50 ±0. 50

4. 00±0. 00

0. 41 ±0. 19

0. 00±0. 000. 06±0. 06

0.0

0. 00±0. 000. 47 ±0. 17

D/Dth

0. 61 ±0. 01

0. 60±0. 01

0.65 ±0.02

0. 45 ±0. 03

0. 35±0. 040. 61 ±0. 03

0. 67 ±0. 17

0. 64±0. 11

0.63

0. 50 ±0.05

0. 58 ±0. 04

0. 53 ±0. 10

0. 63 ±0. 04

0. 56 ±0. 04

0. 69 ±0. 03

0. 50 ±0.02

0.55 ±0.04

0. 84 ±0.02

0. 77 ±0.05

0.44

0. 87 ±0. 10

0. 69 ±0. 03

A'tf,.,

(km)

+ 0. 3±0. 5

0. 0±0. 6

+ 1. 0±0. 7

- 5 . 1±2. 3

- 7 . 0±2. 8

+ 0. 3±0. 7

- 3 . 0±3. 4

- 0 . 7±0. 7

+ 5.3

- 3 . 1±1. 2

+ 2. 4±0. 8

- 3 . 2±1. 7

-1.2±1.4+ 0. 8±1. 1

+ 4. 1±1. 1

+ 9. 5±0. 2

+ 4. 8±1. 0

+2. 2±0. 6

+ 2. 7±1. 2

+ 5.7

+ 2. 1±1. 6

-0. 5±0. 5

No. obs.

413

290

123

26

12

10

2

3

1

1114

6

2

11

42

8

18

5

1

3

20
6 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 2.—The mass {in g) of a zero visual magnitude meteoroid as a function of velocity \\. and zenith angle ZK

To, (km/sec)

zR

0°

30°

45°

60°

75°

85°

10

120

132

151

191

269

617

20

8. 13

8.91

10.2

12.9

18.2

41.7

30

1.66

1.82

2.09

2.63

3.72

8.51

40

0.55

0.63

0.69

0.87

1.23

2.82

50

0.23

0.25

0.29

0.36

0.51

1. 17

60

0. 11

0.12

0. 14

0. 18

0.25

0.58

70

0.062

0.068

0.078

0.098

0.14

0.32

References

JACCHIA, L. G.

1955. The physical theory of meteors, VIII:

Fragmentation as a cause of the faintmeteor anomaly. Astrophys. Journ.,

vol. 121, pp. 521-527.

1958. On two parameters used in the physical

theory of meteors. Smithsonian Contr.

Astrophys., vol. 2, no. 9, pp. 181-187.

1963. Meteors, meteorites and comets; interrelations. In The Solar SyBtem, vol. IV,

ed. by B. M. Middle -hurst and G. P.

Kuiper, Univ. of Chicago Press, pp.

774-798.

JACCHIA, L. G.; VERNIANI, F.; and BRIGGS, R. E.

1965. An analysis of the atmospheric trajectories

of 413 precisely reduced photographic

meteors. Smithsonian Astrophys. Obs.

Spec. Rep. No. 175, 309 pp.; also SrnithBonian Contr. Astrophys., vol. 10, no. 1,

139 pp., 1967.

MCCBOSKY, R. E.

1955. Some physical and statistical studies of

meteor fragmentation. Ph.D. thesis,

Harvard University, Cambridge, Mass.

U.S. STANDARD ATMOSPHERE

1962. U.S. Standard Atmosphere 1962. Prepared under NASA, USAF, and USWB,

Washington, D.C., 278 pp.

VERNIANI, F.

1964. On the luminous efficiency of meteors.

Smithsonian Astrophys. Obs. Spec. Rep.

No. 145, 62 pp.; also Smithsonian Contr.

Astrophys., vol. 8, no. 5, pp. 141-172.

Abstract

The authors have recently completed a general analysis of the atmospheric trajectories of 413 precisely reduced

Super-Schmidt photographic meteors; the results obtained mainly concern physical characteristics of meteors. This

paper mentions only a few of the results as they relate to the subject of the Symposium, namely, physical differences

dependent on the type of orbit, peculiarities of individual showers, and the mass scale for photographic meteors.

Meteors with abrupt beginnings appear at a height where the atmospheric density p is such that pv* is a constant

(v=meteor velocity); this result suggests that heating rather than aerodynamic pressure is the trigger mechanism

in the breakup of such objects.

Explanation of table 1 symbols

va apparent velocity, corrected for atmospheric drag

ZR zenith distance of apparent radiant

Mvm photographic absolute magnitude reached

by meteor at maximum light

HB height corresponding to beginning of

photographic trajectory

//,.5 height of point where absolute photographic

magnitude of brightening meteor reached

the value +2. 5

HUL height of point where meteor reached its

maximum absolute brightness

HM height corresponding to end of photographic

trajectory

I) duration of photographic trail from HB

to HK

Cc a measure of integrated brightness of

meteor, defined by

+

where 7 P is absolute photographic brightness

of the meteor expressed in zero-magnitude

units

photometric mass of meteor, computed

using Verniani's (1964) luminous efficiency

ablation coefficient, defined by

dmjdv
PRECISION-REDUCED 8UPER-SCHMIDT METEOR RE8ULTI5—JACCHIA ET AL.

progressive fragmentation index, defined by

d , b

x=T,lo&VT'

where v is the observed deceleration, vT is

the theoretical deceleration, and

bi —log p.t —x«i where pOb. is the

atmospheric density deduced from the observed deceleration, and p.t

 is the density

tabulated in the U.S. Standard Atmosphere

W, B

D/Dtlk

(1962); 8 was defined in the explanation

of x; A log Peorr is also equal to %

(log p,—log pm)y where pm is the meteor

density and log pm is the mean logarithmic

value of the density of all meteors

wake and blending, respectively, expressed

in an arbitrary scale from 0 to 4 (0=no

wake or blending, 4=maximum)

ratio between observed and theoretical

duration

difference between thje average HJ.J of a

group of meteors and the overall mean of

No. obs. number of observations used

Relation of Meteor Orbits to the Orbits of

Comets and Asteroids

w

L. KRESAK1

Introduction

In the solar system, comets and asteroids are

two potential sources of meteoroids. It has

been demonstrated that both comets and asteroids are able to supply new meteor particles

necessary to replace those being constantly

removed by planetary perturbations, collisions

with the planets, and interplanetary erosion

and spiraling into the sun under the action of

drag effects (Fesenkov, 1942; Whipple, 1951;

Piotrowski, 1954). No dependable quantitative information is available, however, either

on the efficiency of the two sources or on the

potential lifetimes of individual meteoric particles in circumsolar orbits.

With regard to a number of known cometmeteor shower associations and to the abundance of meteor orbits with both high inclinations and eccentricities, the cometary origin of

a large proportion of meteors is beyond any

shadow of doubt. On the other hand, there

are very few, if any, convincing cases of

asteroidal origin. Hence the fundamental

question is not whether the source is cometary

or asteroidal, but rather whether, and in what

proportion, asteroidal meteors are present at

all. According to Jacchia, Verniani, and Briggs

(1965), only 1 of 413 precision-reduced SuperSchmidt meteors was of asteroidal nature.

Conceivably, the mass distributions of cometary and asteroidal meteoroids need not be

the same, and a different proportional representation of the two components may be

expected to appear at different levels of brightness. Curiously enough, Hawkins (1959) finds

' Astronomical Institute of the Slovak Academy of Sciences, Bratislava,

Czechoslovakia.

240-022 O—67 2

an increasing proportion of asteroidal meteors

toward brighter objects, whereas Kresak (1964)

suggests the same for fainter objects.

Insofar as there is no reliable device for

discriminating between asteroidal and cometary

meteors from their behavior during their interaction with the earth's atmosphere (the range

of variability for shower meteors of cometary

origin is even wider than that for sporadic

meteors in general), the orbital characteristics

appear to be the most suitable data for attempting to solve the problem. Unfortunately, the

restriction of observations to the particles

crossing the earth's orbit requires an extrapolation of the systems of cometary and

asteroidal orbits rather than a direct comparison

between them. Our statistics of these orbits

are strongly, and in different ways, biased by

the discovery conditions; also, when dealing

with particles of meteoric size we must take

into account the operation of nongravitational

effects, which are practically negligible for their

parent bodies, and the efficiency of which depends on a number of factors difficult to

evaluate.

The main purpose of this paper is to represent

the virtual distribution of the orbits of comets,

asteroids, and meteors in a common diagram

where, analogous to the Hertzsprung-Russell

diagram, the main features of each distribution

could be fixed and the evolutionary paths indicated. A two-dimensional diagram requires

the choice of two characteristic elements out of

the six defining a Keplerian orbit. Among

these, the time of perihelion passage is obviously,

of no interest for our problem. The longitude

of the node, although able to reveal some rela9
10 SYMPOSIUM ON METEOR ORBITS AND DUST

tion of evolutionary significance to Jupiter's

orbit, can also be omitted. Incidentally, this

is the only element that can be simply determined for individual meteors with high precision and that permits separate studies in terms

of diurnal and annual variations of meteor rates.

The argument of perihelion for meteors encountering the earth is bound to the semimajor

axis and eccentricity by a strict condition.

Neglecting the eccentricity of the earth's orbit,

we have

broken heavy line delimits, to the right, the

region in which the boundary condition of

crossing the earth's orbit,

cos «= - (a—ae?— 1), (1)

and we may discard one of these three elements

without any ambiguity as far as meteor orbits

are concerned. Thus it appears most reasonable to use a set of diagrams in which the semimajor axis is plotted against eccentricity, each

diagram for a specific range of inclination. The

position of every object in this diagram determines the size and shape of its orbit. The

diagrams for higher inclinations will obviously

include only orbits essentially different, by

orientation, from those of asteroids and shortperiodic comets of Jupiter's family.

The representation of the fundamental observational data by the afe diagram—irrespective of inclinations and inherent effects of

selection—is shown in figure 1. In the system

of asteroids (black dots) the fine structure of

commensurability gaps is clearly visible, as well

as the clustering of the Trojans and the Hilda

group. All 1649 asteroids numbered up to the

end of 1963 are indicated; in addition, six unnumbered asteroids of the Apollo group (Apollo,

Adonis, Hermes, 1948EA, 1948OA, and 1950-

DA), for which orbital elements of lower

accuracy are available, are included. All 77

known periodic comets with periods not exceeding 20 years are indicated by open circles,

only two cases of very inaccurate elements,

P/Wilson-Harrington and P/Perrine, being

omitted. The short-dashed ovals indicate the

areas occupied by the members of five major

short-periodic meteor showers (the Quadrantids,

Northern and Southern Taurids, Geminids, and

5 Aquarids); other showers, for which no dependable data on the dispersion of elements

are available, are denoted by crosses. The

is satisfied. Obviously, meteors observed from

the earth's surface can fall only within this area,

with some small overlapping due to the eccentricity of the earth's orbit.

The diagram may be supplemented by the

scales of other significant quantities that are

functions of a and e alone, either in general

(period of revolution, mean daily motion,

eccentricity angle, perihelion distance, aphelion

distance) or for the particular case of bodies

colliding with the earth (heliocentric velocity,

argument of perihelion). The loci of equal

perihelion distance </, aphelion distance Q, and

argument of perihelion w are plotted in figures

2a, 2b, and 2c, respectively. Other quantities,

depending on a, e, and i (such as the geocentric

and no-atmosphere velocity or Whipple's "cosmic weight"), may be similarly indicated in

the a/e diagrams designed for the proper

values of inclination.

The apparent distribution of orbits shown

in figure 1 is strongly biased by the discovery

conditions. For periods of observation long

compared with the periods of revolution

(<20 years in fig. 1), the due correction factors

may be visualized, too, as functions of the

position within the diagram. The form of these

functions is, obviously, different for different

kinds of objects, and a discrimination according

to the inclination is again necessary.

Empirical comet-asteroid criteria

In order to provide a sharp conventional distinction between the cometary and asteroidal

meteor orbits, Whipple (1954) introduced the

K criterion,

1^0, (3)

and demonstrated that K is positive for 96

percent of known comet orbits, and negative

for all but 3 asteroid orbits. Since K is a

function of a and e alone, the borderline K=0

may be indicated in the ale diagram; this is

done in figure 1 by the thinner full curve.

It is evident that, unless there is physical
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 11

&0

70

6 5

SO

5 5

5 0

*i

to

J 5

J O

25

24

15

to

OS

nn

-

-

• *

-

•

' t

*

'•''•r* * '

• ir ^J

-

-

Of 0 ?

\

I \

° \

\

\

\

i

\

t•. * •*

* *

'-^kTtSi ••*'

__

—

V

\

\

\

\

\

\

\

\

\

\

\

\

\

\

\

. • .

"•• •• * *j

5

03 O-*

\

\

\

\

\

\

\

\

\

\

\

> \

\ . \

\

 N

\ o no

\o o

\

.-, . .

*. "* •

—

o

\ °

oo.

o

. °

\

•

•

0 5

O

O

8

\ °

\

\

.

—

0-6

0

O

O

o o

0

° o

o°° ^°°

O o

\ °\

\o o

'

o

o

0

o

0

o

o

o

Jffl

\

•

07

0

o

o

/

o /

7/ °

/

$ °

fi O o

+

\

\

\

as 09

o 1

/

/

1

/

° / +

/

/

/

/

/

/

/

o I

/

/

/

/

/ °

o

o 1

4- j

°+ I

/'"-., i

( /

_ \

\

K

-

-.

;

•

•

—

\

FIGURE 1.—Position of different objects in the a/e diagram. Astronomical symbols= major planets; dots= asteroids; open circles1

comets; short-dashed ovals= dispersion of major meteor streams; crosses=mean orbits of other meteor streams; heavy line=

boundary condition for crossing the earth's orbit; thinner Iine= Whipple's K criterion; dashed line = Pe criterion.
12 SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 2.—a, Perihelion distances (heavy line= boundary condition for crossing the earth's orbit; dashed lines= perihelia at the

distance of Jupiter's perihelion and aphelion, respectively); b, aphelion distances (dashed lines=aphelia at the distance of

Jupiter's perihelion and aphelion, respectively); c, argument of perihelion for the orbits intersecting the orbit of the earth;

d, Tisserand's invariant 7*0 for Jupiter, i=0 (dashed lines= boundary conditions for crossing Jupiter's orbit at its perihelion

and aphelion, respectively).
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 13

reasoning for formula (3) (which is not the

case), a number of other functions of a and e

may be chosen to suit the same purpose.

The measure of suitability is the minimalization

of the number of exceptions not obeying the

criterion, and the simplicity of the function.

Probably the best criterion from this point of

view is

Pe=a3/2e^2.5. (4)

In fact, there are 13 comets moving in asteroidal orbits according to (3) but only 1 according to (4); and 3 asteroids moving in cometary

orbits according to (3) but only 1 according to

(4). The fit is improved against the K criterion

from 99.8 to 99.9 percent for the asteroids and

from 97.8 to 99.8 percent for the comets.

Also the a/e diagram (fig. 1), where the Pe

criterion is indicated by the dashed curve,

proves that the division is now as good as

possible. The lists of exceptions from the K

and Pe criteria, respectively, are given below

(tables 1 and 2). Again, the problematical

case of P/Wilson-Harrington (K=— 0.377?,

Pe=0.95?) is omitted. Of the exceptions

from (4), P/Oterma did not satisfy the Pe

TABLE 1.—Exceptions from the K criterion

TABLE 2.—Exceptions from the Pe criterion

944 Hidalgo

Adonis

1566 Icarus

P/ SchwassmannWachmann 2

P/Whipplc

P/Johnson

P/SchwassmannWachmann 1

P/Kulin

P/Holmes

P/ Ashbrook-Jackson

P/Shajn-Schaldach

P/Tempel 1

P/Reinmuth 2

P/Wolf 1

P/Spitaler

P/Schorr

P/Wolf-Harrington

P/Oterma

K

+ 0.445

+ 0.200

+0.055

-0.106

-0.098

-0.098

-0.081

-0.081

-0.076

-0.053

-0.052

-0.048

-0.020

-0.020 ( + 0.102 before 1922)

-0.019

-0.005

(+0.066)-0.075 in 1924

(+0.083)-0.006 before 1937,

-0.276 in 1958

944 Hidalgo

P/SchwassmannWachmann 1

P/Oterma

Pe

9.15

2.12 2.46 in 1925

(4.92) 3.24 before 1937,

1.14 in 1958

criterion for only three revolutions between

1937 and 1962, and P/Schwassmann-Wachmann

1 was close to the limit at the time of discovery.

Nevertheless, while criteria of this type yield

a practical orientation as to the general character of the orbit of a specific object, there are

two reasons why we cannot rely upon them as

indicators of meteor origin. One of these

reasons, the operation of nongravitational

evolutionary effects necessary to displace the

orbits to crossing with that of the earth, has

already been pointed out by Dycus and Bradford. (1964). The other reason is that observational bias prevents the comets moving in

asteroidal orbits from being discovered even

if such exist. Only a high eccentricity ensures

that a comet becomes bright enough around

the perihelion and, at the same time, does not

age too rapidly in the aphelion part of its orbit

where it spends most of its time. This requirement is evidently not met in the asteroidal

region CK"<0, Pe<2.5). A comet located in

the upper left part of this region would have to

be of abnormal brightness (like P/SchwassmannWachmann 1) to be discovered, and a comet

situated in the lower part of the diagram would

disintegrate rapidly.

It is rather problematical whether comets

can enter at all the lower part of the diagram.

The perturbational capture process by Jupiter

does not allow this and, in fact, with the exception of P/Encke, there is no comet having

aphelion far inside Jupiter's orbit. The concentration of aphelia around Jupiter's orbit

is undoubtedly a characteristic feature of shortperiodic comets. Nevertheless, it is questionable whether the presence or absence of such

concentration among meteor orbits can reveal

anything about their origin: partly because

the Trojan asteroids exhibit such concentration,
14 8TMPO8IUM ON METEOR ORBITS AND DUST

too, and partly because cometary meteors,

which are subject to considerable nongravitational forces unlike the comets themselves,

may much more easily pass Jupiter's perturbational barrier.

It must be pointed out that there may even

be an essential difference between a cometary

and an asteroidal orbit in spite of entirely

identical angular elements, a and e (i.e., an

identical position in the a/e diagram). This

difference occurs at simple commensurabilities

with the mean motion of Jupiter, where the

asteroid orbits are relatively stable, due to

interplay of perturbations preventing any

closer approach to Jupiter (Opik, 1963), whereas the comet orbits are highly unstable, due

to the preceding capture process. A nice

example of this difference is P/Oterma and the

Hilda group of asteroids (Kresak, 1965a).

In figure 1, Comet Otenna appears imbedded

within the Hilda group, but this was the case

only during three revolutions of the comet

and two revolutions of Jupiter. The escape

of the comet from this region (Marsden, 1961)

is indicated in figure 5c.

If we want to establish the difference between comet and asteroid orbits, each object

must be classified either as a comet or as an

asteroid absolutely, regardless of the type of

its orbit. In fact, the aspect of these two

types of objects does not always differ sharply.

On several occasions some asteroids (1 Ceres,

2 Pallas, 3 Juno, 14 Irene, 122 Gerda, 182 Elsa,

224 Oceana) have been observed surrounded

by faint nebulosities. Although such observations are rare, unconfirmed, and doubtful

(Putilin, 1953), the experience of observers

such as Herschel, Hind, Schroter, or Comas

Sola does not allow us simply to neglect them.

On the other hand, some returns of periodic

comets have been recorded during which no

visible coma has developed and the comet

was steadily of asteroidal appearance. The

cometary character of P/Kulin has been recognized only after the determination of its

orbit. Also the aspect of P/Arend-Rigaux

was entirely stellar during its last two apparitions (Roemer, 1966); had the discovery

occurred one revolution later than it actually

did, we should have no reason for classifying

this body as a comet, except for the form of

the orbit. Of course, these are exceptional

marginal cases that cannot affect the general

character of the two distributions of orbits,

but they are perhaps able to influence the

degree of their overlapping.

When speaking about asteroidal orbits we

must define precisely the meaning of this term.

Unfortunately, this necessity is often overlooked and individual orbits (e.g., those of some

meteorites and fireballs) are rather arbitrarily

designated as cometary or asteroidal. Unless a

sharp numerical criterion like (3) or (4) is applied, we can define asteroidal orbits crossing

the orbit of the earth in three different ways:

(1) as orbits of low inclination and eccentricity,

constituting a direct continuation of the asteroidal ring at its inner side; (2) as orbits with

aphelia situated within the main asteroidal belt;

and (3) as orbits that could arise, by any evolutionary process, from typical asteroid orbits.

In fact, definitions (1) and (2) are not fulfilled

by the asteroids of the Apollo group, the

outstanding exception from (1) being 1566

Icarus, and from (2), 1620 Geographos. Exceptions are found in the outer region of the

ring, too—such as 944 Hidalgo (from (1) and

(2)), 279 Thule, the Trojans, and the Hilda

group (from (2)). For investigating the origin

of meteors, definition (3) is most reasonable;

however, before applying it we must discuss

the operation of all potential effects that are

able to transform the original orbits.

Transformations of orbits

PLANETARY PERTURBATIONS.—The secular perturbations by major planets are of less significance for our problem. According to the wellknown Poisson theorem, there are no secular

terms of the first or second order in the perturbations of semimajor axes, and the perturbations of eccentricity are far from sufficient to

displace the perihelia from the asteroidal belt

to the earth's orbit.

Random perturbations at close encounters

are of greater importance; however, an overwhelming majority of asteroids cannot appreciably approach major planets. The extreme

outer asteroids, with the exception of Hidalgo,

are prevented from that by the commensurability with Jupiter's mean motion; some of the

innermost ones can encounter Mars, but its
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 15

mass is too small for efficient changes. For the

comets, close approaches to Jupiter are frequent

(they are responsible for the formation of shortperiodic orbits) and the displacement in the a/e

diagram is often drastic. Four striking examples of such a transformation (P/Oterma,

P/Wolf 1, P/Kopff, and P/Pons-Winnecke) are

plotted in dashed lines in figure 5c.

Owing to the equality of the planetocentric

velocity at the moments of entering and leaving

the sphere of action, the elements of the perturbed body before and after the appulse are

bound by the condition known as the Tisserand

criterion,

T=arl+2A-*»al»(l -e*)1'

2

 cos /=const, (5)

where A is the radius of the orbit of the perturbing planet, assumed circular, and / the inclination to its orbital plane. For a small original inclination of the perturbed body the orbital

plane cannot change appreciably, keeping cos /

very near to 1. Hence we have, for low inclined

orbits, the approximate condition

T0=a1+2A-3'

2

a

l

'

2

(l-e2)

1

'

i=con8t. (6)

The loci of equal To for perturbations by

Jupiter are plotted in figure 2d. They indicate

the lines along which a body situated in the

respective point of the diagram and revolving

near the ecliptical plane would displace after

the approach. Since there is an equal a priori

probability that the nearest approach will

occur ahead of or behind Jupiter, both directions of displacement are equally probable.

A close approach to Jupiter may occur only

within, or not far from, the area situated to the

right of the double dashed lines; this refers to

tangential orbits to Jupiter in perihelion and

aphelion, respectively. In this area

a(l—e)<ga<a(H-e) (lower line), (7)

and

a(l — (upper line). (8)

The probability of encounter increases toward

this boundary.

Similar diagrams may be constructed for the

perturbations by other planets, too, but the

effect of Jupiter is definitely the predominant

one.

ASTEROIDAL COLLISIONS.—If an asteroidal fragment should enter the terrestrial space after

ejection from the main asteroidal belt as a

consequence of collision, the resulting orbit

must obviously fulfill two conditions: it must

cross the region of collision, and the crossing

velocity must be equal to the ejection velocity.

For each original orbit from which the fragment

has separated, the area accessible may be

delimited in the a/e diagram. Furthermore,

for each point within this area the required

velocity of ejection may be determined.

A series of collisions may obviously occur

before one of the fragments reaches the earth's

orbit. Nevertheless, the probability of collision decreases rapidly with increasing separation from the main belt, because better conditions for the distribution of eccentricities

cannot compensate for the decrease of particle

density.

For a single collision, the velocity Ve at which

the fragment must leave the original orbit,

assumed circular with radius Oo and situated

in the plane of the ecliptic, will be

Ve=[3ao-1-a-1-2ao3/

2

a

1

/

2

(l-e2)

1/2

 cos 7]1/

2

 (9)

in the units of the circular velocity of the earth

(29.8 km/sec). The range of semimajor axes

and eccentricities accessible for the fragment

is obviously limited by the condition

a(l—e)<ao<a(l+e). (10)

Furthermore, unless the orbital inclination of

the fragment is zero, the other node must be

situated at the earth's distance from the sun.

This condition is expressed by the relation

a(l-e2)=2a0(a0+iy (11)

Formulas (9) to (11) have been evaluated for

three zones of collision, corresponding to the

commensurability gaps 1:4 (oo=2.065, conventional inner boundary of the main asteroidal

belt), 1:2 (ao=3.278, the outer region of the

belt), and 1:1 (oo=5.203, the region of the

Trojans); and for two values of inclination,

i=0° and 30°. The results are represented in

figures 3a, 3b, and 3c, with the proper velocities
16 SYMPOSIUM ON METEOR ORBITS AND DUST

Ve expressed in km/sec. Full curves apply to

i=0° , dashed curves to i=30°. The fragments

may enter only the area separated by the thin

full envelope. With i = 0°, an encounter with

the earth is possible everywhere within the

overlapping part of the two areas limited by

the boundary conditions (10) and (2) (the full

heavy curve), while with i = 30°, only on the

dashed-and-dotted line representing the additional condition (11).

It is evident from figures 3a to 3c that the

ejection velocities required to bring the fragments from the asteroidal belt to the earth's

orbit are much too high. For most of them a

velocity of 10 to 15 km/sec is necessary, the

absolute minimum amounting to about 4.5

km/sec. If we put, with Opik (1966), the upper

limit of this velocity at 1.0 to 1.5 km/sec, then

even when allowing for a reasonable eccentricity

of the original orbit we do not find regions of

possible encounters with the earth. Even if we

would admit ejection velocities of the order of

10 km/sec, we cannot explain the presence of

asteroidal meteors in the lower left part of the

a/e diagram by collisions within the main

asteroidal belt.

DRAG EFFECTS.—Different nongravitational

drag effects—the Poynting-Robertson effect,

the effect of corpuscular radiation from the sun,

and the Yarkovsky-Radzievsky effect—may be

considered in common, as they all change the

size and shape of the orbit in the same way.

The evolutionary paths due to these effects may

be plotted in the a/e diagram from the relation

(Wyatt and Whipple, 1950)

The paths for different values of the invariant

C, depending upon the initial elements, are

plotted in figure 3d. The arrows indicate the

direction of evolution that strongly predominates and is common to all the above-mentioned

effects except the Yarkovsky-Radzievsky effect

of the direct rotation; this may, however, play

some role only for very rapidly rotating bodies.

The speed of evolution, or the displacement in

the a/e diagram, considerably accelerates downward and in the direction of the arrows.

Figure 3d demonstrates instructively the suggestion of Dycus and Bradford (1964) concerning the changes of Whipple's K criterion due to

the Poynting-Robertson effect. From this

figure the effect may be readily verified for

individual objects without computation.

It is essential that the evolutionary paths

are nearly perpendicular to the direction of

Jupiter's perturbational barrier and to the

prevailing direction of strong perturbations

(fig. 2d). Also, the fragments formed by

asteroidal collisions, which do not at once reach

the boundary a(l— «) = 1, will continue their

evolutionary paths at large angles to the original

displacement, and can eventually become observable in spite of a lower ejection velocity.

Perturbations of the orbital plane will produce

deviations from the nodal line condition (11).

Thus the interplay of more effects may allow

the particles of a given origin to enter also the

regions of the a/e diagram otherwise forbidden.

Distribution in the a/e diagram

ASTEROIDS.—As seen from figure 1, the distribution of the asteroids in the a/e diagram is

strongly influenced by the commensurability

effects, producing a fine vertical structure.

This structure reflects in the smoothed equidensity lines shown in figure 4a, which depicts

the apparent distribution of 1649 numbered

asteroids. The heavy lines delimit the area

occupied by one-half of the objects; each other

line corresponds to a decrease of density by a

factor of two per unit area of the diagram.

The sample of numbered asteroids is obviously biased by the discovery and recovery

conditions, which depend, first of all, upon the

mean opposition magnitude m^. Owing to low

orbital eccentricities of most asteroids, their

short periods of revolution, and small amplitudes of brightness due to the rotation, the

changes of apparent magnitudes from one

opposition to another may be neglected in

the first approximation in the main part of

the asteroidal belt. The selection effect could be

evaluated easily provided that the absolute

magnitude distribution were known with sufficient accuracy; unfortunately, this is not the

case.

At the boundary of the distribution, where

the densities are low, other more intricate effects

appear. Higher eccentricities, yielding considerable variations of discovery conditions at
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 17

. A

-

-

y

/

/

/

/ /

/ /

//

/ h

/ n k

——-—

1

7/

i

f

/

/

/'/ w

/ /

l l

III // /1

/

M/ >

X

1

i

c / 7

/ / / /

/

/

/

/

n

\

\

\

X \

\ \ X

• \ \ ^

1

;

/

i

j

i

1

\

\JA \ \

-

j

is

\

I

FIGURE 3.—Ejection velocities (in km/sec) referred to a circular orbit of: a, commensurability 1:4 (heavy line= boundary condition for crossing the earth's orbit; thinner lines= boundary condition for the orbits of ejected particles, ejection velocities for

»=0°; dashed lines= ejection velocities for i=30°; dashed-and-dotted line=nodal line condition for t=30°); b, commensurability 1:2; c, commensurability 1:1; d, operation of drag effects (constant C) (arrows= the predominant direction of evolution,

common to the Poynting-Robertson effect, corpuscular effect, and Yarkovsky-Radzievsky effect of retrograde rotation).
18 SYMPOSIUM ON METEOR ORBITS AND DD8T

different oppositions, deter the mean opposition

magnitude from being a sufficient measure of

the discovery probability. Systematic searches

for new asteroids by Wolf and Metcalf's

methods are intentionally suited to the bodies

moving in the main part of the belt, as far as

both the mean angular velocity and a small

distance from the ecliptic are concerned. On

the other hand, when an exceptional object

happens to be discovered, the best efforts are

made to follow it and eventually add it to the

list of numbered objects. This applies to the

Apollo group as well as to the Trojans, for which,

in addition, special search programs have been

accomplished.

If we restrict ourselves to the largest asteroids, which are presumably all known, no

correction at all needs to be applied to the

observed distribution. The list of numbered

asteroids is essentially complete down to the

absolute magnitude g= 10.0; selecting 333

objects brighter than this limit from the revised

catalog of asteroid magnitudes (Kuiper et al.,

1958), we obtain the distribution shown in figure

4b. The limiting absolute magnitude 0=10.0

corresponds to a diameter of about 50 km.

The list of numbered asteroids is also essentially complete down to the mean opposition

magnitude mo=15.O; there are 796 objects

brighter than this. We shall use them for

extrapolating the distribution of asteroids in the

a/e diagram down to g= 15.0, or to the diameter

of about 5 km. Since m0 and g coincide at

Ao =1.618 (where a(a—1) = 1), correction factors of F > 1 must be applied beyond this limit.

They increase rapidly and become less and less

reliable with increasing semimajor axis. Assuming the form of magnitude distribution

we have

dN~0' dg, (13)

log F=a3(a-1)2 log 0. (14)

The work of Kuiper et al. (1958) has shown

that the value of the constant 0 varies considerably with the position within the asteroid

ring. Extrapolating the correction factors F

directly from the statistics of absolute magnitudes in the 3 zones delimited by Kuiper et al.

(op. cit.) (2.0<a<2.6, 2.6<a<3.0, 3.0<a<

3.5) and applying them to the sample of 796

asteroids brighter than mo=15.O, we get the

distribution shown in figure 4c. For the Hilda

group, 0=3.6 was adopted; for the Trojans the

reduction was impossible because there are no

objects brighter than mo=15.0, and the magnitude interval covered by the known Trojans is

too narrow to permit a reasonable estimate of 0.

Comparing the figures 4b and 4c we see that

the general picture radically changes when

passing to objects with diameters 10 times

smaller. Unfortunately, the values of A applied

here are still rather uncertain, and the extrapolation has possibly been pushed too far.

Nevertheless, the comparison is instructive at

least in demonstrating the danger of applying

the distribution function of larger bodies to the

smaller ones. Since no asteroids crossing the

earth's orbit appear in figure 4c, we have to

search for another way of linking up the data

on the Apollo group with those on the main

asteroidal belt.

An attempt to do this is presented in figure

4d, which is constructed on a different principle.

The absolute magnitude of the third brightest

asteroid, gif was determined for elementary

square areas in the a/e diagram (Aa=0.2,

Ai = 0.04), and smoothed loci of equal magnitudes '/„ have been drawn. Outside the central

part of the belt, where less than three asteroids

per sampling area have been found, or where

it was guessed that the known asteroids do not

represent the set of absolutely brightest ones,

auxiliary tentative procedures had to be applied. Where the density gradient appeared

low, the sampling area AaAe was extended; in

other cases it was necessary to introduce a

subjective factor by estimating gt from an incomplete set of brightest objects. Here use

was made of the probable sequence of IJU which,

for a given value of 0 in equation (13), yields

log (0.4i-0.2)

(15)

For the Apollo group also this procedure

fails because some of its members are probably

too far from the top of the sequence. In this

zone the estimates of the incompleteness (Opik,

1963) have been applied. The respective equidensity lines are plotted in figure 4d in dashed
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 19

curves; all known asteroids falling within this

region, whether numbered or unnumbered, are

also inserted. The decrease of the asteroid

density between two neighboring lines, which

was 2:1 in figures 4a through 4c, is defined by

an increment of 0.75 mag in g3. This corresponds to a ratio of 2:1 for 0=2.5, 2.5:1 for

0=3.4, and 3:1 for 0=4.3.

Even here the density ratios, in particular

those overarching a number of equidensity lines,

must be taken with much precaution. One

important thing, however, becomes absolutely

clear: the abrupt decrease of the asteroid population at the border of the central part of the

distribution substantially slows down in the

environment. The distribution of orbits in

the Apollo group does not represent a smooth

continuation of the distribution in the main

asteroidal belt; there are, rather, two different

systems superimposed: (1) a compact dense

system, including all large asteroids and concentrated on a small area of the a/e diagram;

and (2) a loose system with a low degree of

concentration, stretching possibly over the

whole area of the diagram between a=\ and

o=4.

Unfortunately, nothing definite can be stated

about the population in the upper right of the

diagram. Unless Hidalgo is a peculiar, extinct

cometary nucleus, its large separation from the

central group would suggest that members of

system (2) are also present here.

An essential improvement of the basic data

on the orbits of faint asteroids may be expected

from the results of the Palomar 48-inch Schmidt

minor planet survey, which are now under

elaboration at the Leiden and Cincinnati Observatories (Herget, 1964).

COMETS.—For the short-periodic comets the

conversion of the observed distribution of orbits

into the virtual one is even more difficult than

for the asteroids: first, because of the considerable variations of discovery conditions from one

return to another, and second, because of the

rapid, irregular, and unpredictable variations

of brightness with the heliocentric distance.

We shall tentatively assume that for comets

with g> 1 the general discovery conditions are

determined by the apparent brightness at the

most favorable perihelion passage occurring in

50 years. With a random distribution of the

earth's longitudes at the time of the comet's

perihelion passage, there is a probability of 0.5

that at this optimum occasion the elongation of

the comet from the earth, measured in radians

from the sun in the ecliptical plane, will be less

than t •'

t = 0.01 TO?*2. (16)

At the same time there is a probability of 0.5

that the angular distance of the comet from the

ecliptical plane will be less than the median

ecliptical latitude of the perihelion in the sample of comets concerned.

Short-periodic comets show a moderate increase of the mean perihelion latitude with

increasing semimajor axis. A least-squares solution for all short-periodic comets falling within

the limit of our diagram (P<20 years) yields

the empirical relation

cos 6= 1.011—0.004a. (17)

Obviously, this relation holds good only within

the interval of about 3<o<7, and cannot be

extrapolated outside it.

At the time of observation adopted, the heliocentric distance r and the geocentric distance

of the comet A will be

A= (q*-2q cos t cos 6+ l)in.

(18)

(19)

Substituting (16) and (17) into (19), and considering that t and b are small angles, we find,

after some simplifications, that the geocentric

distance expressed in terms of a and e will be

A= [(a-ae-1)*+ (1 -e) (0.0010a4

+0.008a»—0.022a)]1/a. (20)

The first term in the brackets alone corresponds

to the most favorable case possible of I =0,

6=0 for each combination of a and e; the second

term gives the correction on the average deviation from this for the best return in 50 years.

Obviously, the best discovery conditions need

not occur exactly at the perihelion; on the other

hand, there is no need for anybody to be searching for comets or observing the proper region

just at the most favorable moment. Assuming

that the brightness of the comet varies with
20 SYMPOSIUM ON METEOR ORBITS AND DUST

the second power of geocentric distance and

with the fourth power of heliocentric distance—

around the perihelion this appears more plausible than the sixth-power law (Kresak, 1965b)—

we can compute the difference between the

apparent magnitude m and the absolute magnitude h in the position defined above,

m—h= 10 log r-f 5 log A. (21)

Again, we assume a distribution law of the form

dN~y*dh. (22)

The distribution of absolute magnitudes of

short-periodic comets suggests, despite the

lack of data, 7=2.0 as the most plausible

approximation. This figure may appear too

low compared with the steeper incremental

laws valid for the meteors and asteroids. It

must be remembered, however, that the brightness of a meteor is approximately proportional

to the cube of its radius, and that of an asteroid

to the square of its radius, whereas for a comet

it depends upon the quantity of gas and dust

forming the coma. This should be roughly

proportional to the square of the radius of the

nucleus, too; however, a linear secular decrease

of the diameters of the nuclei of short-periodic

comets (Whipple, 1964) requires a reduction of

the factor 7, analogous to the effect of sputtering

of meteoroids (Kresak, 1960). Thus a lower

value of 7 does not indicate any outstanding

difference between the mass distributions of

the asteroids and the comets. It may be noted

that Vsekhsviatskij (1958) estimates 7 still

lower.

Combining formulas (18), (20), (21), and (22),

and putting log 7=0.30, we obtain the correction factor F in an arbitrary point of the afe

diagram from

log F=3 log (a-ae) +0.75 log [(a-ae-l)2

+ (l-«)(0.0010a4+0.008a2—0.022a)]. (23)

The observed distribution of semimajor axes

and eccentricities of short-periodic comets has

been determined for two samples of orbits:

(1) the orbits of all short-periodic comets (a

total of 77) at their discovery apparitions; and

(2) the orbits of those short-periodic comets

(a total of 41) that have been observed during

the last return to the sun.

The differences between these two samples,

consisting, in particular, of a considerable enhancement of population below the commensurability gap of one-half, have been discussed

elsewhere (Kresak, 1965a). Sample (2) evidently yields a better representation of the

situation at a given moment; nevertheless, the

comets entering the region below the gap are

probably more efficient in ejecting meteoroids

there than during other periods of their evolutionary history. The observed distributions,

again with the smoothed equidensity curves

indicating the loci of density ratios 1:2:4, etc.,

are shown in figures 5a (sample (1)) and 5c

(sample (2)), the corresponding corrected distributions in figures 5b and 5d, respectively.

The perturbational changes of the orbits of

P/Oterma, P/Wolf 1, P/Kopff, and P/PonsWinnecke, indicated by dashed lines in figure

5c, betray the frequent wandering of individual

comets through the diagram.

Because of the lack of data, the corrected

distributions cannot be extrapolated far to

the left. In the upper left corner a concentration of comets with the perihelia grouping

along Jupiter's orbit may be anticipated.

The lower boundary of the distribution is

fixed by Jupiter's perturbational barrier (fig.

2d), which does not allow the comets captured

from outside to enter the inner region; however,

meteoric particles that are ejected from the

comets and that are small enough can do this

under the action of drag effects, following the

paths indicated in figure 3d.

METEORS.—Th e a/e diagram for meteor

orbits may be supplemented by some quantities that are unambiguously defined only

for the particular case of orbits intersecting

the orbit of the earth. One such quantity,

the argument of perihelion defined by equation

(1), is shown in figure 2c. Other important

quantities are the geocentric velocity and

the no-atmosphere velocity, which, together

with the elements a, e, and i, determine the

probability of collision and the relation between

the meteor's mass and brightness.

Neglecting the eccentricity of the earth's

orbit and expressing all velocities in the units
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS KRESAK 21

of circular velocity of the earth, we have for

the heliocentric velocity VH at the moment

of encounter:

VH=(2-a-iy\ (24)

This, together with the velocity of the earth,

results in the geocentric velocity VG,

Vo=[S-a-1-2a1'

2

(l-e2)

1

'

2

 cos i]1'

2

. (25)

The attraction of the earth accelerates the

approaching meteor; at the he'ght of about

100 km, where most meteors appear, the

resulting no-atmosphere velocity Vm is related

to the geocentric velocity by

= [3.139-a" (26)

1

-2a1/

2

(l-e2)

1

/

2

 cos i]

The values of Va for i=0° , 30°, 90°, and 180°,

expressed in km/sec, are plotted in figure 6.

Just as for the asteroids and comets, the

observed distribution of meteors in the a/e

diagram will differ from the virtual distribution

of meteoroid orbits in space. The selection

effects include the geometric conditions of encounter (the probability of collision) and the

conditions of recording the atmospheric phenomena, associated with the collisions, by a

particular observing technique. For photographic observations, this includes the dependence of the brightness of a meteor upon its

mass and no-atmosphere velocity, the dependence of the detectability of its image on the

plate upon the brightness, distance, and angular

velocity, and the mass (or magnitude) distribution law.

The dependence of the collision probability

P upon orbital elements has been determined

by Opik (1951). Other effects mentioned

above have been considered by Whipple (1954),

who defined the proper correction factor, called

"cosmic weight," as

= VoV-J[2-a-1-a(l-e2)]l/2 sin i. (27)

The cosmic weights have been computed for

all meteors of the Harvard surveys (McCrosky

and Posen, 1961; Hawkins and Southworth,

1961; Jacchia and Whipple, 1961).

There is some uncertainty as to whether the

no-atmosphere velocity exponent, appearing

in (27), correctly takes into account the massvelocity and number-luminosity laws; however,

with the data available at present a reasonable

improvement of (27) may not be possible. Hence

we have adopted this formula with two minor

modifications: (1) we express the velocities

in the units of circular velocity of the earth

instead of the units of 100 km/sec adopted by

Whipple, and (2) we omit the factor sin i.

While the former modification is purely formal,

equivalent to the introduction of a proportionality factor, the latter modification represents

a reasonable adaptation of Whipple's "cosmic

weights" for the application in the a/e diagram.

In investigating the population in different

parts of the diagram, we are driven to deal

with meteor samples of limited range in inclination, and to presume that the distribution in

a and e is the same everywhere within this

range. If formula (27) is used, the meteors

with inclinations near to 0° or 180° would be

assigned very low weights, and the statistical

importance of the sample would decrease. For

instance, in the range of low-inclination orbits,

0

o

<t<30° , the corrected distribution would

essentially depend upon the meteors with orbits

15°<t<30°, and reflect strongly all random

fluctuations found in this less-populated range.

For this reason we adopt the correction factor G:

G=VoV-*[2-a-1-a(l-e2)]l/i

}

 (28)

which is in simple relation to Whipple's "cosmic

weight,"

C.W.=S7.8Gsini. (29)

Since P is the probability of collision per

revolution of the particle, the factor G converts

the observed distribution in the a/e diagram

into the distribution of perihelion passages of

individual meteoroids down to a uniform mass

limit. To compare this with the distributions

of the asteroids and comets (figs. 4 and 5), we

must pass from the frequency of perihelion

passages to the number of bodies in space,

multiplying G by the period of revolution.

Thus we obtain the correction factor G':

-<rl-a(l-*)]lf*. (30)
22

00 02

8YMPO8IUM ON METEOR ORBITS AND DUST

06 OB 10 0 0

FIGURE 4.—Distribution of asteroids in the ale diagram: a, observed distribution of 1649 numbered asteroids (cipher marks=

commensurability ratios with respect to Jupiter); b, distribution of 333 asteroids brighter than g= 10.0or larger than Z)=50

km; c, distribution of asteroids brighter than g= 15.0 or larger than D— 5 km, extrapolated from the distribution of 796 asteroids

brighter than mfc= 15.0 using Kuiper's values of/3;d, distribution extrapolated from the sequence of brightest asteroids in each

region (heavy lines= boundary condition for crossing the earth's orbit, boundaries of the regions occupied by one-half of all

objects). In diagrams a, b, and c each pair of neighboring lines corresponds to a change in the density by a factor of two; for the

explanation of diagram d see the text.
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS KF*«AK 23

OO 02 O* 06 O» HI OO Oi 04 04 O4 H)

FIGURE 5.—Distribution of comets in the a/e diagrim: a, observed distribution of 77 short-periodic comets at their discovery

apparitions; b, same distribution corrected for the effect of selection; c, observed distribution of 41 short-periodic comets

that have been observed during the last return to the sun; d, same distribution corrected for the effect of selection (heavy

lines= boundary condition for crossing the earth's orbit, boundaries of the regions occupied by one-half of all objects; longdashed lincs= aphelia at the mean heliocentric distance of Jupiter; dots = individual comets; short-dashed lines = perturbational displacement of some strongly perturbed orbits. Each pair of neighboring equidensity lines corresponds to a change in

the density by a factor of two).
24 SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 6.—No-atmosphere velocities Vm (in km/sec) of meteors in the ale diagram: a, for »=0° ; b, for »=30°; c, for i=90° ; d, for

j=180° (heavy lines= boundary condition for crossing the earth's orbit).
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 25

Obviously, C.W., G, and G' are not defined

beyond the boundary set by equation (2).

The correction factors G and G' are plotted in

figures 7 and 8 for four selected values of inclination, t=0° , 30°, 90°, and 180°. In our

analysis we shall consider three groups of

meteor orbits delimited by these boundary

values: (1) low-inclination orbits (0°<r<30°);

(2) direct high-inclination orbits (30°<t<90°);

and (3) retrograde orbits (90°<t<180°).

It may be noted that the distribution of

asteroids and short-periodic comets, treated

above irrespective of inclination, referred practically to group (1). In fact, there are only

11, or 0.7 percent, numbered asteroids with

inclinations exceeding 30° and merely 3, or

0.2 percent, with inclinations exceeding 35°

(1580 Betulia, 52?0; 944 Hidalgo, 42?5; and

1373 Cincinnati, 38?9). Also, there are only

6, or 8 percent, short-periodic comets (P<20

years) with inclinations exceeding 30° and

merely 2, or 3 percent, with inclinations exceeding 32° (P/Tuttle, 54?7; P/Pigott, 45? 1).

For the meteors high inclinations are much

more abundant even among short-periodic

orbits, although low inclinations do prevail

here, too.

In addition to the discrimination according to

inclination, a discrimination between bright and

faint meteors was also attempted. For faint

meteors the extensive catalog of Super-Schmidt

orbits by McCrosky and Posen (1961) is available; the lower precision of the graphical

reduction methods used here appears sufficient

for our purpose because of the homogeneity of

the data. Photographic orbits of brighter

meteors, although generally more accurate, are

rather scarce, and the data had to be compiled

from different sources. Even so a sample of

some statistical importance could be obtained

for only low-inclination orbits It consists of

70 orbits measured in Dushanbe (Katasev,

1964; Babadzhanov, 1963), 47 orbits from the

Harvard bright meteor photographic data

(Whipple, 1954), and 17 orbits from the

Ondfejov data (Plavcovd and Plavec, 1960;

Ceplecha et al., 1964). To these data, obtained

by conventional slow cameras, 43 orbits of the

brightest Super-Schmidt meteors (Jacchia and

Whipple, 1961) have been added. In order to

avoid a bias in favor of high-velocity meteors

240-022 O—67 3

and to ensure a relative homogeneity with the

rest of the sample, the choice of these meteors

was not based on the photographic magnitudes

but on the probable rise above the plate limit,

inferred from the absolute magnitude and noatmosphere velocity (Hawkins and Upton,

1958; Kresak, 1964).

A rather difficult problem is the exclusion of

the shower meteors (already not included in the

numbers quoted above). According to Southworth and Hawkins (1963), about 36 percent of

all photographic meteors belong to meteor

streams and associations, the proportion being

even higher among brighter and short-per odic

meteors. It is practically impossible to distinguish between "sporadic" and "shower"

meteors in individual cases, because of both a

low spatial density of minor showers and a

considerable dispersion of many major showers.

It was considered reasonable to discard only

the members of the five major showers indicated

in figure 1—the Geminids, Northern and

Southern Taurids from group (1), the 5 Aquarids from groups (1) and (2), and the Quadrantids from group (2). The possible interference

by other showers has been checked additionally

by comparing the angular elements of meteors

forming clusters in the a/e diagrams.

In connection with the peculiar shape of the

dispersion areas of meteor showers in figure 1,

one important point may be emphasized. As

a consequence of the condition denoted by

equation (1), the dispersions within the a/e

diagram do not indicate a general relation

between the semimajor axis and the eccentricity

in a meteor stream, but only in its part meeting

the earth. By comparing figures 2a, c, we see

that the loci of constant q and o> run almost

parallel unless the aphelion distance is extraordinarily small. Now, for a shower of

short duration, where ft is practically equal

for all meteors, a small dispersion of the lines

of apsides, necessary to keep the stream compact at large heliocentric distance, requires a

small dispersion in the argument of perihelion

(O>=T—Q). In this case only meteors falling

within a narrow range of perihelion distances

can collide with the earth. Thus the large disproportion between the dispersion of the perihelion and aphelion distances (e.g., dq— ±0.006

against 6Q= ±0.7 for the Quadrantids, dq=
26 SYMPOSIUM ON METEOR ORBITS AND DUST

OO 02

OO OS 0-4 OS Ot HI 00 02 0* OS

FIGURE 7.—Correction factors G for conversion of the observed frequency of meteors into the virtual frequency of perihelion

passages in the a/e diagram: a, for i=0° ; b, for i=30°; c, for i=90°; d, for J=180 ° (heavy lines=boundary condition for

crossing the earth's orbit).
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 27

n.3 0-4 O« 0-8 tO OO 0-i 04 0«

FIGURE 8.—Correction factors C for conversion of the observed frequency of meteors into the virtual density in the a/e diagram:

a, for »=0°; b, for i=30°; c, for i=90°; d, for »=180° (heavy lines= boundary condition for crossing the earth's orbit).
28 SYMPOSIUM ON METEOR ORBIT8 AND DU6T

±0.015 against 8Q= ±0.7 for the 8 Aquarids,

or 5?= ±0.007 against 8Q= ±0.15 for the

Geminids—all values determined from the

catalog of McCrosky and Posen (1961)) is no

definite characteristic of the stream's structure.

The dispersion of perihelion distances is obviously underestimated because of the selection

effect, whereas the dispersion of aphelion distances is overestimated because of the lower

accuracy in determining this quantity from the

velocity data.

The a/e diagrams for the low-inclination

group (1) of nonshower meteors are shown in

figure 9: for 176 bright photographic meteors

above, for 1300 Super-Schmidt meteors below.

The Pfibram meteorite, with a=2.42, € = 0.674,

would fall into the lobe close to the left of the

maximum occurrence in figure 9a. Again, the

spacing of the equidensity lines corresponds

to a change by a factor of two in the density

per unit area, the heavy line delimiting the

region occupied by one-half of the meteors.

The observed distributions (figs. 9a, c) are

converted into the respective virtual distributions (figs. 9b, d) by applying the correction

factors G' plotted in figure 8. An interpolation

between the correction factors for i=0° and

i=30° was necessary; it proved sufficient to

do this graphically by halving the angles

formed by the loci of equal G' (0°) and G'

(30°), and averaging the distances between

two neighboring curves throughout the diagram. Analogous diagrams for the groups of

high-inclination direct orbits (2) and retrograde orbits (3) are shown in figure 10. Here

the random fluctuations in density are larger

compared with figure 9c, because of the lower

numbers of orbits included (226 and 125,

respectively).

Minor irregularities in the distributions may

be attributed to meteor showers in only two

cases. The concentration of low-inclination

orbits near a=1.5, e=0.93 (figs. 9c, d) is

associated with a dispersed shower of extremely

low perihelion distance, g~0.10, active around

January 20. The radiant is situated near

a Leo, at about a=150° , 8= + 15°, the orbits

resembling those of the Geminids and 8 Aquarids. The belt of enhanced density of direct

high-inclination orbits, stretching from a =1.9,

e = 0.95 to a=0.7, e=0.80 (figs. 10a, b), is

associated with another stream of extremely

short perihelion distance, g~0.10. The approximate radiant coordinates at the time of

maximum activity (about July 17) are a = 325°,

8= +5°. These meteors are probably connected with the complex of Southern and Northern Aquarid streams meeting the earth a little

later; a resemblance to the intricate system of

Taurid-Arietids is apparent. The large dispersion in the semimajor axes and the occurrence of extremely short aphelion distances

(#=1.3 for Meteors nos. 3356 and 8028) is of

particular interest, insofar as the concentration

approximately follows the evolutionary path

anticipated for the drag effects. A similar

prominence, ending near a—1.0, e —0.50, is

found in the distribution of retrograde orbit*

(figs. 10c, d), but there is no orbital association

among the bodies constituting this concentration.

The group of retrograde orbits exhibits, as

expected, an increasing concentration toward

longer semimajor axes, continuing over the

upper edge of the diagram. A secondary

maximum reveals a concentration of aphelia of

high-eccentricity orbits to the orbit of Jupiter.

This concentration extends downward to the

left, in the proper direction of operation of the

drag effects.

The main change in passing from the retrograde to the direct high-inclination orbits

(fig. 10b) is that a concentration of orbits of

the type of Jupiter's family of short-periodic

comets (around a=3.5, e = 0.70) begins to

appear. This concentration becomes the predominant feature among the direct low-inclination orbits (figs. 9b, d). Here, in the

region of a>2.5, no distinction between brighter

and fainter meteors is apparent. The concentration is not so sharp as for the shortperiodic comets, which may be partially due

to a lower accuracy in determining meteor

orbits. At the lower side, the region of maximum occurrence of brighter meteors ends by a

sharp cutoff, a decrease in the density by a

factor of 10 within less than 0.5 a.u. in a.

This cutoff is absent in the group of fainter

meteors (fig. 9d), although even here the

decrease is steeper than for the high-inclination

orbits. It must be remembered that because

of the brightness-velocity dependence we are
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 29

dealing with smaller particles in the highinclination and retrograde groups. Thus the

comparison of figures 9b with 9d, and 9d with

10b and lOd consistently suggests an increasing

proportion of extremely short-periodic orbits,

situated far inside Jupiter's perturbational

barrier, with decreasing size of the particles.

In figures 9a and 9b, based on the most accurate elements, the separation of a very interesting group of eight low-eccentricity meteors,

forming the secondary maximum at the extreme

left, is clearly indicated. This concentration

appears just in the region accessible to fragments ejected from the asteroidal belt at reasonable velocities, and subsequently decelerated by

the drag effects. It is also essentially the same

region where an anomaly of the magnitude distribution, suggesting a different origin of the

particles, has been found previously (Kresak,

1964). It may be noted that Cook, Jacchia,

and McCrosky (1963) suspected two distinct

classes of orbits for four meteors considered

asteroidal on the basis of their behavior in the

atmosphere. In fact, two of these meteors

(Halliday's iron meteor with a—1.05, 6 = 0.117,

and Harvard Meteor no. 1242 with a=1.33,

e = 0.262) fall just within this region, whereas

the two others (Harvard Meteor no. 19816

with a = 2.24, e = 0.662, and the PHbram meteorite with a=2.42, e = 0.674 (a chondrite))

together with the Harvard Meteor no. 7946

(a=2.49, e = 0.621), classified as asteroidal by

Jacchia, Verniani, and Briggs (1965), fall on

the lower boundary of the region of maximum

occurrence of low-inclination orbits. This is

just the region where the orbits of the asteroids

not belonging to the Apollo group (719 Albert:

a=2.59, e = 0.541; 887 Alinda: a=2.52, e=--

0.540; 1036 Ganymedes: a=2.66, € = 0.543;

1953EA: a = 2.44, 6 = 0.580) approach most

closely to the boundary condition (2), as is

evident from figure 4d.

Conclusions

The application of the a/e diagram to the

distribution of asteroid, comet, and meteor

orbits suggests that there are probably five

distinct classes of short-periodic meteors, each

of which is generically related to a corresponding class of larger bodies:

1. Long-periodic comets supply meteors

with a random distribution of orbital planes,

which are spiraling to the sun under the action

of drag effects. As pointed out by Whipple

(1963), the Poynting-Robertson effect generally

acts much more slowly than the interplanetary

erosion, which prevents the aphelia of all but

the very smallest cometary meteoroids from

displacing appreciably toward the sun. Whipple also suggests, however, that just the highinclination orbits are favored by the PoyntingRobertson effect because of the concentration

of the eroding dust to Jupiter's orbital plane.

Possibly the corpuscular component increases

the efficiency of drag effects not to be entirely

eliminated by the erosion. A relatively slow

decrease in the number of high-inclination

meteors with decreasing aphelion distance suggests that a drag is actually acting on them.

The only alternative explanation, that these

meteors belong to class (5), will be referred to

below.

2. Jupiter's family of short-periodic comets supplies a class of meteoroids that reflects

its characteristic features: the concentration of

aphelia around Jupiter's orbit, and low inclinations. Not more than a few percent of the

orbits have t>30°. For bright photographic

meteors, Jupiter's perturbational barrier, combined with the erosion effects, prevents the

aphelia from drifting toward the sun and produces a sharp cutoff in the semimajor axes.

For fainter meteors, this boundary is less definite, either because of the diffusion of some

particles inward, or because of an increased

degree of overlapping with the orbits of class (5).

3. The system of minor planets is obviously associated with a similar system of

smaller particles, but these are unobservable

from the earth on account of their excessive

perihelion distances. Individual marginal

members of this system enter the region of

observability, in particular as a continuation

of the Albert group of asteroids, near a=2.5,

e — 0.&. They are hardly distinguishable by

orbital elements from the cometary meteors

of Jupiter's family; only their aphelion distances

are generally somewhat shorter (about 4.0).

4. The asteroidal fragments originating

from the collisions in the central part of the

asteroidal belt spiral to the sun in orbits of

lower and decreasing eccentricity, until they
30

SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 9.—Distribution of meteors in low-inclination orbits (0°<»<30°) in the a/e diagram: a, observed distribution of 176 bright

nonshower meteors; b, same distribution corrected for selection effects; c, observed distribution of 1300 faint nonshower meteors;

d, same distribution corrected for selection effects (heavy lines= boundary condition for crossing the earth's orbit, boundaries

of the regions occupied by one-half of all objects; dashed lines = aphclia at the mean heliocentric distance of Jupiter. Each

pair of neighboring equidensity lines corresponds to a change in the density by a factor of two).
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK

frofrifr4 o-a fo oo oi 0-4 M (ye uj

FICUKE 10.—Distribution of meteors in high-inclination orbits in the ale diagram: a, observed distribution of 226 faint nonshower

meteors in direct orbits (30°<i<90°); b, same distribution corrected for selection effects; c, observed distribution of 125 faint

nonshower meteors in retrograde orbits (90°<Ct<[180o); d, same distribution corrected for selection effects (heavy lines = boundary condition for crossing the earth's orbit, boundaries of the regions occupied by one-half of all objects; dashed lines—aphelia

at the mean heliocentric distance of Jupiter. Each pair of neighboring equidensity lines corresponds to a change in the density

by a factor of two).
32 SYMPOSIUM ON METEOR ORBITS AND DUST

become observable around a=1.2, e = 0.2.

Owing to a higher crushing strength they are

much less affected by erosion than the cometary

particles. This class shows a steeper increase

in frequency with decreasing brightness than

do the cometary meteors (Kresak, 1964),

and may be rather abundant at the magnitudes

below the present threshold of photographic

techniques. In the range of fainter meteors

a connection of this area with (3), running

closely along q=l, appears.

5. The fifth component is most difficult

to interpret, because of insufficient information

on the nature and distribution of orbits of the

parent bodies. The largest bodies belonging

to this class are members of the Apollo group

of asteroids. It has been shown that these

objects do not constitute a smooth continuation of the distribution of orbits within the

main asteroidal belt (fig. 4d). It has also

been demonstrated by Opik (1963) that the

perturbations by Mars are inadequate for

supplying this region with the observed number

of asteroids. Opik's assumption that the

members of the Apollo group have originated

from residual nuclei of comets seems plausible.

However, the diameters of these bodies, of the

order of 1 km, are essentially the same as those

of the nuclei of most short-periodic comets

(Roemer, 1966), and the efficiency of the jet

deceleration necessary to reduce the aphelion

distances of the parent comets is problematical

with regard to Jupiter's perturbational barrier.

On the other hand, it is difficult to imagine

how a meteor stream of the type of the Geminids might be of asteroidal origin; and the

orbit of this stream is definitely more similar

to that of 1566 Icarus than to the orbit of any

comet.

Unfortunately, the virtual distribution of

orbits in the Apollo group is rather indeterminate because of the inherent selection effects.

Whipple (see Opik, 1961, discussion) has pointed out

the relatively small angular velocity of most known

Apollo asteroids at the time of the nearest

approach, which increases the chances of discovery of the bodies subject to heavier perturbations by the earth; however, the geocentric velocities of these bodies (18 km/sec on

average) are considerably higher than the velocities of the bodies of class (4), which are not observed among asteroids. Note that there are

no indications of perceptible perturbations by

the earth in the parts of meteor streams intersecting the orbit of the earth (Kresak, 1954),

but this may also be due to much shorter

lifetimes.

Another possible bias, which appears even

more serious, concerns the distribution in inclination. High-inclination orbits of the type of

Apollo yield a much smaller probability of a

close approach to the earth, and bodies moving

in retrograde orbits would imply such rapid

angular motion at the time of approach that

they could hardly be discovered on photographs. In fact, we are not certain that the

orbits of this type are actually of low inclination

only, as indicated by the observations. A

proof that there are also orbits of high inclination and retrograde motion would comply with

the existence of similar meteor orbits. The

origin of these meteors (class 1) in long-periodic

comets and strong drag effects compared with

the erosion effects would not be required in

this case.

A dependable estimate of the relative abundances of these five classes of meteor particles

from earth-based observations is practically

impossible, because of the boundary condition

(2). The relative abundances among the observable particles, and their general trend

toward the unobservable region of the a/e

diagram, may be estimated from figures 9 and

10. With regard to the strong velocity dependence of meteor phenomena and meteor

observing techniques, the relative contributions

to the total influx of meteors down to a uniform

magnitude, or mass limit, essentially differ both

from the virtual and from the observed states;

they also change with the limiting values

adopted.

Acknowledgments

Some computations used in this paper have

been performed with the ZRA-1 electronic

computer, by the courtesy of the Institute of

Mechanics and Automation of the Slovak

Academy of Sciences. Dr. A. Hajduk and Dr.

J. &tohl kindly assisted in the programming,

and Mrs. L. Burkovigova and Mrs. L. SmfSkovA

in the statistical processing of the data. My

sincere thanks are due to all of them.
METEOR ORBITS RELATED TO COMET AND ASTEROID ORBITS—KRESAK 33

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Abstract

The distribution of the orbits of asteroids, short-periodic comets, and meteors is investigated using a series of

diagrams with semimajor axis plotted against eccentricity, designed for particular values ot inclination. This kind

of representation allows a number of significant quantities and conditions to be interrelated and compared with

observations. Empirical comet-asteroid criteria are discussed, and the evolutionary paths in the a/« diagram, resulting from the perturbations by Jupiter, asteroidal collisions, and the drag effects of solar radiation, are computed.

The selection effects inherent in the discovery, or observation, of individual categories of objects are evaluated

as functions of the position within the diagram, and the observing data are converted into the probable virtual distributions. All known orbits of the asteroids and short-periodic comets and all available photographic meteor orbits

are used for this purpose.

The comparison of the corrected distributions and the consideration of potential evolutionary effects suggest

that there are five distinct classes of meteor orbits, generically related to comets or asteroids as parent bodies, which

are concentrated in different regions of the diagram.
Classification of Meteor Orbits

Z. CEPLECHA1

Introduction

This paper will try to answer two principal

questions:

1. Do groups exist among sporadic meteor

orbits that we can recognize?

2. If there are such groups, can we connect them with groups of the known bodies

of the solar system?

These questions were partly answered by

many authors, but complex answers in the

general form that I shall attempt could be

of great importance. My answers, however,

are limited to a small mass region because of

the necessity of dealing with relatively precise

photographic orbits, which are at present

available for meteors of photographic magnitude

from + 2 to —10, with the majority of the

observational material between +1 and —5.

If we do not limit the questions to sporadic

meteors only, the answers are quite clear. We

know the meteor showers, which means "yes"

for the first question. Hence our first question

must be understood to apply to more of the

meteor population than the groups similar to

meteor showers, which are called associations

by Jacchia and Whipple (1961). The second

question applied to classical meteor showers

yields the well-known answer that there is a

direct connection between individual cometary

orbits and individual meteor shower orbits.

For the sporadic meteors we must exclude

every partial case that is induced by meteor

showers and associations.

Whipple's comet-asteroid criterion

Whipple (1954) postulated his K criterion for

the investigation of the origin of short-period

< Astronomical Institute of the Czechoslovak Academy or Sciences,

Ondrejov, Ciechoslovakia.

streams. Later, many authors applied this

criterion to individual sporadic meteor orbits,

thus implying positive answers to both our

questions. To compare the present orbits of

streams, which cross the earth's orbit, with the

present orbital distribution of short-period

cometary and asteroidal orbits, which usually do

not cross the earth's orbit, is, of course, to

some extent risky; but, to apply the same procedure to individual sporadic orbits is quite inadmissible, at least before we know the answers

to both our questions.

Recently, Dycus and Bradford (1964) criticized the application of Whipple's K criterion

to individual sporadic meteor orbits. I had

similar thoughts before reading that paper and

I fully agree with the criticism. In short,

Whipple's criterion is an empirical boundary

line between cometary and asteroidal orbits,

which could hardly be extrapolated down to

perihelion distances equal to and less than 1 a.u.

It is possible to find other empirical expressions

to distinguish, between cometary and asteroidal

origins, but the extrapolation down to the

perihelion distances equal to and less than 1

a.u. differs considerably.

Composition of the meteor particles

Some years ago, I found a double maximum

distribution of a parameter, denoted by kB,

which represents a measure of the heat conductivity, density, and specific heat of the

meteoric particle (Ceplecha, 1958a). In that

paper I implied a positive answer to our first

question, and found it possible to connect the

two maxima with the stony and iron meteorites.

At the same time, I had insufficient data on

the meteor orbits. Thus, the connection was

based solely on the correspondence of theo36
36 SYMPOSIUM ON METEOR ORBITS AND DUST

retical kB with observed values. Such an absolute scale of the kB parameter derived from the

beginning heights is very dubious, and my

results were much criticized. The results of

that paper on meteor composition are today

inadmissible for me, at least before we know the

answer to both our questions. On the other

hand, I shall use the concept of the kB parameter

throughout this paper to clarify the problem of

sporadic meteor orbits.

ADDITIONAL kB PARAMETER.—In addition to the

orbital elements of individual sporadic meteors,

I shall use a parameter kB, which is directly

connected with the composition of the body.

This idea is quite clear if we suppose that individual groups of sporadic meteors could have

not only different orbits but also different compositions.

A simple one-dimensional solution of the

heat-conductivity problem during the first part

of the meteor trajectory, where the ablation

and light production are quite negligible, yields

the temperature T on the surface of the particle

as a function of the air density and other

parameters. Thus,

(1)

2(\Scb cos

where A is the heat-transfer coefficient, X the

heat conductivity, 8 the density, c the specific

heat of the meteor material, zR the zenith

distance of the radiant, p the air density, b

the air-density gradient, va the no-atmosphere

velocity, and T the temperature of the body

before entering the atmosphere. If we now

assume that the temperature at the beginning

of the meteor light as recorded by the photographic emulsion is constant and equal to TB,

we can use equation (1) to compute a certain

value that will be strongly dependent on the

material constants. Let us now define a

logarithmic parameter kB as

(2)

(3)

5 1

p a + - log Va— - log COS ZR.

First we shall deal with equation (2), i.e., the

"theoretical" definition of kB. The density

gradient is changed very little, and the spread

induced in equation (2) by b is hardly greater

than 0.1. Almost all the energy is used in

heating the surface at the first part of the

trajectory of such small particles as we shall

deal with. Thus A will be almost the accommodation coefficient, not far below one. In

most cases A could hardly change from one

meteor to another to such an extent that the

induced statistical spread exceeds 0.3. The

temperature at which we begin to observe the

meteor was estimated by Levin (1961) to lie

between 2000° and 3000°C. But even if we

extend the temperature limits at the meteor

beginning, we are still in the negligible range of

spread, say 0.2, in equation (2).

The weakest point of the theoretical definition

of kB is the range of validity of equation (1).

If the body has dimensions of, say, less than 1

mm, we proceed to a more complicated theoretical solution of the problem (Ceplecha and

PadevSt, 1961). Using the numerical results

of such a solution with a meteor dimension

as one of the parameters to compute kB

from equation (3), I found that the induced

spread due to differences in dimensions is less

than 0.1 in all the cases I will discuss in this

paper.

Since we begin, however, to photograph the

meteor not at the point that is theoretically the

beginning of rapid ablation, the correspondence

of equations (2) and (3) is not certain in

advance. There may be three possible cases.

If we photograph the meteor before the point

of rapid ablation, equations (2) and (3) correspond with the temperature at this point. If

we photograph the meteor just at the point of

rapid ablation, both equations are exactly

satisfied. At this point, theoretically speaking,

there is a jump in brightness of 1 mag for meteors with small velocity and of 3 mag for meteors

with great velocity. Thus the probability of

coincidence of photographic and theoretical

beginnings is not negligible. If we begin to

photograph the meteor after it has started rapid

ablation, equations (2) and (3) have no meaning

and we must speculate qualitatively. If this

point is not too far beyond the point of beginning of rapid ablation, we need only add to the

logarithm of air density (log pB) a certain value

dependent on many parameters to correct
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 37

equation (1). But the direction of the density

correction is the same for all such meteors; thus

the constant correction can be assumed as a

first approximation. Equations (2) and (3)

can, therefore, be used again, but with the

additional uncertainty of an unknown positive

constant.

Thus we can use equations (2) and (3) for

the photographic meteors without a previous

knowledge of the exact theoretical point at

which we begin to photograph the meteors, if

the observational material is homogeneous in

the sense of limiting magnitudes and maximum

brightnesses of the photographed meteors.

These conditions are excellently fulfilled by the

McCrosky and Posen (1961) meteors, which we

shall use as our main observational material in

this paper (42 percent of the meteors have a

maximum magnitude between 0 and 1, and 67

percent a limiting magnitude between 3 and 4).

Equation (3) contains only values accessible

for measurement. We can understand equation (3) so that kB given by the beginning height

density as the main factor is corrected by the

velocity and zenith distance of the radiant.

The influence of cos zR on kB from equation (3)

is in almost all real cases very small. Thus the

velocity is the only factor that can induce

statistical groups of velocities into the statistical

groups of kB, and then there is a real danger that

statistical groups of kB can be wrongly identified

as groups of different composition. We must

first examine this velocity effect before considering the distribution found for kB.

A very great advantage of the kB value is the

fact that it is obtained from data on beginning

meteor heights. At this point the fragmentation of the meteor body is less than at any other

observed point. Even if we assume that the

beginning point is identical with the beginning

of rapid fragmentation, we arrive at correct

results by the following procedure.

Groups according to the kB parameter

I will use the photographic Super-Schmidt

meteors studied by McCrosky and Posen

(1961) as my main observational material

because (1) they give the most extensive

photographic observational material for more

than 2000 sporadic meteors with orbits and

other data necessary to compute the kB parameter; and (2) the limiting and maximum magnitudes of all these meteors have a statistical

distribution that indicates a very good homogeneity of the material. The relatively greatest

drawback of the McCrosky-Posen material is

its lack of accuracy due to the graphical reduction method used. But in all the cases that I

investigated, this inaccuracy resulted in an

additional statistical spread only, which did

not interfere with the main results.

The U.S. Standard Atmosphere (1962) was

used to connect heights with air densities. If

we now compute kB for all the McCrosky-Posen

sporadic meteors, we obtain the histogram

given in figure 1. The interval of kB, in which

the numbers of meteors are plotted, was chosen

as 0.1. (Throughout this paper I shall usually

C B A

2 00

100

50

n

0-P

25 to 35

km/sec

FIGURE 1.—Distribution of the kB parameter for all sporadic

meteors of the McCrosky-Posen Super-Schmidt meteors.

The 25 to 35 km/sec interval of velocities is a good check

that the positions of the maxima do not depend on the

velocity.
38

SYMPOSIUM ON METEOR ORBITS AND DUST

denote intervals by their initial values; for

example, kB=7.7 contains values from 7.70 to

7.79, and so on.)

I must add that kB is at first taken as a

relative value only; thus we can say that the

right-hand part of figure 1 contains denser

particles with greater heat conductivity than

the left, but what is the absolute value of the

density we leave open for the present. At first

sight we observe two maxima of kB distribution,

as I previously found from other data on bright

meteors (Ceplecha, 1958a). The minimum

between these two maxima lies higher than

would be expected if the sample were composed

of the two main groups only, thus indicating the

possible presence of a third group. I denote

these groups in order of decreasing density of the

meteoroids: A group with maximum at kB= 7.6,

B group with maximum at ArB=7.2, and C

group with maximum at kB=6.9. The difference of kB between the A and the C groups is

0.7, which corresponds to a change in height

of 8 to 10 km.

Now we must prove the influence of velocity

on the total distribution. I divided all the

material into groups of different velocities with

10 km/sec intervals. The distribution of kB

for each of these velocity intervals is plotted

in figure 2. The interval of 30 km/sec (i.e.,

from 30 to 40 km/sec) compared with the

total distribution is at first sight a good verification of the reality of all the three groups A,

B, and C, quite independent of the velocity.

The maxima are at exactly the same positions

as for the total distribution. We see that the

interval of velocity below 20 km/sec contains

almost only the A group; on the other hand,

almost all the meteors with c.^6 0 km/sec

belong to the C group. The 20 km/sec interval

has all three groups with the main group A;

the 30 km/sec interval has all three groups with

the main group C; the 40 and 50 km/sec

intervals contain relatively few meteors because

of a minimiun in the velocity distribution, but

there is still an indication of the three groups

in the 40 km/sec interval and a dominant C

group in the 50 km/sec interval.

Summarizing, we see that the A group is well

recognized up to the 40 km/sec interval, the B

group from the 20 to the 40 km/sec interval, and

the C group from the > 60 km/sec down to the

20 km/sec interval.

We can further prove the influence of differences in the meteor magnitudes and masses.

We use the material divided into different

velocity groups and make a further separation

into different magnitude and mass intervals.

The results are summarized in table 1.

The homogeneity of the material is well

demonstrated in table 1, and the ka parameter

is thus confirmed as a very good criterion for

investigating the McCrosky-Posen meteors.

Jacchia (1960) observed an effect similar

to our groups (using the bright Super-Schmidt

meteors), but his material, comprising about 400

meteors, was not sufficient for a detailed statistical study such as I present in this paper.

Distribution of orbital elements of the groups

(preliminary classification)

If we wish at this stage to answer our first

principal question, we must turn to the orbital

elements. We are now in a position to recognize

at least two, possibly three, groups of sporadic

meteors according to their kB parameters (i.e.,

their composition). Thus we can choose the

representatives of each group: A group with

kB interval from 7.5 to 7.8 containing 719

members, C group with kB interval from 6.7 to

7.0 containing 559 members, and B group with

kB interval 7.3. The B group is contaminated

by A and C groups to the extent of about 70

percent, but we can "subtract" the A and C

TABLE 1.—The change of kB maxima between the lowest

and the highest values of meteor mass and magnitude

Velocity

interval

km/sec

20

20 to 30

30 to 40

*

60

kn maximum shift

A

mass magnitude

0. 1 0. 2

0. 1 0.1

0. 1 0.0

C

mass magnitude

0. 0 0. 2

0. 1 0.2

0. 1 0. 1

B

mass magnitude

0.1 0.2

•The number of meteors In the 40 and 00 km/we intervals U too small to

permit a statistical investigation.
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 39

100

n 0—-

20-

20-

2Oto3O

km/sec

n

30 to 40

km/sec

40-

20-

40 to 50 km/sec

C A

'oo

to 60 km/sec

GO km/sec

8

B

FIGURE 2.—Distribution of the kB parameter for the same sample as in figure 1 but divided into different velocity intervals. The

positions of the maxima do not depend on the velocity.

distributions and get some information on this

smaller B group.

Figure 3 illustrates the distribution of orbital

inclinations for all three groups. The A group

shows a very strong ecliptical concentration

with a negligible part of highly inclined orbits

that can be explained by uncertainties in classification due to errors in the beginning heights.

The C group also displays ecliptical concentration, but the highly inclined orbits are very

frequent and cannot be explained by errors.

The B group has ecliptical concentration of

orbits with practically constant numbers between 0° and 30°. Before separating the

observational material according to inclination,

we will find it useful to look at the distribution

of the semimajor axis. We observe in figure

4 that the A group has a maximum of a distribution between 1 and 2 a.u., the B group

a flatter maximum between 1 and 3 a.u.

On the other hand, the C group has a double

maximum, the first one between 2 and 3 a.u.,

and the second one for a « ». (The many

negative values of a are not surprising because

of the approximate reduction method used by

McCrosky and Posen (1961).)

Thus we see that the simple C group is now

separated into two groups according to the

orbit. To check this fact we use the orbital

inclination 50° as a division. All orbits with
40 SYMPOSIUM ON METEOR ORBITS AND DUST

10 in

0-

100-

n

0 -

100-

B

A

FIGURE 3.—Distribution of inclinations of the orbits of all

the sporadic Super-Schmidt meteors divided into the groups

A, B, C according to the preliminary classification.

i>50° represent the nonecliptic component,

and with i<50° the ecliptic component. Such

a separation for the A group is meaningless

since almost all meteors would be in the ecliptic

component. This confirms that wrongly classified meteors mainly are present.

The situation for the C group is quite different. The meteors with t>50° yield the maximum of a = oo, and the meteors with t<50° yield

the maximum between 2 and 3 a.u. This is

really a very good triple coincidence among

the kB parameter, semimajor axis, and inclination. Thus we can divide the C group into two

groups according to inclinations. The ecliptical

short-period group with i^SO" I shall denote as

the Ci group, and the long-period group with

arbitrary inclinations as the Cj group (in practice I take i>50° as the criterion for the C»

group).

The next element I consider is the eccentricity, using the 0.1 interval (fig. 5). The A

group has more maxima, indicating statistical

subgroups; the main maximum is in the 0.6

interval, and the majority of the A meteors

have eccentricities below this maximum. The

( \ group has only one maximum at 0.7, and the

number of meteors with eccentricities below

0.6 is negligible. The i\ group has a maximum

at eccentricity = 1.

The perihelion distance distribution (fig. 6)

for the A group and the C groups is also quite

different. The A group has a strong maximum

in the interval 0.9, while the C| group has

constant distribution starting with g=0.2.

The distribution of q for the B group points to

a relatively great number at very small perihelion distances, less than 0.3, in which the B

group markedly differs from the A and Ci

groups.

In summary, we see that the A group contains denser bodies with smaller semimajor

axes and smaller eccentricities than does the

C group. Both these groups have ecliptical

concentration and short-period orbits. The Cj

group contains particles of the same composition as the Ci group, but with random inclinations and long-period orbits. The B group

contains bodies with densities between the A

and the C groups, with relatively eccentric

orbits, ecliptical concentration, and small

perihelion distances.

It is evident that the velocity can be used

as an additional parameter for the classification.

The A group has a strong maximum in the

velocity interval v* <20 km/sec, the C2 group

has a maximum in the velocity interval P»

>60 km/sec, the C, group in the interval 25

to 35 km/sec, and the B group in the interval
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 41

20

100

n

200-

100-

B

all

all

100 i<50

all

n o

200

100

a

100-

100-

c

i>50°

A

i>50°

.5123 4 610«<0

a(a.u.) -°°

.5 1 2 3 4 610a><0

a(a.u.) -°°

.5 1 2 3 4 610oo<0

a (a.u.) •°°

FIGURE 4.—Distribution of semimajor axes for the same material as in figure 3. The separation according to the inclinations

yields the Q and Cj groups.

from 30 to 40 km/sec. This was used throughout the investigation and yielded the same

results I present in this section, except that the

groups were more distinct and the results

were clearer.

Groups in the e-q diagram (definitive

classification)

The one-dimensional histograms of the preceding

section show clearly the reality of the groups

according to composition, and at the same time

they are also distinct groups according to the

orbital element distributions; however, if we

wish to compare the orbital shape for different

240-022 O—6T 4

groups, we must turn to the two-dimensional

histograms. I chose the eccentricity as the x

axis and the perihelion distance as the y axis,

representing the oribtal shape. My choice

of q instead of the usual o makes it possible to

represent conveniently the short-period and

long-period orbits together on one diagram.

I used the e-q diagram to plot the positions

of all meteors of individual groups. As is

expected on the basis of differences in onedimensional histograms of individual groups,

we can find statistical limits between the groups

in our e-q diagram (fig? 7). The lower line is

the limit where the meteor collides with the
42 8TMPO8IUM ON METEOR ORBITS AND DUST

10

100

10-

100-

0 0.5 1 0 0.5 1 0 0.5 1

FIGURE 5.—Distribution of eccentricities for the same material

as in figure 3.

earth at aphelion. The straight line, with q=l,

is the limit where the meteor collides with the

earth's orbit at perihelion. Real cases can, of

course, be somewhat outside the limits because

of the eccentricity of the earth's orbit. Thus,

the upper part of the diagram contains all

observable orbits of meteors. The statistical

limits given by the solid lines determine where

the balance of observed numbers of meteors

of different groups is attained. In reality, the

interference of groups is present. We can

conclude that meteors with e <0.6 belong to

the A group; meteors with a >5 a.u. belong to

the C2 group; and meteors with q <0.2 and

o <5 a.u. belong to the B group. The boundary region between the A and C2 groups contains many instances of the Ci group, but they

are still less numerous than A or C2. This is

the reason why statistically the Ci group is

limited to lower values of q, where the C,

meteors are more frequent relative to A and C2.

Thus a significant number of meteors of the Ci

0 0.5 1 0 0.5 1 0 0.5 1

n 0

FIGURE 6.—Distribution of perihelion distances for the same

material as in figure 3.

group are in the region between the dashed

lines, but A and C2 groups prevail there.

Other parts of the e-q diagram have stronger

limits and the groups are sharply separated.

The small contamination of these boundary

regions is due mainly to the wrong classification and wrong orbit of individual cases.

We can prove the limits among groups of the

e-q diagram by the following opposite procedure. We choose now the limits in figure 7

as the definition of the groups; to avoid misunderstanding, I denote these defined groups

by A', B', C[, Cj. The kB distribution for each

group will show clearly the contamination of

groups in the e-q diagram (fig. 8). It is not

possible to separate the Ci and C» interferences

in this way, but both groups, mainly Ci, have

a relatively high A-group contamination, which

is mainly present in the upper region of the e-q

diagram between the dashed lines.
CLASSIFICATION OF METEOR ORBITS CEPLECHA 43

10

FIGURE 7.—Boundary lines among groups in the e-q diagram.

The main groups are contained inside the full lines. The

probable extension of the C, group superposed with the A

and Cj groups is marked by the dashed lines.

A small part of A', B', and C[ meteors have

orbits with inclinations greater than 40°. Such

orbits are denoted by A'l, B'l, CJI, and their

kB distribution in figure 8 clearly shows that

these cases are present mainly because of errors

in the basic material. The contamination of

the A group by the Cj group 's well evident

from the distribution of the A'l group.

We are now ready to use two criteria for the

classification of sporadic meteors: the kB value

and the position in the e-q diagram. Thus the

contamination of individual groups, when both

criteria are used, becomes negligible. From

figures 7 and 8, I now define each group to

be inside the limits given in figure 7 and with

the following kB interval: A group with kB=7.40

to 7.89; B group with fcB=7.10 to 7.29; Ci

group with fcB=6.70 to 7.09; and C2 group with

kB=6.70 to 7.29.

Characteristic orbits of the groups

We use the newly defined groups to investigate

characteristic orbits. The results of one-dimensional histograms are summarized in table 2.

The B and Ci groups have a simple distribution

of elements, and one characteristic orbit can

be derived from the maxima of the distributions, which are in all cases close to median

10

20

50-

0

20

0

20

100-

B'l

A'l

B'

B

FIGURE 8.—Distribution of the kB parameter, if the classification is made using the e-q diagram of figure 7. The

groups are marked by "dashes" to be clear that a different

definition of the groups is used from that in the preceding

figures. The contamination of the groups is evident from

this figure.
44 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 2.—Maxima of the one-dimensional histograms of orbital elements. (The values a, e, and q are not quite consistent

since they belong to independently determined maxima of the distribution of the three quantities connected

with strong correlation q=a(l — e).)

Group

a

e

q

i

T

Corresponds to

Main

max.

2.29

0.61

1.00

1°

252°

Second

max.

1.82

0.47

0.88

1°

91°

A,

A

Third

max.

1.31

0.35

0.90

1°

270°

A,

Fourth

max.

1.14

0.17

0.93

2°

164°

A,

Median

1.69

0.51

0.86

B

2.45

0.92

0.17

115°

c,

2.17

0.80

0.41b

6°

124°

Main

max.

0.99

1.00

c,

Second

max.

10.6

0.92

0.81

64° «

230°

Median

35

0.97

0.89

> Very flat maximum, median 14*.

*> Very flat maximum, the given value Is the median.

• Maximum between 100 and 1000 a.u.

* Orbits of this shape have a strong maximum at 80* Inclination Interval: probably a shower In April d Hereullds) with radiant 10* higher In declination

than Lyrids and a similar orbit but with smaller semimajor axis. (Meteor No*. 3010, 7328, and 3238 are surely the member* of thU ttoower.)

values. The Ct group has one dominant

maximum (fig. 9) close to the parabolic orbit

with q=l, and one well-defined secondary

maximum, which is probably caused by a

shower not separated from the original material.

This shower could in some way be connected

with the Lyrids.

The A group covers a relatively large area

in the e-q diagram; thus it is not surprising

that a more complicated statistical distribution

of elements is present. Figure 10 shows the

distribution of eccentricity for the A group,

5CH

FIGURE 10.—Distribution of eccentricities for the A group of

definitive classification.

and at least four groups are present. But

some of these groups are further separated in

the two-dimensional e-q histogram. If we look

for areas of minimal number of meteors in the

e-q histogram, we can find limits among 10

subgroups of the A group (fig. 7), and at the

same time determine the characteristic orbits

of these subgroups (table 3). Dividing lines

in figure 7 are the "valleys," if the meteor

numbers are plotted in the e-q diagram as

heights.

The distribution of inclinations has the

following characteristics (fig. 11):

2040KX)|-j60| fl8,

1-1000 ;30 -14

5 7 9 II 14 18 30 60 I-100 -20 -12 -8-6-4-2

1000-40 -16 -10

a (a.u.)

FIGURE 9.—Distribution of the semimajor axis of the C»

group of definitive classification of the McCrosky-Posen

Super-Schmidt meteors. The numbers of meteors are

reduced to equal I/a intervals.
CLASSIFICATION OF METEOR ORBITS—CEPLECHA

TABLE 3.—Subgroups of the A group

45

a

e

<1

Number of meteors

A,

1. 12

0.17

0.93

88

A,

0.96

0.25

0.72

41

A,

1.45

0.35

0.94

59

A4

1.23

0.38

0.76

17

A5

0.94

0.46

0.51

36

A,

1.84

0.49

0.94

68

A;

2.15

0.61

0.84

88

A8

1.32

0.62

0.50

22

A,

2.80

0.65

0.98

78

Aio

2.69

0.74

0.70

84

A group: ecliptical concentration, two

maxima at 1° and 11°, and a trace of a third

max in in in at 17°.

B group: ecliptical concentration, flat

maximum from 0° to 30°, then a drop from 30°

to 40°.

C| group: strong ecliptical concentration,

one maximum at 5° followed by a drop. The

cases with i>15° are negligible.

Cj group: smooth distribution in the complete 0° to 180° interval. (The local increase

at the 60° interval is explained in c of table 2.)

A subgroups (the maxima of inclination distribution are given in parentheses; the main

maxima are italicized):

two maxima: A, {2°, 13°); A, (1°, 9°);

A, (2°, 12°); A7 (2°, 10°); A, (2°, 10°);

A8 (5

one flat maximum: A5 (5°); A« (5°);

three maxima: A9 (8°, 9°, 18°); A10 (0° to

5°, 10°, 17°).

The distribution of inclination of the complete

A group, and also of all subgroups, is quite

different from the distribution of the Ci group.

Only the Ai0 subgroup is probably contaminated

in the first maximum by the Ci-group distributioD. The third maximum of the A9 and Ai0

subgroups is probably caused by the Ct-group

contamination.

The last element to be examined is the

longitude of perihelion. The distributions with

a 10° interval for different groups are given in

figure 12.

A group has a big maximum in the interval

190° to 340°, with the greatest numbers in the

interval from 230° to 280°. A secondary maximum between 70° and 100° is well defined.

B group contains too few cases for the investigation of any reliable distribution of

longitude of perihelion.

Ct group has a well-defined maximum from

120° to 160°.

Cj group has no maximum, as is expected for

orbits without any ecliptical concentration.

The distribution of longitude of perihelion is

clearly different for the A and Ct groups. The

distribution of r for the A subgroups is given in

table 4. All distributions of r for the A subgroups are different from the Ci-group distribution.

The characteristic orbits of groups are plotted

in figure 13.

Relative number of meteors among the

groups

The observed number of meteors nOb§ for each

group can be corrected for different observational effects. If we use the so-called cosmic

weight (as defined by Whipple, 1954), we obtain

the number of meteoroids np with constant

mass that pass perihelion per unit time. The

characteristic orbits of groups were used, and

thus only a very rough estimation was obtained.

The Cj group with long-period orbits was

seriously affected. The results are valid for

the mass interval from about 1 to 10"4 g. The

A group is dominant. The C-group space

density is about eight times less than that of

the A group. The B-group space density is

about 50 times less than that of the A group

(table 5).

A subgroups and associations

Southworth and Hawkins (1962) investigated

the connection among elements of orbits of a

random sample taken from the same material

we use, but by quite a different method. As

the probability of finding the meteor associations by their method is much higher in those
46

8YMPO8IUM ON METEOR ORBITS AND DUST

3CH

n 5

5 0 -

0° 8° 16° 24° 32° 40°

i

FIGURE 11.—Distribution of inclinations for the definitive

classification.

20-1

10

0

10

30

c2

A r

n

Iflf F

•»

"'I

i n 1 ^nJ JL

" [y

0° 80° 160* 240° 320°

IT

FIGURE 12.—Distribution of longitudes of perihelion for the

groups of definitive classification.

TABLE 4.—Maxima of distribution of r for A subgroups

(the main maxima are unierlined)

Main maximum

230° to 280°

A,

A,?

A,

II

A.

A j.

Secondary

maximum

A,

A,

A,

A,

A,

A,,

Other subgroup

maxima

A, (160°)

A, (140°)

A, (140°)

As (320°)

As (330°)
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 47

TABLE 5.—Percentage number of meteors in the groups

Group

A

B

c,

c,

no k.

54

6

9

31

nv

87

2

5

C

regions where the density of meteor numbers in

the e-q diagram is higher, I was not surprised to

obtain a distinct classification for almost all

the Southworth and Hawkins associations.

The only criterion in table 6 was the orbital

shape.

We see that the associations belong mostly to

the A group. On the contrary, as we shall see

later, the classical meteor showers belong without exception to the B, d , and C* groups, the

C group being the most frequent. Thus the

associations found by Southworth and Hawkins

have, on the whole, different characteristics

from the classical meteor showers.

Classification of small-camera meteors

Before answering the principal questions in the

Introduction, 1 shall try to repeat the same

procedure as adopted above to the observational material of small-camera meteors.

This is, of course, not so simple; first, because

of the small number of meteors available from

individual observatories, and second, if we

summarize all the material, because of possible

inhomogeneities. A further complication is the

much greater number of shower meteors in the

FIGURE 13.—Characteristic orbits of the groups.

TABLE 6.—Classification of the associations of Southworth and Hawkins

X

p

i.

+

a

y

S

V

Association

Geminids

Geminids

Orion ids

Ursa Majorids

Boot ids

Boot ids

Librids

Draconids

Group

c,

A io

A.

A,

AT, A,O

A,,AI 0

B

c,

Association

4> Bootids

{ Cepheids

a) Ursa Majorids

Cyclids

6 Ophiucids

M Draconids

T Herculids

ji Ophiucids

Group

A,

A,

A,

A,

c,

A,

A,

A,

$

a

X

c

V

<T

Association

Herculids

Cetids

Capricornids

Pegasids

Draconids

Geminids

Taurids

Leonids

Group

A,

A,

A,

A* AT

c,

c,

A,

*

•I do not believe that this association has any physical meaning.
48 SYMPOSIUM ON METEOR ORBITS AND DUST

small-camera material compared with the

Super-Schmidt meteors. I use the following

published material of the small-camera meteors:

Harvard (Whipple, 1954), Ondrejov (Ceplecha,

1952, 1953, 1957, 1958b; Ceplecha and Rajchl,

1959; Plavcova and Plavec, 1960; Ceplecha

et al., 1964) (and some unpublished values),

Dushanbe and Odessa (Babadzhanov and

Kramer, 1963). There were altogether 645

meteors, of which 281 belong to showers in

the classical sense. The remaining 364 sporadic

meteors comprise less than 20 percent of the

material we had at our disposal for the SuperSchmidt meteors.

We computed the kB parameter for all these

meteors. We checked the homogeneity of the

material using the k,, distribution for the

material from individual observatories. The

maxima coincide quite well, even though the

sharpness of the maxima is not so good due to

the small number of meteors investigated.

The only correction, which must be applied, is

a small correction of +0.1 of kB for Ondfejov

meteors. But the results are practically the

same without this correction.

If we now summarize meteors from all the

observatories, we get tbe histogram for kB

in figure 14. The result is the same as for the

Super-Schmidt meteors: two maxima of the

distribution separated by exactly the same

difference, 0.7. The third group between these

two main maxima is present at the same

relative place. Thus we can identify the

same A, B, and C groups without any doubt

among the sporadic meteors photographed by

the small cameras.

The numerical values of kB, at which the

maxima occur, are of course slightly different,

mainly because of the differences in the limiting magnitudes. The kB values for the smallcamera meteors are systematically higher by

0.3 than for Super-Schmidt meteors, which

corresponds to systematically lower beginning

heights (due to a decrease of the limiting

magnitude) of 3 or 4 km.

The A group, relative to the C group, is

much weaker for the small-camera than for the

Super-Schmidt meteors. This is in good

agreement with the fact that among the smallcamera meteors many more shower meteors are

present, and practically all these shower meteors

belong to the C group, as we shall see later

(table 7). The same holds for the B group,

which is more prominent among the smallcamera than among the Super-Schmidt meteors.

(Some classical showers belong to the B group,

but there is no clear case of the presence of the

A group.)

The ratio of the observed numbers of meteors

in the A and C groups is 0.92 for the smallcamera and 1.35 for the Super-Schmidt meteors.

30-

n 20

10-

0

11

nJ

8

FIGURE 14.—Distribution of the kB parameter for all sporadic

small-camera meteors from four observatories. The main

groups A, B, C, are well defined.

TABLE 7.—Classification of meteor showers ruing kB

parameter for Super-Schmidt meteors

Shower

a Capricornids

South Taurids

Geminids

South 6 Aquaria*

Lyrid8

Pereeids

Classification

c,

c,

B

B

c,

c,

Shower

Orionids

Quadrantids

X Cygnids

North Taurids

South Arietids

-, Draconids

Classification

c,

Bc,

c,

c,

(C,)"

> B group according to *• but with highly Inclined orbit with 7 new 1.

b

 Its haa a martinnm at 6 9 of the small-camera scale, which could be

caused by the smallest observed density 0.0 (with the extreme possibility

0.4).
CLASSIFICATION OF METEOR ORBITS CEPLECHA 49

The correction for the number of particles

passing the perihelion per unit time could

fully explain this difference. The resulting

constant number ratio for meteors passing the

perihelion per unit time and having the same

mass is 8 for both the small-camera and

Super-Schmidt meteors.

It is surprising that weaker meteors photographed by Super-Schmidt cameras contain

more observed dense particles than the smallcamera meteors. But if we suppose that shower

meteors, which are clearly connected with

comets, have small densities, then the relative

absence of classical showers among the SuperSchmidt meteors could point also to the greater

observed number of heavy particles among the

Super-Schmidt meteors.

It is not possible to present a definition of the

groups using the e-q diagram for the smallcamera meteors because of the small number

insufficient for the construction of two-dimensional histograms. Thus, I use the parameter

kB only for the group definitions: A group, kB

from 7.70 to 8.19 with 99 cases; B group, kB

from 7.40 to 7.59 with 50 cases; and C group,

kB from 6.80 to 7.29 with 122 cases.

Orbits of groups for the small-camera

meteors

The distribution of orbital elements for different

groups of the small-camera meteors is given in

histograms of figures 15,16,17, and 18. Though

the number of meteors is insufficient for a

detailed study, the following conclusions can

be made and compared with the results for the

Super-Schmidt meteors.

INCLINATIONS: A group: ecliptic concentration;

B group: ecliptic concentration

with flat maximum;

C group: ecliptic concentration

with many meteors of highly

inclined orbits.

The distribution of inclinations is, for all

groups, similar to that for the Super-Schmidt

meteors. Thus the same dividing inclination

of 50° was used to separate the C group into

the d and Cj groups. This separation by

inclinations also divides the short-period orbits

from the long-period orbits; thus the double

maximum of semimajor and eccentricity distributions for the whole C group is well separated

0° 40° 80° 160°

FIGURE IS.—Distribution of inclinations for small-camera

meteor groups.

into a single maximum distribution for the Ci

and Cj groups.

SEMIMAJOR AXIS: A group: maximum of distribution in interval from

2 to 3 a.u.;

B group: maximum from 2

to 3 a.u.;

Ci group: maximum from 3

to 4 a.u.;

C j group: maximum = «.
50 SYMPOSIUM ON METEOR ORBITS AND DUST

n o

10-

i<50€

0

20

0

.5 1 2 3 4 610 oo

a -oo<o

FIGURE 16.—Distribution of semimajor axes for small-camera

meteor groups.

The groups with ecliptical concentration have

the maxima of distributions of semimajor axis

about 1 a.u. greater than for the Super-Schmidt

meteors. This we can explain by the greater

average mass of the small-camera meteors,

which are thus, because of the PoyntingRobertson effect, much nearer to the original

starting orbits than the lighter Super-Schmidt

meteors.

5-

0

20 H

10-

n

0

20-

10-

0

B

i<50c

1.0

FIGURE 17.—Distribution of eccentricities for small-camera

meteor groups.

The C» group has relatively less negative

values of a, if compared with the Super-Schmidt

meteors. This, of course, is due to the more

precise orbits of the small-camera meteors than

of the McCrosky and Posen meteors. Also

lower values, below 10 a.u., of the Ci group can

be explained by the higher accuracy of a.
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 51

0

10

n 10

20-

10

0

B

~~| i <50'

L-n nc2

A

i<50°

~li r~

i—

_r

0.5

q

1.0

FIGURE 18.—Distribution of perihelion distances for smallcamera meteor groups.

ECCENTRICITIES: A group: one maximum in

the 0.7 interval is 0.1

higher, if compared with

the main maximum for the

Super-Schmidt meteors.

The structure is not so

complicated as that for the

Super-Schmidt meteors;

B group: very flat maximum

with no values below 0.5,

and relatively more values

in the 0.8 and 0.9 intervals,

if compared with the SuperSchmidt meteors;

Ci group: one maximum in

the 0.7 interval and a relatively lower number of

meteors in the 0.6 interval,

if compared with the SuperSchmidt meteors;

Ci group: one maximum = 1

and very small differences

when compared to the distribution of the SuperSchmidt meteors.

The eccentricity distribution for the A, B, and

Ci groups confirms that the small-camera

meteors are nearer to the original starting orbits.

PERIHELION DISTANCES: A and CI groups: more

concentrated at q

= 1 than for the Super-Schmidt meteors;

B group: more distinct

maximum at q from

0.1 to 0.2 than the

Super-Schmidt meteors, which show

only a flat maximum at small perihelion distances.

Note that the A group contains more highly

inclined orbits than for the Super-Schmidt

meteors. This can be explained by the greater

number of meteors of the C» group, which are

wrongly classified as the A group in some cases,

and so the contamination of the statistical A

group by the C» group is expected to be higher

for small-camera meteors; this is rarely observed.

The limits among groups in the e-q diagram

(see fig. 7) hold for the Super-Schmidt meteors

and are not applicable to the small-camera

meteors. Generally speaking, the limits for

the small-camera meteors are shifted to the

right and up (greater e and q).

Poynting-Robertson effect: age and origin

Results for the small-camera meteors, if

compared with the Super-Schmidt meteors,

point to the possibility of estimating the age of

the ecliptical groups taking into account the

Poynting-Robertson effect. As the material
52 8YMP0SIUM ON METEOR ORBITS AND DUST

for the B and Ct groups is not too extensive,

and both these groups seem to be connected

with a cometary origin, I use the procedure of

this section exclusively for the A group of the

McCrosky and Posen meteors with »<B<20

km/sec.

Wyatt and Whipple (1950) give the equations

of changes of orbital elements due to the

Poynting-Robertson effect as

a=- (4)

where C is a constant given by a known pair

of a, e, and

(5)

where r is the radius and 6 the density of the

meteor particle.

The computation was made from the individual data on each meteor of the A group.

The density 1 was assumed and also used for

the computation of the meteor radius r from

the mass TO. The choice of density is equivalent to the choice of the time scale only and

has no influence on the element distribution.

We first computed the C constant, and its

histogram is shown in figure 19. There is one

great maximum at 2.2, which is connected with

the A8 and A9 subgroups. The e-q diagram is

used to present the results of the distribution

of A-group meteors today and 2, 5, and 9

million years ago (see fig. 20). The lines in the

40-

n 20-

today diagram have the same C, i.e., the direction of the motion of the points due to the

Poynting-Robertson effect.

If we now choose the statistical semimajor axis

of a starting asteroidal orbit to be 2.8 a.u., we

can follow individual groups back in time up

to this limit and hence determine the age.

Thus we have found at least five age groups of

< 1 , 3, 4, 8, and 12 million years. They correspond to the following A subgroups:

<10* years A,-fA7

3X10* years As

4X10* years At+ A,+ AW- A8

8X 106 years A,

12X109 years A,

The subgroups A,o and A» are not present in

this A-group sample because of the limitation

imposed by vm<C2Q km/sec.

The time scale for the A group seems to be

higher than previously supposed. But the

absolute scale of time is dependent on the mass

scale, and thus on the luminosity coefficient

T0. As r8oc(62/To)

1/3

 and the value $7To can be

determined from the observations (Verniani,

1964), the time scale of equation (5) is estimated

to be about by 30 percent less than the assumed

value. On the other hand, the results in this

paper on the meteor densities tend to increase

the deduced ages. Even if we assume the

results of Verniani, the ages are still too large

and the original starting orbit can be not only

asteroidal, but also subasteroidal. In particular,

I2XI06

FIGURE 19.—Distribution of the Poynting-Robertson constant C for the sporadic meteors with P 0 O < 2 0 km/sec belonging to the A

group of the Super-Schmidt meteors.
CLASSIFICATION OF METEOR ORBITS CEPLECHA 53

1

0.5H

TODAY

0.5

q

•

1.0-

0.5-

•:••.••• • - A

' •''" - • • • :

2 x 106 YEARS AGO

Mi:-

0.5

z.oA

0.5

9x1Ov YEARS AGO

1.5H

5x10° YEARS AGO

<P\ * .

0.5

e

0.5

e

FIGURE 20.—Poynting-Robertson effect plotted as points for each meteor in the e-q diagram. The A group with p.,,^20 km/sec of

sporadic Super-Schmidt meteors is used.
54 8TMPO8IUM ON METEOR ORBITS AND DUST

the orbits with observed eccentricities less than

0.30, which are very usual among the SuperSchmidt meteors, can hardly originate from an

eccentric cometary orbit, since the Poyn tingRobertson effect cannot change such orbits

into observed orbits during periods shorter than

some tens of million years.

Our starting asteroidal orbit with a=2.8 a.u.

is chosen on the assumption that collisions with

large asteroidal bodies change the semimajor

axis in both directions. It would be difficult to

find a collision mechanism that shortens only

the semimajor axis. If we wish to reduce the

ages, we must suppose the existence of a great

number of small asteroidal bodies with semimajor axes between 1 and 2 a.u. It is interesting that the same assumption appears to be

necessary for a stony meteorite origin (Anders,

1965). The asteroidal origin of the A group is

not excluded on the basis of the Poyn tingRobertson effect.

Absolute scale of the ku parameter

The theoretical values of the kB parameter from

equation (2) are of no importance for the

absolute scale of this parameter. On the other

hand, if we know the absolute scale, we can

obtain rough estimates of meteor-particle densities for our groups. We can calibrate the kB

scale from photographed meteors of known

composition. I will use two meteors with pure

iron spectra without any indication of sodium,

calcium, and magnesium lines, and the

McCrosky-Soberman (1963) artificial iron meteoroid. The first grating spectrum with 12 lines

and 340 A/mm was published by Halliday

(1960). The second grating spectrum was

recently photographed and reduced at the

Ondfejov Observatory, and has 189 lines with

58 A/mm dispersion. The spectrum and the

normal small-camera photographs of this meteor, taken from two stations, were obtained;

thus, all the necessary data are at our disposal

(Meteor no. 36221 and Spectrum no. S 912).

There is no doubt that, with such a great dispersion, the Ondfejov S 912 spectrum is a pure

iron spectrum with Fe I and Fe II lines and

some clearly resolved Ni I lines. The lines for

Na I, Ca I, Ca II, Mg I, Mn I, and Cr I, usual

in normal meteor spectra, are absent. This

confirms the iron composition of the meteor

body.

The kB parameter for this Ondfejov iron

meteor was found to be 7.94. But this value

must be corrected for the increase in brightness

of the meteor over the average brightness of the

small-camera meteors investigated in this paper.

The average brightness magnitude m,t (median

of the distribution) of all the meteors in the

small-camera samples is —4.2, and the brightness of Meteor no. 36221 is —11.0 mPl. The

change of kB per magnitude can be estimated

from the difference between the small-camera

and Super-Schmidt meteors. The median of

the limiting photographic magnitude for the

Super-Schmidt meteors is +3.3, and for the

small-camera meteors is — 1.0. The change of

kB in this interval is 0.30; hence the ratio

Aifca/Aro,,=0.070 mg"1. Thus the correction

for kB is 0.48, and the corrected £,=8.42. To

check such a small correction, we can use the

separation of the small-camera meteors into

two groups according to magnitudes. The

median photographic magnitudes of these

groups with the same number of meteors are

—2.9 and —5.6. Although the kB distributions

for both groups do not define the maxima as

clearly as for the complete material, we can

definitely conclude that the difference of kB

between these two groups is close to 0.10. This

indicates that the correction of kB used for

Meteor no. 36221 could be somewhat overestimated but it could hardly be smaller than

the real value.

The Halliday iron meteor has the great

advantage that its magnitude has exactly the

median value of our small-camera sample. The

kB parameter is 8.38, and no further correction

is necessary. This value checks our correction

0.07 of kB/m.

The most important data we use are those

on the artificial iron meteoroid. The great

advantage is the use of Super-Schmidt cameras

for the records. Thus the kB value can be

directly compared with the main sample of the

Super-Schmidt meteors we use. The only

slight drawback is the very small velocity 9.8

km/sec. But the Super-Schmidt sample is so

extensive that we can determine the A maximum of the kB distribution for meteors with
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 55

poo<12 km/sec. The resultant value Jtfl=7.55

is only 0.10 less than for the whole sample.

(For meteors with 12<ca ,<13 km/sec, the

kB maximum is exactly the same as for the

whole sample.) The resultant value of kB,

according to the whole sample of the SuperSchmidt meteors, is thus 8.05 for the artificial

iron meteoroid.

All these three values of kB are in good

agreement. If we scale these values to correspond to the Super-Schmidt meteors we have

8.12, 8.08, and 8.05. The mean value ArB=8.08

can be accepted for the iron body. The difference of this value from the maxima of the kB

distribution for the Super-Schmidt meteors

determines the absolute scale of kB, and thus

the product X5c.

Now we can use a rough dependence of X6c

on 6 for the different materials examined (fig.

21). *If we use the data from Levin's book

(1061) and the data on the stainless steel 304

from McCrosky and Soberman (1963), we get

the following rough estimates of the density:

A group 6=4.0 g/cm3,

B group 5=2.2 g/cm3,

C group 5=1.4 g/cm3.

These estimates are not precise since no strict

dependencies exist among X, 6, and c. But

there is a tendency for c to be constant and

independent of the porosity, which could cause

a low density for the C group. Thus we can

reduce the problem to the 5-X dependence only.

If we assume for a porous body of stony composition

Xoc6", (6)

then the value of n could be between 1 and 3,

with 2 as the most probable value. The value

2 corresponds to the data given by Levin (1961).

Even if we use n=l, we obtain 6=0.9 for the C

group as the lowest acceptable limit.

Thus we see that the A group with the

shortest semimajor axis and the smallest

eccentricities has a density close to that of the

average stony meteorite. On the other hand,

the C group has a density not much greater

than one, a value quite unknown among meteorites. At the same time, the separation of this

IRON MET.

STEEL 304

/ / SANDSTONE

«*>/' ? >• c

POROUS. BODY

0

log 8

FIGURE 21.—Log b is plotted against % log \6c. Different

materials (iron meteorite, steel 304, meteoric stone, sandstone, hypothetical porous body) are each represented by a

point. The y axis is also the ka parameter + constant.

The constant is easy to determine as the observed values of

ka for three iron bodies must be at the place where iron

meteorite and steel 304 are plotted. Thus the observed

ka parameter for the A, B, and C groups can be plotted in

this figure (arrows). Thus a rough estimation of the density

of the meteor material is possible.

C group into the Ci group with ecliptical

concentration and short-period orbits and the

Cj group without ecliptical concentration and

with long-period orbits indicates that the C

group is connected with comets.

The B group has a density close to two. As

the orbits of the B group have very great eccentricities with aphelion distances near the

Jupiter orbit, a cometary origin is highly

probable. The increase of density could be

caused during the close approach to the sun, as

the perihelion distances are all below 0.35 a.u.,

with the most probable characteristic value of

0.17 a.u. The temperature of about 500° C

can join the individual grains of the conglomerate more closely together, thus increasing the

heat conductivity. On this assumption the

change in the density could be less than the

given change of 0.8. If n in equation (6) is 3,

then we proceed from the C-group density 1.4

to the B-group density 1.9 and to the heat

conductivity 1.3 X10s. The increase in the heat

conductivity of five times, due to the solar

heating, seems quite reasonable. If no changes

of density are present (n=«), the heat conductivity must change 10 times.
56 SYMPOSIUM ON METEOR ORBITS AND DUST

The iron particles among the Super-Schmidt

meteors can be estimated from figure 1 in a

maximum of 10 cases, i.e., 0.5 percent of the

whole sample.

The results on the densities differ from the

recent data given by Verniani (1964). The

density of our C group is five times greater than

the density of the whole Verniani sample. I

shall present here some remarks on the meteor

densities derived in the Verniani paper. I think

that the absolute T0 value, which depends

mainly on the McCrosky and Soberman experiment (1963), is quite acceptable. On the other

hand, the absolute value of r/S2 was determined

from equation (11) of the Verniani paper, where

the measured meteor deceleration, drag, and

shape coefficients enter to the third power.

As the fragmentation is effective, it is not quite

clear to what particle the deceleration belongs.

At the same time we must suppose knowledge of

the drag and shape coefficients. I think that

the "absolute" values of T/62 determined in the

Verniani paper could be systematically overestimated. The resulting density could be

between the density of the particle, or dropcloud, and that of the main meteor body.

If the ratio TA/(dv/dt) in Verniani's equation

(11) is increased by only three times, the Cgroup density 1.4 will coincide with 0.25 given

by Verniani for the complete sample. It is

evident that systematic change due to all three

quantities, r, A, and dv/dt, could be much

greater than three.

If we suppose that the dimensions of fragments or drops do not depend too much on the

main body dimension, then the fragmentation

will change the decelerations more at the end

of the trajectory, as is observed. But then the

brighter meteors are less affected by the fragmentation, and it is quite clear why Verniani

arrived at twice the density for the smallcamera meteors than for the Super-Schmidt

meteors. The Verniani meteoroid densities are

not identical with the density of the main

meteor body.

On the other hand, our results are based on

the beginning heights, where the fragmentation

is not so important as later, and no measurements or assumptions of decelerations were

used at all. The absolute scale of our densities

was obtained by direct comparison of three iron

bodies with the sample. Thus I think my results on densities are closer to reality than

Verniani's.

The question of the fragmentation of the Agroup meteors can arise if they have stony

densities. Fragmentation of meteors was well

established by Jacchia (1955) to explain the

faint meteor anomaly. But if only our C group

contains fragile meteors, then this contradicts

the fact that the C group is relatively more

numerous for brighter small-camera meteors

than for the Super-Schmidt meteors. The

same holds for shower meteors. But I think

that the fragmentation necessary to explain the

faint meteor anomaly must be understood quite

generally, without assuming that the material

leaves the body as solid particles only. The

separation of drops is another form of "fragmentation." The study of meteor and wake

spectra of very bright meteors (Ceplecha, 1964,

1965) shows such a great luminous volume

where meteor light is produced at very small

excitation temperatures that there must be a

transport of meteor mass behind the body by

means other than gas. "Fragmentation" of

big bodies in the general sense is also present,

but from the observational point of view has

little importance for the measured decelerations,

as the drops or fragments are much less than

the body itself. The smaller the meteor body,

the greater the effect on the measured velocity.

This is the reason for deceleration anomalies for

faint meteors and at the meteor ends. Thus

we can conclude that fragmentation in this

general sense is important for all the groups we

have found, without strong dependence on the

meteoroid density. The A group is no exception, even if its density and composition are

those of the stony meteor.

Theoretical and observed beginning of the

meteor

The small difference in the kB values between

the Super-Schmidt and the small-camera meteors points to a steep increase of the light curve

just at or before the beginning of the photographed trail. The change of kB by 0.30 is

equivalent to the change of beginning height of

about 3.5 km, and is accompanied by a change

of the limiting magnitudes between the two
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 57

used samples of 4.3 mpg. The resulting slope of

the light curve at the meteor beginning is 1.2

mp#/km, about seven times greater than is

usually observed after the beginning. The

majority of the observational material has

maximum magnitudes in the interval from 2 to

4 mpt above the plate limit equally for both

samples. The sudden increase of brightness at

the beginning could to some extent be related

to the theoretical considerations of Levin (1961).

We can compute the ratio of the temperature

to the heat-transfer coefficient from the theoretical equation (2). We get for iron bodies,

which we use as the definition of the absolute

kB values:

log TB/A = 3.60 for the Super-Schmidt meteors,

=3.90 for the small-camera meteors,

and thus,

Super-Schmidt meteors

A TB

1 4300° K

0. 65 2800° K

small-camera meteors

A TB

1 8200° K

0. 65 5400° K

We see from the resulting temperature values

that the theoretical beginning point of a meteor

as defined by Levin (1961) is practically identical

with the beginning photographed for an average

meteor by the Super-Schmidt camera. The

small camera is able to record the average

meteor about 4 km lower than the corresponding

theoretical beginning point.

Classification of shower meteors

There is not too much observational material

for a statistical distribution of the kB parameter

for the shower meteors because of the dearth of

observational material for the small-camera

meteors and the small percentage of shower

meteors among the Super-Schmidt sample.

The Super-Schmidt sample is sufficient to

classify, according to the kB distribution,

Orionids as C2 group, Perseids as C2 group,

and Geminids as B group. The small-camera

sample has enough cases for the Perseids,

which are put into the same Cj group. This

is consistent with the cometary origin of the

C group in general.

Only indications of the classification can be

given for other showers, mainly based on the

Super-Schmidt meteors (see table 7).

240-022 O—67 5

The classification of the showers corresponds

well to the orbital characteristics except for

the Quadrantids, which are classified according

to kB as the B group, but they have highly

inclined orbits. It is interesting that among

the classical showers no case with A-group

classification is present. This supports the

idea that the A group is not connected with

comets.

As we know, 7 Draconids are very young

meteors recently separated from the parent

comet. We can assume that the density of the

cometary particles, when they leave the parent

comet and lose their volatile material, is somewhat lower than the 7 Draconid value of 5=0.9.

This value is about twice Whipple's theoretical

value (1955) derived on the basis of bis cometary

model. If all the volatile material is lost by

the meteor body soon after leaving the comet,

the results of this paper show that there could

be some contrary process that makes the

meteors more conductive for the heat flow and

probably also somewhat denser. Heating by

solar radiation could be the reason. Thus the

evolution could proceed from 7 A Draconids

type to the C type and to the B type at

close approach to the sun.

The ka distribution for other sporadic

meteor samples

Hawkins and Southworth (1958, 1961) published

all available data on a random sample of SuperSchmidt meteors taking every tenth meteor

from the complete material. The precise reduction method was applied to these meteors.

Thus we can use this sample of 285 sporadic

meteors for checking the results on the kB

parameter distribution. The strong maxima

at kB intervals 7.5 and 6.9 and a weak maximum at 7.2 coincide almost exactly with the

maxima obtained for the McCrosky and Posen

meteors. It means that there is no systematic

error, especially in the beginning heights. The

A group is again the most prominent. Also the

orbital elements have similar distributions in

both samples.

Kecently Verniani and Hawkins (1965)

published data on 320 radio meteors available

for computation of the kB parameter. Even if

the physical meaning of the beginning height

for a radio meteor is different from that of an
58 SYMPOSIUM ON METEOR ORBITS AND DUST

optical meteor, some of the considerations of

the second section of this paper still hold. It

is interesting that the two strong maxima of

kB distribution are again present. The maximum at kB=7A to 7.7 contains the majority

of the material and could correspond to the

A group. The maximum at A:fl=6.9 could

correspond to the C group. I do not have

the orbits of individual meteors at my disposal,

thus nothing final about the groups can be

concluded. But statistics of radio meteor

orbits as a whole (Hawkins, Southworth, and

Rosenthal, 1964) give the distribution of

semimajor axes, eccentricities, and inclinations similar to the A group of the SuperSchmidt meteors with more cases of smaller

a and e than the A group of the Super-Schmidt

meteors.

The ratio of meteor numbers in the groups

A/C=3.8 for radio meteors indicates the continuing tendency of relative increase of the

observed meteor numbers of the A group with

the decrease of the meteor brightness (TO,,, = 8

for the radio meteors).

Results

The main results of this paper answer the

two principal questions in the introduction:

1. Four groups exist among sporadic

meteor orbits. Three groups denoted A, B, C,

can be separated using the kB parameter, which

represents to a good measure the product of

heat conductivity, density, and specific heat.

The A group has the greatest density, the C

group the least. The C group can be further

separated into the Cx and Cj groups by semimajor axes and orbital inclinations. Characteristics of the A group are the greatest meteoroid

density, short-period orbits with small eccentricities, and ecliptical concentration; of the

Cx group, the lowest meteoroid density, shortperiod orbits, but with longer semimajor axis,

and with greater eccentricities than the A

group, ecliptical concentration; of the Cj

group, density identical with the Ci group,

long-period orbits with eccentricities near 1

and without any ecliptical or other concentration; and of the B group, density between the

A and C groups, short-period orbits with great

eccentricities, and ecliptic concentration, small

perihelion distances. The A group is the most

numerous among the observed Super-Schmidt

meteors, and the C among the observed smallcamera meteors.

2. The C, group is clearly connected with

short-period comets and the C, group with the

long-period "parabolic" comets. The B group

is probably connected with the short-period

comets. The A group as a whole is probably

connected with asteroids. The A-group

meteors with eccentricities below 0.30 are

probably connected with smaller asteroidal

bodies having orbits with semimajor axes

between 1 and 2 a.u.

Further results of this paper are the following:

1. The distribution of the kB parameter

has two main maxima (A and C groups) independent of the observational material used

(McCrosky and Posen, Hawkins and Southworth, small-cameras of four different observatories, radio meteors).

2. The independence of the kB maxima

on the velocity, mass, and magnitude was

verified.

3. The parameter kB defined by equations

(2) and (3) is a very good relative measure of

the meteoroid composition. The heating theory

of the meteoroid before the rapid ablation is

the most certain of all the meteor-phenomenon

theories.

4. The absolute scale of the kB parameter

can be obtained using two meteors with pure

iron spectra and the artificial steel meteoroid.

5. Using the absolute values of kB, we get

the probable average density 4.0 for the A

group, 2.2 for the B group, and 1.4 for the C

group. The lowest acceptable limit of the

density for the C group is 0.9.

6. The absolute kB values if compared

with the theoretical values of equation (2)

demonstrate that the observed beginning of

the average Super-Schmidt meteor is almost

identical with the theoretical beginning as

defined by Levin (1961). This is not the case

for the small-camera meteors.

7. A sudden increase of brightness is

present at the meteor beginning, and is seven

times greater than the normal slope of the

first part of the light curve.

8. The extensive A group can be statistically separated into 10 subgroups using twodimensional e-q histograms.
CLASSIFICATION OF METEOR ORBITS—CEPLECHA 50

9. The differences in orbital elements for

the small-camera meteors and for the SuperSchmidt meteors, if compared in A and Ci

groups, are quite consistent with the greater

average mass of the small-camera meteors

with orbits less changed by the PoyntingRobertson effect.

10. The different times of the origins of

individual meteor subgroups of the A group

are due to the Poynting-Robertson effect.

11. The results of Verniani (1964) on

meteor densities are at least five times smaller

than our results. Verniani uses meteor decelerations, and absolute values of the drag and

shape coefficient, which I do not require.

Also, meteor fragmentation affects my results

much less than the results of Verniani.

12. Whipple's K criterion is an empirical

boundary line between cometary and asteroidal

orbits, which cannot be extrapolated down to

perihelion distances equal to and less than

1 a.u.

13. My previous results based on theoretical values of kB and connecting the two

main groups of sporadic meteors (now denoted

A and C) with iron and stony meteorites are

incorrect. If there is some group of iron

particles among the Super-Schmidt meteors, it

contains less than 0.5 percent of all the sample.

14. Classical meteor showers studied by

the its-parameter distribution belong mainly

to the C group and some to the B group.

No A group was found.

15. The associations of Southworth and

Hawkins (1962) mainly belong to the A group.

16. The heating by solar radiation could

be the reason for the change of C-group

properties to the B-group properties.

17. The C group and the shower meteors

dominate in the observed number of the smallcamera sample. The A group dominates in the

observed number of the Super-Schmidt sample,

which has a distinct lack of the observed

shower meteors. The ratio of meteoroid

numbers passing the perihelion per unit time

and having the same mass is A/C = 8 for both

the samples.

Very recently Jacchia, Verniani, and Briggs

(1965) published data on relatively brighter

Super-Schmidt meteors, which can be used for

the computation of the kB parameter and fully

confirm the results of this paper.

Acknowledgment

I am very much indebted to Miss M. JeSkova

for assistance with the numerical computations,

which were mainly made with the ZUSE

Z-23 electronic digital computer of the National

Research Institute of Heat Engineering in

Prague.

References

ANDERS, E.

1965. Tisserand's criterion: A link between meteorites and Mars asteroids. Enrico

Fermi Institute for Nuclear Studies

[preliminary draft].

BABADZHANOV, P. B., and KRAMER, E. N,

1963. Methods and some results of the photographic researches of meteors. In

Ionosphere and Meteors, Sec. V of IGY

Program, no. 12, Publ. House Acad. Sci.

USSR, Moscow.

CEPLECHA, Z.

1952. Double photographed meteor, 1949 Apr. 21.

Bull. Astron. Inst. Czechoslovakia, vol. 3,

pp. 13-15.

1953. Meteor photographs, I: Air densities. Bull.

Astron. Inst. Czechoslovakia, vol. 4,

pp. 55-59.

1957. Photographic Geminids 1955. Bull.

Astron. Inst. Czechoslovakia, vol. 8,

pp. 51-61.

1958a. On the composition of meteors. Bull.

Astron. Inst. Czechoslovakia, vol. 9,

pp. 154-159.

1958b. Photographic Perseids 1956. Bull. Astron.

Inst. Czechoslovakia, vol. 9, pp. 225-234.

1964. Study of a bright meteor flare by means of

emission curve of growth. Bull. Astron.

Inst. Czechoslovakia, voL 15, pp. 102-

112.

1965. Complete data on bright meteor 32281.

Bull. Astron. Inst. Czechoslovakia, vol.

16, pp. 88-101.

CEPLECHA, Z.; JEZKOVA, M.; NOVAK, M.; RAJCHL, J.;

SEHNAL, L.; and DAVIES, J. G.

1964. Ondrejov double-station meteors during the

IGY and IGC. BulL Astron. Inst.

Czechoslovakia, vol. 15, pp. 144-155.

CEPLECHA, Z., and PADEVET, V.

1961. The beginning of rapid evaporation of

meteors of different dimensions. Bull.

Astron. Inst. Czechoslovakia, vol. 12,

pp.191-195.

CEPLECHA, Z., and RAJCHL, J.

1959. Photographic meteors 1955 and 1956.

Bull. Astron. Inst. Czechoslovakia, vol.

10, pp. 133-135.
60 SYMPOSIUM ON METEOR ORBITS AND DUST

DTCUS, R. D., and BRADFORD, D. C.

1964. The origin of meteors inferred from orbital

elements. Icarus, vol. 3, pp. 306-310.

HALUDAY, I.

1960. The spectrum of an asteroidal meteor fragment. Astrophys. Journ., vol. 132, pp.

482-485.

HAWKINS, G. S., and SOTJTHWORTH, R. B.

1958. The statistics of meteors in the earth's

atmosphere. Smithsonian Contr. Astrophys., vol. 2, no. 11, pp. 349-364.

1961. Orbital elements of meteors. Smithsonian

Contr. Astrophys., vol. 4, no. 3, pp. 85-

95.

HAWKINS, G. S.; SOUTHWORTH, R. B.; and ROSENTHAI,, S.

1964. Preliminary analysis of meteor radiants

and orbits. Harvard Radio Meteor Project lies. Rep., no. 7, 32 pp.

JACCHIA, L. G.

1955. The physical theory of meteors, VIII:

Fragmentation as a cause of the faintmeteor anomaly. Astrophys. Journ., vol.

121, pp. 521-527.

1960. Individual characteristics of meteor families. Astron. Journ., vol. 65, pp. 53-54.

JACCHIA, L. G.; VERNIANI, F; and BRIGOS, R. E.

1965. An analysis of the atmospheric trajectories

of 413 precisely reduced photographic

meteors. Smithsonian Astrophys. Obs.

Spec. Rep. No. 175, 309 pp.; also in

Smithsonian Contr. Astrophys., vol. 10,

no. 1, 139 pp., 1967.

JACCHIA, L. G., and WHIPPLE, F. L.

1961. Precision orbits of 413 photographic

meteors. Smithsonian Contr. Astrophys.,

vol. 4, no. 4, pp. 97-129.

LEVIN, B. J.

1961. The Physical Theory of Meteors and Meteor

Matter in the Solar System. Trans, by

F. Bartel, ed. by N. Richter, AkademieVerlag, Berlin, 130 pp.

MCCROBKY, R. E., and POSEN, A.

1961. Orbital elements of photographic meteors.

Smithsonian Contr. Astrophys., vol. 4,

no. 2, pp. 15-84.

MCCROSKY, R. E., and SOBERMAN, R. K.

1963. I {••suits from an artificial iron meteoroid at

10 km/Bee. In Proceedings of the Symposium on the Astronomy and Physics

of Meteors. Smithsonian Contr. Astrophys., vol. 7, pp. 199-208.

PLAVCOVA, Z., and PLAVEC, M.

1960. Heliocentric orbits of six photographed

sporadic meteors. Bull. Astron. Inst.

Ciechoslovakia, vol. 11, pp. 226-227.

SOUTHWORTH, R. H , and HAWKINS, G. 8.

1962. Statistics of meteor streams. Geophys.

Res. Papers 75, p. 261, AFCRL 62-497,

May. See also, Proceedings of the Symposium on the Astronomy and Physics of Meteors. Smithsonian Contr.

Astrophys., vol. 7, pp. 261-285, 1963.

U.S. STANDARD ATMOSPHERE

1962. U.8. Standard Atmosphere 1062. Prepared under NASA, USAF, and U8WB,

Washington, D.C., 278 pp.

VERNIANI, F.

1964. On the luminous efficiency of meteors.

Smithsonian Astrophys. Obs. Spec. Rep.

No. 145, 62 pp.

VERNIANI, F., and HAWKINS, G. S.

1965. Masses, magnitudes, and densities of 320

radio meteors. Harvard Radio Meteor

Project Res. Rep., no. 12, 34 pp.

WHIPPLE, F. L.

1954. Photographic meteor orbits and their distribution in space Astron. Journ., vol.

.59, pp. 201-217.

1955. On the mass-luminosity relation for meteors. Astron. Journ., vol. 60, pp. 182-

183.

WYATT, S. P., Jr., and WHIPPLE, F. L.

1950. The Poynting- Robertson effect on meteor

orbits. Astrophys. Journ., vol. Ill ,

pp.134-141.

Abstract

An additional kB parameter proportional to log \6c of the meteoroid is used together with the orbital elements

Four groups are found among sporadic meteors: the A group has the greatest density and short-period orbits with

small eccentricities and ecliptical concentration; the C group has the least density and can be separated into a Ci

group of short-period orbits with ecliptical concentration but with longer semimajor axes and with greater eccentricities

than the A group, and into a C, group with long-period orbits of eccentricities near one and without any ecliptical or

other concentration. The B group has a density between that of the A and the C groups, and short-period orbits

with great eccentricities, small perihelion distances and ecliptical concentration. The C| group is clearly connected

with short-period comets, the C2 group with the long-period "parabolic" comets. The B group could be connected

with the short-period comets. The A group is probably connected with asteroids. The observed number of SuperSchmidt meteors is maximal in the A group, a little less in the C group (the C:

 group being a greater contributor than

the Ci group), and only small in the B group.
Comments on Ceplecha's Paper "Classification of Meteor

Orbits"

F. VERNIANI 1

In his paper "Classification of Meteor Orbits"

(supra), Ceplecha finds essentially the existence

of two groups among sporadic meteors: One

(A group) containing meteors with greater

density and short-period orbits, and another

(C group) containing meteors with lower

density and long-period orbits. He then estimates the density of meteors of the A group to

be about 4 g/cm8 and hence infers that they are

of asteroidal origin. In conclusion, he finds

that 54 percent of the meteors observed photographically and about 90 percent of the true

meteoric population should be considered as of

asteroidal origin.

The existence of some physical differences

between short-period and long-period meteors

was first discovered by Jacchia (1958, 1960,

1963). A systematic difference in density was

later explicitly pointed out by Verniani (1964a),

and confirmed by Jacchia, Verniani, and Briggs

(1965). The explanation of these differences

was given on the basis of Whipple's theory of

comets and meteors (1950, 1951). Therefore,

while the existence of the two different groups

found by Ceplecha confirms well-established

facts, his conclusions about the asteroidal

origin and the high density of most meteors

differ from the generally accepted results and

theory.

The present evidence shows that nearly all

photographic meteors are of cometary origin.

Referring for all details to Jacchia and Whipple

(1961), Jacchia (1963), and Jacchia, Verniani,

and Briggs (1965), I point out the following

facts:

1

 Smithsonian Astrophysical Observatory, Cambridge, Massachusetts; on leave from Ccntro Nazionale per U Fisica dell' Atmosfera e la

Meteorologia del CNR, Rome, Italy.

1. The orbits of many meteor showers and

associations have been clearly identified with

those of some comets.

2. The physical characteristics of sporadic

and shower meteors not related to known comets

do not show any systematic differences from

those of the shower meteors connected with

comets.

3. Fragmentation is of common occurrence, as i& shown beyond any reasonable doubt

by the deceleration anomalies, and by the

blending of the exposed segments.

4. The average meteor density, directly

computed by decelerations, is about 0.25 g/cm3.

5. Among over 400 precisely reduced

meteors, only one has all the expected characteristics of an asteroidal meteor, and this in

spite of the fact that especially long trails were

selected, thus favoring the inclusion of asteroidal meteors.

From all these facts we must conclude that

the great majority of meteors are of cometary

origin, and because they are also light, porous,

and crumbly, they conform to Whipple's theory

of comets and meteor production.

Ceplecha finds values of average meteor

densities one order of magnitude larger than

the currently accepted values (Whipple, 1963;

Verniani, 1964a,b; Jacchia, Verniani, and

Briggs, 1965). In particular, he criticizes the

procedure used in my paper (1964a) to obtain

meteor densities. He claims that, in the case

of fragmenting particles, the meaning of decelerations is not clear, and quoting his own words,

"it is evident that systematic changes due to

(the drag coefficient) y, (the shape factor) A,

and (the deceleration) dv/dt could be much

61
62 SYMPOSIUM ON METEOR ORBITS AND DUST

greater than 3." I must remark, first of all,

that the drag equation is sound, because it

expresses the conservation of momentum; and

as far as y and A are concerned, there is indeed

little danger of systematical error. The SuperSchmidt photographic meteors are small; freemolecule flow should occur in most cases, and

therefore y must be 1.1 or very close to it. In

any case, y could only be smaller than the assumed free-molecule-flow value; hence the computed densities would become even smaller than

0.25 g/cm3. It is also very difficult to see how,

on the average, A could be different from 1.5

by more than 10 or 20 percent. Let us not forget that the increase in cross section due to

fragmentation is properly taken into account

by means of the fragmentation index.

For a good part of the precisely reduced

photographic meteors used in my paper (1964a),

the fragmentation index is close enough to 0 to

make it useless to question the meaning of the

decelerations, and consequently of the densities,

which turn out to be about 0.25 g/cm3. The

aforementioned asteroidal meteor has a deceleration 1 order of magnitude smaller than that

of the other little-fragmenting meteors, and we

do find for the former a density of about 4

g/cm3. Should we, for any reason, scale the

density of the ordinary meteors to Ceplecha's

value, we would find for the asteroidal meteor a

density of the order of 50 g/cm3. As far as the

most-crumbling meteors are concerned, the

meaning of the measured decelerations may be

rather obscure, but the use of the fragmentation index reduces their decelerations to a

standard point in the trajectory where the

effects of fragmentation are unimportant.

Moreover, the resulting densities are in general

agreement with those of meteors scarcely affected by fragmentation. Should we question

the validity of the densities calculated for the

severely fragmenting bodies, it is clear that

those meteors could not in any case be stronger

and denser than nonfragmenting bodies.

I must also point out that I have determined

meteor densities using solely the heights of

maximum light for 359 photographic meteors

for which the decelerations were unknown

(Verniani, 1964b). In spite of the different

method employed, the results are in very good

agreement with those obtained directly by

decelerations.

It is natural now to ask ourselves why

Ceplecha arrives at such different values. The

discrepancy in Ceplecha's results is due mainly

to the definition and use of his kB parameter,

not to mention the large uncertainties in heat

conductivity, specific heat, and surface temperature of meteoric material. In fact, his equation (1), the basis for the definition of kB, is

at great variance with some well-established

observational results. Ceplecha's equation (1)

may be written as:

log pB=constant—2.5 log vm

+2 log (p» COB ZM), (1)

where pB is the atmospheric density at the

height of meteor beginning, r. the apparent

meteor velocity outside the atmosphere, pm

the meteor density, and AH the zenith angle.

Now, the analysis of 413 precisely reduced

Super-Schmidt meteors gives (Jacchia, Verniani, and Briggs, 1965):

log pfl=constant—3.5 log p.—0.25 log m., (2)

where m. is the initial mass of the meteoroid, and

the standard deviation of the coeflBcient of log

r«, is ±0.15. Accordingly, Ceplecha's kB

turns out to contain a term (—log P») that

may explain why his average kB for fast meteors

(flco~60 km/sec) is roughly 0.5 smaller than

his average kB for slow meteors (t?..~20

km/sec). Even if we divide the meteors into

2 groups of different orbital characteristics

(long- and short-period), the coefficient of

log Vm is still close to —3.5.

The lack of agreement between Ceplecha's

theoretical equation (1) and the observational

equation (2) is probably due to the effect of

radiation cooling, neglected by Ceplecha. Incidentally, radiation cooling probably accounts

also for meteors beginning some 6 km lower

than expected on theoretical grounds (Jacchia,

Verniani, and Briggs, 1965). If, for the sake

of simplicity, we take a spherical body, the

ratio R between the energy radiated by the

meteor and the heat produced on the meteor
COMMENTS ON CEPLECHA's PAPER—VERNIANI 63

itself in the collisions with the atmospheric

molecules is given by

R= (3)

where e is the emissivity, a the Stefan-Boltzmann constant ( = 5.67X10~8

 cgs), T the

temperature, A the heat-transfer coefficient,

v the velocity, and p the air density. Assuming,

again for simplicity, that T=1 > we find

(4)

The average Super-Schmidt meteor with a

velocity of 18 km/sec begins at 90 km (Jacchia,

Verniani, and Briggs, 1965), where p~3.2X 10~9

g/cm3, while the beginning height of a meteor

having a velocity of 70 km/sec is about 116 km,

where p~4.0X10~n g/cm3. Assuming T=

2000°K, equation (4) yields i?~0.4 and

/?~0.5, respectively, which means that at

meteor beginnings radiation is not at all

negligible. With T=3000°K, we would find

/?>2; i.e., such a temperature cannot be

reached. Incidentally, this shows also that

the temperatures derived by Ceplecha in his

section 13 (up to 8200 °K) are physically

impossible: a further proof of the unrealistic

approach represented by his equation (1).

Acknowledgment

The author is grateful to Dr. Luigi G. Jacchia

for discussions on several points touched on

in this paper.

References

JACCHIA, L. G.

1958. On two parameters used in the physical

theory of meteors. Smithsonian Contr.

Astrophys., vol. 2, no. 9, pp. 181-187.

1960 Individual characteristics of meteor families

(abstract). Astron. Journ., vol. 65,

p. 53.

1963. Meteors, meteorites and comets; interrelations. In The Solar System, vol. 4,

ed. by B. M. Middlehurst and G. P.

Kuiper, Univ. of Chicago Press, Chicago,

pp. 774-798.

JACCHIA, L. G.; VERNIANI, F.; and BRIGGS, R. E.

1965. An analysis of the atmospheric trajectories

of 413 precisely reduced photographic

meteors. Smithsonian Astrophys. Obs.

Spec. Rep. No. 175, 309 pp.; also in

Smithsonian Contr. Astrophys., vol. 10,

no. 1, 139 pp., 1967.

JACCHIA, L. G., and WHIPPLE, F. L.

1961. Precision orbits of 413 photographic meteors. Smithsonian Contr. Astrophys.,

vol. 4, no. 4, pp. 97-129.

VERNIANI, F.

1964a. On the luminous efficiency of meteors.

Smithsonian Astrophys. Obs. Spec. Rep.

No. 145, 62 pp.; also in Smithsonian

Contr. Astrophys., vol. 8, no. 5, pp.

141-172, 1965.

1964b. On the density of meteoroids, II: The

density of faint photographic meteors.

Nuovo Cimento, vol. 33, pp. 1173-1184.

WHIPPLE, F. L.

1950. A comet model, I: The acceleration of

Comet Encke. Astrophys. Journ., vol.

Ill, pp. 375-394.

1951. A comet model, II: Physical relations for

comets and meteors. Astrophys. Journ.,

vol. 113, pp. 464-474.

1963. On meteoriods and penetration. Journ.

Geophys. Res., vol. 68, pp. 4929-4939.

Abstract

The present evidence pointing to a cometary origin and to a low density for the overwhelming majority of meteors

is briefly reviewed. Account is given for some of the reasons leading Ceplecha to the wrong conclusion that most

meteors are asteroidal and have a density of about 4 g/cms.
Abstract of Ceplecha's Reply to Verniani's Comments

Verniani omitted the difference between the

Ci and C2 groups.

The sporadic C group and shower meteors

begin 9 km higher than the sporadic A group,

and 15 km higher than each of the three iron

meteors. These are observational values.

Table 16.1 in Special Report 175 (Jacchia,

Verniani, and Briggs, 1965) shows a systematic

difference in log a of at least 0.2 between

the shower meteors and the sporadic A group,

if the distribution is plotted instead of using

the average values only. All three phases—

solid, liquid, and gas—are transported behind

the body. It is not necessary to explain the

faint meteors anomaly as due only to fragmenting bodies produced by comets.

The 0.25-g/cm3 density could be systematically shifted because of the unknown physical

meaning of y, A, and dvjdt in the free molecule

flow drag equation, if applied to ablating

meteors. I do not use any theoretical values

of heat conductivity, specific heat, and surface

temperature to derive the densities. My assumption could be shortly written: iron=iron.

The velocity exponent 2.5 is verified beyond

any doubt from figures 1 and 2 of my paper.

The velocity exponent 3.5 results if the

64

two groups A and C are put together in one

group and the difference of the beginning

heights is explained by the velocity difference.

But this is not correct (see figs. 1 and 2). The

masses published for Super-Schmidt meteors

are not direct observational values, but they

are computed theoretically from the light

curves.

As the meteor surface temperature rises

in direct proportion to the air density p in

the case of heat conductivity, and p '•'* in the

case of radiation, there exists some "reference

height" not very much higher than the observed

beginning, where radiation is negligible and my

equation (1) holds. This "reference height"

is strictly dependent on the heat conductivity,

density, and specific heat, and it is to some

extent related to the observed beginning height,

though radiation could be the main process

at the beginning.

My paper contains a more general view independent of any theoretical value (the only one

is 2.5 log Vm, which exactly corresponds to the

observations). My densities are obtained by

direct comparison of the relative kB of three

iron meteors with the relative values on the

same scale for the whole sample.
Further Comments by F. Verniani

Among the 413 precisely reduced meteors of

Jacchia, Verniani, and Briggs (1965), shower

meteors begin on the average 3.1 km higher

than sporadic meteors, mostly because of their

greater velocities: after reduction to a standard

velocity and mass, the difference in beginning

height is about 1 km. These are observational

values.

The small difference (0.09) in the average

value of log a between sporadic and shower

meteors is, again, mostly due to the different

mean velocity (33.7 km/sec for sporadic and

39.3 km/sec for shower meteors). Moreover,

as Jacchia, Verniani, and Briggs (1965, p. 45)

state, there is no appreciable difference in log

a between short- and long-period meteors when

groups of the same velocity are compared

(ibid., table 17.1.2).

The drag equation, the meaning of the deceleration, and the effect of the drag coefficient

have been fully discussed in my previous

comments.

Ceplecha does assume theoretical (and very

uncertain) values of the heat conductivity and

specific heat of the meteoric material in order

to derive his values of the density (see his

eq.2).

I do not question Ceplecha's "reference

height" where the atmospheric density p could

be ~t?~2'

6

, but it is obvious that these "reference heights" have very little to do with the

observed beginning heights, which follow the

law p~t?~8'

5

.

Reference

JACCHIA, L. G.; VERNIANI, F.; and BRIGGS, R. E.

1965. An analysis of the atmospheric trajectories

of 413 precisely reduced photographic

meteors. Smithsonian Astrophys. Obs.

Spec. Rep. No. 175, 309 pp. Also in

Smithsonian Contr. Astrophys., vol. 10,

no. 1, 139 pp., 1967.

66

Orbits of Bright Photographic Meteors

P. B. BABADZHANOV

 X and E. N. KRAMER 2

During the period 1957 to 1963, systematic

photographic observations of meteors were

carried out at the Astrophysical Institute of the Year

Academy of Sciences of Tadjikistan (Dushanbe) Month

and at the Odessa and the Kiev astronomical

observatories. The photographs were taken Day

with cameras NAFA 3C/25 (D=100 mm, F =

250 mm, and field of vision 40°X50°); a pan- Com rad.

chromatic emulsion of 19-cm width with a

sensitivity of 1100 to 1300 units of GOST

(approx. 350-450 ASA) was used. The base

lines between the stations at each observatory

were from 20 to 40 km. The exposures, which Sin Q

were carried out automatically, had a duration

of 30 to 60 minutes. Time signals were made

on the star trails by a special transducer. The Cos ZR

limiting magnitude of the system was approximately + 1 mag. The precision of the deter- «

mination of the coordinates of any points on

the negatives was about 5 sec of arc.

The results are given for about 500 meteors Hb

photographed in Dushanbe and Odessa. Some Hmtx

of the results were published by Babadzhanov He

and Kramer (1963); those that include the V'a

observations of the period from 1960 to 1963

are given in table 1 (Dushanbe) and table 2 VG

(Odessa); these tables consist of the following V*

data:

 a

No. Meteor number. In table 1 the

 e

first two digits signify the year 2

of observation minus 1900; the 2

next three digits signify the num-

 w

ber of exposures in the current

year; and the last digit signifies ®

the number of the camera. In

1

 Astrophysical Institute of the Academy of Sciences of Tadjikistan.

USSR.

1

 Odessa State University, USSR.

table 2 the first column denotes

the meteor number.

Year of observation minus 1900.

Number of the month of observation.

Day of the month in Universal

Time given to 0?001.

Radiant (right ascension a and

declination 8) after correction for

the earth's attraction and diurnal

aberration, in degrees and minutes. Equinox 1950.0.

Q is the angle between the great

circles traced by the meteor, as

seen from two stations.

ZR is the zenith distance of the

radiant.

Elongation of the corrected radiant from the apex of the earth's

motion, in degrees.

Height at beginning, in km.

Height at maximum light, in km.

Height at end, in km.

Velocity outside the earth's atmosphere, in km/sec.

Geocentric velocity, in km/sec.

Heliocentric velocity, in km/sec.

Semimajor axis, in a.u.

Eccentricity.

Perihelion distance, in a.u.

Aphelion distance, in a.u.

Argument of perihelion, in degrees. Equinox 1950.0.

Longitude of the ascending node,

in degrees. Equinox 1950.0.

Inclination of the orbit plane to

the ecliptic, in degrees. Equinox

1950.0.

67
68 SYMPOSIUM ON METEOR ORBITS AND DUST

No.

600051

600153

600165

600185

630215

610502

630621

630674

630684

630054

631512

631712

611902

631811

631006

632141

620384

601242

601443

620611

620631

620644

620681

620606

620662

620672

632341

620762

612376

632395

612451

632421

612474

632432

632441

632494

632521

632652

632665

632632

632725

632762

620886

620962

621025

621105

621134

621204

621234

612992

621354

621402

621694

621892

621973

614003

600361

622063

632943

622123

600522

622215

622372

614654

622512

614715

614713

614764

614794

622563

622571

622713

Year

fiO

60

80

60

63

61

63

63

63

63

63

63

61

63

63

63

62

60

60

62

62

62

62

62

62

62

63

62

61

63

61

63

61

63

63

63

63

63

63

63

63

63

62

62

62

62

62

62

62

61

62

62

62

62

62

61

60

62

63

62

60

62

62

61

62

61

61

61

61

62

62

62

Month

1

1

1

1

1

2

2

2

2

3

6

fi

7

7

7

7

7

7

7

8

8

8

8

8

8

n

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

9

9

9

9

9

9

10

10

10

10

10

10

10

10

10

10

11

12

12

12

12

12

12

12

12

12

Day

1.725

4.898

4.924

4.877

22.898

13.885

17.658

18.703

18.783

26.657

16.804

22.890

11.892

15.733

20.846

23.868

25.787

26.903

31.863

2.734

2.829

2.878

3.788

3.874

4.818

4.042

10.681

10.902

11.704

12.773

12.946

13.742

13.750

13.776

13.852

14.849

15.747

15.867

15.879

17.734

18.875

23.795

24.717

28.734

3a 850

31.912

1.774

2.850

3.688

9.002

10.017

23.757

2.851

6.898

9.915

16.878

20.817

21.802

23.940

26.792

28.939

30.728

1.989

3.662

3.826

8.925

8.957

11.749

11.880

17.618

17.714

22.706

TABLE 1.—Orbital elements of

Corr. radiant

a

93°16'

118 34

228 63

220 65

101 16

258 06

07 15

141 42

160 45

175 58

271 33

343 27

304 31

266 25

34 38

21 69

25 51

319 38

31 02

47 34

34 03

32 56

342 34

332 49

36 36

332 30

276 45

38 66

48 31

48 29

68 23

46 56

41 22

47 56

30 48

47 26

66 15

40 35

60 24

314 62

22 13

264 35

36 66

335 43

92 30

68 07

91 36

91 21

276 17

101 13

85 30

366 33

84 40

79 37

110 39

37 46

00 37

04 18

06 20

46 24

52 38

331 58

50 33

99 17

84 23

72 43

151 33

82 03

81 37

83 48

102 57

274 50

1

-28°U'

26 34

49 45

49 17

16 U

63 08

8 4 0

12 17

5 02

2 01

- 1 6 15

9 5 3

49 40

25 26

46 32

61 43

51 60

- 9 12

63 62

83 36

54 48

64 40

- 1 5 36

- 1 2 34

56 60

31 15

42 51

56 03

65 39

57 19

65 58

59 27

58 25

58 11

54 02

54 40

56 51

57 18

59 17

4 08

34 46

61 57

69 66

- 5 08

62 40

26 24

56 29

58 35

44 08

40 00

- 1 0 34

- 2 37

50 33

33 17

- 4 49

10 20

14 30

15 27

15 29

11 25

0 3 8

- 1 2 55

13 34

27 34

24 28

- 9 48

21 05

26 45

16 33

24 50

12 37

71 51

Sin Q

0.171

0.026

0.064

0.063

0.196

0.372

0.942

0.328

0.190

0.196

0.424

a 375

0.220

0.669

0. Ill

a 181

0.060

0.184

0.366

0.244

a 193

am

0.660

0.273

a 401

0.268

0.194

0.575

0.104

0.133

0.246

0.146

a 061

<l. 272

0.202

a 075

0.166

0.629

0.143

0.394

0.067

0.306

a 201

0.641

0.130

0.172

0.092

0.040

0.482

0.226

0.168

0.625

0.157

0.704

0.227

0.255

0.037

0.100

0.104

0.365

0.083

a630

0.479

0.208

0.838

0.336

0.405

0.347

0.275

0.206

0.179

0.573

CosZ,

0.394

0.961

0.537

0.635

0.751

0.644

0.909

0.804

0.788

aoos

0.601

0.602

0.004

tt077

a 512

a 7 »

a487

0.666

asM

0.683

a 610

a 764

a44O

a 040

0.694

0.912

a006

0.810

0.488

0.460

0.800

0.396

0.400

0.474

0.713

0.600

0.356

a 701

0.726

0.807

0.808

0.758

0.558

0.668

0.601

a 801

0.289

0.501

0.965

0.516

0.311

0.761

0.740

0.892

0.403

0.875

0.652

0.460

0.884

0.867

0.684

0.669

0.778

0.996

0.966

0.942

0.909

0.923

0.881

0.575

0.622

0.400

meteors

90:1

77.il

»3. 6

63.7

33.,',

75.5

137.8

98.3

7V. 1

98.0

H3.ll

19.4

73 4

106.7

35.8

40.4

30 7

73 9

30.6

ISN.H

40 0

30 0

63 5

71 0

41 4

a, n

103.0

38.2

88.1

10.6

38. 9

41.0

40.7

40.3

36.7

36.5

38.6

38.8

40.8

95.6

31.6

95.2

51.2

89.9

44.9

9.2

38.8

30.0

109.4

27.0

34.4

95.2

30.2

24.8

27.3

75.2

28.9

25.6

25.5

76.5

77.0

158.1

78.1

63.4

76.6

96.0

22.5

86.8

87.9

90.9

72.8

91.5

(Dushanbe)

88.2

64. fi

84 S

93.9

108.8

88.9

74. 1

81.3

95.7

H 4 4

01.9

ua4

99.6

91.3

113.0

uas

111.6

102.0

100.0

!•• > 7

na4

100.6

99.2

91.4

112.3

88.8

94.4

109.0

103.8

106.2

103.0

111.2

113.4

109.3

111.1

104.5

108.5

108.9

107.7

87.8

106.0

90.9

106.4

95.4

95.4

109.4

107.0

104.8

91.7

100.3

114.7

83.5

112-0

110.8

97.7

104.0

129.3

111.5

100.2

03.2

98.6

77.4

101.1

94.6

96.8

90.9

66.3

92.3

89.9

98.8

102.4

80.8

78.9

83 3

7ft 8

08.6

102.2

70.5

BO, B

74 4

010

—

79.8

100.0

96.0

80.0

uas

i'»i.'.

84.3

Wfl 0

H4 'i

BIO

NO 4

w 6

88.1

S3.9

101.3

88.0

88.5

98.4

101.5

—

92.0

108.5

96.0

92.0

93.0

87.5

104.0

99.0

102.2

79.3

92.0

7& 0

98.11

84.8

91.0

96.6

98.5

95.8

72.9

98.2

—

61.0

94.5

94.3

94.5

74.2

_

99.6

98.5

78.8

85.0

_

76.2

75.6

83.0

81.9

60.3

81.0

76.9

89.fi

90.7

85.3

11.

77.5

SO. 1

7.1. 7

67.8

97.0

88 1

41. s

71.8

7ft fi

40 2

77.4

101.9

90.4

81.7

108.6

97.0

83. 5

M •-•

7H 7

n .-> 87.3

80.8

H « 3

78.4

K 3

7M B

74 fi

Od H

03.7

90. U

H9.0

87.9

03. 8

80.2

90.9

82.9

05.8

04.4

97.6

74.9

90.2

72.6

95.7

82.1

88.7

95.9

90.2

92.7

72.2

92.4

84.2

58.2

87.6

94.1

90.4

68.7

89.9

93.8

91.8

75.9

80.9

36.2

69.7

69.9

72.0

73.3

58.6

53.5

72.8

77.9

86.8

82.9

Vm

36.2

23 4

37 •:

37 4

68.1

33 7

14 3

.'1 4

32 5

.'1 3

2* 1

.',0 1

41 'I

31. fl

82 .'.

60.0

«) 1

17.6

10 7

42.5

6a 7

eao

a t

34.2

59. M

45 ii

21.0

61.8

00 0

61.9

57.3

60.0

63.9

60.8

«l.n

59.0

58.6

«O.H

59.2

•IT. 2

64.5

23.5

50.1

27.9

58.2

72.7

60.9

56.4

19.3

67.0

64.0

23.5

66.6

68.9

67.1

32 3

74.9

67.5

67.9

30.3

34.4

13.5

29.9

41.0

31.9

24.2

28.6

26.4

24.6

25.9

40.4

26.1

VQ

28.0

sa7

18.1

IS, S

61 y

11.0

8 0

IS 1

30 4

17.0

:n a

87 I

30 8

11 4

61 3

68 1

Bfl, 8

M.0

M S

41 n

SB 5

M H

4-) fi

n 4

IN fi

43 H

18 0

saa

59 6

80.7

5&1

58.6

02.7

59.fi

59.7

57.8

57.4

59.6

58.0

24.8

63.4

20.9

48.7

25.4

56.9

71.6

59.7

55.0

15.8

65.8

62.7

20.6

65.4

67.9

65.9

30.4

73.8

66.3

6fi.9

38.1

32.8

8 . 0

27.7

39.2

29.9

21.8

26.3

23.8

22.1

23.1

38.5

23.6

1 , ,

M.4

13 8

34 s

18.0

4.' 1

37 8

37 3

37 3

as a

87.0

37 1

31 7

41 U

31 1

41 3

41 1

40 N

80.6

40 J

40 0

41 B

40.0

3* (I

M l )

41 4

40 1

31 6

41.0

40 8

42.5

88.0

41 4

44 1

41.7

40 2

38.4

39.0

41.0

40.6

40.3

41.3

37.6

38.0

38 9

41.6

42.8

41.1

37 6

37.9

41.7

41.8

37.6

42.4

42.7

41.7

36. H

49.7

41.4

41.9

36.0

39.1

37.6

36.4

37.3

37 3

39 1

11.7

37.4

36.8

38.4

41.4

38 9

2.70

1 20

1 40

LSI

27.0

2.42

118

X30

2 Hi

3 1H

3 31

1.20

-78.2

3.73

1.08

10.2

10.5

8.09

8.07

11 fi

33 H

11.4

3.90

1.08

23.2

0.38

3 31

•

v.ao

-17.1

ISA

25.7

-3.52

83.2

0.30

3.16

3 77

13.0

8.45

0.08

18.8

2.62

2.84

3.03

31. 8

-13.0

1X8

2.53

2.71

81.8

88.0

2.5 1

-34.0

-10.5

23.1

2.07

-1.29

12.2

28.0

1.81

3.47

2.36

1.92

118

2.15

3.22

0.633

2.20

1.98

2.68

9.58

3.04
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS—BABADZHANOV AKD KRAMER 69

No.

600051

600163

600166

600186

630215

61OS02

630621

630674

630684

630064

631612

631712

611002

631811

631006

632141

620384

601242

601443

6206U

620631

620644

620681

620605

620662

620672

632341

620762

612376

632305

612451

632421

612474

632432

632441

632494

632521

632552

632555

632632

632725

632762

620886

620962

621025

621105

621134

621204

621234

612992

621364

621402

621694

621892

621973

614003

600361

622063

632943

622123

600522

622215

622372

614564

622612

614715

614713

614764

614794

622663

622571

622713

Year

GO

60

60

60

63

61

63

63

63

63

63

63

61

63

63

63

62

60

60

62

62

6'.'

62

62

62

62

63

62

61

63

61

63

61

63

63

63

63

63

63

63

63

63

62

62

62

62

62

62

62

61

62

62

62

62

62

61

60

62

63

62

60

62

62

61

62

61

61

61

61

62

62

62

Month

1

1

1

1

1

2

2

2

2

3

6

6

7

7

7

7

7

7

7

H

8

8

H

8

8

K

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

9

9

9

9

9

9

10

10

10

10

10

10

10

10

10

10

11

12

12

12

12

12

12

12

12

12

TABLE

Day

1.726

4.898

4.924

4.877

22.898

13.885

17.658

18.703

18.783

26.667

16.804

22.890

11.892

16.733

20.846

23.868

26.787

25.903

31.853

2.734

2.829

2.878

3.788

3.874

4.818

4.942

10.681

10.902

11.794

12.773

12.946

13.742

13.750

13.776

13.852

14.849

15.747

15.867

15.879

17.734

IS.875

23.795

24.717

28.734

30.850

31.012

1.774

2.860

3.688

9.902

10.917

23.767

2.851

6.898

9.915

16.878

20.817

21.802

23.940

26.792

28.939

30.728

1.989

3.662

3.826

8.925

8.967

11.749

11.880

17.618

17.714

22.796

e

0.728

0.630

0.343

0.361

0.980

0.693

0.658

0.675

0.874

0.668

0.812

0.386

1.01

0.763

0.960

0.941

0.910

0.954

0.881

0.921

0.972

0.916

0.970

0.801

0.067

0.018

0.704

1.000

0.904

1.054

0.712

0.963

1.28

0.988

0.843

0.697

0.760

0.926

0.888

0.903

0.961

0.614

0.645

0.865

0.974

1.08

0.938

0.690

0.633

0.978

0.983

0.748

1.03

1.03

0.958

0.862

1.48

0.953

0.979

0.818

0.894

0.583

0.816

0.958

0.854

0.774

0.946

0.768

0.723

0.788

0.977

0.678

1.—Orbital elements of meteors

q

0.736

0.442

0.979

0.976

0.533

0.986

0.962

0.714

0.362

0.725

0.448

0.738

0.938

0.921

0.796

0.958

0.948

0.229

0.962

0.914

0.957

0.062

0.067

0.100

0.051

0.515

0.978

0.970

0.935

0.943

0.824

0.956

0.992

0.959

0.999

0.969

0.902

0.958

0.949

0.650

0.739

1.011

1.009

0.528

0.818

0.973

0.784

0.786

0.997

0.688

0.985

0.632

0.902

0.656

0.970

0.286

0.617

0.571

0.683

0.328

0.354

0.984

0.352

0.091

0.314

0.728

0.029

0.513

0548

0.669

0.219

0.979

1'

4.66

1.96

2.00

2.08

53.5

3.86

3.40

3.68

5.40

3.64

4.32

1.66

-157.2

6.54

3.88

31.4

20.0

9.81

15.2

22.4

66.6

21.8

5.71

3.68

43.4

12.0

5.64

OO

18.4

-35.5

4.89

50.4

-8.0 4

165.4

11.7

5.36

6.63

25.1

16.0

12.7

36.8

4.23

4.67

6.73

62.8

-26.9

24,8

4.28

4.44

62.9

115.0

4.38

-69.0

-39.6

45.3

3.85

-3.20

23.8

55.4

3.29

6.57

3.74

3.48

4.21

3.99

5.72

1.04

3.90

3.41

4.79

18.9

5.10

w

66?2

295.0

169.0

166.2

265.8

175.3

22.2

70.1

111.0

251.3

284.3

269.2

212.3

218.6

123.5

162.1

149.2

305.0

152.8

142.4

151.9

153.0

148.7

132.8

150.6

271.6

203.9

161.8

146.8

149.9

123.5

152.1

164.4

151.4

165.9

150.4

138.4

152.8

160.2

255.8

243.2

181.3

175.0

87.9

128.0

201.2

124.1

117.4

194.0

111.0

343.3

82.2

216.3

251.2

340.5

122.7

68.7

82.8

80.7

119.3

111.1

14.5

115.8

31.2

298.7

66.3

355.5

276.0

93.2

267.6

235.1

188.4

a

10«2

282.4

282.4

282.4

302.0

324.8

148.1

149.1

149.2

6.2

84.7

90.5

109.2

112.3

117.2

120.1

122,2

122.8

128.4

129.8

129.8

129.9

310.8

310.8

131.8

131.9

137.1

137.6

138.7

139.1

139.8

140.1

140.6

140.1

140.2

141.1

142.0

142.1

142.1

143.9

145.0

149.8

150.9

154.8

156.8

157.8

158.7

159.9

160.5

166.8

347.5

0.1

189.0

193.0

15.9

23.1

27.3

28.1

29.6

32.7

35.4

36.9

38.9

251.1

251.0

76.4

256.5

259.3

79.4

264.9

85.1

269.6

(Dushanbe)—Continued

i

147?2

1 5

65.2

65.4

137.3

54.0

3.5

1.4

1 0

0.1

7.2

148.3

63.4

21.8

123.7

112.6

113.8

11.4

113.3

67.9

113.6

113.1

25.9

2.2

111.2

71.6

27.1

116.4

116.4

114.9

113.7

110.8

114.1

113.2

117.5

116.9

114.3

115.0

111.4

15.2

134.4

33.6

91.5

41.0

106.3

169.6

117.2

111.4

22.8

146.3

122.2

0.7

132.1

159.6

134.0

6.0

162.0

163.2

163.6

7.0

25.8

0.3

5.5

13.6

1.5

19.7

312

2.9

5.0

1.1

20.1

37.3

•w

166?4

217.4

91.4

88.6

207.8

140.1

170.3

219.2

260.2

256.5

9.0

359.7

321.5

330.9

240.7

272.2

271.4

68.7

281.3

272.2

281.8

282.9

119.5

83.6

262.4

43.5

341.0

299.4

285.5

289.0

263.3

292.2

305.0

291.5

306.1

291.5

280.4

2919

292.3

39.7

28.2

331.1

325.9

242.7

284.8

359.0

282.8

•277.3

354.5

277.8

330.8

82.3

45.3

84.2

356.4

145.8

96.0

110.9

110.3

152.0

146.5

51.4

154.7

282.3

189.7

142.7

252.0

175.3

172.6

172.6

320.2

98.0

-2.0

- 1 2

- 1 1

-5.7

-1.9

-0.9

-2.2

-0.2

-

—

-2.0

-2.3

-2.1

0.1

-1.6

-2.0

-6.8

-1.6

- 1 0

-1.0

-2.8

-2.4

^3.2

-2.7

- 1 0

-1. 0

-1.0

-0.8

-2.7

—

-2.8

-3.0

-3.0

-2.4

-2.4

-2.8

-2.5

-1.9

-1. 4

-1.7

-6.5

-0.7

-0.2

0.4

-1.4

-2. 9

-2. 8

-2. 4

-3. 1

-1. 6

—

-3. 0

- 1 0

-2. 2

-1. 9

-1. 5

bolide

- 1 2

-2. 8

-0. 6

-1. 4

bolide

-3. 9

1.0

-1. 7

-1. 4

-2. 8

-1. 9

-0. 8

-2. 2

-0. 8

t

1.02

0.30

0.44

1.02

0.24

1.36

1.03

0.55

0.76

2.92

0.88

0.22

0.23

0.66

0.21

0.30

0.49

0.89

0.66

0.43

0.64

0.37

0.70

0.66

0.45

0.26

0.99

0.26

0.30

0.33

0.30

0.96

0.63

0.71

0.46

0.55

0.59

0.34

0.23

0.55

0.31

1.12

0.33

0.74

0.23

0.24

0.46

0.43

1.06

0.22

0.76

1.61

0.50

0.28

0.27

0.90

0.55

0.24

0.65

0.77

5.17

1.42

1.40

0.75

1.65

0.29

1.66

0.77

1.97

0.62

0.42

771 oo

192

2.65

140

38.6

0.071

1.49

218

0.955

_

_

2.76

0.069

0.347

0.577

0.036

0.109

3.06

0.898

1.14

0.095

0.382

0.210

0.943

1.40

0.461

0.088

170

0.031

0.330

—

0.366

1.15

0.48

0.379

0.266

0.461

0.526

0.121

0.056

1.28

2.09

2.15

0.061

0.341

0.059

0.089

0.604

0.216

3.46

0.029

—

25.3

1.08

0.637

0.069

0.616

1.05

0.121

0.423

0.636

—

7.34

0.168

5.57

0.668

11.7

1.68

1.94

0.413

0.480

Shower or

parent

comet

Quadr

Quadr

1766 II

67

72(73)

1764

Per

Per

Per

V

Per

Per

VII

Aqu

Per

73(72)

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

«Cyg

IX

1864II

IX

IX

17901

1723

S. Ari

Ori

Ori

Ori

8. Ari

S. Taur

XV?

XV

XV

X V

19171
7

0 SYMPOSIU

M ON METEOR ORBITS AND DUST

TABLE 2.—Orbital elements of meteors (Odessa)

No.

197

198

200

201

202

203

205

206

207

162

208

209

164

209a

210

212

215

214

213

219

221

222

220

224

226

223

227b

227

227a

225

229

188

232

233

228

230

231

236

168

235

166

165

169

190

238

173

170

234

167

239

172

241

240

243

249

237

252

251

177

178

176

253

179

244

248

250

245

244a

246b

255

256

257

259

Year

61

61

61

61

61

61

61

61

61

60

61

61

60

61

61

61

61

61

61

61

61

61

61

61

61

61

61

61

61

61

61

60

61

61

61

61

61

61

60

61

60

60

60

60

61

60

60

61

60616061616161616161606060616061616161616161616161

Month

344455666t>777888888888H88888888888888888888888888888888888888888888888888

Day

20.087

8.830

15.801

10.802

9.024

9.058

15.883

21.070

22.074

20.004

11.008

2a ooo

23.847

1.840

3.080

0.882

7.002

7.035

7.053

7.871

0.032

0.030

0.037

0.820

0.800

0.072

0.080

0.000

10.015

10.023

10.024

10.901

10.055

10.077

10.081

11.000

11.051

11.704

11.827

11.834

11.804

11.881

11.881

11.881

11.882

11.922

11.926

11.035

11.035

11.065

11.983

12.000

12.010

12.014

12.044

12.054

12.841

12.846

12.852

12.874

12.895

12.919

12.981

13.007

13.007

13.018

13.010

13.037

13.045

13.957

11017

14.021

14.037

Corr

a

237°51'

195 07

207 07

156 44

202 11

280 10

222 10

200 43

205 12

272 33

204 11

14 31

370 10

300 02

343 11

30 44

47 20

30 34

40 27

311 35

42 10

43 32

12 43

41 35

44 58

328 01

44 80

44 40

42 82

48 27

48 12

47 20

45 44

382 36

343 34

343 35

80 54

47 13

44 19

46 00

80 48

48 22

45 54

47 15

50 34

44 47

41 04

342 06

48 10

46 20

49 04

46 00

47 17

328 15

48 03

347 33

50 40

37 38

47 12

46 46

45 42

47 40

50 03

45 40

40 31

43 08

40 18

51 38

48 27

83 00

56 17

51 11

61 61

radianta

i'ir

-0 45

10 40

-0 03

-0 27 42 28 05 30

-4 38

10 00

-1 37

02 11

53 40

44 04 1 67

-14 15

67 23

68 28

60 40 66 22

6 42

67 32

47 12

02 88

88 32

67 86

-7 00 50 30 50 20 57 27 00 40 80 63 87 18 88 30

-12 00

-0 36

-11 16

58 10

50 17

50 05

57 40

57 04

57 52

57 40

50 58

50 17

01 30

50 26

-13 10

58 41

88 08

55 10

57 10

50 00

53 39

60 31

48 10

57 37

59 24

58 47

58 08

50 45

58 23

58 14

57 66

56 60

56 37

88 00

57 38

67 14

50 47

61 41

50 16

58 57

SinQ

a 881

0.444

0.090

0.670

0.182

0.110

0.278

0.802

0.180

0.461

0.008

0.229

0.328

0.066

0.006

0.288

0.016

0.208

0.200

0.147

0.237

0.128

0.132

0.201

0.126

0.914

0.194

0.284

0.123

a 041

0.309

0.078

0.147

0.570

0.413

0.701

0,125

0.370

0.021

0.270

0.220

0.122

0.210

0.060

0.201

0.098

0.240

0.502

0.837

0.217

0.009

0.224

0.310

0.810

0.200

0.177

0.180

0.180

0.110

0.400

0.091

0.157

0.372

0.268

0.100

0.180

0.038

0.174

0.470

0.202

0.221

0.061

0.995

CosZ,

0.700

a 628

0.722

a 713

a 578

0.841

0.037

0.574

0.807

0.000

0.842

0.805

0.907

0.077

0.606

0.603

0.788

0.884

0.012

0.772

0.880

0.830

0.062

0.424

0.424

0.006

0.790

0.864

0.888

0.884

0.848

0.002

0.727

0.626

0.088

0.850

0.880

0.308

0.472

0.401

0.402

0.601

0.864

0.552

0.523

0.081

0.705

0.800

0.696

a 750

0.705

0.810

0.833

-0.050

0.017

0.908

0.481

0.556

0.608

0.554

0.598

0.049

0.764

0.840

0.819

0.872

0.841

0.800

0.801

0.699

0.813

0.844

0.870

«

3»'3

91.9

90.3

168.5

118.0

04.7

108.2

00.2

00.1

M.9

W. 0

43.0

111.3

70.3

fil.U 41 •-'

M.1

41 4

30.0

MO. 7

4 0. H

30.4

51.0

no4O.fi

H2.fi

42.«

SO. 4

IB. 4

43.x

39.9

39.9

41. 2

59.3

64.0

6O.fi

41.1

41.7

41.5

40.2

39.5

40.2

40. 0

39.3

38. S

43.9

42.0

69.9

41.0

40.6

35.5

39.7

40.4

69.3

42.6

56.8

39.5

42.2

40.9

40.2

38.9

40.6

40.3

40.1

39.0

39.8

40.2

39.8

39.4

39.0

43.8

41.3

40.9

v

m

Va

101.5

07.0

101.0

87.8

06.2

108.0

83.3

01.4

79.8

90. 0

88.6

107.3

04.0

84.7

08.8

1U.6

107.0

100.0

100.2

8&8

106.7

104.0

07.0

111. 2

107.7

00.6

100.1

116.0

100.0

108.4

108.1

104.8

103.3

95.0

98.0

99.6

102.2

107.3

100.0

108.0

HZ 6

110.7

113.0

104.0

102.5

100.5

98.6

107.6

113.0

1010

110.0

1011

106.2

108.0

103.9

100.6

105.5

106.0

110.8

107.9

111.3

110.0

110.0

1015

107.5

112.0

100.2

108.0

100.5

106.3

111.8

100.5

08.8

93.0

70. 8

•8.2

BA..'-

70. s

7M.3

87.8

78.2

M»3

HX 0

1*7 0

Hl.fl

7H. 4

•K. 3

08.8

97. 2

M. 3

89.0

M.6

90.4

W.5

89.9

89.0

91.9

99.6

93.0

102.0

8 10

101.1

81.6

83.1

101.0

00.4

96.0

95.0

88.5

98.0

99.7

98.5

101.6

80.7

92.5

87.0

98.0

81.4

90.9

91.2

100.0

95.0

100.3

O il

77.5

K3 11

8 10

70.2

50.1

78.2

IV9.0

75 5

H5.0

H .3

7fl V

Sfl.O

TV 0

St. 9

U3 2 77 0 75 6

U3.0

W.O

H3.4

WO

uo.u

*e.«

07.8

NO. 4

87.5

94.7

9Z5

87.9

95.7

H9.0

86.1

80.4

90.7

90.0

97.5

93.9

92.0

80.0

96.4

98.0

83.0

97.0

715

9Z0

79.3

84.3

95.4

88.6

85. H

92.0

86.4

99.3

95.5

93.0

92.5

94.9

05.6

79.1

8 10

86.3

93.5

80.0

99.0

90.8

89.0

05.0

8 15

96.7

80.1

28. 1

28.4

16.3

18.0

47.7

14 4

2ZS

35.5

23 7 n i

62.5

BLl

40 7

41 V

80.3

m 3

ami M B 24 1

fll.5 fJ i

,'J «

fiO «

aao

11.8

M) *

60.8

60. 6

M.O

61.1

59.9

59.6

40.6

41.5

40.2

59.6

61.1

60.8

00.5

58.1

60.4

60.4

59.9

62.5

62.6

61.5

38.7

62.2

61.0

60.1

60.3

60.6

43.1

60.0

46.6

60.9

60.2

60.2

61.4

60.9

60.1

60.8

60.2

60.3

63.4

61.1

58.4

60.1

60.8

57.8

50.9

50.6

54. a

214

28.0

12.3

15 4

40.1

0.5

10.8

33. H

21 1

27.1

01 3

19.4

3H.0

40 4

a§ H

50.0

W 0 at 7

21.1

M 3

02.0

53 4

50.1

50.0

so. a

59. 5

80. S

50.3

57.3

50.8

68.8

58.3

39.0

39.9

38.7

58.3

59.8

50.5

59.2

56.7

59.0

59.0

58.5

61.2

61.3

60.2

37.0

60.9

59.6

58.8

59.0

59.3

41.8

57.8

45.4

59.6

58.8

68.0

60.0

59.6

58.8

59.4

58.9

59.0

6Z1

59.8

57.1

58.9

59.5

56.4

58.6

58.4

36.3

38. 5

41 5

41.3

38.7

42.8

33.5

37 9

4U.M

37. e

41 4

45.0

38. 2

44.0

17.1

41 5 40 7

41. N

41 2

30.2

42.6

30.5

40 V

40.7

41.8

39 0

4ZH

41.3

41.1

41.4

41.8

40.6

41.4

34.8

37.8

35.3

41.0

42.6

4Z2

41.4

38.8

41.2

41.1

40.3

4Z5

45.0

43.0

38.5

43.2

41.9

39.7

40.9

41.5

41.8

41.3

38.2

41.4

4Z0

41.4

42.1

41.1

41.1

41.6

41.1

40.6

43.0

41.9

39.3

40.7

41.0

40.7

41.3

40.9
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS—BABADZHANOV AND KRAMER

TABLE 2.—Orbital elements of meteors (Odessa)—Continued

71

No.

197

198

200

201

2ff2

203

205

206

207

162

20M

209

164

209a

210

212

215

214

213

210

221

222

220

224

226

223

227b

227

227a

225

220

188

232

233

228

230

231

236

168

235

166

165

169

190

238

173

170

234

167

239

172

241

240

243

249

237

252

251

177

178

176

253

179

244

248

250

245

244a

246b

255

256

257

259

Year

61

61

61

61

61

61

61

61

61

60

61

(H

GO

(11

fil

61

61

til

01

61

61

61

61

61

61

fil

61

61

61

61

61

60

61

61

61

61

61

61

60

61

60

60

60

60

61

60

60

61

60

61

60

61

61

61

61

61

61

61

60

60

60

61

60

61

61

61

61

61

61

61

61

61

61

Month

3

4

4

4

S

S

6

6

6

t»

7

7

7

8

8

8

8

g

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

Day

20.057

8.836

15.801

16.862

9.024

0.058

15.883

21.979

22.974

29.094

11.998

20.996

23.847

1.849

3.986

6.852

7.002

7.035

7.053

7.871

9.032

9.036

9.037

9.826

9.890

9.972

9.989

9.990

10.015

10.023

10.024

10.901

10.055

10.077

10.081

11.000

11.051

11.794

11.827

11.834

11.864

11.881

11.881

11.881

11.882

11.922

11.926

11.935

11.935

11.965

11.083

12.000

12.010

12.014

12.044

12.054

12.841

12.846

12.852

12.874

12.895

12.919

12.981

13.007

13.007

13.018

13.019

13.037

13.045

13.057

11017

11021

11037

a

1.90

3.03

19.85

13.67

3.40

-11.70

1.42

2.86

-2.01

2.64

27.32

3.18

3.09

-4.82

2.38

32.87

9.14

147.30

18.13

2.02

-1183

1 7 2

11.49

9.04

23.1

3.77

-11.15

18.35

13.86

22.4

105.72

8.84

21.27

1.65

175

1.74

12.06

-13.6

-27.59

21.20

3.62

16.99

1115

6.99

-16.74

-3.31

-8.56

3.30

-7.58

-227.32

5.09

11.40

29.04

107.2

18.68

3.06

25.138

-73.85

22.44

-42.65

13.83

1145

45.80

13.30

8.45

-9.46

1862.20

1 25

0.16

12.38

0.18

17.56

11.27

t

0.828

0.813

0.064

0.927

0.751

1.085

0.287

0.743

1.371

0.739

0.963

1.310

0.684

1.077

0.967

0.971

0.901

0.993

0.947

0.690

1.064

0.797

0.912

0.893

1.000

0.894

1.090

0.948

0.931

0.958

0.991

0.804

0.956

0.054

0.968

0.922

0.025

1.070

1.035

0.055

0.750

0.044

0.933

0.865

1.055

1.202

1.115

0.946

1.127

1.004

0.818

0.017

0.968

0.992

0.949

0.752

0.963

1.014

0.958

1.022

0.930

0.034

0.080

0.028

0.880

1.104

0.000

0.786

0.807

0.926

0.903

0.047

0.018

1

0.328

0.566

0.716

1.004

0.848

0.996

1.014

0.733

0.746

0.690

1.015

0.985

0.979

0.372

0.079

0.950

0.901

1.003

0.960

0.627

0.956

0.958

1.014

0.964

0.943

0.398

0.944

0.945

0.957

0.935

0.921

0.933

0.944

0.076

0.088

0.137

0.905

0.046

0.064

0.951

0.905

0.951

0.954

0.943

0.926

0.965

0.981

0.179

0.563

0.952

0.929

0.051

0.045

0.878

0.946

0.761

0.929

0.996

0.954

0.959

0.965

0.949

0.938

0.062

0.936

0.984

0.942

0.911

0.944

0.915

0.894

0.035

0.929

1'

3.47

5.50

39.03

26.34

5.95

1.83

4.98

160

53.56

5.20

166

6177

17.38

203.00

35.26

3.41

8.48

21.97

17.11

4618.02

7.14

35.76

26.76

43.9

210.52

16.74

41.60

3.22

5.42

3.35

23.22

41.45

6.34

33.02

27.36

13.04

6.42

9.26

21.85

57.14

213.5

36.41

5.36

49.35

43.93

26.69

27.95

90.53

25.82

15.96

3723.

7.50

17.38

23.84

17.46

3120

21.61

M

296?8

271.8

245.5

177.8

308.7

193.2

172.9

249.4

237.4

255.0

1814

161.1

2014

77.2

151.1

150.6

220.1

192.2

207.1

265.7

152.8

151.0

182.9

153.7

149.4

73.4

150.3

140.3

152.2

147.3

1416

146.4

149.3

206.6

328.9

323.5

140.9

150.6

1519

151.0

138.6

156.9

151.5

148.2

146.2

156.2

160.1

226.0

155.1

151.5

1416

isa 7

149.6

223.0

149.6

245.2

146.2

165.1

151.6

153.5

1514

150.2

157.8

153.6

147.0

161.0

149.2

140.5

148.9

143.0

138.9

147.3

145.7

a

359? 1

198.6

25.4

206.5

228.8

48.9

84.4

90.2

91.1

08.1

109.2

117.8

120.8

129.2

311.2

1310

1311

1311

1312

1319

136.0

136.0

136.0

136.8

136.9

137.0

137.0

137.0

137.0

137.0

137.0

138.1

137.9

317.9

137.9

137.9

138.0

138.7

130.0

138.7

139.0

135.0

139.0

139.0

138.8

139.0

139.1

318.8

139.1

138.9

139.1

138.9

138.9

138.9

139.9

138.9

139.7

139.7

140.0

140.0

140.0

139.8

140.1

139.0

130.9

139.9

139.9

130.9

130.9

140.3

140.8

140.8

140.8

i

122?8

2.4

20.7

6.2

0.0

76.6

15.6

10.9

33.4

14.2

41.1

110.5

28.5

31.9

23.4

111.6

115.4

111.1

115.3

15.8

113.3

126.4

95.0

115.1

113.0

7.5

110.3

1115

1111

107.4

114.3

113.2

111.6

29.6

19.6

48.0

111.8

111.6

111.5

119.1

112.6

112.9

113.1

113.8

116.6

109.6

111.0

11.3

112.9

112.9

116.6

113.6

113.0

68.1

109.0

82.6

1112

109.8

111.9

113.4

1110

112.4

113.2

112.9

1117

117.5

113.6

1114

1110

115.3

106.9

111.5

111.8

297?9

110.4

270.9

213

177.5

242.1

257.3

339.5

328.5

3510

293.6

279.0

325.2

206.3

102.3

2815

3512

326.3

341.3

40.6

288.8

287.1

318.9

290.5

286.3

210.3

287.3

286.3

329.2

2813

281.6

2814

287.2

1614

106.8

101.6

278.9

289.3

293.9

289.8

277.6

280.9

290.6

287.2

285.0

295.2

200.1

1710

2012

290.4

283.7

289.6

288.5

1.0

280.5

211

285.8

3018

291.6

205.5

2914

290.0

297.9

293.5

286.9

300.8

280.1

280.5

288.8

283.3

279.7

281.1

286.6

-5.1

-2. 2

-1. 1

-3.6

-6. 7

- 1 6

-2. 5

-2. 5

-3.1

-2. 6

-6.7

- 1 6

- 1 8

-3. 7

- 1 4

-2. 0

- 1 6

-3. 3

-5. 2

-3. 5

- 1 1

- 1 3

-5.9

-5.9

-3.9

- 1 6

- 8

-3. 5

-3.7

-3. 3

-3. 5

-6.4

- 1 6

- 1 5

- 1 8

-3. 3

-3. 3

- 1 1

-3.4

-3.7

- 1 8

-7. 4

- 1 0

-5. 2

- 1 9

771 oo

2.57

5.67

50.8

1124

6.62

0.85

6.89

2.00

6.97

20.45

0.97

0.094

1.05

1.32

1.31

1.42

0.24

1.04

0.47

2.83

0.90

3.18

7.24

0.91

1.86

25.05

0.52

0.26

6.95

0.45

19.24

1.56

1.25

0.28

0.24

0.36

1.20

0.66

0.54

1.46

11.75

1.12

3.88

0.14

Shower

or parent

comet

1834

f Dra

III

Per

Per

Per

Per

1457 II

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Aqu

VII

VII

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

a Aqu

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per

Per
72 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 2.—Orbital elements of meteors (Odessa)—Continued

No.

258

261

263

264

265

181

185

184

267

268

269

271

270

187

273

272

274

194

196

Year

61

61

61

61

61

60

60

60

61

61

61

61

61

60

61

61

61

60

60

Month

8

8

8

8

8

8

8

8

8

8

8

8

8

8

9

9

9

9

10

Day

11040

11026

11078

16.037

16.071

17.787

10.700

19.882

10.807

21.061

21.068

22.041

22.063

26.071

1.812

1.824

1036

10.818

20.871

Corr.

a

22 56

S3 50

53 24

356 02

56 00

52 40

57 20

22 32

10 21

210 33

288 45

65 11

4 10

261 10

206 31

208 60

340 28

335 38

36 30

radiant

I

- 1 1 00

60 14

57 53

- 1 3 47

50 01

57 23

58 17

24 41

21 45

63 30

61 31

58 28

- 1 3 17

64 63

61 04

12 17

3 41

- 0 40

:t 4H

SlnQ

0.433

0.665

0.488

0.438

0.173

0.387

0.207

0.081

0.380

0.201

0.375

0.660

a 447

0.626

0.188

0.838

0.660

0.842

0.765

CoaZ,

0.520

0.646

0.748

0.466

0.743

0.363

0.386

0.668

0.600

0.625

0.808

0.848

0.407

0.682

0.994

0.833

a 616

0.708

0.782

•

38.9

42.0

39.6

610

40.3

38.3

38. H

30.5

41.6

95 4

H». 4

38. 9

61.8

H7. 1

06.6

110.6

80.3

no :

78.0

106.6

100.1

107.5

08.6

111.8

103.0

113 4

117.4

06.3

Hi 4

02.1

106.2

08.0

H9 1

HO. 5

Hi. 7

89.9

93 4

OH. 1

95.3

94.0

92 9

97. 2

90.6

M.I

H6.4

9Z5

H3.5

H7. 1

90.5

H9.3

Hfl.2

7« 3

Hi 7

HI.9

11.

96.9

90.1

91 4

Hfc 4

94.8

H9.6

8 1 7

H3.4

90.0

77 0

81 3

96.0

85.0

H2 6

70.7

73.2

70.3

79 4

Vm

60.7

60.4

60.1

38. 9

60. 2

65.0

61.0

6 1 9

61.0

M. 2

29 9

61.0

46.0

25.0

2 1 9

31.5

27.7

2 . 0

» 9

59.6

59 1

811

36 H

58.9

63. H

59. H

63 fi

59.7

21. 7

28 0

59.8

4 1 5

22.H

22. 3

29 5

23 2

IH 9

Jfl 5

VM

41.1

42.1

40.7

35.5

41 1

416

41.2

41.0

42.4

38. 2

40.5

41.2

40 2

M.2

38 7

51 0

35 4

40 3

36 0

Longitude of perihelion («+Q), in

m

Shower or

parent comet

Maximum photographic absolute

magnitude of the meteor's trail.

Duration of photographed trails,

in seconds of time.

Initial mass of meteor body, in

grams.

Meteor shower, association, or

parent comet.

The meteors that belong to the associations

discovered from observations in the USSR are

designated by Roman numerals and those discovered by Jacchia and Whipple (1961) by

Arabic numerals.

Determination of the instant of the meteor

was made either by reduction of meteor photographs obtained at one of the stations by both

driven and undriven cameras or by using a

moving-blade shutter (Kramer, 1953).

The velocity of the meteor outside the atmosphere was computed on the basis of the interpolation formula V=Va-\-kce*t

. Reduction

methods for meteor photographs have been

described in detail by Babadzhanov and Kramer

(1963).

From the distribution of maximum luminosity

of all meteors (fig. 1) it follows that on the whole

they refer to the class of bright meteors (M<1

mag), the maximum being —3 mag. For comparison, figure 1 also shows the distribution of

30

20

10

0

*

BRIGHT METEORS

FAINT METEORS

-

-

•

I ' r r---

1

i

-9-8-7-6-5-4-3-2- 1 0 I 2 3 Mmox

FIGURE 1.—Distribution of maximum magnitudes of meteors.

maximum luminosity of faint meteors photographed by Baker Super^Schmidt cameras

(McCrosky and Posen, 1961). The distributions partly overlap; hence the results given
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS BABADZHANOV AND KRAMER

TABLE 2.—Orbital elements of meteors (Odessa)—Continued

73

No.

258

261

263

264

265

181

185

184

267

268

269

271

270

187

273

272

274

1U4

IM

Year

61

61

61

61

61

60

60

00

61

61

61

Cl

61

60

61

61

61

60

60

Month

8

8

8

8

8

8

8

8

8

8

8

8

8

8

<J

g

g

g

10

Day

14.040

14.926

14.976

16.937

16.971

17.787

19.799

19.882

19.897

21.961

21.968

22.041

22.053

25.971

1.812

1.824

4.036

19.818

20.871

a

13.64

-43.68

9.25

1.80

13.90

-3.73

14.50

12.92

-18.99

3.02

7.44

15.77

6.52

2.95

3.38

—1.05

1.76

6.20

1.81

i

0.971

1.021

0.900

0.927

0.033

1.260

0.934

0.959

1.015

0.679

0.866

0.942

0.984

0.658

0.717

1.834

0.767

0.873

0.778

9

0.399

0.928

0.926

0.131

0.929

0.970

0.951

0.531

0.292

0.968

0.997

0.914

0.102

1.010

0.058

0.878

0.410

0.787

0.403

1

26.91

17.56

3.46

26.89

28.03

25.29

5.07

13.88

30.60

12.96

4.89

5.81

3.10

11.60

3.22

H

356.6

146.4

145.1

144.0

146.1

157.8

151.0

268.4

65.7

153.4

194.3

143.3

144.4

177.4

208.4

216.9

68.4

237.6

248.9

Q

320.8

141.7

141.8

323.6

143.7

144.7

146.6

146.7

146.5

148.5

148.5

148.5

328.6

152.6

158.9

159.0

161.1

176.7

27.3

i

131.6

110.9

113.8

28.3

112.9

118.2

115.3

148.8

133.8

32.7

43.6

115.5

53.7

36.5

33.5

19.8

7.6

4.6

4.7

*

317.5

288.1

286.8

107.7

289.8

302.5

297.6

55.0

212.2

301.9

342.8

291.8

113.0

330.0

7.3

15.9

229.5

5 1 3

276.2

-2. 6

-4. 5

- 5

-3.5

-4. 0

-2.0

-2. 7

-2. 0

-2.8

TOco

1.26

0.91

1.82

0.26

3.62

1.70

7.45

2.76

2.55

Shower

or parent

comet

Per

Per

VII

Per

Per

Per

VI

VI?

73?

73?

Per?

K Dra

*Cyg

1907IV

XCet

below supplement the results obtained for faint

meteors.

Distribution of orbits

The distributions of orbital elements for bright

meteors were studied in order to show how they

differ from corresponding distributions for faint

meteors. For sporadic meteors we considered

only the semimajor axis, eccentricity, inclination, and aphelion distance. Cosmic weight

was not included in our data, which were thus

uncorrected for this factor.

Semimajor axis

The distribution of orbits of all sporadic meteors

in reciprocal semimajor axis I/a is given in

figure 2. For comparison the distributions for

faint photographic and radar meteors are also

given. For l/a<0.6(a.u.)~1, in all three distributions brighter meteors prevail; for l/a>0.6

(a.u.)~\ the faint meteors become predominant.

In the distribution of all meteors the maxima

are at o«2.5 a.u. The second maximum for

bright meteors is observed near the parabolic

limit.

The percentage of orbits of sporadic meteors

with l/a<0.2(a.u.)"1 is given in table 3. The

bright meteors were photographed in Dushanbe

and Odessa, the faint meteors in the USA, and

the radar meteors were observed in Kharkov

(Kashcheyev, Lebedinets, and Lagutin, 1965).

In spite of the fact that the data in this table

240-022 O—67 6

12

I

BRIGHT METEORS

FAINT METEORS

. RADAR

<-3 -Z 0 2 .4 .6 .8 10 1.2 1.4 1.6 1.8 20

FIGURE 2.—Distribution of orbits of sporadic meteors in

reciprocal semimajor axis l/a(a.u.)-1.

TABLE 3.—Orbits of sporadic meteors

Meteors

Bright

photographic

Faint photographic

Radar

Photographic

magnitude

« - 3

+ 0.8

«+6 to + 7

Percentage of

orbits with I/a

<0.2 (a.u.)-»

34 7

27.4

7.8

are distorted by different observational selection, we may consider that among faint meteors the short-period orbits are predominant.
74

SYMPOSIUM ON METEOR ORBITS AND DUST

It is necessary to note the existence of a

considerable percentage of hyperbolic meteors,

whereas among radar meteors it is low. This

may be explained by the specific character of

radar observations of meteors moving at great

velocity. There is no reason to believe that all

hyperbolic orbits could be explained as due to

observational errors.

Inclination

The distribution of inclinations of sporadic

meteors (fig. 3) shows that among faint meteors

orbits with small inclination (less than 20°)

predominate. The maximum in the distributions falls at i=140° both for bright and for

faint meteors. In addition, the second maximum for bright meteors can be observed at an

inclination of about 180°.

Eccentricity

The distributions of the eccentricity of bright

and faint sporadic meteors are given in figure

4, which shows that bright meteors move on

more eccentric orbits than faint meteors.

Orbits with an eccentricity less than 0.65 are

found more often among faint meteors, while

those with a large eccentricity are found more

often among bright meteors. A strongly pronounced maximum at «=1 for bright meteors

should be noted. There is no such maximum

for faint meteors (McCrosky and Posen, 1961).

Here the relative number of meteors from t —

0.65 to e = 1 is nearly stable.

35

30

25

20

15

10

BRIGHT METEORS

FAINT METEORS

120 160 180 i°

FIGUKE 3.—Distribution of orbits of sporadic meteors in

inclination t.

16

14

12

10

— BRIGHT METEORS

— -FAINT METEORS 1

0 6 0 8 I.OX.Oe

FIGURE 4.—Distribution of orbits of sporadic meteor* in

eccentricity t.
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS BABADZHANOV AND KRAMER 75

Aphelion

The distribution of meteor orbits in aphelion

distance up to g' = 10 a. u. is given in figure 5.

The maxima at 2'= 1.5 a. u. and 4 a. u. may be

noted in the distribution of aphelion of faint

sporadic meteors. Bright meteors have one

maximum at g' = 3.5 a.u. Small aphelion

distances (g'<3 a. u.) are found among faint

meteors relatively more often. The percentage

30

cr

CD

20

O

O

LJ

0

BRIGHT METEORS

---FAINT METEORS

H

L_

J

"\

8 IO>IO q1 (a.u.)

FIGURE 5.—Distribution of orbits of sporadic meteors in

aphelion distance g'(a.u.).

of orbits with aphelion distances of more than

10 a. u. (g'>10 a. u.) is higher for bright than

for faint meteors.

The relation between all the other orbital

elements for both bright and faint meteors is

the same.

From the above we see that bright meteors

move in more eccentric orbits than faint

meteors and that the inclinations of the orbits

of bright meteors are on the average larger

than those of faint meteors. It is possible that

the differences between bright and faint meteors are due to the Poynting-Robertson effect

and the perturbations of the planets.

Meteor associations

In addition to the meteors belonging to showers,

there is a separate class of meteor associations

which occupies an intermediate position between sporadic and shower meteors. It would

be simpler to identify them as weak showers.

The data on the associations discovered mainly

from the observations in Dushanbe and Odessa

are given in table 4. The Harvard observations were also used in the identification of

some associations. The first column of table

4 gives the ordinal number of the association;

the second column gives the meteor number

(D, O, and H corresponding to observations in

Dushanbe, Odessa, and according to the Harvard Meteor Program, respectively); the remaining columns give the date of observation,

radiant coordinate, meteor velocity, and the

identification of associations with meteor showers (the number is from the list published by

Astapovich (1962)). Table 4 contains 16 associations, 4 of which coincide with weak showers

in Astapovich's list. The Soviet observations

also support the associations discovered by

Jaccbia and Whipple (1961) (see tables 1 and

2).

Perseids

Among the orbits of meteors observed in

Dushanbe and Odessa there are 167 Perseids,

which constitute more than 60 percent of all

known photographic Perseid orbits. On the

basis of 188 orbits of Perseid meteors observed

in the USA, the USSR, and Czechoslovakia,

the dependence of the radiant on the solar
76 SYMPOSIUM OX METEOR ORBITS AND DUST

No.

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

XIII

XIV

XV

XVI

Meteors

D 590541

0 39

0 121

D 59198 7

D 57067 3

D 570706

D 570774

D 592351b

D 592524

H 8089

O 130

D 641623

D 641872

O 1

H 3377

D 620511

II 8215

I) 582652

O 64

O 184

O 267

O 228

O 230

O 264

D 620581

O 237

O 243

D 621025

D 621134

D 621204

O 19

H 3861

O 220

D 583464

D 583587

D 572181

D 572182

D 572384

H 4657

O 87

H 9030

D 573027

O 90

O 104

D 622553

D 614764

D 614794

D 614715

H ' 5557

Year

59

58

59

59

57

57

57

59

59

53

59

64

64

57

52

62

53

58

58

60

61

61

61

61

62

61

61

62

62

62

57

52

61

58

58

57

57

57

52

58

53

57

58

58

62

61

61

61

52

TABLE

Month

3

3

6

7

7

7

7

7

7

7

7

8

8

7

7

8

8

H

S

8

8

8

8

8

Q

8

8

8

9

4

8

8

8

9

9

Q

9

9

9

10

10

10

10

10

12

12

12

12

12

4.—Meteor associations

Day

6. 7

18.8

29.9

1.9

26. 7

26.8

27.8

12.9

27.8

20. 4

29. 0

8. 8

12. 8

30. 0

24. 3

2. 7

5.4

13.9

12. 0

19. 9

19.9

11. 0

11. 0

16. 9

4. 8

12. 0

12. 0

31. 8

2. 8

3. 8

28.8

30. 5

9.0

17.9

22.9

25.7

25.7

27.8

27. 5

1 3 . 0

10. 4

28. 9

1 9 . 1

23. 1

17.6

11.7

12.9

9.9

9.3

a

159°

176

285

287

280

278

278

278

280

281

291

284

281

15

10

48

60

17

20

22

10

343

344

356

342

348

328

92

92

91

10

17

13

9

15

0

0

2

3

20

16

102

106

102

84

82

82

73

68

a

78°

65

-17

-20

49

51

48

49

51

51

49

46

46

35

37

84

83

30

27

25

22

1

-11

-14

-16

48

54

63

56

59

62

61

63

7

11

-9

-9

-9

-8

4

12

38

32

27

25

27

17

-10

-10

km/sec

19

20

30

30

31

28

27

30

31

31

28

25

25

65

65

42

44

58

00

65

61

41

40

38

42

47

43

58

61

56

52

52

54

33

32

26

24

21

24

24

24

71

71

70

26

26

25

24

23

Associations

0 Andromeda

(No. 177)

7 Aqua rids

(No. 163)

X Andromeda

(No. 181)

IJ Arietids

(No. 246)

longitude was computed (Kramer and Roudenko, 1965) and found to be:

a=-126?32+l?25(±0?01)Xo ,

<5=29?67+0?20(±0?01)XG.

Thus, the daily motion of the radiant in

right ascension is l?20 and in declination 0?20.

Computed heliocentric orbits of Perseids

change within wide limits. The distribution

of heliocentric velocities of photographic Per-
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS—BABADZHANOV AND KRAMER 77

seids is given in figure 6. The solid curve

corresponds to the observations made up to

1959, and the broken curve corresponds to

the meteors given in tables 1 and 2. The

maximum of these two distributions falls on

41.5 km/sec, which is about 0.3 km/sec less

than the parabolic limit. A number of orbits

are hyperbolic, in all probability partly due

to observational errors; however, we can give

some definite data about the existence of

hyperbolic orbits in the Perseid shower. Meteors with strongly pronounced hyperbolic orbits

were found by different observers, for example,

Meteors nos. 9792, 14581, 16091, and 21232

from observations at Ondfejov (Ceplecha et al.,

1964); nos. 1910, 1918, 2578, 8136, 8666, 8725,

8761, 10570, 11752, etc., from observations

at Harvard (Whipple, 1954; Hughes, 1959);

nos. 159, 167, 173, 181, 207, 209, 272, etc.,

from observations at Odessa; and Meteors

nos. 582514, 582561, 583191, 592964, 594472,

etc., from observations at Dushanbe. Many

of them are Perseids, since the date of observation and the radiant and orbital elements,

except for a and e, are close to the average

data for the Perseid shower. The orbital

elements of meteors are computed on the

basis of the earth's coordinates and the vector

of the meteor velocity at the moment of observation. When obtained in this way, the

orbit is osculating, i.e., we know the motion

of the meteor particle at the time of its collision with the earth, but the original orbit

is usually unknown. The calculation of the

original orbit for each meteor is very difficult

indeed, since it is connected, for example,

with the effect of various physical factors

on the orbit of meteor particles.

Since meteor particles are usually small

in size, they are subjected to the PoyntingRobertson and Yarkovsky-Radzievsky effects

(Radzievsky, 1952). The forces connected

with these effects may considerably change the

initial orbit over a long period of time.

To explain the origin of the hyperbolic orbit

of individual meteors, we must emphasize once

again that these orbits are hyperbolic at the

place of collision of a meteor particle with

the earth, and that even among the meteors

of known elliptic showers, such as the Perseids,

individual meteors moving in hyperbolic orbits

39 40 41 42 43

v (km/sec)

44

FIGURE 6.—Distribution of Perseid orbits in heliocentric

vebcity Fg (km/sec).

are observed. On the other hand, meteors

whose orbits are smaller than the mean orbit

are observed in the same shower (Babadzhanov,

1958). The considerable dispersion of the

semimajor axis of shower meteor orbits cannot be

explained by observational errors. Hence the

force that causes a great scatter of orbits

in space remains unknown. In any case,

it is clear that the hyperbolic nature of some

meteor orbits does not necessarily mean that

the meteors are of interstellar origin. It is

necessary to note that hyperbolic orbits are

found more often among bright meteors. It

is possible that the distinguishing feature

of bright meteors is that some of them move

in hyperbolic orbits. We are inclined to

believe that hyperbolic orbits can originate

within the solar system as the result of physical

processes to which some meteor bodies are
78 SYMPOSIUM ON METEOR ORBITS AND DUST

exposed during their "last" approach to the

sun (Kramer, Vorobyeva, and Roudenko, 1963;

Babadzhanov and Kramer, 1963; Ceplecha

et al., 1964).

There is no doubt that more precise observations are needed to reveal the hyperbolic

orbits, and it is also necessary to investigate

the mechanisms that are capable of transferring a meteor particle from an elliptical to

a hyperbolic orbit.

Relation between meteor bodies and other

bodies of the solar system

Photographic observations of bright meteors

confirm their relation to comets. In the last

columns of tables 1 and 2 the names of the

known showers as well as the parent come Us

are indicated. Sometimes they are individual

sporadic meteors. Their relation to comets

may be purely formal, but according to their

general orbital characteristics (e.g., eccentricity,

inclination) bright meteors appear to be connected with comets. It can be remarked that

Whipple's K criterion for these orbits suggests

a cometary relationship. However, the identification of meteors for which lf<0 with

asteroids does not seem to have sufficient basis,

since orbital characteristics alone are insufficient to draw conclusions regarding the "generic" connection between meteors and asteroids

or comets.

In 1964 experiments were made in the USSR

on the photography of meteors by the method

of instantaneous exposure. Photographs with

an exposure of 0.5 msec were obtained by

Babadzhanov and Kramer (1965). Meteor

images on these photos were very little distorted

by the motion of the meteor on the emulsion.

For slow meteors these images may be considered instantaneous. From such photographs

the instantaneous structure of meteors can be

studied. The photographs presented here illustrate instantaneous images of some meteors.

The first (Meteor no. 641541, plate la) belongs

to a Perseid, and the second (Meteor no.

641872, plate 16) to a weak shower (association

III, table 4). It is interesting to note that the

photographs of all Perseids are nearly the

same as in plate la, i.e., they have short tails.

Meteor no. 641623, according to its orbital

characteristics, belongs to the same association

III as does Meteor no. 641872 according to its

instantaneous image (plate lc). The tails of

Meteors nos. 641872 and 641623 are similar

in size and shape. Thus, the luminosity

characteristics of these two meteors confirm

their common origin and the reality of meteor

associations.

References

ASTAPOVICII, I. S.

1062. Astronomical Calendar. Permanent section, pp. 616-637.

BABADZHANOV, P. B.

1958. Photographic observations of Perseids.

A-tmphN.-. ln.-t Acad. tSci. Tadjikiszan,

no. 20, pp. 13-20.

HABADZIIANOV, P. B., and KKAMEK, K. N.

1963. McthodH nnd no me n -ult- of the photographic researches of meteors. In Ionosphere and Meteors, Hoc. V of IGY

Program No. 12, Publ. House Acad.

Sci. USSR, Moscow.

1965. Instantaneous meteor photography preliminary results. Astron. Journ. USSR,

vol. 42, pp. 660-665.

CEPLECHA, Z.; JE2KOVA, M.; NOVAK, M.; RAJCHL, J.;

SEHNAL, L.; and DAVIES, J. G.

1964. Ondfejov double-station meteors during

the IGY and IGC. Bull. Astron. Inst.

Czechoslovakia, vol. 15, pp. 144-155.

HUGHES, R. F.

1959. Meteor trains. Smithsonian Contr. Astrophys., vol. 3, no. H, pp. 79-94.

JACCHIA, L. G., and WHIPPLE, F. L.

1961. Precision orbits of 413 photographic

meteors. Smithsonian Contr. Aatrophys., vol. 4, no. 4, pp. 97-129.

KASHCHEYEV, B. L.; LEBEDINETS, V. N.; and LAGUTIN,

M. F.

1965. The motion of small meteoric bodies.

Doklady Akad. Nauk SSSR, vol. 164,

pp. 1256-1259.

KRAMER, E. N.

1953. On the detcrminat on of flash times of

meteors by means of a chopping shutter.

Astron. Circ. USSR, no. 135, pp. 10-12.

KRAMER, E. N., and ROUDENKO, O. A.

1965. Photographic observations of the Perseids.

Astron. Journ. USSR, vol. 42, pp.

416-423.

KRAMER, E. N.; VOROBYEVA, V. A.; and ROUDENKO,

O. A.

1963. The experiences of the Astronomical Observatory of Odessa in meteor surveillance

during the International Geophysical

Year. Astron. Obs. Odessa, vol. 5,

pp. 5-63.
ORBITS OF BRIGHT PHOTOGRAPHIC METEORS BABADZHANOV AND KRAMER 79

MCCROSKY, R. E., and POSBN, A. of asteroids and meteorites. Astron1961. Orbital elements of photographic meteors. Jo urn. USSR, vol. 29, pp. 162-170.

Smithsonian Contr. Astrophys., vol. 4,

no. 2, pp. 15-84. WHIPPLE, F. L.

RADZIEVSKY, V. V. 1954. Photographic meteor orbits and their

1952. On the effect of an isotropic reemission distribution in space. Astron. Journ.,

of solar radiation on the orbital motion vol. 59, pp. 201-217.

Abstract

The distributions of orbital elements of bright meteors (M<1 mag), which were photographed in 1957-1963

in Dushanbe and Odessa, are studied. It is concluded that bright meteors move in more eccentric orbits than faint

meteors, which were photographed by Baker Super-Schmidt cameras. The inclinations of orbits of bright meteors

arc on the average larger than those of faint meteors. The reality of hyperbolic meteor orbits is discussed. Photographic observations of meteors made by the method of instantaneous exposure show that meteors belonging to

different showers or associations have respectively different luminosity and fragmentation characteristics. Data

about orbital elements of meteors photographed in 1960 to 1963 in Dushanbe and Odessa are presented.
8 0 SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 1

a, Meteor no. 641541, which belongs to the Perseid shower, observed August 6, 1964. b, Meteor no. 641872, observed

August 12, 1964. c, Meteor no. 641623, observed August 8, 1964.
Inferences from Photographic Meteors

C. C. DALTON

The masses of a random sample of 285 sporadic

photographic meteors (Hawkins and Southworth, 1958, 1961) were recalculated according

to the physical theory of Opik (1958) with

rescaled mass. Weighting functions were derived for the minimization of the effects of

several sources of physical selectivity. A

five-variable statistical analysis was made for

log mass, log velocity, arithmetic celestial latitude of radiant, eccentricity, and radiant

full-angular displacement from the apex of

the earth's way. (For a detailed analysis,

see Dalton (1965).)

Table 1 shows the top-of-the-atmosphere

level-surface mean cumulative flux formulas

that were found by comparing the weightedsample cumulative distributions with the results

of Hawkins and Upton (1958) for the cumulative flux with respect to absolute photographic

magnitude for similar photographic meteors.

The spatial weighting factor was used for a

population of meteoroids in space, and it is

proportional to the terrestrial weighting factor

divided by Opik's (1951) earth-encounter

probability.

The construction of the spatial weighting

factor is illustrated in figure 1. After weighting

inversely with the square of meteor height at

maximum brilliance, the 3/2 power of the airentry velocity, the apparent fraction of the

circle of celestial latitude through the meteor

radiant, and the earth-encounter probability,

we found that weighting inversely with exp

(0.18Z) gave maximum symmetry. Because

the meteors more than 42° below the ecliptic

were obscured by the horizon, the meteors

TABLE 1.—Summary of results

2.24 g mass for zero absolute visual magnitude

meteor at 30 km/sec

log FMp=0.537 My-13.81 ±0.15

log ^ m =-1.3 4 log m-14.24±0.60

log F m c=-1.09 log (mv)-12.62±0.60

log F m r

2

=-0.92 log (mv1)-13.78±0.60

log ^ m r

3/2=-log -12.00±0.06

Partial correlations

Terrestrial weighting/,

0.097 for log m vs log v

0.103 for log m vs |&|

—0.403 for log v vs |/8,|

0.882 for log v vs X

Spatial weighting/j

0.107 for log m vs |/3e|

—0.200 for log m vs e

0.516 for |fr| vs e

— 0.799 for X vs e

1

 Aero-Astrodynamics Laboratory, Marshall Space Flight Center,

National Aeronautics and Space Administration, Huntsville, Ala.

81
82 SYMPOSIUM ON METEOR ORBITS AND DUST

150.0

135.0

120.0

105.0

90.00

75.00

60.00

45.00

30.00

15.00

.0000

-

-

2

-

a

I

r

t

a

|

r

o

I

f

I

o

f

1

p

1

•

«

if

1

«a

L

if

Tf

1

i

1

0

*>

•

1

I

>

1

O • ~ (im

-

•

r

.0000 10.00 20.00 30.00 40.00 50.00 60.00

±/?e. Celestial Latitude

70.00 80.00 90.00

FIGURE 1.—Cumulative distributions of celestial latitude, for either positive or negative (Jt separately, of radiant weighted

exp (-0.18Z) for zenith angle Z.

more than 42° above the ecliptic were subsequently given double weight for arithmetic

consideration of celestial latitude.

Figure 2 shows separate cumulative distributions of radiant celestial latitude over two

regimes of mass. Each regime has half the

sample weight.

A similar treatment for log velocity appears

in figure 3; but the correlation with log mass is

not so apparent as in the preceding figure.

It can be seen in figure 4 that the cumulative

concentration of meteoroids in space has unit

negative slope when the smaller meteoroids are

ignored because of the lack of any magnitudeabove-plate-limit weighting. Beard's (1963)

results for the slope of cumulative concentration

with respect to particle dimension, from zodiacal

light and solar F-corona data, support this

result.

When the earth-encounter probability is removed, the slope in figure 5 is the same as in

Hawkins and Upton (1958).
-ou 'x

m suqop A"jtnouio3 pus "8961

g a '

sn&i8A xng 8ApBp\unio-3o| JOJ 'fr£i — 'adojs

a ares aq^ 8AT3 A*aq^ ^nq f^uaoaad 01 J°

^xoopA Soj pn« ssuui 3

-JOO jBt}.red juaaiad o

puv sup[A^Bjj ^q pa^BpqB^ sanjBA SSBUI

"6 8>m3g in aaAiS si XSiaua put?

um^uaraora jo u^axu ou^amoaS aq'j

q^iM xng aAi^Bpirano JOJ ado|s

y A*3jaua oi^8upj| JOJ paounouoid ajom uaAa

aq o^ iCouapua^ siq'j sAioqs 8 ajnSy pn"B ISSBUI

o^ ^aadsaa q^iA^ ^-niSg Smpaoaad aqi in SB daa^s

os iou si 'i ajnSy UT imoqs SB 'nnnuaraoiu o^

^iM xnp aAi^Bpuino aq^ jo adojs aqj^

uo^dfi puB sup(

pa^jodajt SB apn^iuSBui oiqdu.i3o^oqd

JOJ adojs auiBS aq^ s^oqs 9

ssrui ,,-MOJ,, pur u-q JOJ Xjajwrdas 'auBipcj jo

(Bap)

jo suonnqujsip 3Aue[nuin3 3[dni«§—-j

p

fr'O8 VOL fr'09 VOQ

^ T TTTT T T T T

( 1

- i ! '

i

. , , ! r : c

i i « •'

o t « " ! ' '

ssc

I SSOl

I...:::::..::.....:::::::::::::::::::::::: t • •• :

it..::::...:.:....::::..:::::::::::::::::::

i

fr'Ofr fr'OC fr'02 t'OI 6C

"*"TT "*" 1111 i l/i

I'll 1BI TITUBII

I Ifav ]

jBWT T

1 If] 1 1 J

1 jp

T WT ff

F TT JT

• i r Tjj TT

X i iff LI

ittj' TT jt

ii iX i +1 1

f. Jp i IE I

, i' "•_

i' | 9\_

t

[

 *''' i r

i * * tt

i i J »

' ' J i i t c ' HI' '

i i c B'

UJ MOI s D L -

II •*

U Ublli sX t i. .

x ti l

000'

O'QZ

0 0 5

osz

001

OSl

SZl

002

Q 2 2

xoxivo—saoxiaK onwvaoojoHj KOHJ
84 SYMPOSIUM ON METEOR ORBITS AND DUST

cDU. 1 1 ! [ 1

1

rT' —

zoo.

1 f 0.

IOU.

125. --^-U-4-l

i

i uu. — — ^ j

ii 7(f

7*n I---I II, tt 750

 :: --flit

! J

1

-i •! - I

J j l l

•

f

*~f 4

I

-r

•_f_ - i *B - -

+ &

Mi ^ J

i 1

iT I '

g • i l

jrri

r 1

x * high mo

H a II

D

5J

S

1 K

J

i l l

• H « l l LllL E1 • •

• J ^

10.6 20.6 30.6 40.6 50.6

Velocity, v ( km/sec)

60.6 70.6

FIGURE 3.—Sample cumulative distributions of air-€ntry velocity, separately for "high-" and "low-" mass regimes with

terrestrial weighting ft.

DALTON, C. C.

1965. Statistical analysis of photographic meteor

data, I: Opik's luminous efficiency and

supplemented Whipple weighting. NASA

Tech. Memo. X-53325.

HAWKINS, G. S., and SOUTHWORTH, R. B.

1958. The statistics of meteors in the earth's

atmosphere. Smithsonian Contr. Astrophys., vol. 2, no. 11, pp. 349-364.

1961. Orbital elements of meteors. Smithsonian

Contr. Astrophys., vol. 4, no. 3, pp.

85-95.

HAWKINS, G. S., and UPTON, E. K. L.

1958. The influx rate of meteors in the earth's

atmosphere. Astrophys. Journ., vol. 128,

pp. 727-735.

OPIK, E. J.

1951. Collision probabilities with the planets and

the distribution of interplanetary matter.

Proc. Roy. Irish Acad., vol. 54, A, pp.

165-199.

1958. Physics of meteor flight in the atmosphere.

In Interscience Tracts on Physics and

Astronomy, no. 6, Interecience Publ.,

New York.
INFERENCES FROM PHOTOGRAPHIC METEORS DALTON 85

1

2.39

2.19-

1.99

1.79 J

1.59 -

1.39

1.19

.992

.792

592

392 .

-

"1

4 B. U H ft i i

1 r

i k

I t

w

i

i i

M

ai_4_

r*

ml

lm 1 1 %l

Vi\ VI Sv

\ \

\ \

1

V

1 \

IrE

- log m + 1.0 3

y

V

k

1k

\

i

\

K

'V

y

J y

\

w

v

sy. i

V

Ms

i

-2.14 -1.84 -1.54 -1.24 -.949 -.649 -.349 -049 .250 .550 .850

log m, g

FIGURE 4.—Logarithm of sample cumulative spatially weighted distribution /, of meteoroid mass.
86 SYMPOSIUM ON METEOR ORBITS AND DUST

2.49

2.24

1.99

1.74

1.49

1.24

.990

.740

.490

.240

-.009

h

•

i *

iff

Jlhl

\

Vn

m

J

\ 1

1.34 log m + 0.66

•

\

"I

i

\

i

\

\

-

\

>

\

V

k

i

v

>\

1

I

-2.14 -1.84 -1.54 -1.24 -.949 -.649 -.349 -.049 .250 .550 .850

log m, g

FIGURE 5.—Logarithm of sample cumulative terrestrially weighted distribution/,of meteoroid mass.
INFERENCES FROM PHOTOGRAPHIC METEORS DALTON 87

i

2.49

2.24

1.99

1.74 J

1.49-

1.24

.990

.740

.490-

.240-

0 0 9

i

-i

"1

ft

]

4

/

/

/

/

?

I

/

. A _i

it

j

L

Li

Jjn

: H

I 1

1

l l

i;

7

if

l'

- r

± t nrl

tt---1^^

j& • - A?

T0Ti ::_

Jtx

frx T l

>.537 Mp + 1.29

r

4UJ—1—^.

-2.90 -1.90 -.899 .100 1.10 2.10

Absolute Photographic Magnitude, Mp

3.10

FIGURE 6.—Logarithm of sample cumulative terrestrially weighted distribution / , of absolute photographic magnitude.
88

SYMPOSIUM ON METEOR ORBITS AND DUST

2.49;

2.24-

1.99-

1.74:

1.49-

1.24

i

990

.740-

490r

240

[)09

i

-

-

-

a.

-

+

n if

1r

Pi

—

44- n

A1

+

±

xJ i

HI 1 Tk

nis pi s u

n^

1 1 * •

1.09 log (mv) + 2.32

i

V

• S•

J

> * X

^

>

s

s

—

-

-

n

•

-

-.741 -.441 -.141 .158 .458 .758 1.05 1.35 1.65 1.95 2.25

log (mv), g(krn/sec)

FIGURE 7.—Logarithm of sample cumulative terrestrially weighted distribution / , of meteoroid air-entry momentum.
INFERENCES FROM PHOTOGRAPHIC METEORS DALTON

j

2.32

1.97

1.62

1 ?7

.920-

.570

.220

-.129 -

-.479

.829

•1.17.

•4 #•

"* ' ! 1

< » •

—

—

1

—

i

iy

i

i J>> 1

I

l

J

| L

L

1 M -

TV

r TLI

-0.92 log (mv2)+3.46

TM

-444-

X

s,

1

s

s A

t

1V

'v

s

-

X

\

-

S

_

I--

( •

) -

s

•

!

.544 .894 1.24 1.59 1.94 2.29 2.64 2.99 3.34 3.69 4.04

log (mv), g(km/sec)2

FIGURE 8.—Logarithm of sample cumulative terrestrially weighted distribution ft of meteoroid air-entry kinetic energy.

240-022 O—67 7
90 SYMPOSIUM ON METEOR ORBITS AND DUST

2.32-hI CO _ .

I.Oc

l.tr

- -

.0 tU

. . _

.tLcSj

1 9Q

.i &y

-A7Q . - -

ft f jf

- fi 9Q . - -

— 11 7 "t"

I I I

TTT

-HT

4-

4—

f

_

4-f

•4- -_

in

TTT

JVml

r

-log(mv3/2) + 2.

J

4-

f

h

KV

1

95

- i- •

ss

1;

!

l

4

Ok

!

T" -

•—

P

m

\

H

1

s

-

H

—

k

• --(

!

j

s,

i

{

S

. _ _

V

-

j

-

z

—

s

I

f

-051 .248 .548 .848 1.14 1.44 1.74 2.04 Z34 2.64 2.94 3.24

log(mv3/2), g (km/sec)3/

2

FIGURE 9.—Logarithm of sample cumulative terrestrially weighted distribution / , of the geometric mean of msteoroid air-entry

momentum and kinetic energy.
Equipment for the Observations of Meteor Trails1

J. DELCOURT2

Last year a program of radioelectrical

observations of meteoric trails was undertaken

by the CNET. A 40-MHz forward-scatter

path was used. In August 1965, a new program was begun with a 30-MHz forward-scatter

path and a 30-MHz radar.

An accurate localization of the reflection

point on each meteor trail is obtained from

an angle-measuring system from which one

component of the meteor speed vector can

be deduced. These data can be obtained

easily for a great number of meteor echoes

(some tens/hour).

The forward-scatter path is 1000 km long,

in the north-south direction, between the

Hague (Netherlands) and Toulon (France).

The bistatic radar transmitting and receiving

stations are 30 km apart, in the west-east

direction.

Measurement of angle of arrival

To determine the direction D of a meteoric

echo, the same equipment is used in both

forward-scatter path and radar: the phase

difference 4> between the field received by two

antennas Ax and A2 is measured. The angle

a'=(A~A2,D)

is deduced from the * measurement by the

expression

= —r~ cos a

A

where X is the wavelength and d the distance

1

 This work is supported by the Centre National d'Etudes Spatiales

(CNES) and the I.Q.S.Y.

'Centre National d'Etudes des Telecommunications (CNET),

Issy-lcs-Moulineaux (Seine). France.

Let A XA 2 be perpendicular to the path axis,

and A3 be a third antenna, AiA3 being aligned

along the path axis. When the latter pair of

antennas is used, the angle

can be determined in the same way as a'.

The azimuth a and the elevation 0 of the

direction D are given by

cos a'=cos a cos /3,

cos /3'=sin a cos 0.

The two waves with phase difference $ enter

two receivers Rx and i?2 and are mixed with a

wave arising from a common local oscillator. The

IF waves thus obtained have the same phase

difference *. These signals, Ex cos Qt and E2

cos ($#+$), enter a modulator which yields a

voltage proportional to Ex cos <t>. Similarly,

after changing one of the phases by T/2, the

same signals enter a second modulator which

yields a voltage proportional to Ex sin «t>. The

voltages Ex cos $ and Ex sin $ are applied to

the plates of an oscillograph, producing a polar

diagram (Ex, <i>).

The various possible errors in a' and fi' are:

Reading error: $ can be read from a film

record with a precision of the order of 2°.

Phase shifts due to variations in a circuit

element: it is necessary to verify frequently

the zero position of the phase comparator.

Noise superimposed on the echo: the phase

comparator introduces an error A4> which

gives rise to the errors Aa' and A/3' between

0?3 and 0?7 for a SNR of 30 db, and between

0?2 and 0?4 for a SNR of 25 db.

91
92 SYMPOSIUM ON METEOR ORBITS AND DUST

Frequency variations in the transmitter or in

a local oscillator: supposing A4>= 1°, it would

be necessary for the transmitter and the first

receiver oscillator to have a relative stability

of the order of 10~7.

Errors due to tropospheric and ionospheric

refractions are negligible compared to the

preceding errors.

Doppler measurement

The two origins of doppler frequency shifts are

doppler effects due to (1) movement of the

meteor: its duration is of the order of 0.1

sec—the frequency shift is very high, a few

hundred Hz; and (2) winds after the formation

of the trail. This shift is much lower than

that of (1).

The meteor speed is deduced from the doppler

shift A/, by using the relation

?. AT,

•

where y is the scattering angle, \' is the speed

->

vector of the meteor, and TV is the inner normal

to the equiphase surface.

Forward-scatter path

The phase difference <f>(0 is measured between

the reflected wave and the wave generated by

an oscillator. In the cylindrical approximation

of the Fresnel ellipsoid we have

where r is the cylinder radius, and Vx is the

speed component orthogonal to the axis.

Radar

The phase difference $(/) is measured between

the reflected wave and the wave directly

transmitted through a ground link. We have

where r is the radar distance, and Vis the speed.

The error in <l> is composed of the errors in

(1) the phase of the echo, and (2) the phase of

the reference wave. It can be shown that in

the measurement of a speed component of the

meteorite, the errors that dominate are due to

the noise.

The errors in V, are AF, = 2 m/sec for

SXR = 10 db, and AV,= l m/sec for SNR = 20

db.

Preliminary experimental results

Plate 1 shows a sample of meteoric echo record.

The scope on the upper left corner gives the

amplitudes as a function of time. The two

other scopes on the right give polar diagrams

of amplitude and angles of arrival also as a

function of time: elevation (upper right scope)

and azimuth (lower right scope). Time is

marked every 10 msec, with a larger mark

every 100 msec.

From the elevation and azimuth vulues so

obtained, and from an approximate value of

altitude, the geographic distribution of the

echoes can be determined. Figure 1 shows an

example of such a distribution (at 11 a.m.);

it can be seen that the echoes only appear in

the eastern half of the region where the antenna

diagrams overlap, indicated by a dashed line.

Figure 1 also shows the location of the radar

relative to the forward-scatter path.

FIGURE 1.—Geographic distribution of echoes.
EQUIPMENT FOR THE OBSERVATIONS OF METEOR TRAILS DBLCOURT

The velocity component orthogonal to the

->

axis V± is completely determined: the amplitude

V± is known from the doppler-effect measure-

->

ment, and the angle 0 between V± and the horizontal is deduced from the values of a' and /3'.

Figure 2 shows such a distribution of d as a

function of local time, established for a few

days of 1964. It can be seen that most of the

meteors come from the west in the morning

and around midday, and from the east in the

evening and around midnight, following the

movement of the apex.

Acknowledgment

I am indebted to MM. Giraud, Masseboeuf,

Revah, and Spizzichino for their work on the

described apparatus.

20 22 24

LOCAL TIME ' 0T0 0 5 ECHO/ HOUR

1 0.9 TO I ECHO/HOUR

j I TO 2 ECHO/HOUR

FIGURE 2.—Variation in the direction of meteoric trails as a

function of time.
94 SYMPOSIUM ON METEOR ORBITS AND DUST

•

1

1

•

2.

i

1

r

• • MPS

| |

PHASE

;

0

k

\

8

- 2

•

i

1

6 1 1 i

' 4

AFFA»B! r

1j

-

1

4.

1

AZIM

•ft*

PLATE 1

Sample meteoric echo record.
Meteor Photography with an Image Orthicon System

G. T. HICKS, 1 G. G. BARTON, JR., 1 and W. J. DAMBECK1

Introduction

For the past several years, we at the U.S. Naval

Research Laboratory have been interested in

the application of electronic imaging techniques

at night under starlight conditions to view,

and if necessary to photograph, an otherwise

invisible scene. At the same time, we have

also been interested in viewing and recording

objects that might appear in a clear night sky.

The objects that we have photographed include

satellites, auroral phenomena, and meteors.

As an example of our earlier work, plate 1

shows successive 16-mm frames of a meteor

photographed at 24 frames/sec from an image

orthicon television monitor. The field of view

of this system is approximately 15° in diameter,

and this particular meteor had an apparent

angular velocity of 15 deg/sec. The meteor

reached its peak brightness in the 9th frame

and "disappeared" in the 14th frame, leaving

residual ionization along the trail, which persisted throughout the 28th frame. It should

be pointed out that there is an inherent property

of an image orthicon tube that does not permit

complete erasure of information recorded on

the tube target from one frame to the next.

Consequently, for meteor work involving persistent ionization trails the image orthicon tube

must be calibrated for moving targets of various

brightnesses and speeds in order to get a correct

measure of the ionization along a meteor trail.

At its brightest this meteor is estimated to have

been about +2 mag. The ionization trail is

estimated to be down to approximately + 8 or

+ 9 mag near the last frame.

Equipment

Plate 2 shows a military version of an image

orthicon system with a 105-mm lens and a

focal ratio of 0.75. We still use the same lens

but with a much smaller portable system.

Figure 1 is a schematic presentation of an

image orthicon camera tube, which is the heart

of the system. The object of interest is focused

by the lens to form an image on the photoelectric surface of the tube. This surface has

a quantum efficiency of approximately 10 percent. Photoelectrons are accelerated by a

potential of 500 volts to the target, where for

each striking the target 5 or 6 secondary electrons are emitted and collected by a positive

voltage on the mesh, which is variable with

respect to the target. The target has the

property of extremely low lateral leakage of

charge compared with its leakage perpendicularly. Consequently, an electronic charge

image is left on the target. This image, which

corresponds to the optical image formed originally on the photoelectric surface, is scanned

with a scanning beam of electrons from the

OUTPUT

'SIGNAL

' E.O. Hulburt Center for Space Research. U.S. Naval Research

Laboratory, Washington, D.C. FIGURE 1.—Schematic drawing of image orthicon camera tube.

05
96 SYMPOSHM OX METEOR ORBITS AND DUST

image orthicon tube. The return beam is a

modulated signal as determined by the amount

of charge seen at a particular point on the target. This modulated beam is amplified approximately 1000 times by a 5-stage electron

multiplier and then coupled into the video

amplifiers.

We have recently developed a new method

of recording meteors with the image orthicon

system.

1. A timing comb (see fig. 2) is now impressed on the photocathode so as to suppress

photoelectric emission during preselected intervals. These pulses occur on the 1 sec, %

sec, Xo sec, and J«o sec, and have a duration

of approximately 10 msec, 5 msec, 200 ft&ec, and

100 usec, respectively, thereby establishing

by comparison four breaks occurring in the

photographed meteor trail where the meteor

was at some particular point in real time. The

meteor trail can now be measured and the

READOUT PULSE TFT SEC WIDE (0-12 VDC)

SHUTTER PULSE (RECORDING CAMERA) 0-40 VDC

SHATTER PULSE ON"g: SEC "OFFIrl ^jr SEC

TIMING COMB (PHOTOCATHODE) PULSE) 0-5O0 VDC

-^L SE C _ 100 M SEC p WIDTH

-fo SEC ~ 200 M SEC "

j SEC - 5 m SEC "

I SEC - 10 m SEC "

0 2 10 14 18 22 26 30 34 38 42

FIGURE 2.—Timing-comb photocathode voltage pulses.

Total information meteor recording system (TIMRS).

velocity determined for each 60-see interval iti

its evanescent life.

2. A shutter-driving amplifier and logic

circuit synchronized to the circuit above opens

a recording camera shutter for

 2So sec and

cycles the shutter in :*JO *©<'•

3. An integrating network and amplifier,

which turns the scanning beam on and off in

synchronism with the above-mentioned circuits, allows storage of information on the target

for %0 sec and subsequent readout in the

%o-sec interval. This circuit and the shutter

are so synchronized that the shutter is open

during five readouts and cycled between the

fifth and sixth readouts so us to allow photographic recording of the total information falling

on the photoeathode. This last circuit can be

disconnected so as to allow normal scanning

of the image orthicon tube. In this mode of

operation approximately 90 percent of the

information appearing on the kinescope is

recorded and 10 percent is lost during the

shutter cycle.

Some preliminary results obtained July 30,

1965, with this system for meteor photography

are shown in plates 3 to 7. Time breaks at

Ko-sec intervals are noticeable in these meteor

tracks, but the breaks at %Q sec are not so

definite as they need to be for data reduction

and trajectory computation. It should be

remembered that this is a first attempt at

reducing the amount of film used and the attendant processing and data reduction. We will

lengthen the %o-sec pulse widths to make

them more prominent.

The duration of the pulses occurring at any

of the preselected intervals can be adjusted

for optimum visibility on the photograph, and

this will be done as more meteors are recorded

and data reduction commences.
METEOR PHOTOGRAPHY WITH AN IMAGE ORTHICON SYSTEM HICKS ET AL. 97

I- 6

< 2
98 SYMPOSIUM ON METEOR ORBITS AND DUST

•i

6

x
METEOR PHOTOGRAPHY WITH AN IMAGE ORTHICON SYSTEM HICKS ET AL. 99
100 SYMPOSIUM ON MKTEOR ORBITS AND DUST
METEOR PHOTOGRAPHY WITH AN IMAGE ORTHICOX SYSTEM—HICKS ET AL. 101

5 1
PLATE 6

Meteor photographed with new electronic ihutter technique.
PLATE 7

Meteor photographed with new electronic shutter technique. OCO

Some Characteristics of the Major Meteor Showers

P. M. MlLLMAN

 l

The various physical parameters of meteors are

determined by widely different methods that

make use of a number of observational techniques. A selection was made here of some of

those quantities that are likely to show correlation with the physical nature of the original

meteoroid. The average values of these selected parameters, for meteors belonging to the

major showers, were reduced to a simple qualitative index ranging from 0 to 10 and are listed

in table 1. These indices are plotted in figure 1,

where the relationships among the various

showers can be seen at a glance.

The first three parameters listed, AH, x>

and <r, were taken directly from a recent paper

by Jacchia, Verniani, and Briggs (1965). The

parameter AH is the average height difference

in kilometers between the shower meteors and

the nonshower meteors of the same geocentric

velocity, and all heights are taken at the point

near the beginning of the trail where the meteor

reaches a photographic absolute magnitude of

-f2.5. For heights greater than the nonshower

average, AH is positive. The index was taken

as 10 for the greatest heights (Giacobinids),

and 0 for the lowest (5 Aquarids).

The parameter x represents the degree of

fragmentation of the meteoroid, determined

from the variation in deceleration along the

meteor trajectory. The value of x is zero

for virtually no fragmentation and increases

as the tendency to fragment increases. For its

derivation, see Jacchia, Verniani, and Briggs

(1965). The index was graded from 0 to 10 in

the same sense as the x values.

The ablation coefficient a is defined by

dm=a mv dv, the mass equation in basic meteor

i National Research Council, Ottawa, Canada.

240-022 O—67 8

theory (m is meteoroid mass, and v its velocity

in the atmosphere). From this it can be shown

that <r=A/2IY, where A is the heat transfer

coefficient, T the drag coefficient, and f the

effective latent heat of vaporization of the

material in the meteoroid. When a is large,

the ablation from the meteoroid surface is

relatively high. As is pointed out in the paper

already referred to, there is no marked correlation between a and \, although each tends

to cluster for any given group of meteors. A

mean a for the entire trajectory was used for

each meteor, and only the meteors with fairly

standard light curves were considered in compiling the mean a and x for the various showers.

The <r index used here was taken in the reverse

sense, i.e., 10 for the lowest a value.

The meteoroid densities p were taken from

Verniani (1964), who used the observational

data from the Harvard program of meteor

photography (Hawkins and South worth, 1958).

The index was given high values corresponding

to the lowrest densities. If the density variations listed in Jacchia, Verniani, and Briggs

(1965) are used, the only marked change in the

p index would be almost an interchange of the

values for the 8 Aquarids and the Geminids.

This point has to be investigated further.

The ratio between the numbers of meteors

in successive whole magnitudes is designated r.

The various determinations of this parameter

from visual data show a wide range, and it has

been difficult to arrive at satisfactory values.

The values listed are my tentative estimates,

and I used, in the main, unpublished material

from the Ottawa visual meteor program,

supplemented by various published results

(Levin, 1965; Opik, 1955, 1958; Millman and

105
106 8YMPO8IUM ON METEOR ORBITS AND DUST

TABLE 1.—Physical parameters and corresponding qualitative indices for meteor showers. (The qualitative indices plotted in figure 1 are given in parentheses following the corresponding value of the parameter. A colon between

the parameter and the index suggests uncertainty due to small quantities of observational data or other

causes. Where two values are listed for nonshower meteors, the first corresponds to the first half of the year,

the second to the second half of the year.)

Nonshower

Quadrantid

Lyrid

Arietid, f Perseid

6 Aquarid

Perseid

Giacobinid

Orionid

Taurid

Geminid

Nonshower

Quadrantid

Lyrid

Arietid, f Perseid

5 Aquarid

Perseid

Giacobinid

Orionid

Taurid

Geminid

(N)

(Q)

(Y)

(AZ)

(D)

(P)

(J)

(0)

(T)

(G)

(N)

(Q)

(Y)

(AZ)

(D)

(P)

(J)

(0)

(T)

(G)

A// (km)

0. 0 (2)4)

+ 0.3 (2)4)

- 0 . 7:(2)

- 3 . 1 (0)

+ 0.8(3)

+9.5 (10)

+ 4.8(6)4)

+2.3 (4)4)

-0. 5 (2)

Log T^ (sec)

-0.95 (0)

-1.37(3 )

-1.33(2)4)

-1.23 (2)

-1.02 (H)

- 1 . 20:(2)

-1.95(7)

-1.61 (434)

-1.12(1)

X

0.27 (2)4)

0. 44 (4)

0.08:(X)

0. 52 (5)

0.28 (2)4)

1. 89:(10)

0.46 (4)4)

0.04 (0)

0.21 (1)4)

6 04)

12 (1)4)

33 (3)4)

7(1)

23 (2)4)

8(1)

26 (3)

(10)

8(1)

46(5)

Log a (sec'/cm1)

-11. 16 (1)4)

-11.48 (5)

-11. 17:(H)

-11.40 (4)

-11.26 (2)4)

-14.9 :(10)

-11.20 (2)

-11.32 (3)

-11.23 (2)4)

NV D

7 ()4)

13(1)4)

40 (4) 1

5:(0) 2.

24

20:(2) 20

50 (5) 5

p (gm/cm1)

0.22 (5)

0.27 (5)

0. 49 :(0)

0.14 (7)

0 . OO l Id :

0. 18 (6)

0. 17 (6)

0.32 :(4)

(days)

(0)

(0)

(6)4)

5 (4)

:(1)4)

:(1)

(3)

(10) 0.05(10)

25 (3) 6

30

50 (5) 5

(2)4)

:(H)

(3)

3.

:i

2.

J.

2

9 (•

0.98

0.92

0.22

0.07

0.95

0.99

0. 57

0. 34

0. 14

r

0 (4)

2:(2)

0:(4)

5 (10)

6:(9)

H:(6)

u.)

(10)

(9)

(2)

(1)

(934)

(10)

(6)

(4)

(1)

S (sec-')

/1.05 (0)

(0.75 (2)4)

0.50 (4H)

0.40 (5H)

0.60 (4)

0. 60:(4)

0.25 (7)

0.40 (5)4)

0. 45 (5)

qx (*.u.)

5.2 (2)

55 (10)

ao(i )

5. 6 (2)

55 (10)

6.0 (2)

30 (7)

4.0(1)4)

2.6(1)

Burland, 1961). All values of r listed here

should be considered as tentative. The index

was chosen with high values corresponding to

low r.

The next two parameters, S and TA, were taken

from a paper by Millman and Mclntosh (1964,

1966): S is the slope between log N and log T,

where N is the number of meteor echoes, and T

the echo duration in seconds. Since the larger

and brighter meteors produce, on the average,

echoes of longer duration, S will be larger where

the number ratio between successive magnitudes is high. The S index was chosen high

for low S and, since no comparable radar records

are available for the Giacobinid shower, the

peak S index was set at 7 to allow for the possibility of still lower S values.

The parameter TA is the equivalent average

duration of meteor echoes at the faint threshold

of the records produced with the Ottawa meteor

patrol radar (Millman and Mclntosh, 1963).

This value was found by extending the log N vs

log T curve to the T that corresponds to N for all

echoes recorded. Here again, high values of

the TA index correspond to low values of TA.

It will be noted in table 1 and in figure 1 that,

commencing with the parameter S, two values

are given for the nonshower meteors. The first

of these corresponds to the period through

February, March, and the first part of April,

and is typical of nonshower meteors encountered

during the first half of the year. The second

corresponds to the last part of August, September, and the first part of October, and is typical

of the nonshower meteors recorded during the

second half of the year.

The parameter NR is the hourly echo rate of

shower meteors at shower maximum, as deter-
AH

SOME CHARACTERISTICS OF MAJOR METEOR SHOWERS—MILLMAN

X a p r S TA NR N v D

107

FIGURE 1.—Plot of the qualitative indices for various physical characteristics of meteor showers. J=Giacobinid; O=Orionid;

AZ=Arietid, f Pcrseid; T=Taurid; P=Perseid; Q=Quadrantid; N=Nonshower, lower line first half of year, upper line

last half of year; G=Geminid; Y=Lyrid; D=6 Aquarid. The physical parameters are defined in the text. The index

increases with increasing values of the parameters for A//, x> M?> -^v, q, and q\ and with decreasing values of the

parameters for a, p, r, S, TA, and D.

mined from the Ottawa patrol radar for echoes

of duration 2 sec or greater. High index values

correspond to high rates. Maximum index for

the Ottawa records was set at 5, and the index

for the Giacobinid shower was arbitrarily taken

as 10.

The visual hourly rate for a single observer

for shower meteors at shower maximum is represented by Nv, taken from a table published

by Millman and McKinley (1963). High index

values correspond to high rates, and again the

index for the Giacobinid shower was taken

arbitrarily as 10, with a maximum index for the

regular annual showers as 5.

The shower duration D is measured between

points where the hourly rate for the shower

meteors is one-quarter the maximum rate.

The values of D listed in table 1 are the average

between those listed in the table by Millman

and McKinley (1963) and measures made from

the radar rates of echoes with durations 2 sec

or greater (Millman and Mclntosh, 1964, 1966).

The D index is high for short duration.

The range of distances from the sun experienced by any group of meteors can be very

significant in relation to their past history and

current physical makeup. The last two parameters included in this summary are the perihelion distance q and the aphelion distance gi.

These values come from the orbital elements

Us ted by Jacchia (1963). In both cases, high

index corresponds to large values of distance.

The most striking feature in figure 1 is the

exceptional character of the Giacobinid shower

on the basis of almost every parameter. There

is some tendency for the 8-Aquarid shower to

lie at or near the other extreme. Additional

points to note are the high indices of the Perseid

shower for both S and TA, the difference in

these same two parameters between nonshower

meteors appearing in the two halves of the

year, and, except for the Giacobinids, the
108 SYMPOSIUM ON METEOR ORBITS AND DUST

apparent lack of correlation between fragmentation and low density. It must be remembered that the density values are still in some

doubt, as was noted earlier, particularly in the

case of the Geminids and the S Aquarids. The

p and /• values used here are probably the least

reliable when the differences found for the

various showers are considered.

In summary, it may be concluded that the

picture is far from simple, and there is evidence

for a wide variety of basic physical characteristics even within the members of a single

shower. When we remember the great diversity found in asteroidal fragments, it is not

surprising that there should be a similar

diversity in cometary fragments.

References

HAWKINS, G. S., and SOUTHWORTH, R. B.

1958. Statistics of meteors in the earth's atmosphere. Smithsonian Contr. Astrophy«.,

vol. 2, no. 11, pp. 349-364.

JACCHIA, L. G.

1963. Meteors, meteorites, and comets; interrelations. In The Solar System, vol. IV, ed.

by B. M. Middlehurst and G. P. Kuiper,

Univ. of Chicago Press, Chicago, pp.

774-798.

JACCHIA, L. G.; VEBNIANI, F.; and BRIGGS, R. E.

1965. An analysis of the atmospheric trajectories

of 413 precisely reduced photographic

meteors. Smithsonian Astrophys. Obs.

Spec. Rep. No. 175, 309 pp.; also in

Smithsonian Contr. Astrophys., vol. 10,

no. 1, 139 pp., 1967.

LEVIN, B.

1965.

MlLLMAN,

1961.

Mll.I.M \N,

1963.

1964.

1966.

Mll.I.M \.N,

1963.

OPIK, E. J

1955.

1958.

VERNIANI,

1964.

J.

Physical theory of meteors and the study

of the structure of the complex meteor

bodies on the basut of visual meteor

observations. In Meteons, t»d. by T. R.

Kaiser, Spec. Suppl. Journ. Atmot*.

Terr. Physics, vol. 2, Pergamon Press,

New York, pp. 131-143.

P. M., and BORLAND, M. S.

Meteor magnitude distribution!*. Astron.

Journ., vol. 66, pp. 291-292.

P. M., and MCINTOBH, B. A.

A preliminary report on radar meteor

counts. In Proceeding* of the Symposium on the Astronomy mid Physics

of Meteors. Smithsonian Contr. Antrophys., vol. 7, pp. 45-51.

Meteor radar statistics. I. Canadian

Journ. Phys., vol. 42, pp. 173U-1742.

Meteor radar -t:iti-uc- II. Canadian

Journ. Phy«., vol. 44, pp. 1593 1602

P. M., and MCKINLEY, 1). W. It.

Meteors. In The Solar System, vol. IV, ed.

by B. M. Middlehurst and G. P. Kuiper,

Univ. of Chicago Press, Chicago, pp.

674-773.

The inn.-.*••- of meteors. Mem. Soc. Roy.

Sci. Liege, ser. 4, vol. 15, pp. 125-146.

Statistical results from the Arizona Expedition for the study of meteors. Contr.

Armagh Obs., no. 26, pp. 1-82.

F.

On the density of meteoroids, II: The

density of faint photographic meteors.

Nuovo Cimento, vol. 33, pp. 1173-1184.

Abstract

Twelve physical parameters, found for the major meteor showers, were reduced to simple qualitative indices,

which were plotted in relation to the indices for nonshower meteors. The general lack of correlation among these

indices suggests a wide spread of physical characteristics within the members of any given meteor shower.
Research on Orbits of Minor Meteor Streams

A. K. TERENTJEVA

 l

Already in the 19th century the classical founders

of meteor astronomy, G. V. Sehiaparelli, G. A.

Newton, and F. A. Bredikhin, suspected that

meteor streams did exist in large quantities.

The streams characterized by high meteor rates,

duration of activity, and ease of observation

were the first to be studied. The best known

of these streams, 10 in number, are usually

called major streams.

In recent years the development of instrumental techniques has made it possible to

investigate the less numerous, but no less

significant, minor streams.

The author has made a detailed analysis of

the published data on the photographed orbits

(about 3600) of individual meteor bodies and

on numerous visual observations made in the

second half of the 19th and the first half of the

20th centuries. The most reliable data concerning visual weak shower radiants (about

2000), whose velocities had been determined,

were used. A study of this material resulted

in the finding of 374 minor meteor streams.

A monograph discussing the most authentic of

these streams (154) will be published in Russian

(Terentjeva, in press); brief reports have appeared (Terentjeva, 1963; 1964a, b; 1965a).

The remaining 220 streams, which are less

certain, as a rule include those that have no

more than 2 photographic orbits (or 1 photographic orbit if a visual radiant exists).

Generally, the existence is accepted of several

hundred minor meteor showers with a duration

of not less than 3 to 7 days and an average rate

not exceeding 2 meteors per hour. However,

more observational material of high quality is

needed in order to recognize these showers.

1

 Kiev State University, USSR.

We found a curious phenomenon of radiants

located in symmetrical positions with respect

to the ecliptic: several geocentric radiants

(sometimes groups) are symmetrically located

to the north and south of the ecliptic at a

distance of up to 50°; the elements of corresponding orbits are the same, except for the

180° difference in u and Si. Therefore, the

orbital planes, which cut across a common line

of nodes, are symmetrical with respect to the

ecliptical plane. Perhaps this phenomenon

should be considered as a regular feature and

be studied by means of celestial mechanics.

Ten of the minor streams are said to have a

northern (N) and a southern (S) branch. As

an exception, the S-Arietids stream (8-17

December) has three clearly defined branches—

northern (N), ecliptic (Q), and southern (S)

(Terentjeva, 1965b).

The great number of homogeneous visual

observations of minor meteor showers, carried

out by I. S. Astapovich in 1942-1945, show

that their radiants near the ecliptic possess a

considerable area of radiation. Some ecliptic

minor showers have several small secondary

radiation centers located within this large

area (for example, Scorpionids, Virginids,

Sagittarids, Librids). The position and relative

activity of these centers change during the

period of one night and from night to night.

It is as if the meteor stream is dispersed into

filaments. Because of the relative shortness

of these filaments, the radiation center disappears after several hours or days and is

replaced by other radiation centers in the same

large radiation area. As a rule the radiation

area of a minor shower, located at a distance

from the ecliptic, is small.

109
110 SYMPO8IUM ON METEOR ORBITS AND DUST

Other meteor showers have a more homogeneous radiation area; their secondary centers

of radiation are not as distinct (in some cases

owing to the weakness of the shower), and the

radiation area is more or less uniformly filled

with individual radiants.

In some cases the activity of every secondary

radiation center varies during its diurnal

displacement, so that during the displacement

from west to east the intensity increases in

western and decreases in eastern radiant centers,

respectively. This effect could produce the

phenomenon of a stationary or even a backward-moving radiant, but, in reality, this does

not occur.

The activity of minor showers is an extremely

complicated and intricate dynamic problem to

solve. It will take many years of investigation

to obtain an approximate answer. One of the

reasons is the rapid evolution of minor streams.

Even Super-Schmidt meteor cameras are incapable of obtaining the necessary data because

of the deficiency in or the total absence of

bright meteors in minor showers. Many

streams vary so rapidly that it is impossible

to determine their structures before they assume

a new form. Sometimes a shower can appear,

reach its maximum, and then disappear for

a period of some 10 years (for example, the

Bootids of the Comet Pons-Winnecke). Other

minor showers, which are little perturbed by

major planets, exist for hundreds and thousands

of years, making apparitions every year, just

as Perseids, Geminids, and other major showers

do.

Approximately half of the 374 recognized

streams were visually observed in the 19th

century. Reobservations of radiants of the

end of the 19th and of the beginning of the 20th

centuries, carried out by A. M. Bakharev in

1938 and by I. S. Astapovich in 1926, 1933,

and 1942 to 1945, show that during approximately half a century, one-third of the old

radiants were replaced by new ones; one-third

noticeably changed their positions, visibility

epochs, and activity; and only the remaining

one-third of the radiants underwent a minimum of change. The last third, in the main,

include long-periodic streams with significant

orbital inclinations that are little influenced

by planetary perturbations.

When analyzing the orbits of meteoric bodies

not associated with any streams, we see that

sporadic meteor matter shows traces of original

homogeneity.

To determine the connection between the

meteor streams under study and other minor

bodies of the solar system, the author calculated

the value of Tisserand's criterion C---(\/a) +

(2/a/"2) yp

 co s

 * (perturbed planet Jupiter) for

all comet orbits (except hyperbolic orbits) in

Porter's catalog (1961), which number 738

(502 comets) in all; for orbits of 154 minor

meteor streams (Terentjeva, in press); and for

the orbits of the 1650 asteroids listed in 1965

(Institute of Theoretical Astronomy, Acad.

Sci., USSR, 1964). The C distribution is

shown in intervals of </ 0.02*7, and is illustrated

in figure 1. For comets that had several

perihelion passages, C was taken as the arithmetical mean of the values of every observed

return; and for meteor streams, as the arithmetical mean of the values of every individual

stream orbit.

The maximum overall distribution for meteor

streams, short-periodic comets, and asteroids

falls on the modal value f?«0.6. The longperiodic and parabolic comets with the modal

value C~0 differ greatly from the former and

stand in a group by themselves.

The similarity of distribution for long-periodic

and parabolic comets is evidence that parabolic

comets can be considered to have elongated

elliptic orbits.

In the course of a consistent transition from

asteroids to comets and then to meteor streams,

the overall range of values of C increases (see

fig. 1). The distribution of asteroids is more

compact as compared with that of comets;

meteor streams have the greatest C dispersion

and reveal their main maximum between +0.55

and +0.58 in the region of the maximum shortperiodic comets of Jupiter's group. A deviation of the main mode is observed for streams

with respect to comets at +0.02 in the direction

of the higher values of C, which apparently is

the result of a general evolution of meteor particles due to the action of various physical

factors (corpuscular and photon radiation,

interstellar medium, etc.).

If we compare the C-distribution graph for

minor streams with the graphs for short-
ORBITS OF MINOR METEOR STREAMS TBRENTJEVA 111

A (3)

4-

-0.4

FIGURE 1.—Distribution of minor bodies according to Tisscrand's criterion: (1) minor meteor streams (#=154); (2) short-periodic

(P <200 years) comets (#=95); (3) asteroids (#=1650); (4) long-periodic comets (#=117); (5) parabolic comets

(#=290). The encircled dot belongs to curved line (4).

periodic comets and asteroids on corresponding

parts of the abscissa (fig. 1), we see a noticeable

similarity, even to the smallest details. In

several cases the secondary maxima coincide,

and this is hardly fortuitous. The same holds

true if we carefully compare the distributions

of long-periodic and parabolic comets with the

distribution of minor streams.

More precise structural details of the C

distribution can be seen in figure 2, where the

interval chosen (d=0.0lC) is smaller. The

general character of the distribution remains

the same as in figure 1.

Hence, meteor streams can be connected

with all the indicated minor bodies; the majority, however, with comets. If we interpret

this connection from the standpoint of meteor

streams originating from other minor bodies,

the proportion of the asteroid component with,

possibly, the meteorite component (Terentjeva,

1964c) will be not less than 23 percent, and that

of the comet component not more than 74

percent, most of which is comprised of shortperiodic comets of Jupiter's group. Some

streams may have come directly from longperiodic and parabolic comets.

An insignificant portion of minor streams

(3 percent) is found in the region of C^> 1 (fig.

1). They are streams with small eccentricity

(in the main, e=0.15 to 0.24) and with large

semimajor axes (a=0.87 to 1.18). If we calculate C for the particles in the zodiacal cloud,

they will be located in the region of C> > 1.

Here, apparently, the influence of physical

effects is present (Poynting-Robertson, etc.)

and increases with the growth of dispersion of

meteor matter. In the process of evolution

the particles, apparently undergoing disaggregation, grow smaller and gradually approach

the sun in spiral orbits. This evolutionary

process, which is connected with secular variations of a and e, leads to "secular" variations

in the values of C, and is consistent with the

decrease of full particle energy.

At present the search for connections between

streams and comets on the basis only of their
112

SYMP08IUM ON METEOR ORBITS AND DUST

(3)

-0.4 -0.2

FIGURE 2.—Distribution of (1) minor meteor streams, (2) short-periodic comets, (3) asteroids, accordinjc to Tisserand's criterion.

orbits coinciding (as is frequently done) is

limited and inadequate; this is particularly

true for minor streams. If we consider the

catalog of theoretical comet radiants (Kramer,

1953), it is possible to find a connection with

comets for only 18 minor streams out of 154

(Terentjeva, 1964b), i.e., 12 percent. It is

most likely that the remaining 88 percent can

be related to: (1) minor streams of comet origin

that have lost contact with the comet because

of perturbations, (2) streams (also of comet

origin) whose parent comet disintegrated or

was lost sight of for some reason or another,

(3) streams resulting from the disintegration

of other greater streams and having lost contact

with the parent stream (possibly as a result

of partial perturbation), (4) possible streams

of asteroid-meteorite origin, and (5) streams

of other possible origin. If we make a comparison with major streams, we see that the parent

comet is evident in approximately 80 percent

of the cases. This may be due to a more

favorable location of their orbits in the solar

system at a great distance from perturbed

planets. The greater portion of minor streams

are less well located. They undergo frequent

and greater perturbations, and in the entire

process of evolution have progressed much

further than major streams; apparently the

minor streams are in a relatively later stage

of evolution (although in reality they might be

younger). This is affirmed by the greater number of cases of considerable radiation area as

compared with that of major showers.

From the above discussion we must conclude

that it is becoming more and more difficult to

find connections between minor streams and

comets. A careful study should be made of the

history of the stream and of its associated

comet; they certainly are not identical. It is

necessary to utilize celestial-mechanical criteria

(e.g., those of Tisserand, Callandreau) in order

to judge whether the individual orbit of a given

stream of the past could correspond to the orbit

of one or another comet, and to what extent

the conclusion of their genetic connection is

probable. By such an approach the author

was able to discover more stream-comet associations and, in part, the connection between

separate comets and groups of meteor streams,

in spite of the great differences today in their

dates of visibility and radiant positions (simultaneously with a general similarity of physical

properties of such meteors). There also possibly exists a family of minor streams connected

with a comet, which, in turn, is a member of a

comet family that originated from a parentcomet, i.e., the presence of complex cometmeteor systems is observed.

Data on possible families of meteor streams

associated with Comet Pons-Winnecke 1951 VI

and Comet Helfenzrieder 1766 II are given in
ORBITS OF MINOR METEOR STREAMS TERENTJEVA

TABLE I.—Possible families of meteor streams associated with Comet Pons-Winnecke 1951

1766 II

113

VI and Comet Helfenzrieder

Comet and meteor streams

Pons-Winnecke 1951 VI

17 Virginids (41)

April 6-12

71 Virginids (46)

April 7-21

f Draconide (88)

May 22-June 13

Bootids (90)

June 13-July 2

f Draconids (91)

June 16-25

Helfemrieder 1766 II

0 Cancrids (9)

January 13-19

ft Leonids (17)

February 3-6

40 Leo Minorids (21)

February 12-17

* Virginids (29)

March 1-18

a

(a.u.)

_

2.90

2.95

3.27

2.67

2. 56

—

2. 53

2.54

2.36

2.65

c

0.653

0.722

0. 758

0.690

0.620

0.603

0.852

0.837

0.838

0.770

0.800

q

(a.u.)

1. 161

0.795

0.716

1.00

1. 010

1. 015

0. 403

0.420

0.407

0.525

0.527

deg.

264.6

258.7

271.9

267.5

276.0

265.0

254.3

220.7

242.6

240.0

262.7

ft

deg.

94.4

19.5

21.8

72.5

85.5

90.0

76. 1

115.7

315.7

325.5

349.4

i

deg.

21.7

4.8

10.8

39.5

19.8

33. 1

7. 9

2.7

2.5

13.0

P C

(years)

6. 12 0. 5125

±0.0016

0. 54

±0.02

0. 525

±0.0003

0. 48

±0.03

0.58

±0.03

— 0.57

±0.02

4. 51 0. 5107

0. 542

±0.006

0.54

±0.05

0. 59

±0.07

0. 55

±0.04

n

15

4

2

2

4

3

1

3

3

2

5

table 1 (see also figs. 3 and 4). The duration

of activity of showers is noted in the first

column of the table, and its number (Terentjeva, 1963) is shown in brackets. The values

of the orbital elements of the comets are taken

from Porter's catalog. The last two columns

list the mean values and mean absolute deviations of Tisserand's criterion C in n returns of

the comet or in n individual orbits of the

meteor stream.

FIGURE 3.—Pbssible family of meteor streams associated

with Comet Pons-Winnecke 1951 VI (projection on the

ecliptic plane).

FIGURE 4.—Possible family of meteor streams associated

with Comet Helfenzrieder 1766 II (projection on the

ecliptic plane).
114 SYMPOSIUM ON METEOR ORBITS AND DUST

The short-periodic Comet Pons-Winnecke,

after returning to the perihelion not fewer than

15 times, was systematically perturbed by

Jupiter, which gradually increased the comet's

perihelion distance (Porter, 1961). Figure 3

depicts two orbits of this comet in its returns of

1819 and 1951. During this period the absolute brightness of the comet decreased by 5.3

mag (Vsekhsvyatskii, 1958).

Special attention should be paid to the need

for studying the connection between Comet

Pons-Winnecke 1951 VI and Comet Helfenzrieder 1766 II. Possibly these two comets are

in some way related to Comet van Biesbroeck

1954 IV ((7=0.5102) and Comet Neujmin (3)

1951 V (C= 0.5054±0.0006).

Naturally only a detailed investigation of

gravitational perturbations, as well as lightpressure and corpuscular perturbations, can

really substantiate the author's assumptions

regarding comet-meteor families discussed in

this article and earlier.

Do minor showers of telescopic and ultratelescopic meteors exist? Yes, they do, but it

is very difficult to observe them. For example,

6 days a year the activity of telescopic meteors

is enormous (Skalnate Pleso, Ashkhabad).

This means that every year the earth meets six

minor streams of telescopic meteors. For

July 20 to 24, this stream may be a "big"

stream of telescopic meteors. It is necessary to

find (by means of radar) the coordinates of the

radiants and the velocity of these streams and

to determine their orbits in the solar system.

The orbits of telescopic and especially ultratelescopic meteor streams are unknown.

If we consider that the general evolution of

meteor matter in the solar system is accompanied by the disaggregation of meteor systems

and meteor bodies themselves, we may conclude

that among telescopic and weaker meteors the

fraction organized into meteor streams as compared with the sporadic fraction will be much

less than among ordinary and bright meteors,

where this ratio is near to 1.

References

INSTITUTE or THEORETICAL ASTRONOMY, ACAD. 8CI.,

USSR

1964. Ephemeride« of minor planets for 1965.

Nauka, Moscow-Leningrad, pp. 13-42.

KRAMER, E. N.

1953. Comctary radiant* and the connection of

meteor Bhowers with cometa. IBV.

A-tron. Obs. Odessa State University,

vol. 3, pp. 163-247.

PORTER, J. G.

1961. Catalogue of comotary orbit*, I960. Mem.

BAA, vol. 39, no. 3, 97 pp.

TEHENTJEVA, A. K.

1963. Orbitu of minor meteor stream*. Aatron.

Ciro. Acad. 8ci. U88R, Moacow, no.

249, pp. 1-4; no. 264, pp. 1-8.

1964a. Sunn- peculiarities and properties of minor

meteor atreama. Aatron. Circ. Acad.

Sci. USSR, Moacow, no. 277, pp. 1-3.

1964b. On the interconnection between minor

meteor streama and comets. Aatron.

Circ. Acad. Sci. USSR, Moscow, no. 307,

pp. 4-7.

1964c. On the interrelation of minor bodies of the

solar system. Informational Bull.

("Materials International Geophysical

Year" Geophysical Committee of the

Ukrainian SSR), Kiev, no. 6, pp. 11-15.

1965a. On the space structure of some meteor

streams. Astron. Circ. Acad. Sci.

USSR, Moscow, no. 313, pp. 7-8.

1965b. Concerning the space structure of 4-

Arietids and Leonids. Bull. Comm.

Comets and Meteors, Acad. Sci. USSR,

no. 11, pp. 33-35.

1966. Minor Meteor Streama. Collection of

works "Meteor Investigation," no. 1,

from series "Investigation Results According to International Geophysical

Projects," Nauka, Moscow.

VSEKHSVYATSKII, S. K.

1958. Physical characteristics of comets. Fizmatgiz, Moscow; trans, from Russian by

The Israel Program for Scientific Translations, Jerusalem, 1964.
On Two Problems of Sporadic Meteor Activity

J. STOHL1

The seasonal and diurnal variations of meteor

rates obtained at different locations and by

different methods of observation have been

analyzed. The results will appear in extenso

elsewhere (Contr. Astron. Obs. Skalnate Pleso).

Only two problems of broader interest, concerning the comparison of the Northern and

Southern Hemisphere data, are discussed here:

the dependence of the seasonal variation upon

the geographic latitude, and interstellar meteors.

Seasonal variation of sporadic radiant

distribution

The model distribution of apparent radiants of

sporadic meteors consisting of three constant

sources—apex, helion, and antihelion (Hawkins,

1956; Hawkins and Prentice, 1957)—is a

reasonable approximation to the mean wholeyear distribution only, subject to considerable

seasonal variations. As Keay (1963) has shown

for the Southern Hemisphere, the actual

strength varies from 0.8 to 3.7 for the helion,

and from 1.1 to 4.0 for the antihelion sources,

referred to the apex source. This variation is

evidently connected with the changes of distribution of meteor orbits along the earth's orbit.

On the basis of the available observations, in

particular of the extensive radar data from

Ottawa (Millman and Mclntosh, 1963), it is

possible to estimate the variation of the individual source strength for the Northern Hemisphere. If we adopt a model of the radiant

distribution with three point sources (apex,

Xo—90°; helion, Xo—30°; antihelion, Xo—150°),

strengths /,, and a continuous sporadic background with the uniform strength /0, then the

observed frequency/, of the sporadic meteors in

each time interval can be expressed by the sum

(1)

1

 Astronomical Inst'tute of the Slovak Academy of Sciences, Bratislava, Czechoslovakia.

where we assume n=\. The mean zenith

distances 2, of individual sources can be

calculated for arbitrary time intervals. The

strengths /< and Jo are considered constant

throughout the day. Deriving an equation of

the form (1) for each hour of the day, we obtain

24 equations of condition for 4 unknowns/< and

/„, which can be evaluated by the method of

least squares. By the solution of the equation

systems for a number of the year's intervals,

we obtain the seasonal variation of the strength

of individual sources.

The numerical calculation was carried out by

means of the electronic computer ZRA-1, on

the basis of the Ottawa radar observations

(</>=-f45?4) for 12 monthly intervals. The

contribution of shower meteors, included in the

radar observations, has been considered qualitatively in the discussion of the results. Figure

1 shows the calculated seasonal variation of

activity of the sources (in units of the mean

Ottawa frequency). The mean errors, which

are also indicated, have been calculated from

the residuals in the equations of condition.

Keay's results for the Southern Hemisphere

(<p=— 43?6) are shown in figure 2.

A comparison of the results for the Northern

and Southern Hemispheres leads to the following conclusions:

1. The helion source in the Northern

Hemisphere (fljv) exhibits an extensive maximum in the first half of the year, with an

extreme activity in June. The activity of this

115
116

SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 1.—Seasonal variation of the radiant sources in the

Northern Hemisphere (Ottawa). //=helion, AH=anuhelion, A=&pex, S— sporadic background.

source in the Southern Hemisphere (Hs) is

relatively constant, with a slight maximum in

the summer months. On the contrary, in the

Northern Hemisphere the antihelion source

(AHff) shows a relatively constant activity,

whereas in the Southern Hemisphere (AHS) an

extensive maximum from October to December

appears. The agreement in the strengths of

the sources Hn~AHs and AH^-Hs in amplitude,

combined with a phase displacement of 180°

between Hy-AHs and 90° between AHN-HS,

suggests the activity of two extraordinarily

diffuse streams of meteors. These may be

tentatively identified with the northern summer

daytime showers and the southern complex of

Velaid-Puppids; the radiants of these intricate

systems are so diffuse that they can hardly be

separated from the sporadic background.

2. The activity of the apex source has,

both in the Northern and Southern Hemispheres,

the same trend with a maximum in the second

half of the year and a minimum in April-May.

This can be attributed to a real variation of the

meteor density. The activity of the sporadic

background is practically constant throughout

3 -

0 -i 1 1 1 1 r

12 -

10 -

a -

a -

* -

3 -

o

FIGURE 2.—Seasonal variation of the radiant source* in the

Southern Hemisphere (Christchurch). //=hclk>n, /// / =

antihelion, ^ = apex, S = »poradic background.

the year, with a moderate decline in FebruaryMarch; this result is in complete agreement

with the variation of the telescopic meteor

activity (Kresak and Kresakova, 1963).

3. The total annual strengths of individual

sources of sporadic meteors are equal in both

hemispheres. The integrated relative strengths

are as follows: apex, 18 percent; helion, 31

percent; antihelion, 35 percent; uniform background, 16 percent.

Interstellar meteors

One of the main objections to the existence of

interstellar meteors is the fact that no geocentric velocities in excess of 80 km/sec have

been measured by radio methods. It can be

shown that this objection is not entirely justified. McKinley (1961) has already pointed out

that the heliocentric velocity of interstellar

particles is given by the energy equation for

their velocities in the earth's distance from the

sun, rather than by the vectorial composition

of the velocities. Hence, assuming a velocity

of 20 km/sec with respect to the sun, the maxi-
TWO PROBLEMS OF SPORADIC METEOR ACTIVITY STOHL 117

mum geocentric velocity is not 92 km/sec, but

only 76.5 km/sec.

This velocity obviously applies only to

meteors with heliocentric radiants situated

exactly in the earth's apex; however, this case

is not representative for interstellar particles,

at least not for the overwhelming majority of

them. The sun's motion relative to the medium

of interstellar particles is about 20 km/sec in

the direction toward the point with equatorial

coordinates a = 276°, 6=4-37°. The heliocentric radiant of the main source of interstellar

meteors would shift from this point in the

direction of the antihelion point by an effect

analogous to the zenith attraction. The geocentric radiant, resulting from the vectorial

composition of the heliocentric meteor velocity

and the earth's orbital velocity, would displace

during the year, with the position of the earth

in its orbit. As the numerical computation

shows, the elongation of the geocentric radiant

from the earth's apex can acquire the values

from 39?5 to 78?0 only. The corresponding

geocentric velocities are surprisingly low, never

exceeding the value of 65.5 km/sec, and with a

lower limit of 42.5 km/sec.

The random dispersion of individual velocities of the interstellar particles results in a

dispersion of the above-mentioned values of

the geocentric velocity. Nevertheless, even in

this case the geocentric velocities should group

predominantly within the velocity interval

quoted above. It is obvious that interstellar

meteors are rare, if they do exist. Thus it is

not surprising that there are no velocities in

excess of 72 km/sec, even if some interstellar

meteors actually exist. Perhaps there is another, more promising procedure for verifying

the presence of interstellar meteors. If they

actually exist, there must be some excess of

the velocities 43 to 65 km/sec in the northern

velocity distribution compared with the southern one, since the northern declination of the

solar apex is high. Comparable and representative velocity data from both hemispheres

would obviously be required for this purpose,

and meteor showers with geocentric velocities

falling within the interval in question would

have to be discarded carefully.

References

HAWKINS, G. S.

1956. Variation in the occurrence rate of meteors.

Astron. Journ., vol. 61, pp. 386-391.

HAWKINS, G. S., and PRENTICE, J. P. M.

1957. Visual determination of the radiant distribution of sporadic meteors. Astron.

Journ., vol. 62, pp. 234-240.

KEAY, C. S. L.

1963. The annual variation in the radiant distribution of sporadic meteors. Journ.

Atmos. Terr. Phys., vol. 25, pp. 507-513.

KRESAK, L., and KRESXKOVA, M.

1963. The density distribution of telescopic

meteors around the earth's orbit. In

Proceedings of the Symposium on the

Astronomy and Physics of Meteors.

Smithsonian Contr. Astrophys., vol. 7,

pp. 253-258.

MCKINLEY, D. W. R.

1961. Meteor Science and Engineering. McGrawHill Book Co., New York, 309 pp.

MILLMAN, P. M., and MCINTOSH, B. A.

1963. A preliminary report on radar meteor

counts. In Proceedings of the Symposium on the Astronomy and Physics

of Meteors. Smithsonian Contr. Astrophys., vol. 7, pp. 45-51.

Abstract

Seasonal changes of the sporadic radiant distribution are investigated on the basis of Ottawa radar records

using a simplified four-source model. The results are compared with the Southern Hemisphere data from Christchurch. Low amplitude and parallel variations of the apex source and of the uniform sporadic background contrast

with peculiar changes of the helion and antihelion source; the possible reasons of this effect are discussed.

It is shown that the observed absence of geocentric velocities exceeding 73 km/sec does not exclude the existence

of some hyperbolic orbits. The comparison of the geocentric velocity distribution in the Northern and Southern

Hemispheres is suggested as a potential check of the reality of the hyperbolic component.

Remark on a Cosmic-Probe Investigation of Meteor Showers

with Retrograde Motion

V. GUTH1

Up to the present it has been possible to study

the structure of meteor showers only once, or

perhaps twice, a year, when the earth crosses

the shower. If it were possible to send a cosmic

probe along the meteor shower orbit, with the

same heliocentric velocity but in the opposite

direction, this probe could continuously collect

the necessary data on the density of the dust

and the micrometeoroids in the stream, as a

function of the distance from the parent comet

and the sun during a half period of the stream.

Several probes with slightly different inclinations and launched at different times could

measure the function of the density inside the

shower. The launch into showers with retrograde motion is somewhat easier, since smaller

velocities than for directly moving showers are

needed. Studies of this kind would be especially

valuable for showers where the matter is not

yet uniformly distributed along the whole comet

orbit as, say, for the Leonids (the return of the

richer part of which we are now expecting) and

for H alley's comet showers. The latter case is

more important, since we expect the return of

Halley's comet in 1986, and by this time we

shall probably have rockets efficient enough to

reach the required velocity.

Let us suppose that such a probe will be

launched on May 5, 1986 (the date when the

1

 Astronomical Institute of the Czechoslovak Academy of Sciences,

Ondfejov, Czechoslovakia.

earth reaches the shortest distance from the

comet's orbit), first on the parking orbit, and

later on the orbit with apogee 0.064 a.u. to

reach the comet's orbit at the closest point. At

this moment it is necessary to accelerate the

probe at the geocentric velocity 0.97F (earth),

that is, at the heliocentric velocity 1.40V but

in the opposite direction to the comet's motion.

If we suppose (according to Prof. Kempinski)

that the passage of Halley's comet will be on

November 18, 1986 (1986.88), the probe will

then be 4 a.u. distant from the comet at the

time of launch. The probe will pass the

perihelion on June 13 (0.8 a.u. from the earth),

and on the last day in August it will meet

Halley's comet with the true anomaly 106? 7 at

a distance of 1.60 a.u. from the sun and 1.56

a.u. from the earth. Later, in mid-October, the

comet will approach the earth at a distance as

near as 0.16 a.u., just at the beginning of the

Orionids' activity. At the time of the comet's

perihelion passage the probe will be 2.7 a.u.

from the sun. This probe could therefore

measure the dust in parts of the orbit preceding

and following the comet, and elucidate some

processes of disintegration of comets. Naturally

the given data are only tentative, as the return

orbit in 1986 is not yet precisely known. (See

fig. 1.)

119
120 SYMPOSIUM ON METEOR ORBITS AND DUST

PROBE

HALLEY'S COMET

FIOURB 1. Trajectory for comet probe.

Point

1

2

3

4

5

6

Date

1986

May 5

June 13

August 31

Oct. 19

Nov. 18

Dec. 27

Earth

L

223 ?9

261.4

337.0

25.0

55. 1

94.6

Z

R

1.009

1.016

1.009

0.996

0.988

0.983

Probe

V

-81?0

0.0

106.7

120.7

125.8

130.8

r

1. 00

0.59

1.60

2. 28

2. 67

3. 14

Comet

V

13O?8

125.8

106.7

69.4

0 . 0

-81. 0

C

r

3. 14

2.67

1.60

0.86

0.59

1.00

lit mark

launch

probe perihelion

prob e !ii«-i-t- come t

Orionids

comet perihelion

/. = longitude in degrees, v=true anomaly in degrees, r, li - minis vector in a.u.
Incidence of Meteors on the Earth Derived from Radio

Observations

W. G. ELFORD1

1. Introduction

Radio observations of meteors have been used

to investigate the incidence of meteors over a

wide range of magnitudes. From hourly rate

counts made with equipment operating on

wavelengths between 4 and 18 m and at pulse

power levels ranging from tens of kilowatts to

several megawatts, data are now available on

the flux of meteors between 0 and +13 mag.

Meteors are counted by radio equipment in

terms of the electron density or the equivalent

radio brightness (see equation (1)). A meteor

trail formed within the radiation pattern of a

radar system will be detected if the orientation

of the trail satisfies the geometrical conditions

of specular reflection and if the echo exceeds

the threshold level for the system. Although

the determination of meteor-echo rates is

precise and objective, the brightness counts are

not necessarily simply related to the total

influx of meteors above a prescribed limiting

brightness or to the total influx above a

prescribed limiting mass. The transformation

of rates to fluxes above a limiting brightness

requires assumptions concerning the distribution of ionization along a meteor trail, the

ablation process, and, in the case of sporadic

meteors, a knowledge of the geocentric radiant

distribution. Further, the extension of the

transformation to determine the influx of

meteors above a prescribed limiting mass

requires a knowledge of the ionizing probability,

a parameter still subject to considerable uncertainty. It is not surprising, therefore, that

1

 Department of Physics, University of Adelaide. Adelaide, South

Australia.

240-022 O—67-

relatively few workers have attempted to reduce

their rate observations to incident fluxes.

Earlier results have been summarized by

Kaiser (1963), who also compared the radio

results with those of optical observations.

Kaiser has shown that over the magnitude

range —5 to +10 the estimates of the incident

flux of meteoroids capable of producing trails

brighter than a given magnitude vary by about

a factor of 10. The major part of this variation

between estimates is almost certainly due to

the difficulty in accurately allowing for the

severe selection effects imposed by the various

methods of observation.

In this paper we are chiefly concerned with

the fluxes of meteors that produce line densities

in excess of prescribed limiting values. The

effect of the meteor velocity on the probability

of detection is severe, and the brief discussions

in sections 4 and 6 on the flux of shower and

sporadic meteors in terms of a limiting value

of mass have been introduced mainly to indicate

the order of magnitude of the corrections.

A meteor radar system of a given wavelength

has an effective height ceiling due to a combination of the effects of the initial radius of the

trail and the diffusion of the ionized column on

the strength of the returned echo (McKinley,

1961). A number of workers have claimed, on

theoretical grounds, that the reduction in the

true echo rate due to this height ceiling is

severe. However, in order to make reliable

corrections to the echo rates and hence to the

flux estimates, we require experimental evidence concerning the magnitude of these effects. No corrections for this radio ceiling

121
122 SYMPOSIUM OX METEOR ORBITS AND DUST

have been attempted in the following discussions, but the problem is further examined in

section 6.

It is convenient to introduce a scale of radio

magnitude by the definition

j=40—2.5 (1)

where qt is the zenithal line density in electrons,'

m. We assume that the maximum electron line

density q in a trail is proportional to the cosine

of the zenith angle x of the path, so that

qt=q/cos xIt is of interest to note that the radio magnitude defined by equation (1) differs by only 0.6

mag from the photographic magnitude Mp,

according to a recent analysis by Verniani and

Hawkins (1964), who find that

Mp=39.40—2.5 log,0 qt.

2. Detection of meteor fluxes from radio

meteor rates

In order to relate the rate of detection of

meteors with a radar system to the absolute

rate of influx of meteoroids into the atmosphere

we must determine the fraction of the incident

meteor population detectable by the radar

system. The factors on which the rates of

detection of meteor trails depend are: (1) the

number distribution of meteors as a function of

maximum electron line density, (2) the geocentric radiant distribution, (3) the distribution

of ionization along the trail and the nature of

the radio reflection process, and (4) the parameters of the radar system. The main sources of

uncertainty arise in factors (2) and (3). These

are discussed in sections 5 and 6.

The first step in solving the problem is to

determine the response of the radio system to

meteors from an element of the celestial sphere

of unit radiant density, producing trails with

line densities in excess of a prescribed limiting

value. The description of the echo rate for all

positions of the element in the altitude-azimuth

coordinate system is termed the response function of the system. Graphical methods for

determining the response function for any

system have been given by Kaiser (1960,

1961a), and a computer method suitable for

either coincident or spaced transmitting and

receiving stations has been developed by Elford

(1964). In general, the response function of

any system will be a function of both elevation

and azimuth of the radiant. However, for an

omnidirectional antenna system sucli as used

at Ottawa and Christchurch for surveys of

meteor activity, the response function varies

only in elevation.

The incident flux of meteors whose radiants

lie within an element of the celestial sphere

of solid angle dil and which produce zenithal

line densities greater than q, can be written as

N(qt)(lil. This is the flux across a plane

normal to the meteor paths. It Is assumed

that the cumulative distribution function

N(qt) can be represented by a simple power

law of the form

N(q.)=Kq*,. (2)

Alternatively, the distribution function can be

defined in terms of the number of meteors

dN(q,) that produce line densities between

q, and q,+dqt. It is customary to write this

incremental distribution function as a simple

inverse power law with exponent s, i.e.,

dN(q,)xq-'dqt. (3)

The two exponents in equations (2) and (3)

are related by the expression c=l—«. The

exponent s is not constant but in general varies

slowly with magnitude. Its value lies between

1.4 and 2.7. In calculating the response function of a system we usually assume a constant

mean value for .s (and hence for c) appropriate

to that portion of the meteor population near

the limiting magnitude of the system. This

is justified by the fact that the radar echo rate

is determined predominantly by those meteors

whose radio brightness is within 2 or 3 mag of

the limiting magnitude. However, it is shown

later that the use of a mean value for s and c

breaks down for shower meteors brighter than

+ 3 mag.

For narrow-beam meteor radar systems the

form of the response function is relatively

insensitive to the value of c. In the case of

radar systems that use antennas with broad

polar diagrams, the response function can vary

significantly with changes in the value of c.

This is illustrated in figures 1 and 2, where

the response functions for the omnidirectional
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS—ELTORD 123

V

J

/

\

\

c—0 6

\

\

V

\ \

\ \ \

0 10* 20* 30* 40° 5O* 60* 70* 80* 90°

ELEVATION OF RADIANT

FIGURE 1.—Response functions for the 33 Mc/sec-meteor

patrol radar at the Springhill Meteor Observatory, Ottawa.

The functions have been calculated for several values of the

exponent c in the cumulative distribution relation N{q.)

J

/

1

/

V

c-14

> ^

^0. 6

\

\ V

3O* 40* 50° 60"

ELEVATION OF RADIANT

FIGURE 2.—Response functions for the 70 Mc/sec-meteor

patrol radar at Christchurch, New Zealand. The functions

have been calculated for several values of the exponent c in

the cumulative distribution relation N(q,) = Kqe,.

meteor radars at Ottawa (Neale, 1958) and

Christchurch (Ellyett and Keay, 1963) have

been calculated for a number of possible values

of c. Thus the radiant elevation at which a

broad-beam system has its peak response will

depend on the value of c. This effect must be

taken into account when the rates of shower

and sporadic meteors observed with such

systems are compared.

The value of the exponent s in the incremental

distribution function for sporadic meteors has

been estimated by various workers. From a

detailed analysis of photographic meteors

Hawkins and Upton (1958) obtained a value of

2.34 for sporadic meteors brighter than +4 mag.

For fainter meteors the most direct method of

estimating s is from a comparison of radio echo

rates obtained at two different levels of transmitter power or minimum detectable signal

level. The results of a number of estimates of

s for sporadic meteors are summarized in

figure 3. Estimates of error are available only

for data marked (2), (5), and (6); it is therefore

not possible to assess whether all the data are

consistent. It appears, however, that there is

a change in s of about 0.5 in going from meteors

of 0 mag to meteors of +9 mag, and that in the

magnitude range +9 to +13 the value is 2.0

±0.05.

In the case of meteor showers the value of s

has been determined only for those showers

whose echo rate is such that they can readily be

distinguished from the sporadic background.

The distributions of maximum line density for

six meteor streams have been determined by

Browne et al. (1956), Weiss (1961), and Kaiser

(1961b). As in the case of sporadic meteors, it

was assumed that over a limited range of

magnitudes the incremental distribution function could be represented by a simple inverse

power law with exponent s. The combined

results of these studies extend from 0 to +10

mag and are summarized in figure 4. The

variation of s with magnitude is much greater

than in the case of sporadic meteors, and for

26

2 5

24

2 3

I

22

2 I

(1)

(2)

-

-

(1) WEISS (1961) Radio

(2) HAWKINS and UPTON (1958)

Photographic

(3) KAISER (1961a) Radio

(4) WEISS (1961) Radio

(5) McKINLEY (1961) Radio

- (6) ELFORD (1964) Radio

(3)

(4) (6)

(51

.i 1 1 1 1 1 1

FIGURE 3.—Values of the exponent s in the incremental distribution function of sporadic meteors, determined by optical

and radar methods. The length of the line indicates the

range of radio magnitudes appropriate to each determination.
124 SYMPOSIUM ON METEOR ORBITS AND DUST

0(2)

G(2)

E12>

0(1)

All)

0(2)

G(2)

E(2)

A ARIETIDS

0 8AQUARI0S

E ^AOUARIDS

C GEMINIOS

P PERSEIDS

0 OUAORANTIOS

(1) BROWNE 1L81-

(1956)

(2) WEISS (1961)

(3) KAISERU96I0)

FIGURE 4.—Values of the exponent s in the incremental distribution function for six meteor showers. The length of

the line indicates the range of radio magnitudes appropriate

to each determination.

meteors brighter than +3 mag the assumption

of an inverse power-law distribution is clearly

not justified even over a limited range of

magnitudes. For the Geminid and fl-Aquarid

streams the increase in s for meteors brighter

than +1.5 mag is so steep that it effectively

amounts to a cutoff of meteors larger than those

corresponding to 0 mag. The same argument

applies to the Arietid stream, which is composed

mainly of meteors fainter than +4 mag. For

MR> + 8 all the showers have a value of 8 well

below the value of 2.0 for sporadic meteors, and

thus these showers must eventually become

swamped by the sporadic background as the

magnitude limit is extended to fainter meteors.

3. Sporadic meteor flux

Estimates of the flux of sporadic meteors that

produce trails with zenithal line densities above

prescribed limiting values have been made by

a number of workers. Kaiser (1961a) has used

sporadic meteor rates obtained with a 17 Mc/sec

radar system at Sheffield to determine the

sporadic flux down to a limiting line density of

5XlOnm-I(M«=10.8). The mean influx at

this limit was estimated as 1.9X10~10m~2sec~\

and the value of the exponent s in the distribution law was found to be 2.17 over the

magnitude range + 8 to +11. From observations carried out at a frequency of 27 Mc/sec at

Adelaide, Weiss (1957a) estimated the sporadic

flux down to a limiting line density of 10um~'

as 3.8X10"13m~2sec~1, and the value of s for

meteors between + 5 and + 7 mag to be 2.0.

Lebedinets (1964) has discussed observations

made at Kharkov with a 38 Mc/sec radar

system that could detect meteors above a

limiting zenithal line density of 10l2m~'. When

the estimates of the sporadic flux were extrapolated to the limiting line density of 5X 10nm~~'

quoted by Kaiser for the Sheffield system,

Lebedinets arrived at an incident flux of

2.6X10"10m"2sec"'. This is in close agreement

with the Sheffield result. A recent analysis

(Elford and Hawkins, 1964) of observations

carried out with the Harvard-Smithsonian 41

Mc/sec meteor radar system at Havana, Illinois,

during March 1963 has extended the estimate

of the flux of sporadic meteor* down to a rudio

magnitude of +13.4. The mean influx of

meteors estimated from these observations was

1.0X10"8m~2sec-'.

The various estimates of sporadic influx

are shown in figure 5. There is general agreement among the results derived from the observations made at Adelaide, Kharkov, and

Sheffield, which together extend over the magnitude range +4 to +11. However, when the

Harvard-Smithsonian and Sheffield results are

RADIO MAGNITUDE

6 8 10

l<f"L

S SPORADICS

A ARIETiOS

G GCMINIDS

P PERSEIOS

(1) ELFORD (1964)

(2) KAISER (1953,1955,19610)

(3) LEBEDINETS (I9C4)

(4) WEISS (19371

• SO)

5 io

 1C(-

10

P(2)<

/G(2)

I013 10'" I01 3

ZENITHAL LINE DENSITY (m"')

FIGURE 5.—Mean incident flux over the whole earth of meteoroids capable of producing meteors with zenithal electron

line density greater than q,. Solid lines, sporadic flux;

broken lines, shower flux.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS ELFORD 125

compared by extrapolating each to +11.5 mag,

there is a discrepancy in the incident flux of a

factor of 4, the higher flux being predicted by

the observations of the fainter meteors. This

discrepancy is too large to be explained by

uncertainties in the radiant distribution or the

response functions for the systems. Further,

the single-body ablation theory predicts the

reverse effect, i.e., as the radio observations are

extended to fainter meteors there should be a

decrease in the proportion of the meteor population detected. On the other hand, there is

experimental evidence (Hawkins, 1964) that

meteors fainter than + 5 mag occur at progressively lower heights, an effect that has been

attributed to a decrease in the degree of fragmentation of the meteoroid for meteors fainter

than + 5 mag. Thus the disparity between the

estimates of the flux based on the 10th- and

13th-mag observations may be the result of a

change in the degree of fragmentation of the

meteroids over this magnitude range.

4. Shower meteor fluxes

The incident flux for eight showers has been

estimated by Weiss (1957a) for meteors with

zenithal line densities in excess of K^m"1,

using data on hourly rates obtained at Jodrell

Bank and Adelaide. From observations made

at Sheffield and Jodrell Bank, Kaiser (1953,

1955, 1961a) has determined the incident flux

for the three showers, Geminids, Arietids, and

Perseids, over a considerable range of limiting

line densities. The results of these various

determinations are summarized in table 1,

together with estimates of the sporadic flux

made by Weiss and Kaiser. It can be seen

from the table that for meteors fainter than

MR= +5(5=1014m~1) the sporadic background

dominates over any of these major streams.

In order to obtain the rate of incidence of

particles above a limiting mass, Weiss (1957a)

applied a velocity correction of the form »*e.

For meteors whose mass exceeds that equivalent

to a zenithal line density of lO^m"1 at a velocity

of 60 km/sec, the three showers—Arietids, £

Perseids, and 5 Aquarids—all have a similar

flux, which is about 40 percent of the sporadic

background. In contrast, the contribution

from the three high-velocity showers, Perseids, 17

Aquarids, and Orionids, is in each case only 1

to 2 percent of the sporadic background.

In figure 5 the variation with magnitude of

the incident flux of the three showers, Arietids,

Geminids, and Perseids, is compared with the

variation for sporadic meteors. Here again

we consider the mean flux over a sphere. The

graphs emphasize the dominant role played

by sporadic meteors fainter than radio magnitude + 5. For meteors brighter than +10

mag sporadics outnumber any one of the three

showers by a factor of 10 or more, and the

trend of the graphs suggests that if the magnitude limit were +13 the sporadics would outnumber any of these showers by a factor of the

order of 102.

TABLE 1.—Shower meteor flux

Tvpe of meteor

Sporadic

Germinid

Perseid

Arietid

Quadrantid

£ Perseid

5 Aquarid

rj Aquarid

Orionid

Flux (m->

10» m-1

45X10-18

100X10-"

sec"1) above limiting zenithal line density*

10" m"1

35X10-"

30X 10-"

15X10-"

25X10-"

20X10-"

18X10-"

37X10-"

18X10-"

23X10-"

10" m-i

56X10-"

12X10-"

8X10-"

20X 10-"

10" m-1

90X10-"

5X10-"

13X 10-"

Reference

(1), (2)

(2)

(1), (2)

(1), (2)

(1)

(1)

(1)

(1)

(1)

*To facilitate comparison between shower and sporadic fluxes the values for the former are given as the mean flux over a sphere (i.e., one-quarter of

the flux through a plane normal to the radiant direction).

References: (1) Weiss (1957a), (2) Kaiser (1953, 1955,1961a).
126 SYMPOSIUM ON METEOR ORBITS AND DUST

It should be noted that the ratios of sporadicto-shower fluxes discussed above refer to the

total sporadic flux compared to the flux of an

individual shower. The ratio of the total incidence per year of sporadic meteors to the total

incidence per year of shower meteors will depend

on the number of meteor showers per year and

their strength and duration. An objective

method of defining a meteor stream in terms of

the degree of similarity of meteor orbits has

been developed by Southworth and Hawkins

(1963), and has been applied to 3000 orbits

determined from observations made with the

Harvard-Smithsonian meteor radar system during the period January to August 1962 (Hawkins, Southworth, and Rosen thai, 1964). The

radio magnitude limit for these orbital data

was estimated as +11. It was found that 24

percent of the orbits associated into streams

(value of association parameter Z>=0.1). A

somewhat similar analysis (Nilsson, 1964) has

been carried out on 2200 orbits determined

from observations of meteors brighter than

+6 mag, made at Adelaide during 1961.

From an examination of real and chance associations of orbits Nilsson concluded that 17

percent of the total orbits could be classed as

definite streams, while a further 8 percent could

probably be classed as members of minor

streams. An examination of Nilsson's data

using the method of Southworth and Hawkins

(Elford, unpublished) gave essentially the same

result as obtained by Nilsson if the association

parameter D was chosen as 0.10 to 0.15. It

would thus appear that over the radio magnitude range + 6 to +12.5 the ratio of the total

annual incidence of sporadic-to-shower meteors

is about 3:1.

For meteors brighter than visual magnitude

+5, Hawkins (1964) has stated that approximately 50 percent of the meteor flux comes from

the major and minor streams. If the stream

activity is defined in terms of the sporadic rate

by the expression N,=kN cos x, where N, is

the shower rate, N the sporadic rate, and x the

zenith distance of the shower radiant, Hawkins

gives values of & as high as 5.5.

Keay and Ellyett (1961) have pointed out

that hourly rates obtained from radio observations of meteor showers are strongly dependent

on the geographical latitude of the observing

station and, in general, do not give a reliable

indication of the relative fluxes from different

meteor showers. They have developed a simple

method of determining the relative significance

of meteor showers, and have shown that when

applied to the shower rates determined at

Adelaide, Christchurch, and Jodrell Bank, there

is general agreement concerning the relative

strengths of showers. They find that the *-

Aquarid shower is the strongest of the regular

meteor showers.

The latitude variation in optical observations

of 24 meteor showers has been investigated by

Kresak (1964), who has determined the relative

number of meteors from a given shower that

penetrate the atmosphere at different geographic

latitudes. The proportion of these that can

be observed optically has also been determined.

It is of interest to note that the fractional

influx into the equatorial zone (±10° latitude)

for 17 of the 24 major showers varies by only

±4 percent. Only those showers with radiants

of high declination show a distinct deficiency

at the equator, and even among these the effect

of zenithal attraction on showers with low geocentric velocity can partially compensate for

the high declination.

5. Annual variation in the incidence of

meteors on the earth

The daily echo rate of meteors observed at any

point on the earth's surface varies throughout

the year. Observations carried out at midnorthern latitudes (Hawkins, 1956; Vogan and

Campbell, 1957; Evans, 1960; Millman and

Mclntosh, 1963) have shown that the daily echo

rate has a maximum between June and September and a minimum during February and

March. In the Southern Hemisphere the daily

echo rate, as determined at Christchurch, 43?5 S

(Ellyett and Keay, 1961), and at Adelaide,

35° S (Weiss, 1957b), has a maximum in December and a minimum between June and

September. Some features of these annual

variations in daily rate can be explained by the

occurrence of the major meteor showers. However, even when the effect of the major showers

is removed, Hawkins (1956) and Weiss (1957b)

have shown that there remains a significant

annual variation.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS—ELFORD 127

It is generally accepted that the radiants of

sporadic meteors are concentrated in a number

of groups. For meteors brighter than MR ~ 6

three groups lying on the ecliptic are recognized,

one at the apex and two centered on points

lying about 70° in longitude from the apex

(Hawkins, 1956; Weiss and Smith, 1960;

Davies and Gill, 1960). The last two groups,

generally referred to as the sun and antisun

groups, have diameters~60° to 70°. At fainter

magnitudes there is increased activity from

regions lying about 60° north and south of the

apex (Davies and Gill, 1960; Hawkins, 1962).

For 10th- to 12th-mag meteors the average

strength of this high-latitude activity is about

50 percent of the sun and antisun concentrations (Elford, Hawkins, and Southworth, 1964).

Over a period of 1 year the declinations of

the various sources of sporadic radiants, as

viewed from one locality, vary in a cyclic

manner, and it would be expected that the

observed echo rate would be a maximum when

the apex lies highest in the sky, that is, during

March in the Southern Hemisphere and during

September in the Northern. The observed

rates for the Northern Hemisphere in general

follow this pattern. However, the Southern

Hemisphere observations contradict the expected annual variation. Weiss (1957b> interpreted these facts to mean that there is a real

variation in the space density of meteors

around the earth's orbit, and he derived an

annual variation in relative density that was

very similar to the results of telescopic studies

of meteors by Kresakova and Kresak (1955).

These results indicated that the incidence of

meteors on the earth during the second half

of the year is about 50 percent greater than

during the first half.

This variability in the space density of

meteors encountered by the earth during the

course of the year has been confirmed by precise

hourly rate observations carried out over a

period of 1 year at Christchurch, 43?5 S

(Ellyett and Keay, 1963; Keay, 1963). These

observations were made with a 70-Mc/sec-wide

aperture system that could detect meteors

down to +8.2 mag. The response function

for this system has already been discussed and

is given in figure 2. From a comparison of the

observed echo rate and the expected echo rate

based on a triple-source radiant distribution

(apex, sun, and antisun), Keay (1963) has

shown that the increase in meteor flux in the

second hah* of the year is due primarily to an

increase in the strength of the antisun group

and, to a lesser extent, to an increase in the

strength of the apex group. The strength of

the sun group remains essentially constant

throughout the year. In a recent investigation of meteor streams based on measurements made at Adelaide (35° S) of orbits of

meteors of +6 mag or brighter, Nilsson (1964)

has shown that the antisun group predominates

during the 6 months July to December, in agreement with the conclusion reached by Keay for

somewhat fainter meteors. Moreover, as

shown in figure 6, the predominance of the

antisun group during these months is due to a

large number of minor streams through which

the earth passes during the second half

of the year. When meteors that are members

of these streams are removed, the strengths

l40r

100

60

o

u 20 -

0l_c£3=C i

180 2"

all orbits

270

ac

UJ

ffl 40

z 30

90 180

nonshower

180 270 0 90 180

LONGITUDE RELATIVE TO THE APEX

FIGURE 6.—The distribution of meteors with ecliptic longitude

as observed at Adelaide (35° S) for 4 months, July-October

1961 (Nilsson, 1964).
128

SYMPOSIUM ON METEOR ORBITS AND DUST

of the sun and antisun groups over this period

are essentially the same. If it is assumed that

there is no marked change in the radiant distribution as the limiting magnitude is lowered

from + 6 to +8, the increase in the incidence

of meteors of + 8 mag or brighter during the

second hah* of the year is most likely due to the

occurrence of a large number of unresolved

meteor showers.

Additional evidence for the presence of minor

showers during the second half of the year

comes from the results of an extensive investigation of hourly echo rates carried out at the

Springhill Meteor Observatory, Ottawa (45° N)

over a period of 5 years 1958 to 1962 (Millman

and Mclntosh, 1963). These observations

were made with a 33-Mc/sec-wide aperture

system omnidirectional in azimuth. The response function for this system has already been

given in figure 1. There is no published

information on the minimum signal that can be

detected with this equipment, but, if it is

assumed that the equipment will just detect a

signal equal to the average cosmic noise, it is

estimated that the radio brightness threshold

for the equipment is +7.5. This is very close

to the threshold level for the Christchurch

equipment. Thus it appears that the two

precise echo-rate surveys carried out at Ottawa

and Christchurch have investigated essentially

the same portions of the meteor population.

Further, these two surveys have been made

from two points almost equally spaced either

side of the equator, 45° N and 43?5 S. In

publishing the statistics of the survey, Millman

and Mclntosh have compared the daily rate of

all echoes with the daily rate of echoes with

duration greater than 8 sec. The percentage

of echoes with durations > 8 sec shows strong

correlation with the major meteor showers, the

percentage for the Perseids and Geminids rising

to as much as 10 percent compared with a

nonshower value of 1 to 2 percent. It is of

interest to note that the average value of the

percentage of long-duration echoes during

February and March is 1.22 ±0.20 percent, and

the average value during September and the

first half of October is 1.76±0.20 percent. If

it is assumed that the percentage of longduration echoes is an index of meteor shower

activity, this result adds weight to the suggestion made earlier that during the second half of

the year the earth passes through a large

number of minor meteor streams.

Since the Christchurch and Ottawa surveys

refer to essentially the same portion of meteor

population, it is of interest to compare the

meteor influx deduced from the two sets of

observations. The average meteor influx for

each month of the year has been determined

from the Ottawa hourly rate data by a comparison of the observed diurnal rates with those

predicted when the radiant distribution is

approximated by a triple-source model and

the response function is that given in figure 1

for c= —1.0. The three sources, each of

diameter 65°, were centered on the ecliptic,

one at the apex and the other two at points

±70° from the apex. The relative strengths

of the sources and the uniform background were

adjusted to give the best match between the predicted and the observed diurnal rates. Using

a similar procedure, Keay (1963) has deduced

the average meteor flux for each month of the

year from the Christchurch data. The radiantdistribution model assumed by Keay consisted

of three point sources on the ecliptic and a uniform background. The strength and position

of the sources were as follows: Source of

strength 1 unit at the apex, two sources each of

strength 2 units at points ±60° from the apex, a

uniform background of integrated strength 1

unit. The results are shown in figure 7 together

°1

Mar | »DI

l a « A0CLAI0C.1T SlaCISS.ItST) •

» • » CMOI5TCMU«CH. 4S»» S

(«eAY.i»«si

A J

Ho,

9 0 *

J»» 1 J.l •<g

180*

Sap ' Oet Nc>

270* i | OT X

Dae | Ja» | 'a» j Mar j

FIGURE 7.—The incidence of meteors on the earth as a function

of ecliptic longitude; observed at mid-northern and midsouthern latitudes.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS—ELFORD 129

with an earlier result obtained by Weiss (1957b)

from observations made at Adelaide. No attempt was made to remove the effect of meteor

showers from the original rate data for either

Christchurch or Ottawa. Keay justified this

approach for the Chr.stchurch data on the basis

that for wide-aperture systems the ratio of

shower to sporadic rates is greatly decreased as

compared with observations made when narrowbeam antennas are used, and that faint shower

meteors are swamped by the sporadic background. However, the Ottawa observations

(Millman and Mclntosh, 1963) do not support

the latter contention. During May and June

the echo rate from the daytime streams is comparable to the sporadic rate, and as a result

the flux estimates based on the Ottawa data

show an anomalous peak in June. The absence

of a similar peak in the Christchurch result is

due to the fact that the response functions of the

Ottawa and Christchurch systems for shower

meteors (c=—0.4 to —0.6) are markedly different from the response functions for sporadic

meteors (c= —1.0). As a consequence, the

probability of detecting Arietid and £-Perseid

meteors at Ottawa is enhanced compared

with sporadics, while the reverse is true at

Christchurch.

With the exception of the 3 months, April,

May, and June, there is good agreement between the three estimates of the relative meteor

influx throughout the year as shown in figure 7.

It is therefore of interest to compare the absolute values of the meteor flux determined from

the Ottawa and Christchurch data. This has

been carried out for the month of March 1960.

The limiting zenithal line density of the Ottawa

system was estimated by assuming that the

minimum detectable echo power was 7.0X10"14

watts. This gave a limiting density of 8.9 X

lO12!!!"1, or radio magnitude +7.5. The incident flux was determined from a comparison of

observed and predicted diurnal rates with the

use of the triple-source radiant distribution

discussed earlier. It was assumed that all

trails were uniform in electron density along

their length and that the difference in heights

between the beginning and the end of the trails

was 6 km. A similar analysis was carried out

with the Christchurch data, and the results are

shown in table 2. The Christchurch result is

Station

TABLE 2.—Sporadic meteor flux

Ottawa, 45° N

Christchurch,

43 ?5 S

X(m)

9.2

4.3

Limiting

8. 9X 1012

5. 1X1012

Limiting

MR

+ 7.5

+ 8.2

Flux (m-2

sec"1)

(March

1960)

1.25X7O-"

1.08X10"

very close to the previous estimates shown in

figure 5, but the Ottawa result is a factor of 2

higher. Since the response functions for these

two systems can be calculated accurately and

the assumed model radiant distribution is the

same for the two calculations, this discrepancy

between the two estimates of flux reflects either

an incorrect estimate of the limiting zenithal

line density for the Ottawa system or the failure

to account properly for the effect of wavelength

on the echo rate. This point should be

examined further when the actual value of the

minimum detectable echo power for the Ottawa

system is known.2

In comparing measurements of meteor flux

made by different workers at different times one

should note that the maximum in the diurnal

echo rate averaged over 1 month can show

year-to-year variations of as much as 50 percent

(Millman and Mclntosh, 1963; Ellyett and

Keay, 1964; Mclntosh and Millman, 1964).

6. Selection effects due to meteor velocity,

trail diameter, and diffusion

Estimates of meteor fluxes down to a given

limiting mass from radio echo-rate data are

subject to considerable error due to the severe

selection effect of velocity and to uncertainties

in the dependence of the ionizing probability

/3 on velocity. In a recent review of the

ionizing efficiency of meteors, Verniani and

Hawkins (1964) conclude that /3ocy40 with an

uncertainty in the exponent of about ±0.5.

A velocity correction of v* was applied to shower

fluxes by Weiss (1957a), and it was shown

in section 4 that this greatly reduces the

significance of the high-velocity showers.

2 Recently B. A. Mclntosh (private communication) has pointed out

that the minimum detectable echo power for the Ottawa system is

probably closer to 2X1(H« watts. This would bring the Ottawa and

Christchurch fluxes into closer agreement.
130

SYMPOSIUM ON METBOR ORBITS AND DUST

Recently (Elford, Hawkins, and Southvvorth,

1964), an estimate has been made of the mass

limit for sporadic meteors observed in March

1963 with the Harvard-Smithsonian meteor

radar system. From the observed velocity

distribution and the value of the ionizing probability given by Verniani and Hawkins, it was

estimated that the flux of sporadic meteors

with mass greater than 1.3X10"8 g is 1.0X

lO-^n"2 sec"1.

The effect of diffusion and finite initial trail

radius on the radar echo rate of meteors has

been discussed by a number of workers (Peregudov, 1958; Fialko, 1960; Greenhow and Hall,

1960; Lebedinets, 1964), who have predicted

that equipment operating on short wavelengths

« 1 0 m) will detect only a fraction of the meteor

population. Lebedinets estimates that for

equipment operating on a wavelength of S m

and at an effective minimum detectable line

density of 1012m~', the true sporadic rate is

about a factor of 30 greater than the observed

echo rate. Greenhow and Hall (1960) estimate

that the percentage of the true influx of meteors

detected by a radio system varies from 1.5 at

4-m wavelength to 40 at 17 m. However, the

estimates of sporadic flux discussed in section 5,

which have been derived from observations at

frequencies of 70, 38, and 17 Mc/sec, do not

differ by more than a factor of 2 to 4. The

lack of agreement between the predicted and

the observed variations in rate as a function of

wavelength has been attributed to the effect of

a decrease in fragmentation among meteors

fainter than + 5 mag (Hawkins, 1964).

References

BBOWNE, I. C ; BULLOUQH, K.; EVANS, S.; and KAISER,

T. R.

1956. Characteristics of radio echoes from meteor

trails, II: The distribution of meteor

magnitudes and masses. Proc. Phyg.

Soc. London, vol. 69B, pp. 83-97.

DAVII!8, J. G., and GILL, J. C.

1960. Radio echo measurements of the orbits of

faint sporadic meteors. Monthly Notices Roy. Astron. Soc., vol. 121, pp.

437-462.

ELFORD, W. G.

1964. Calculation of the response function of the

Harvard Radio Meteor Project Radar

System. Harvard Radio Meteor Project

Res. Rep., no. 8.

ELFORD, W. G., and HAWKINS, G. S.

1964. Meteor echo rates and the flux of sporadic

meteors. Harvard Radio Meteor Project Res. Rep., no. 9.

ELFORD, W. G.; HAWKINS, G. S.; and SOUTHWORTH,

R. B.

1964. The distribution of sporadic meteor radiants. Harvard Radio Meteor Project

Res. Rep., no. 11.

ELLYETT, C, and KEAY, C. 8. L.

1961. All-sky meteor rates in the Southern Hemisphere. Journ. Geophys. Res., vol. 66,

pp. 2590-2591.

1963. Southern Hemisphere meteor rates.

Monthly Notices Roy. Astron. Soc., vol.

125, pp. 325-346.

1964. Meteors: An unexpected increase in 1963.

Science, vol. 146, p. 1458.

EVANS, G. C.

1960. Radio echo observations of metoor activity

between 1054 December and 1958 December. Astron. Contr. Univ. Manchester (1), Jodrell Bank Ann., vol. 1,

pp. 280-337.

FIALKO, E. I.

1960. The dependence of the mean hourly rates of

recorded meteors on the parameters of

meteoroids, the atmosphere, and the

radar system. Sov. Astron.—AJ., vol.

4, pp. 711-721.

GREENHOW, J. S., and HALL, J. E.

1960. The importance of initial trail radius on the

apparent height and number distributions of meteor echoes. Monthly Notices Roy. Astron. Soc., vol. 121, pp.

183-196.

HAWKINS, G. S.

1956. A radio echo survey of sporadic meteor

radiant?. Monthly Notices Roy. Astron.

Soc., vol. 116, pp. 92-104.

1962. Radar determination of meteor orbits.

Astron. Journ., vol. 67, pp. 241-244.

1964. Interplanetary debris near the earth. Ann.

Rev. Astron. Astrophys., vol. 2, pp.

149-164.

HAWKINS, G.S.; SOUTHWORTH, R. B.; and ROSENTHAL,S.

1964. Preliminary analysis of meteor radiants

and orbits. Harvard Radio Meteor

Project Res. Rep., no. 7.

HAWKINS, G. S., and UPTON, E. K. L.

1958. The influx rate of meteors in the earth's

atmosphere. Astrophys. Journ., vol. 128,

pp. 727-735.

KAISER, T. R.

1953. Radio echo studies of meteor ionization.

Adv. Phys., Phil. Mag. Suppl., vol. 2,

pp. 495-544.

1955. The incident flux of meteors and the total

meteoric ionization. In Meteors, ed. by

T. Kaiser, Pergamon Press, New York,

pp. 119-130.
METEOR INCIDENCE ON EARTH FROM RADIO OBSERVATIONS ELFORD 131

KAISER, T. R.—Continued

1960. The determination of the incident flux of

radio-meteors. Monthly Notices Roy.

Astron. Soc, vol. 121, pp. 284-298.

1961a. The determination of the incident flux of

radio-meteore, II: Sporadic meteors.

Monthly Notices Roy. Astron. Soc, vol.

123, pp. 265-271.

1961b. The incidence of interplanetary dust. Ann.

Geophys., vol. 17, pp. 50-59.

1963. Meteors and the abundance of interplanetary matter. Space Sci. Rev., vol. 1,

pp. 554-575.

KEAY, C. S. L.

1963. The distribution of meteors around the

earth's orbit. Monthly Notices Roy.

Autron. Soc, vol. 126, pp. 165-176.

KEAY, C. 8. L., and ELLYKTT, C. I).

1961. The latitude dependence of radar meteor

HIIOWIT observations. Journ. Geophys.

Res., vol. 66, pp. 2337-2343.

KKEHAK, L.

1964. The latitude variation of the meteor shower

influx. Bull. Astron. Inst. Czechoslovakia, vol. 15, no. 2, pp. 53-62.

KHESAKOVA, M., and KKEBAK, L.

1955. On the activity of telescopic meteors and

some related problems. Contr. Astron.

Obe. Skalnat6 Pleso, vol. 1, pp. 40-77.

LEBEDINET8, V. N.

1964. Density of meteoric matter in the vicinity

of the earth's orbit, from radar observations of meteors. Sov. Astron.—AJ,

vol. 7, pp. 549-558.

MCINTOSH, B. A., and MILLMAN, P. M.

1964. Radar meteor counts: Anomalous increase

during 1963. Science, vol. 146, p. 1457.

MCKINLEY, D. W. R.

1961. Meteor Science and Engineering. McGrawHill Book Co., New York, 309 pp.

MILLMAN, P. M., and MCINTOSH, B. A.

1963. A preliminary report on radar meteor

counts. In Proceedings of the Symposium on the Astronomy and Physics of

Meteors. Smithsonian Contr. Astrophys.,

vol. 7, pp. 45-51.

NEALE, M. J.

1958. A low-power continuously-operating meteor

radar. Bull. R. and E. E. Div. Nat.

Res. Counc. Canada, vol. 8, no. 3.

NlLSSON, C. S.

1964. A Southern Hemisphere radio survey of

meteor streams. Australian Journ.

Phys., vol. 17, pp. 205-256.

PEREQUDOV, F. I.

1958. On the effect of meteor velocities on the

hour number in radio-echo detection of

meteors. Sov. Astron.—AJ, vol. 2, pp.

833-838.

SOUTHWORTH, R. B., and HAWKINS, G. S.

1963. Statistics of meteor streams. In Proceedings of the Symposium on the Astronomy

and Physics of Meteors. Smithsonian

Contr. Astrophys., vol. 7, pp. 261-285.

VERNIANI, F., and HAWKINS, G. S.

1964. On the ionizing efficiency of meteors.

Astrophys. Journ., vol. 140, pp. 1590-

1600.

VOOAN, E. L., and CAMPBELL, L. L.

1957. Meteor signal rates observed in forwardscatter. Canadian Journ. Phys., vol.

35, pp. 1176-1189.

WEISS, A. A.

1957a. The incidence of meteor particles upon the

earth. Australian Journ. Phys., vol. 10,

pp. 397-411.

1957b. The distribution of the orbits of sporadic

meteors. Australian Journ. Phys., vol.

10, pp. 77-102.

1961. The distribution of meteor masses for

sporadic meteors and three showers.

Australian Journ. Phys., vol. 14, pp.

102-119.

WEISS, A. A., and SMITH, J. W.

1960. Southern Hemisphere survey of the radiants of sporadic meteors. Monthly

Notices Roy. Astron. Soc, vol. 121, pp.

5-16.

Abstract

Published estimates of the average flux over the earth of meteors with line densities in excess of prescribed limiting values are compared. The results for sporadic meteors are shown to be consistent within a factor of 2 over the

radio magnitude range 0 to +1 0 and within a factor of 4 between radio magnitude +10 and +13.5. The annual

variation in flux is deduced from the precise echo-rate observations made at Ottawa (45° N) and compared with the

annual variation determined from a similar survey at Christchurch (43?5 S). The 40 to 50 percent increase in the

incidence of meteors during the second half of the year is confirmed. The results of a Southern-Hemisphere orbit

survey suggest that this increase is due to a large number of minor showers.

For meteors fainter than + 5 mag the sporadic flux dominates over any of the major showers, a sporadic/shower

ratio of 10:1 being typical for lOth-mag meteors. However, over the range + 6 to +1 2 mag the integrated flux of all

shower meteors- is about 30 percent of the sporadic flux.

The reduction from electron density to mass is still subject to considerable uncertainty. A preliminary study

of 13th-mag meteors suggests that the flux of sporadics with mass greater than 1.3 X 10~« g is 1.0X 10~8 m-*sec~1.

Radar Observations of Meteor Deceleration

J. V. EVANS1

Introduction

In a previous paper (hereafter referred to as

paper 1) Evans (1965) has described observations of sporadic and shower meteors at a radar

wavelength of 68 cm. In these measurements

the meteors were seen when traversing the

antenna beam at right angles. The mean rate

of sporadic meteors observed per hour at night

was 40, and for shower meteors the hourly

rates occasionally rose to well over 100. In

view of these high rates it was considered

possible that, by directing the antenna at the

radiant point of a strong shower, a small

number of meteors might be seen approaching

the radar directly down the beam. This was

successfully accomplished during the 1961

Geminid and Perseid and the 1962 Quadrantid

showers, and very precise determinations of

velocity and deceleration were achieved.

In this paper we review briefly the theory

for the behavior of the velocity of a meteor

when it encounters atmospheric drag. In

subsequent sections the experimental observations are presented and a comparison made

between theory and experiment.

Theory

Contributions to the theory of the deceleration

of a meteor in the earth's atmosphere have been

made by a number of authors over the last

40 years. Contemporary reviews of this work

have been given by Whipple (1943), Hawkins

and South worth (1958), Whipple and Hawkins

(1959), McKinley (1961), and Verniani (1961).

The most useful treatise on the whole subject

is that by Opik (1958). In view of this large

1

 Lincoln Laboratory (operated with support from the U.S. Air Force),

Massachusetts Institute of Technology, Lexington, Mass.

body of literature we will not do more than

outline the development of the basic equations

in this paper.

The physical assumptions employed in the

derivation of an expression for the deceleration

are as follows. It is generally assumed that

the dimensions of the meteoroid are small

compared with the mean free path of the air

molecules. At a height of 100 km the mean

free path X in the air is 16 cm (U.S. Standard

Atmosphere, 1962), and since most meteors

probably have dimensions measured in millimeters, this assumption is almost certainly

valid. At a 80-km height, however, X has

become 0.40 cm and this assumption probably

no longer holds. The air molecules impinging

on the surface of the meteor do so individually,

and if the mean free path is very much larger

than the size of the meteoroid no air cap will

be formed. If the mean free path becomes

comparable with the dimensions of the meteoroid then air molecules that have collided with

the advancing meteor cannot escape freely.

Instead, they suffer a collision with other

air molecules before they have traveled far

from the meteor. Thus, air becomes trapped

in front of the meteoroid and this reduces the

rate of heating of the meteor. It is probable

that cap formation commences in the middle

of the meteor region. This complication is

ignored in many reviews and, of those listed,

only Opik (1958) has treated the problem in

detail.

The next assumption that is widely made

concerns the mechanics of the impact of the air

molecules. It seems probable that most of the

air molecules are occluded onto the surface of

the meteor and liberated a short time later.

133
134

SYMPOSIUM ON METEOR ORBITS AND DUST

Most theories simply assume that the collisions

are largely inelastic and, on the average, the

angle through which the air molecule will be

scattered is that of specular reflection. During

1 sec the meteor will encounter a total air mass

of apv, where a is the physical cross section of

the meteor, p the air density, and v the meteor

velocity. Because it is widely thought that the

collisions are mostly inelastic, an amount of

kinetic energy % optf is given up by the meteor

each second, and some fraction A of this goes

toward heating the meteor. The quantity A is

called the heat-transfer coefficient and is the

net coefficient of transfer, i.e., the difference

between the kinetic transfer and the loss

through radiation and sputtering.

The heat given to the meteoroid is usually

presumed to be distributed initially only over

the surface. Thus the heat is assumed to be

expended in vaporizing the surface layers and

not in heating the meteor as a whole. If I is

the heat of ablation (the heat required to ablate

1 g of the material), then from conservation of

energy it follows that

dm

(1)

where dm/dt is the rate of loss of mass by the

meteor. The velocity v is, of course, not

constant. However, since vac(dm/dt)1/3, v may

be taken as constant until a very large fraction

of the meteor mass has been ablated. Equation (1) is generally known as the mass equation.

A second equation of importance can be obtained by considering conservation of momentum. The momentum given in unit time to the

air molecules in completely inelastic collisions

would be the air mass (apt) times the velocity

(v), i.e., app2. However, the final velocity of

the air molecules may be somewhat less than v,

and hence the meteor momentum destroyed per

unit time can be written as ypav*, where y is a

dimensionless drag coefficient. Hence, we have

dv

(2)

This is the drag equation. The meteor height

will change at a rate dh/dt=v cos % km/sec,

where x is the angle between the meteor path

and the zenith, and h is the height,

that (2) can be written

dv _ vypc sec x

dh~ m

It follows

(3)

The observations of the deceleration of the

meteors presented in later sections give r,

dv/dh, and sec x &s functions of time. Thus,

provided that y can be estimated theoretically,

the variation of ap/m as a function of time ran

be obtained.

By combining the drag and the mass eq nations we obtain

2k V~~m' (4)

where £=yl/A is the effective ablation energy

for unit mass. The observations described

here permit the value of this constant U> be

estimated. By integrating (4) we obtain

= mm exp (5)

where vw and mm are the initial velocity and

mass of the meteor, respectively. This has a

solution

where pn^ is the atmospheric density at the

height of maximum ablation rate. We shall

not continue the development of the various

other possible equations, as these may all be

found in the paper by Verniani (1961). Equations (5) and (6) are only approximately correct.

Verniani (1961) shows that an exact value for

the velocity can be obtained by solving

=HP

•[*(&>

(7)

where 6 is the density of the meteoroid, g is the

acceleration due to gravity, E{x) indicates the

logarithmic integral, and F is a shape factor

employed by Verniani and defined by

v^Fxr1, (8)

where r is the equivalent radius of the meteor.
RADAR OBSERVATIONS OF METEOR DECELERATION—EVANS 135

The difference between the solution of (7) for

a meteor with initial velocity POB = 4O km/sec and

equation (6) is illustrated in figure 1; the difference in the behavior of the equivalent radius

r for the two solutions is illustrated in figure 2.

In equation (3) we developed an expression

containing the meteor mass m and cross section.

The mass m depends upon both the size and the

density of the meteor, whereas the cross section

a depends upon the shape and the size. One of

these variables can be removed if assumptions

are made concerning the shape of the meteor.

Thus, Opik (1958) introduces the equivalent

radius r defined in

4

m = 3

(9)

where 6 is the meteor density. The cross

section may then be expressed as

a=4Jrr3, (10)

where J is a shape factor that would have a

value of 0.25 if the particle were in fact a sphere.

For an average solid meteoroid of not-toounusual shape, Opik adopts a value

J=0.5±0.1. (11)

We also need to know the drag coefficient y

in equation (3). Opik (1958) adopts a value

-

( 0 ) (b)

FIGURE 1.—Theoretical variation of velocity of a meteor with

initial velocity 40 km/sec as a function of atmospheric

density p normalized to density p,,, , at point of maximum

ablation rate: a, the approximate solution of equation (6);

b, the full solution of equation (7), after Verniani (1961).

FIGURE 2.—Theoretical variation of equivalent meteor

radius r as a function of atmospheric density p: a, the

approximate solution given in equation (21); b, the more

rigorous solution (Vernianj, 1961).

of unity for small meteors in which no air cap

is formed. Thus, the product ya becomes

7<r=2*T2=6.28r2. (12)

We have adopted this value in the calculations

that follow. We note, however, that different

assumptions have been made by Hawkins and

Southworth (1958), Whipple and Hawkins

(1959), and McKinley (1961); the last has

followed the formulation of Whipple and

Hawkins. In this treatment the cross section

of a sphere is written as

(13)

thereby removing the equivalent radius r as one

of the parameters. Any object other than a

sphere has a cross section that may be written

a—no 7/1 , K1*)
136

SYMPOSIUM ON METEOR ORBITS AND DUST

where A is a dimensionless shape factor having

a value (9x/16)1/3(=1.2) for a sphere. For a

cube entering the atmosphere face on, A=\.O;

for a cube with one edge leading, A= 1.4. When

a cube moves with one corner leading, A=2.5.

Thus, there is a very approximate relationship

between the shape factor Jused by Opik and A,

namely, J~A/4.

The drag coefficient y will have a value of

1.0 for free molecular flow, but will be reduced

to about 0.4 when an air cap is completely

formed. Whipple and Hawkins (1959), therefore, favor values of A>\ and 7<1 and

consequently adopt for an average value,

7^4=1.0. (Jacchia (1955) employed 1.0 for the

value of the product yAb~2/3.) Thus, from (14),

according to Whipple and Hawkins (1959), we

have

7<r=«-2/3ro2/3. (15)

When expressed in terms of Opik's equivalent

radius r, (15) yields

/4-\8/3

yo=v£)r2=

We see then that Opik's value for ya is ~2.4

times that suggested by Whipple and Hawkins

(1959).

Combining equations (3), (10), and (11) we

obtain (following Opik)

sec

_ A'

dh~2 ~S

in which all the quantities in parentheses are

functions of height. It follows that if dv/dh, p,

sec Xf and v are known, we may obtain r8 as a

function of height. Had we chosen to follow

Whipple and Hawkins (1959), the values of rb

would be uniformly reduced by 2.4.

Observations

The equipment has been described in some

detail in paper 1. During the operations

described here, in which a search was made

for meteors traveling along radial paths toward the radar, the receiver must be detuned

from the transmitter frequency (by as much

as 179 kcps in the case of the Perseids). This

is required in order to bring the center filter

of the receiver filter bank to the expected

doppler-shifted frequency of an approaching

meteor for the particular shower being odserved.

During the course of the 1961 Geminids,

attempts were first made to observe meteors

traveling directly toward the radar by pointing

the antenna beam at the meteor radiant.

These observations were attempted only for

the Quadrantids, Perseids, and Geminids.

With a narrow (2°) beam, directed at an

elevation of only 3°, the amount of sky through

which a shower meteor may pass and give

rise to an echo is reduced in the "radiant"

tracking position by about a factor of 10 from

that in the "right-angle" point position (paper

1). At elevations greater than 3°, the useful

area is still further reduced, and it wax considered worthwhile to direct the antenna at

the radiant only when the radiant elevation

was below about 20° to 30°. An additional

reduction in the rate could be expected to

arise as a result of the reduced crosH section

of the meteors when observed "head on."

(The rates observed for these three major

showers were in fact reduced to the order of 2

shower meteors/hour.) Thus, for successful

observations of meteors traveling toward the

radar, one requires a strong shower having

a radiant whose declination is substantially

different from the latitude of the observer.

The radiant will then rise and set slowly, thus

spending a long period of time at low elevations.

The separation of the meteors traveling

directly down the beam from those that traverse it at an angle proved less difficult than

anticipated. In the first place, the receiver,

which employs a bank of doppler filters, is

sensitive only to meteors having a radial

component of velocity in the range ±9 km/

sec. Thus, with the receiver detuned so that the

center filter of the receiver filter bank corresponds to the frequency of an approaching

shower meteor (with velocity rt), meteors

traveling through the antenna beam can be

detected only if they possess a radial component

of velocity in the range v, ± 9 km/sec. That

is, any meteor with velocity v (measured in

km/sec) traversing the beam at an angle 0 to

the axis will be detected only when the relation

cos"

(18)
RADAR OBSERVATIONS OF METEOR DECELERATION—EVANS 137

is satisfied. From geometrical considerations

alone one would expect to observe more meteors

for which »>P, than for t><c,. Yet, because

the available number of sporadic meteors

decreases as v >40 km/sec (paper 1), the net

effect will be an extremely large reduction in

the rate of sporadic meteors when the receiver

is detuned. Three tests are then applied to

select meteors traveling toward the radar: (1)

the duration should be large—a minimum

value of about 0.5 sec was taken; (2) the

velocity computed on the assumption that the

meteor is traveling directly toward the radar

should be close to the known velocity of the

shower in question; and (3) the mean rate of

change of radial velocity must be small (<2

km/sec *).

In figure 3 the mean radial velocity is plotted

against the mean derivative of the radial

velocity, and there is a distinct group of meteors

with long durations centered on a mean radial

velocity of 35.5 km/sec and a mean deceleration

of 1 km/sec2. The members of this group were

37

36

35

34

33

32

DURATION (sec)

0 1 to 0 2

• 0 2 to 0.5

• >05

2

-2 0 2 4 6 8 10 12 14 16

MEAN APPARENT DECELERATION (km/sec2)

FIGURE 3.—Mean radial velocity of possible Geminid meteors

plotted against mean apparent deceleration. The members

of this group that have long durations are believed to be

Geminids.

240-022 O—87 10

accepted as Geminids and all others rejected,

although in fact some of those shown in figure 3

might also have been Geminids. A similar

selection procedure was employed for the

Quadrantids and Perseids, although here the

problem was made much easier by the higher

value of v, and correspondingly lower number

of sporadic meteors observed.

These selection procedures will not preclude

the acceptance of a meteor traveling at a

small angle (less than, say, 5°) to the axis.

Thus, the angular extent of the radiant will

play some part in limiting the accuracy obtained by this technique. We can, however,

show that meteors traveling at angles larger

than 5° to the axis cannot remain within the

beam long enough to give rise to the observed

durations. For a 5° difference between the

meteor direction and the beam, the radial

velocity observed will be only 99.4 percent of

the true meteor velocity. The finite width of

the beam (2°) precludes the aspect of the meteor

changing by more than 2°. It follows that,

though the meteor velocities may be systematically low (by as much as 0.6 percent), the

amount of this error will not change significantly during the course of the observation.

There was evidence of fragmentation in 40

percent of the sporadic meteors observed traveling through the beam at right angles (paper 1).

Since meteors with durations of more than 0.5

sec have been selected, however, we shall have

largely excluded from this sample cases where

the meteor fragmented. Obviously the exclusion of fragmenting meteors should improve

the likelihood of agreement between theory and

observation.

Results

VELOCITIES.—Tables 1 to 4 summarize the

results of these observations. In the case of

the Perseids (table 2) the durations were mostly

shorter than the Geminids (table 3) and

Quadrantids (table 4). In general, the Perseid

meteors showed little or no evidence of deceleration, but instead seemed to exhibit wider

scatter of values for the radial velocity than

did the Geminids or Quadrantids. An example

of this is presented in figure 4, where the radial

velocity is plotted as a function of time for

Perseid 7. Thus, the extrapolated velocities
138 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 1.—Comparison of initial velocities of shower

meteors

Mean of first six returns

(this paper)

Extrapolated value !•„

(this paper)

t>oo obtained by curve fitting (this paper)

Va> (Whipple and Hawkins,

1959)

Mean value of t>» from

Hawkins and Southworth (1958)

Geminids

(km/

sec)

42. 25

42.42

42.46

42.7

42.6

Quadrantids

(km/

sec)

35. 98

36. 55

36. 73

36.5

36.2

Perseids

(km/

sec)

60. 03

>60. 26

—

60. 4

60. 6

va for these meteors cannot reliably be obtained.

We attribute this behavior to the apparent

ability of the Perseids to fragment readily.

The initial observed velocity has been computed

from the mean of the first six returns, and the

averages for the three showers are listed in

table 1.

For most of the Geminids and Quadrantids,

the radial velocity showed a smooth uniform

decrease with time. Representative examples

are given in figures 5 to 10. Where the

duration exceeded about 0.75 sec, a smooth

curve was fitted to the points and extrapolated

TlMt IHC)

Ku.i »»• 4.— Observation* of radial velocity v» time for

Pcrteid 7 (1961)

backward in time until the gradient of the curve

became zero. The velocity at which this

occurred is given in column 5 of tables 2 to 4

as vm together with an estimate of the accuracy

of this value. Weighted mean values for vm

are given in table 1. The mean velocity given

in column 4 of table 2 has been taken as the

lower limit of v^ for the Perseids. From table

1 it can be seen that these values are in close

agreement with values for vm obtained from

photographic observations by means of the

Super-Schmidt meteor cameras. We are forced

to conclude, therefore, that though the reflecTABLE 2.—Perseids (1961)

Number

1

2

3

4

5

6

7

8

9

10

11

Date

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Aug. 13

Start time

(EST)

1536. 56

1546.27

1607. 28

1620. 56

1733. 51

1835. 52

1841. 25

1844 20

1905. 15

1912. 32

1917. 16

Mean values=

Observed initial

velocity*

60.003

59. 953

60.469

60.089

59. 317

59. 503

60. 534

59. 812

60.693

59.848

60. 134

60.032

Vm

(extrapolated)

60.003

~60. 53

60.26

Duration

(sec)

0. 59

0.30

0.74

0.34

0.24

0.52

1.37

0.32

0. 58

0.28

0. 49

'Mean of first six returns.
RADAB OBSERVATIONS OF METEOR DECELERATION—EVANS

TABLE 3.—Geminids (1961)

139

Number

1

2

3

4

5

6

7,8

9

10

11

12

13

14

15

Date

Dec. 12

Dec. 12

Dec. 12

Dec. 12

Dec. 12

Dec. 12

tDec. 12

Dec. 12

Dec. 13

Dec. 13

Dec. 13

Dec. 13

Dec. 13

Dec. 14

Start time

(EST)

0819. 23

0825. 26

0827. 25

0827. 28

0844. 28

1006.41

1829. 34

1907. 17

0917.31

1801. 47

1833. 40

1904. 48

1927. 16

1941.21

Mean values=

Observed initial

velocity*

35.028

35. 605

34.921

35. 840

35. 723

36. 731

36.209

36. 781

35. 396

36. 475

36.41

36. 936

36.441

35. 217

35. 979

(extrapolated)

35. 70 ±0.05

36.6 ±0.20

36. 72 ±0.05

36. 80 ±0.05

37.2 ±0.20

37.0 ±0.05

35. 80 ±0.20

36.55

Duration

(sec)

0.40

1.08

0.56

0.92

0.55

0.85

1.06

1.39

0.62

1.97

0.53

1.17

0.27

2.78

'Mean of fint six returns.

tTbls meteor appears to have fragmented Into two pieces.

TABLE A.—Quadrantida (196X)

Number

1

2

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Date

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 2

Jan. 3

Jan. 3

Jan. 3

Jan. 3

Jan. 3

Jan. 3

Start time

(EST)

1714. 02

1839.00

2047.54

2145. 46

2151. 10

2159. 10

2254 14

2303.34

2309. 19

2314.05

2337. 19

1735. 17

1745.54

1753.30

2017. 12

2316. 25

2340.08

VIean values=

Observed initial

velocity*

42.357

42.598

43.189

42.407

42.673

42.785

42.121

42.962

41.092

41.766

42 225

41.040

41. 975

41.940

41. 935

42.970

40.755

42. 252

(extrapolated)

42.90±0. 10

42. 64±0. 05

43. 32 ±0.05

42.82±0. 10

42.90±0. 10

42. 44±0. 10

43. 52 ±0. 10

41. 68 ±0.10

41.90±0. 10

42. 24±0. 05

41. 16 ±0.05

42. 20±0. 10

42. 00±0.10

42.416

Duration

(sec)

0.72

0.87

1.08

1.62

1.96

0.50

2.17

1.65

0.67

1.00

0.96

1.25

1.75

1.20

0.31

0.41

0.34

•Mean of first six returns.

tions come from electrons surrounding the

meteoroid, the echoing region has the same

velocity as the meteor itself.

In photographic observations the quantity

measured is the angular distance traveled by

the meteor. The first derivative with respect

to time is, of course, the velocity; the second

derivative is the deceleration. A reduction

procedure required to determine velocity and

deceleration from photographic plates has been
140

SYMPOSIUM ON METEOR ORBITS AND DUST

.5 »<

1. JL02 04 06 OS \

FIGURE 5.—Observations of radial velocity vs time for

Geminid 2 (1961).

04 06 08

TIME (sec)

FIGURE 6.—Observations of radial velocity vs time for

Geminid 9 (1961).

given by Whipple and Jacchia (1957), who

emphasize the care that must be taken in the

process. In these radio measurements the

velocity is measured directly and deceleration

is the first derivative. It seems, therefore,

that the values of deceleration obtainable from

these plots of velocity vs time, e.g., figures 5

to 10, are the best now available.

Unfortunately, even with an accurate plot

of velocity vs time (such as obtained here),

we cannot compute from theory unambiguous

values for the mass of the meteor without

assuming either its radius or its density. The

principal difficulty is simply that there are too

TIME (tec )

FIGURE 7.—Observations of radial velocity vs time for

Geminid II (1961).

< 40 0

10 15

TIME (sec)

FIGURE 8.—Observations of radial velocitv vs time for

Quadrantid 5 (1962).

many unknowns in the equations. It is possible,

however, by comparing these results with

theory, to estimate the effective ablation

energy for unit mass and the product of the
RADAR OBSERVATIONS OF METEOR DECELERATION EVANS 141

410 -

40 0

> 39 0

38 0

: r o

FIGURE 9.—Observations of radial velocity vs time for

Quadrantid 8 (1962).

radius and density for most of the meteors.

These results are presented on pp. 142-146.

AMPLITUDE.—We have enumerated earlier (in

paper 1) the difficulties encountered in measuring echo amplitude. Problems arise because

the basic detection scheme (which employs

the filter bank) provides an output that is not

linearly related to the input. For the observations of meteors traveling radially toward the

radar, echo-power measurements were made

with a separate IF channel having a bandwidth

of 5 kcps. A larger filter would have been

desirable to accommodate the wide range of

doppler shifts encountered. This was not

practical because the signal-to-noise ratio of

most of the returns was very low and a larger

filter would cause all but a few returns to be

undetectable. The output from a 5-kcpswide IF channel was connected to a detector

having a logarithmic law, which gave as its

output a voltage proportional to the received

„ 42.0 -

10 I 5

TIME (sec)

FIGURE 10.—Observations of radial velocity vs time for

Quadrantid 9 (1962).

power expressed in db. This voltage was

sampled by an analog-to-digital converter

on command. The command to "sample"

was derived from the trigger pulse generated

at the output of the filter bank on receipt of

an echo. The digital word representing the

echo power, together with the other information pertinent to each echo (time, range,

doppler, etc.) was stored in the CG24 computer,

which is an integral part of the radar system

(paper 1). This recording system provided

a large dynamic range (better than 30 db),

but unfortunately this precaution proved unnecessary as most of the returns were near

the lower limit of detectability. The undesirable consequence of using the narrow (5

kcps) filter is that only a fraction of the amplitude data (lying within ±2 kcps of the

center frequency) can be regarded as valid.

The logarithm of the power of these returns

is plotted on an arbitrary scale (labeled amplitude) in figures 5 to 10. The system was

calibrated by means of a pulsed signal generator

connected to the receiver via a directional

coupler. The conversion of these values of

signal power is shown in table 5. The majority

of the returns lie between 5 and 10 on the
142 SYMPOSIUM ON M1CTEOR ORBITS AND DUST

TABLE 5.—Conversion table

Amplitude value

1

10

100

Signal power (dbm)

Geminids

-12 9

-11 5

- 9 8

Quandrantids

-12 7

-11 3

- 9 6

amplitude scale, i.e., roughly equivalent to

echo powers of between —118 and —114 dbm.

If the mean range is taken to be 300 km, the

corresponding target cross sections lie between

10 and 25 cm3. These cross sections are substantially lower than the average cross sections

of the meteors viewed from the side, which

are of the order of 1 to 2 m* for the sporadics,

and larger for the Quadrantids or Geminids

(paper 1). Since the same meteor is not

observed both from the side and approaching

the radar, it seems a doubtful procedure to

compare the cross sections observed in the

two cases with calculations based upon models

for the electron distribution such as a truncated

cone. There is no method by which we can

reliably establish the visual magnitude of

individual meteors in either case.

Comparison with theory

VELOCITY.—The results for the velocity of

the approaching meteors (figs. 5 to 10) provide

velocity as a function of time with respect

to the commencement of the event. Curves

were plotted for all the meteors with durations

greater than about 0.75 sec. Values for the

initial velocity va were estimated from these

curves and are presented in table 1.

Tables of values of the velocity as a function

of height were next computed in the following

manner. The smooth curves for velocity vs

time were read off at 0.05-sec intervals to

provide tables of velocity vs time. The height

of the first point in this table was computed

from the mean of all the values for the range

in the 0.1-sec interval centered on this time,

with the assumption that the meteor lies on

the axis of the beam. Because of the finite

width of the beam this assumption probably

introduces an error of no more than ±2 percent of the range. The range values lie between

about 200 and 400 km, and hence there Is

an uncertainty in the absolute height of as

much as ±1 scale height (7 km). This is

unfortunate and in principle could have been

overcome by the use of a split-beam technique.

It was not practicable to employ such a

procedure at the time.

The values for the height at subsequent

times were computed with the assumption

that the meteor continues to travel toward

the radar along the axis of the beam, and that

it travels a linear distance of 0.05P km in each

0.05-sec interval (where v is the mean of the

velocities at the beginning and the end of this

interval). The tables of velocity v« height

constructed in this manner have been published

(Evans and Brockelman, 1964).

The aforementioned tables provide a smooth

variation of velocity vs height and do not

reflect the large errors in the individual range

measurements. The absolute height of the

whole meteor is, however, uncertain by as

much as 1 scale height. Errors in the velocity

curve due to the meteor intersecting the antenna

beam at a small angle cannot, of course, be

corrected. As we have seen, the effect of

assuming that the meteor is traveling radially

toward the radar will tend to cause a small

but systematic underestimate in the absolute

meteor velocity. Unfortunately, it can introduce a far larger error in the computed height.

Because the meteors are all observed at large

zenith angles (x>70°), a small error in the

assumed value of x can cause the height scale

to be considerably altered. For example, in the

worst case when the meteor is descending either

more or less steeply than assumed by the maximum allowable amount (~5°), the computed

height scale may be as much as 40 percent

in error. Thus, it is possible for the beginning

height of the meteor to be ~ 1 scale height

in error, and in the worst possible case the

difference between the beginning and the end

heights may be in error by as much as a scale

height also. These errors could in principle

be reduced if an even narrower pencil beam

were used, but unfortunately the meteor rate

could be expected to vary as the square of

the beam diameter, and might, therefore,

become exceedingly low.
RADAR OBSERVATIONS OF METEOR DECELERATION—EVANS 143

Attempts have been made to compare the

observed deceleration with that predicted

theoretically, with the assumption of free

molecular flow (i.e., no air cap). Curves of

v/vm were prepared for different values of the

effective ablation energy ( (=6, 10, 14, 18, and

22 km'/sec1) for both the Geminids and Quadran tids (with p.=36.0 and 42.5 km/sec,

respectively) from the approximate expression

given in equation (6). These curves were

plotted on a height scale marked off in kilometers, with respect to the height AMI

 at

which the maximum rate of ablation occurs.

To do this it was necessary to assume that the

scale height // is independent of altitude, and

a value ff=6.5 km was employed. Because

we have no way of determining A*** from our

observations, the observed velocity ratios v/vm

were plotted against an arbitrary height scale

and the two graphs were then adjusted for best

alignment between the observed and any one of

the theoretical curves. In practice, it was

also necessary to adjust the graphs vertically

to correct for errors in the estimated value of

vm. It is easy to show that the first-order

effect of a small error Av in estimating the true

value of vm alters all the values of vjvw by the

same amount (Av(vm). Hence, the true value

of vm together with ( and Ann, can be obtained

by this fitting procedure. The results of this

work are summarized in table 6.

In some cases the duration of the meteor

was insufficient to distinguish between different

theoretical curves. An example of this is

provided in figure 11, where Quadrantid 13

can be seen to fit the curves for (=14 km*/sec*

and (=18 tan'/sec*. In these cases both

solutions are given in table 6. In a small

number of cases only one solution seemed

possible—Geminid 9, for example (fig. 12).

In six cases no proper fit could be obtained

to any of the curves because the deceleration

was not sufficiently rapid toward the end of the

event. Examples of this behavior are shown in

figures 12 and 13 by Geminid 11 and Quadrantids 5 and 8. Two of these cases might be

attributed to the use of the approximate solution for the velocity (eq. (6)) in place of the

more rigorous one (eq. (7)). The difference in

predicted behavior for these two solutions is

TABLE 6.—Doum-the-beam meteors

Estimated t .

Qeminid- 2

4

0

9

11

IS

Mean value

Quadrantid 1

2

4

5

8

8

9

10

11

12

13

14

Mean value

S5.7±0.06

86.8 ±0.2

36.72*0.06

a6.8te0.06

37.2 ±0.2

37.0 ±0.06

1*8.66

42.9 ±0.2

42.84^0.06

43.32±0.1

42.82dba\

42.9 ±0.1

4X44±0-l

43.82±ai

41.88±0.1

41.90±0.1

42.24±aO6

41.18±a06

4X20±ai

t42.42

]

f

14

18

8

18

18

First solution

• m

16.89

Mi 43

94.8

91.6

Second solution

I

18

22

36.92

38.47

(appears to have fragmented)

36.92

37.20

37.18

101.0

96.4

96.96 14 37.16

Mean o( all solutions f,,,-36.73

10

6

6

10

18

22

22

18

18

14

14

18

42.80

42.79

43.47

42.83

43.00

42.44

43.41

42.03

42.21

42.45

41.34

42.12

10L65

106.3

86.75

99.0

101.6

98.8

93.76

94.8

101.9

106.0

103.25

109.85

10

10

14

18

14

18

18

22

4X79

43.47

4X89

43.41

48.14

42.65

41.38

42.16

Mean of all solutions t .-42.46

u

93.2

9a 75

98.0

103.8

83.2

97.86

94.75

102.8

1012

102.1

109.2

Comments

Fits both solutions equally

Fits both solutions equally

Fits no solution

Fits this value only*

Poor fit below 96 km

Fits both solutions equally

Fits this value only

Fits these and other solutions

Fits these and other solutions

Poor fit below 99 km*

Poor fit below 78 km*

Poor fit below 106 km*

Poor fit below 96 km

Fits this value only

Fits both solutions equally

Lies between these values

Fits f-18 better*

Poor fit below 112 km

Assumed

34,76

34.98

36.38

36.86

35.98

35.58

42.00

4X31

4X97

41.93

41.90

41.11

4X17

4a 96

4X21

41.53

40.41

40.94

41.62

Mean

H

a 088

0.123

a 784

a 064

a 127

a 054

0.207

a 056

a 069

3.836

a 138

0.055

a 078

a 172

a 120

0.035

0.027

0.039

a oil

a 386

Mean

height

96.48

9X66

89,10

101.35

93.65

101.03

96.7

10X13

106.33

86.00

96.48

10X27

99.25

94.40

9X78

10X86

106.78

104.83

111.88

100.4

Mean

oo»x

a 3368

a 3353

a 1683

0.2876

0.1969

a 2974

a 2687

0.2015

a 1723

0.1882

a 1942

a 2266

0.2324

a 2366

0.2468

0.2409

0.2311

0.2279

•Values plotted (ftp. 14 to 16).

tValues obtained from tables 3 and 4.
144 SYMPOSIUM ON METEOR ORBITS AND DUST

100

O M

O M

O M

O M

0 * 0

O M

O M

KCf UMttON CUMVCC 'OR

OUMMUNTIO MCTCOftf

OUMXUNTO NO 5

•—-y'

AW1VI

^::

FIGURE 11.—Variation of velocity observed for Quadra mid 13

superimposed on theoretical curves for different values

of ablation energy {. It can be seen that this event was of

insufficient duration to define | precisely.

100

OM

o.tt

O M

O H

o.to

O M

O H

8EMMI0 NO II

DECELERATION CURVES FOR OEMWM) METEORS

*^-

~^

t

(

(

(

(

oimwo no »

CssX

^ \

\V\\\\

• ^^oPr v \ VL

• »<XA\ \ \ I

• %^ \ \ \ \ 1

\

FIGURE 12.—Variation of velocity for Geminids 9 and 11.

In the case of 9 it is believed that {= 8 represents the only

likely solution. Geminid 11 departs by an amount too

large to be attributed to the use of the approximate solution

for the velocity.

illustrated in figure 11 for {=10, and seems

sufficient to explain why Quadrantids 6 (fig. 13)

and 14 do not fit the theoretical curve. However,

in the other four cases (Geminid 11, Quadrantids

5, 8, and 9), the departure of theory from experiment is too marked to be explained by the

use of the approximate theory, and one is

tempted to conclude that an air cap had formed

around the meteor. When this happens, the

drag coefficient is decreased and consequently

£ (equal to 71/A) is also reduced. Thus, a

meteor that begins by following a particular

curve for £ (e.g., Geminid 11 follows £= 18) will

FIGURE 13.—Variation of velocity for Quadrantids 5, 6, and 8.

F.vent 6 depart* from the theoretical curve by an amount

that can be attributed to the fact that approximate solutions

(see fig. 11) were used. Both events 5 and 8 depart from

theoretical curves in a manner too large to be attributed

to this cause.

gradually depart from this line toward curves of

lower values of £. We note from table 6 at

what height cap formation seems to begin from

the height at which agreement between theory

and observation becomes poor. In one case

(Quadrantid 6) this is 78 km, but in the remaining cases it is 96 km or higher and throws

some doubt on an explanation in terms of cap

formation.

Ameanfor all the values of £ listed in table 6 is

15.4 km'/sec', which is in remarkable agreement

with the value employed by Verniani (1962)

(16 km'/sec*) in his reduction of photographic

data published by Whipple (1954). The spread

of values is large and suggests that individual

meteors may have values widely different from

this average value. There is no clear-cut

difference between the Geminids and Quadrantids in table 6, and we cannot comment on

the conclusion reached by Jacchia (1958) that

£ increases with velocity.

RADIUS.—A more sensitive test of whether the

meteor is behaving according to the theory for

a single particle with free molecular flow is

achieved by computing the equivalent radius

and comparing its behavior with that expected.

From equation (17) we have

(19)
RADAR OBSERVATIONS OF METEOR DECELERATION EVANS 145

in which v, p, sec x, and dv/dh are known functions of height for each meteor. It follows that

rb may be computed as a function of height,

and if the assumption is made that the meteor

density 6 does not change with height, the

behavior of r with height is obtained.

We obtained values of rS for each of the

velocity values (at 0.05-sec intervals) listed in

the tables (Evans and Brockelman, 1964).

First, the values of dv/dh required in equation

(19) were obtained from the difference between

adjacent values of velocity and height in the

tables. A better approach might have been to

perform a least-mean-squares fit, but our

method gave values sufficiently accurate for the

present purpose. Next, we found the atmospheric density p (from the U.S. Standard

Atmosphere, 1962) by making a table of density

and scale height at 2-km intervals above 70

km. By interpolation using the appropriate

scale height, we obtained the density at any

given height. The remaining term (sec x)

 was

obtained from the range R (computed at the

time the height h was computed), together

with the value of the antenna elevation angle

a from

tions are given in figure 14a-h for some of the

meteors; the approximate theoretical variation

cos x =

R-\-Rg sin a

(RZ+R2+2RRB sin a)1

(20)

in which RK is the radius of the earth.

We now form a table in which the corresponding values of c, dv/dh, h, sec x, and p are

known. Hence, r& can be computed from

equation (19). These values are tabulated in

the published tables (Evans and Brockelman,

1964).

It is to be expected that if the meteor atoms

are ablated singly the density 5 would remain

constant. The variation of rh with density

should then follow the curve given in figure 2.

A check has been made to see whether this is

so. By taking the value of h^x given in table

6 for each point in the tables, we computed the

ratio p/pmix. The corresponding values of

r/rm were plotted against these values of p/pmKXThe initial radius of the meteor r» is not

known. Hence, use was made of the fact that

rm»x=2r«,/3, and the values of r/r<» were simply

forced to pass through the value 2/3 at the

point p/pmM = l. The results of these opera-

°° \ (21)

is also shown.

Upon inspecting these results we find that in

some cases (Quadrantids 10, 11, 12, and 13)

(fig. 14e-h) there is fair agreement between

theory and experiment. However, in many

cases (Geminids 2, 4, and 11, and Quadrantids

1, 5, 8, and 9) there is violent disagreement.

Three of these meteors (Quadrantids 5, 8, and 9)

are illustrated in figure 14a, c, d. These cases

were recognized in the previous section as being

events in which the velocity behavior was

anomalous; however, the plots of r/rm provide

a more sensitive, test of anomalous behavior.

We note that in six cases (Geminids 4 and 13,

and Quadrantids 1, 5, 8, and 9), where the

departure of theory from observations seems to

exist from the very commencement of the event,

the mean height at which these events were first

observed is 104 km. It seems impossible to

attribute these discrepancies to cap formation

since this could hardly occur at such a great

height. We note that the anomalous cases are

all those in which the duration was large ( ~ 2

sec), and hence they are also the cases where

an error in the assumed zenith angle will introduce the largest error in the difference between

the beginning and the end heights. This could,

in the worst case, be ~6 km, which would be

sufficient to account for the difference between

theory and experiment. Those meteors for

which the zenith angle is larger than assumed

will descend less rapidly than expected and will

appear to have decelerated less than they

should. On the other hand, those meteors

descending more rapidly than assumed may

simply be found to match a theoretical curve

for a value of $ lower than the true value.

One meteor (Geminid 6) suffered a very rapid

deceleration, which can only be attributed to

fragmentation. In effect, the cross section a

increased as the meteor descended. Most other

cases exhibited a decrease of r with increasing

atmospheric density p, which is less than that

predicted by theory, but this is probably due

to errors in the height scale. Only in one case

(Quadrantid 6) does it seem reasonable to
146

SYMPOSIUM ON METEOR ORBITS AND DUST

CO 2. 0

<

a

UJ

N

1.5

1.0

Z

o

Z 0.5

a) QUADRANTID NO 5 20

1.5

a

0?

Q

Ul

M

3 1.0

* — •••••* • • • t

J 'j* 1 L

0.5

b) QUADRANTID NO 6

1L

1.0 2.0 3.0 4.0 5.0

NORMALIZED PRESSURE

1.0 2.0 30 4.0 5.0

NORMALIZED PRESSURE

2 0

1.5

10

2

DC

i 0.5

c) QUADRANTID N0.8

Q

a:

Q

UJ

N

_)

<

2

or

O

1.5

1.0

0.5

d) OUADRANTID NO 9

•/'X -

1.0 2.0 3.0 40 5.0

NORMALIZED PRESSURE

1.0 2.0 3.0 4.0 5.0

NORMALIZED PRESSURE

FIGURE \4a-d.—Observed and predicted variation of meteor radius plotted as a function of atmospheric pressure: a,

Quadrantid 5; b, Quadrantid 6; c, Quadrantid 8; and d. Quadrantid 9.

attribute the anomalous behavior to the gradual

formation of an air cap as the meteor descended.

Meteor masses

Despite the differences between theory and

experiment, the mean values of rS do have some

significance. They are plotted as a function of

height in figure 15 and are listed for each meteor

in table 6. It can be seen (fig. 15) that the

values are spread in height approximately along

the curve representing the variation of the air

density. This is an effect that can in part be

explained by the large uncertainty in the true

height of the meteor (±7 km). This alone

would distribute the values of rS over one order

of magnitude. We can arrive at crude estimates of the average mass and radius by assuming a value 6 for the density. The mean values

of rS (table 6) are biased by two very large

values (Geminid 6, which appears to have

fragmented and been given an erroneous value,

and Quadrantid 4, which is so large that it is not

included in fig. 15). If we eliminate these and

Quadrantid 14, which is particularly low, the

mean value of rh is ~0.08 g/cm2. There seems

to be no pronounced difference between the

values for the Geminids and the Quadrantids,

although such a difference has been found by

Verniani (1964). If we assume &~\ g/cm8,

in agreement with the density deduced by

Verniani (1964) for photographic Geminid

meteors, then the average radius is ^0.08 cm,
RADAR OBSERVATIONS OF METEOR DECELERATION—EVANS 147

zo

1.5

1.0

0.5

e) QUADRANTID NO. 10

1.0 2.0 3.0 4.0 5.0

NORMALIZED PRESSURE

w 2.0

Q

*l. 5

Q

I d

N

-• 1.0 ORM

A

z 0.5

_

_

f) QUADRANTID NO. II

1 " M 1 1

1.0 2.0 3.0

NORMALIZED

4.0 5.0

PRESSURE

2 0

1.5

1.0

0.5

-

-

- t*

X, -

1

t

1

1

QUADRANTID NC

J I 1

1.0 2.0 3.0 4.0 5.0

NORMALIZED PRESSURE

co2.0

z>

a

*l. 5

o

Ul

N

3 1.0

<

tr

10.5

h) QUADRANTID N(

-

-

1 I •• J I 1

1.0 2.0 3.0 4.0 5.0

NORMALIZED PRESSURE

FIGURE I4e-k.—Observed and predicted variation of meteor radius plotted as a function of atmospheric pressure: e,

Quadrantid 10; /, Quadrantid 11; g, Quadrantid 12; and A, Quadrantid 13.

and with considerably more uncertainty the

average mass is ~10~2 to 10~3 g.

Most estimates of the mass of zero visual

magnitude meteors lie between 1 and 10"1 g

(McKinley, 1961). The observed value for

the mean mass of the meteors observed in this

work (10~2 and 10~3 g) therefore implies that

the meteors are approximately of + 5 visual

magnitude. This estimate seems reasonable in

view of the fact that the limiting magnitude of

sporadic meteors seen traversing the beam at

right angles was estimated to be -f 8 (paper 1).

We should expect the shower meteors observed

here to be brighter because the trail cross section must be reduced when viewed from the end;

in any event, the showers contain many more

bright members than does the sporadic background (paper 1).

Conclusions

No previous reports of meteors observed

traveling directly toward the radar have been

published. It is most unfortunate that the

observations of meteor deceleration reported

here could not be used to yield accurate mass

values. The principal requirement for detecting

meteors approaching directly toward the radar

is that the elevation of the radiant be low.

Evidently, simultaneous photographic observations would require a number of wide-angle

cameras at considerable distances from the

radar in an area beneath the intersection of the
148 SYMPOSIUM ON METBOR ORBITB AND DUST

FIGURE 15.—Mean value* of the product of radius and density

of the meteors plotted as a function of the mean height of

each event. The value* show a range of two orders of magnitude; some of this spread must be attributed to errors in

the determination of height.

beam with the meteor region. Such combined

observations could yield accurate values of

mass; thence the density and radius would also

be known. Since the velocity would be determined by the radar, the cameras need not have

rotating shutters and could be relatively simple.

Such a program requires a much larger staff

than was involved in running the radar equipment and hence could not be considered.

Acknowledgments

I would like to express my thanks to Mr. R. A.

Brockelman, who wrote the computer programs required during the data-gathering operations and subsequently performed the reduction

of these data; to Dr. G. H. Pettengill and Mr.

V. C. Pineo for stimulating our interest in this

work; to other members of the staff of Millstone

Radar Observatory who assisted in the setting

up of the equipment for these observations;

and to Drs. G. S. Hawkins and T. Hagfors for

helpful discussions.

References

EVANS, J. V.

1965. Radio-echo studies of meteors at 68-eentimeter wavelength. Journ. Geophys. Res.,

vol. 70, pp. 5395-5416.

EVANS, J. V., and BROCHLMAN, H. A.

1964. Radio echo studies of meteors at 68 cm

wavelength, Part II: Shower meteors.

Tech. Rep. 341, Lincoln Lab., Lexington,

Mass.

HAWKINS, G. 8., and SOCTHWORTB, H. B.

1958. The statistics of meteors in the earth's

atmosphere. Smithsonian Contr. Aatrophy«., vol. 2, no. 11, pp. 349-364.

JACCHIA, L. O.

1955. The physical theory of meteor*. VIII:

Fragmentation as a oauae of the faintmeteor anomaly. Astrophys. Journ., vol.

121, pp. 621-527.

1958. On two parametera used in the physical

theory of meteor*. Smithsonian Contr.

Astrophys., vol. 2, no. 9, pp. 181-187.

MCKINLCT, D. W. II.

1961. Meteor Science and Engineering. McGrawHill Book Co., New York, 309 pp.

OPIK, E. J.

1958. Physics of Meteor Flight in the Atmosphere. Interacienoe PubL, New York.

174 pp.

U.8. STANDARD ATMOSPHERE

1962. U.8. Standard Atmosphere 1962. Prepared under NASA, USAF, and USWB,

Washington, D.C., 278 pp.

VEKNIANI, F.

1961. On meteor ablation in the atmosphere

Nuovo Cimento, vol. 19, pp. 415-442.

1962. On the density of meteoroids, I: The density

of bright photographic meteors. Nuovo

Cimento, vol. 26, pp. 209-230.

1964. On the density of meteoroids, II: The

density of faint photographic meteors.

Nuovo Cimento, vol. 33, pp. 1173-1184.

WHIFFLE, F. L.

1943. Meteors and the earth's upper atmosphere.

Rev. Mod. Phys., vol. 15, pp. 246-264.

1954. Photographic meteor orbits and their distribution in space. Astron. Journ., vol.

59, pp. 201-217.

WHIPPLE, F. L., and HAWKINS, G. S.

1959. Meteors. In Handbuch der Physik, vol.

52, ed. by S. Flugge, Springer-Verlag,

Berlin, pp. 519-564.

WHIFFLE, F. L., and JACCHIA, L. G.

1957. Reduction methods for photographic meteor trails. Smithsonian Contr. Astrophys., vol. 1, no. 2, pp. 183-206.
RADAR OBSERVATIONS OF METEOR DECELERATION—EVANS 149

Abstract

By means of a narrow-beam high-power radar operating at 68 cm it has been possible to detect meteors traveling

radially toward the radar. In these observations the antenna is directed at the radiant point of an intense meteor

shower and the receiver tuned to the expected doppler-shifted signal. Because the actual doppler shift can be measured with precision, both the velocity and deceleration of the approaching meteor can be determined. The behavior

of the velocity is compared with the theory for a solid particle entering the earth's atmosphere at heights where no

air cap is formed. Anomalous behavior was observed in several cases, but the height at which this appears to begin

is too great to be accounted for by cap formation. We conclude that errors in the computed height of the meteor

may be responsible for the anomalous cases. A mean value for the effective ablation energy of 15.4 km'/sec* was

obtained, but individual meteors showed wide departures from this value. The mean mass of the meteors is estimated to be in the range 10~» to 10

 Jg, corresponding to a visual magnitude of +5 .

Radar Meteor Echoes

P. M. MlLLMAN

 l

Since 1047 radio observations of meteors,

accompanied by group visual observations, have

been carried out near Ottawa, Ontario, Canada.

In particular, since October 1957, a patrol

meteor radar has been operated continuously

at the Springhill Meteor Observatory (45?2 N,

75?5 W), while visual observations have been

conducted sporadically at Springhill and have

been collected from numerous outside observing

groups in various parts of the USA and Canada.

The data collected since 1957 now consist of

visual observations of some 150,000 meteors

and over 10,000,000 tabulated meteor echoes.

The statistical reduction of this material is

progressing steadily, and detailed results are

appearing in a series of papers (MiUman and

Mclntosh, 1966). I wish here to deal briefly

with certain aspects of the analysis of meteor

rates and the problems of the comparison

between radar rates and visual rates. The

discussion is more in the nature of a current

progress report rather than a statement of

final results and conclusions, and I will welcome helpful comments on the points raised.

It is my feeling that often a series of observational data are accepted without sufficient

attention being paid to the significance of the

figures involved and the possible errors that

may lie hidden in the statistics.

To keep the subject in the observational

field rather than in the theoretical, the standard

reference frame will be taken as the visual

absolute meteor magnitude M, i.e., the visual

magnitude of a meteor at 100-km height in

the zenith. It will be convenient first to

consider what is involved in deriving a visual

hourly rate.

1

 National Research Council, Ottawa, Canada.

Visual meteor rates

In Canada we have always stressed the visual

group count as approaching closer to the complete picture of what is seen from one station.

Counts are normally reduced to a standard

team of six observers, although the actual

observations at Springhill generally involve a

team of eight observers and one recorder.

Factors that can seriously affect the counts are

clouds, haze, moon, aurora, and artificial illumination. Most analyses are carried out only

with Weather I observations, defined as those

made when all the above disturbing factors

are virtually absent.

The ratio of the numbers of meteors seen,

counted down to two successive magnitude

limits, is defined as r. This ratio generally can

be assumed roughly constant over a short

magnitude range, but caution must be used in

extending this assumption to a long range of

magnitude. From a study of the Ottawa visual

records, and assuming that r exhibits no sudden

discontinuities, MiUman and Burland (MiUman,

1957) concluded that a team of six visual observers recorded the foUowing percentages of

the meteors actuaUy visible.

apparent magni- 0 1 2 3 4 5

tude

percentage 100 60 30 10 2 H

recorded

Group visual programs carried out in

Weather I conditions result in a mean visual

apparent magnitude in the range between two

and three. Hence, much the greater portion

of the meteors contributing to the visual hourly

rates are from magnitude classes where 70 to

90 percent are never recorded. The situation

151
152

SYMPOSIUM ON METEOR ORBITS AND DUST

is probably even worse for most single-observer

data. When one adds the problems of subjective variations in magnitude scale, and unknown personal equation factors, it is not

surprising that visual hourly rate data can be

misleading if not reduced carefully.

It is of interest to note the elevation distribution of the meteors recorded by group counts.

For the Ottawa team, where all eight observers

are in standard observing positions, this distribution is surprisingly constant for any given

set of weather conditions. Three examples of

the percentages of meteors observed at Springhill in various elevation ranges are given in table

1. The observations made on December 13/14,

1958, are representative of exceptional transparency and maximum darkness of the sky

background. These conditions resulted in over

1000 meteors being recorded in a watch of just

over 8 hours. It is evident that the better the

weather, the greater the percentage of meteors

recorded at low elevations.

If we take into account the area of the sky

contained in each elevation range of table 1,

we can find the relative density of meteors per

unit sky area. These values are listed in table

2, where the relative densities are found by

dividing the figures of table 1 by the percentage

of sky area in each elevation zone.

The determination of r from visual records

is discouraging. At the bright end of the scale

one is hampered by inhomogeneity and the

small numbers of observations available; at

the faint end one is faced with the problem of

deciding how to allow for the large percentage

of meteors not observed. In addition to these

problems, the effective magnitude scale adopted

by the visual observers may vary considerably

from one observing group to the next and

between the bright and the faint magnitude

ranges. Figure 1 is reproduced from a paper

presented by Millman and Burland (1956) at

the New York Meeting of the American Astronomical Society in 1956. Here, an attempt

was made to bring together the evidence from

several independent methods of estimating r.

Later, these authors published additional material from the Ottawa program (Millman and

Burland, 1961). In spite of the collection of

a large amount of new data during the IOY,

little improvement has yet been made in the

consistency of the results.

We can summarize the situation by saying

that visual programs generally give r in the

range 2.5 to 3.5, and that the adoption of

r=3.0 for an overall average is probably as

good a guess as any. This corresponds fairly

well with Opik's results from the Arizona

Expedition (Opik, 1958). There is no doubt

that the determination of r from any given

set of observations is quite sensitive to a

number of conditions. For example, some of

the best visual observations from Springhill

were analyzed by determining r from meteors

observed at various elevation ranges. It was

found that r varied from roughly 3.5 for meteors

seen near the zenith to as low as 2.3 for meteors

around 20° above the horizon. It can be

TABLE

Elevation (degrees)

December 13/14, 1958

1957-196l(^ea*JerJT

I Weather II

1.—Percentages of meteors recorded in various elevation ranges

0

1

1

1

10

8

7

4

20

21

16

12

30

24

21

19

40

21

21

21

50

13

17

20

60

7

11

15

70

4

5

7

80 90

1

1

1

TABLE 2.—Relative sky density of meteors recorded in various elevation ranges

Elevation (degrees)

December 13/14, 1958

1QV7 i Qfii /Weather I

1 Weather II

0

0.

0.

0.

10 20 30

1

1

1

0.5

0.4

0.2

1.3

1.0

0.8

1.

1.

1.

40

7

5

3

1.7

1.7

1.7

50 60 70

1.3

1.7

2.0

1.0

1.5

2.0

0.9

1. 1

1.6

80

0.

0.

a

90

7

7

7
RADAR METEOR ECHOES MILLMAN 153

1

O

*

•

I

ft

UAC COjNI

MAC COUXTS -

ntvATicm

1

OUT

i

1

--. :--0 -

VISUAL

^OTOO.A -

tlBUTIOM -

i

1 1 1

v.^i:.:.

*

VISUAL

1 1 J 1

FIGURE 1.—Representative value* of r, the ratio in numbers

of meteor* counted down to successive whole magnitude

limits, plotted against the corresponding absolute visual

magnitude range for the data used in each case. Taken from

an unpublished paper presented by Millman and Burland

(1956) at a meeting of the American Atsronomical Society,

December 1956.

shown that, on the basis of normal meteor

heights and atmospheric extinction factors, there

should be no great variation in the r for apparent

magnitudes at different elevation ranges, provided the r for absolute magnitudes is reasonably constant. The above observational result

emphasizes once again the difficulty of deriving

good r values from visual programs.

Radar meteor rates

The Springhill patrol radar (33 Mc/sec, 20 kw

peak power) records meteor echoes on 35-mm

film with a continuous range-time presentation.

Film readers then transfer these echo data

manually to IBM cards (Millman and

Mclntosh, 1963). The antenna system is

omnidirectional, recording fairly uniformly

down to 15° to 20° above the horizon. Reduction factors have been developed to allow for

the subjective errors of the film readers and for

the effects of interference, particularly serious

in 1957-1958. The smallest echoes recorded

correspond to underdense trails and are aspect

sensitive. This will cause uncertainty in the

cutoff at the lower limit and will vary with the

integrated pattern of the meteor paths in the

atmosphere. Echoes with appreciable duration

correspond to overdense trails and will be little

subject to aspect sensitivity, as was early shown

by McKinley and Millman (1949) and further

confirmed in more recent data (Millman, 1962).

The Springhill data are read in five duration

240-022 O—67 11

classes: all echoes, duration > 1 sec, duration

> 2 sec, duration >4 sec, and duration > 8 sec.

Mean hourly rates for each day of the year

have been determined for each of these five

classes for the 5-year period 1958-1962. Tables

for all echoes and for > 8-sec echoes were published by Millman and Mclntosh (1964), and

data for the other classes appear in a paper by

Millman and Mclntosh (1966).

If we concentrate on the echoes > 1 sec

in duration, we are dealing in the main with

overdense trails. Here the standard equation

for echo duration T is

where X is the wavelength, D is the upper-air

diffusion coefficient, and q is the number of

electrons per meter of path length. If we

assume X and D constant for the patrol program,

we have T=Kiq, where Kt is a constant. If

the visual magnitude is related to q by an

expression of the form M=A+B log q, and if

N is the number of echoes with duration > T,

it can be shown that

log N=K2-K3 log r log T,

where K3 log r is the slope between log N

and log T, designated by S. If q is proportional

to the intensity /, K3 will be 2.5. It is convenient to write S=Y(2.5 log r). Where the

parameter Y will indicate the nature of the

relation between q and /, if F=l, then qccl.

The slope S for seventy-three 5-day periods

during the year is plotted in figure 2, taken

from Millman and Mclntosh (1966). It will

be noted that <S varies considerably throughout

the year, reaching minima at the time of the

major annual meteor showers. One of the

unexpected features of this plot is a fairly

regular variation of S between the shower

periods. This is particularly marked during

the first quarter of the year. The nonshower

meteors also exhibit a difference in S between

the first part of the year and the last 6 or 7

months of the year.

The values of S range from 1.1 down to an

extreme low of 0.2 for the Perseid meteors on

the date of the maximum of this shower. If
154 SYMPOSIUM OK METEOR ORBITS AND DUST

I m I iw I M I an I M I NL I I OCT I aov I

FIGURE 2.—The annual variation of the slope S of log N vt

log T, plotted in black dot* for seventy-three 5-day interval* from the records of the Ottawa meteor patrol radar.

The open circles refer to single-day values for all meteors,

and the crosses to shower meteors only for the day of

shower maximum. [Taken from Millman and Mclntosh

(I960]

Y—l, the range of S means a range of r from

2.7 to 1.2. This is an impossibly low range,

particularly for the lower values, which correspond to most of the shower meteors. It is

obvious that Y must be considerably less than

1 in many cases, perhaps as low as 0.3 or 0.2.

We are in the process of comparing the visual

rates from the IGT period with the radar rates,

using the diurnal variation of the radar rates so

that the comparison is made for the same hours

of local mean time. Only the top category of

visual records has been reduced so far. The

radar rates for > 1-sec echoes average 85 percent of the visual rates for six observers. This

would indicate that the radar rates for > 1-sec

echoes correspond to a complete recording of

meteors down to about +1.5 visual apparent

magnitude. There is a difference in the radar/

visual ratio during the December-March period

as compared with the July-November period.

In the first case the ratio is well over 1, while in

the second it is only 0.75.

It must be remembered that the nature of the

cutoff at the faint limit of the records will be

different for the visual and for the radar programs. This is now being investigated. Unfortunately, with r values near 3, small differences in the nature of the cutoff will make major

differences in the hourly rates. No comparison

has yet been made between the probable distribution in elevation of the patrol radar meteor

echoes and the data in table 1. For meteors

observed visually at Ottawa, however, there is a

tendency for those observed high in the sky to

have a greater probability of an associated echo

on the high-power meteor radar. The average

probability of a visual meteor having a radar

echo drops from about 65 percent for elevations

greater than 60° to about 45 percent for elevations under 15°. This type of relation will not

necessarily hold true for the faintest echoes

recorded on the radar meteor patrol, as most of

these correspond to meteors that have not been

detected visually.

Acknowledgment

A portion of the data reduction for this paper

was carried out under Duke University Contract No. DA-31-124-AROD-59.

References

MCKIHLBT, D. W. R., and MILLMAN, P. M.

1949. A phenomenologieal theory of radar echoes

from meteors. Proc. lost. Radio Eng.,

vol. 37, pp. 364-375.

MILLMAN, P. M.

1957. The relative numbers of bright and faint

meteors. Joum. Roy. Aatron. Soe.

Canada, vol. 51, pp. 113-115.

1962. The meteor radar echo: an observational

survey. Astron. Journ., vol. 67, pp.

235-240.

MILLMAN, P. M.t and BURLAND, M. 8.

1956. The magnitude distribution of visual meteors. Presented at 96th Amer. Astron.

Soe. meeting, New York, December.

1961. Meteor magnitude distributions. Astron.

Journ., vol. 66, pp. 291-292.

MILLMAN, P. M., and MCINTOSH, B. A.

1963. A preliminary report on radar meteor

counts. In Proceedings of the Symposium on the Astronomy and Physics of

Meteors. Smithsonian Contr. Astrophys., vol. 7, pp. 45-51.

1964. Meteor radar statistics, I. Canadian

Journ. Phys., vol. 42, pp. 1730-1742.

1966. Meteor radar statistics. II. Canadian

Journ. Phys., vol. 44, pp. 1593-1602.

OPIK, E. J.

1958. Statistical results from the Arisona Expedition for the study of meteors. Contr.

Armagh Obs., no. 26, pp. 1-82.
RADAR METEOR ECHOES MILLMAN 155

Abstract

The problems of comparing visual meteor rates with the echo rates recorded by meteor radar equipment are

discussed. The uncertainty in the determinations of the magnitude distribution for visual meteors is noted. For

most of the visual magnitude range the ratio between numbers in successive whole magnitude groups may be taken

as approximately three. Recent studies of the data from the Ottawa radar meteor patrol show marked variations

throughout the year in the ratio between the numbers of short- and long-duration echoes. Comparison with the

\ i-ual data suggests that the ionization in a meteor trail is not proportional to the visual luminosity, and that this

relation may vary considerably for different groups of meteors. Preliminary results indicate that visual rates for

six observers average 15 to 20 percent higher than the patrol rate for meteor echoes with durations greater than

or equal to 1 sec.

Structure of the Major Northern-Hemisphere Meteor Streams

L. M. G. POOLE

 l

1. Introduction

Of the meteor streams that produce regular

annual showers observable in the Northern

Hemisphere, the Quadrantids (which occur in

early January), the Perseids (mid-August), and

the Geminids (mid-December) are among the

most important. These are all characterized

by a reliably high level of activity and are

separated in date of occurrence from other

periods of significant shower activity. Since

these showers all occur during hours of darkness,

they lend themselves to observation by both

visual and radar techniques. The only other

regular northern showers of comparable intensity are those due to the daytime streams,

Arietids, and f Perseids. These both occur

early in June and can be observed only by

radar, so that unless special radiant-determining equipment is used it is difficult to distinguish

between the activity of the two showers (see

Evans, 1960).

Radio observations on various meteor showers

have been carried out at Sheffield since 1962,

with the emphasis on the accurately controlled

recording of echo-amplitude information, in

order to achieve reliable determinations of the

absolute incident flux and magnitude distribution of the shower meteors. These quantities

are related, respectively, to the spatial density

and mass distribution of a stream's population

in the vicinity of the earth, so that a study of

their variation with solar longitude (in the

cases where the shower activity persists for a

sufficient length of time) enables us to deduce

the structure of the stream at its intersection

1

 Department of Physics, The University, Sheffield, England; now

with Department of Physics, Rhodes University, Grahamstown, South

Africa.

with the earth's orbit. Hence, further inferences can be made concerning the formation

and history of the stream.

Kaiser (1960) has given, in a practical form,

the theory relating absolute incident flux of

shower meteors to the observed radio-echo rate

and equipment parameters. The application

of this theory to the present series of experiments is described in some detail by Kaiser,

Poole, and Webster (1966). It may briefly be

summarized as follows.

The absolute radio magnitude of a meteor

is defined as

Mr=35-2.5 logI0 (at), (0

where at cm"1 is the zenithal electron line

density (produced by a vertically incident

meteor) and is given by a,=am sec x> where

am cm"1 is the maximum line density of a

meteor whose zenith angle is x- The magnitude

distribution can thus be described in terms of

the exponent s in the relation

(2)

where B(a,) is the incident flux producing

zenithal line densities greater than at, and c is

a constant. The form of equation (2) has been

established empirically, and is found to give

an adequate representation of the meteor

magnitude distribution over a reasonably wide

magnitude range.

"Decay-type" echoes occur when the electron

line density a at the reflection point is ^2X1012

cm"1, and in this case the maximum returned

echo power is given by

157

(3)
158

SYMPOSIUM ON METEOR ORBITS AND DUST

when the quantities are in units of gaussian

cgs. Here, PT is the transmitted power, 0 is

the power gain of the antenna in the direction

of the reflection point, which is at slant range R

from the observing station, and X is the radio

wavelength used. If a>2X10 w cm"1, the echo

becomes of the "persistent" type with Pmccaxi*.

The transition between the two echo types

occurs at Mr~+4 (see eq. (1)).

At any instant the reflection points on trains

associated with a particular shower can to a

good approximation be assumed to lie along a

line, the "echo line," drawn through a surface

at the mean height of meteoric ionization, which

for radio meteors is usually taken to be about

100 km. If the equipment sensitivity is such

that echoes are predominantly of the decay

type, the rate of echoes obtained from an echo

line associated with a particular shower with

echo power greater than P« is given by

J w,

where H is the atmospheric scale height,

Axo, «) is a function given by Kaiser (1960,

fig. 8), p=a9jari where a,,0 is the minimum

value of ap, which is the value of a at any

point along the echo line required to give an

echo power PR, and dt is an element of the

echo line. The parameter p thus accounts

for the variation of equipment sensitivity

along the echo line. The direction of maximum aerial sensitivity is that for which p— 1,

and does not necessarily intersect the echo

line at a given instant. Provided NP is determined over an interval of time during

which the quantities of /(x«, «) and fp*~ldl

do not change appreciably, we see from equations (2) and (4) that log NP should be a linear

function of log (aPi) such that

d(\ogNF)

d(\og^-8 1'

(5)

The left-hand side of equation (5) is an experimentally determinable quantity (see section 2),

and the value of « thus obtained can be substituted back into equation (4) to allow explicit

evaluation of 6 as a function of aH (or, using

«q. (1), of Mr). Figure 1 shows contours

of equal p projected onto a surface at a height

500 400 300200 100 200

SLANT RANGE (km)

300 400 S00

FIGURE 1.—Meteor sensitivity contour* at a height of 100 km

for the 17 MC/KC rhombic aerial. The positions of the

echo line at various times, T (hours), before transit of the

Perseid radiant (Dec.—S3*) are shown for the case when the

aerial is directed westward. The broken curves represent

the range limits 250 to 4SO km.

of 100 km for the 17 Mc/sec equipment described in section 2. Superimposed upon these

contours is shown the position of the echo line at

various times relative to the transit of the

Perseid radiant. For given shower radiant

coordinates and known aerial geometry, the

movement of the echo line with time can be

used to predict the time variation in the range

distribution of echoes associated with a particular shower (the "range-time motion"). Equation (4) can be used to predict the expected

variation of shower echo rate within any given

range limits (the "rate curve") by evaluating

the quantity fp*~xd\, over the intercept of the

echo line between the chosen range limits

(represented in fig. 1 by dotted curves).

2. Equipment

The equipment used in the present investigation

is located at the Edgemont research station

(53°26/ N, 1°53' W) near Sheffield, England.

Most of the data have been obtained with a

noncoherent pulsed radar system operating at

a frequency near 17 Mc/sec with a mean pulse

power » 7 kilowatts, pulse length 100 jisec, and

repetition frequency 50 sec"1. The rhombic

antenna system, used for transmission and

reception, produced a beam of width =20°

(to half-power points) directed due west at

an elevation of 17°. The beam was capable

of being directed due east should the occasion

demand (see section 3.C). The overall effective power gain of this antenna over an isotropic
STRUCTURE OF MAJOR NORTHERN-HEMISPHERE METEOR STREAMS—POOLE 159

radiator was 21.3. The receiver output was

recorded on magnetic tape, which had a

dynamic range of more than 40 db, and the

system was calibrated with sets of standard

pulses graduated in increments of 6 db from

an equivalent signal source replacing the

aerial. The recorded meteor echoes were subsequently displayed on a large-screen oscilloscope with a free-running time base adjusted

so that echoes appeared as amplitude-time

profiles. A photograph of two such profiles

is shown in plate 1. The echoes were selected

between range limits chosen so as to minimize

the contribution of sporadic meteors to the

total observed rates, and the left-hand side

of equation (5) was evaluated by counting

the rate of decay-type echoes with amplitudes

above various levels on the screen defined by

the calibration pulses.

The minimum value of a# observable under

average noise conditions is determined by the

equipment parameters (equation (3)). For the

17 Me/see equipment, this value corresponded

to M,— +8.3. When meteors brighter than

Af,~+ 6 are counted, the proportion of persistent-type echoes observed begins to become

appreciable, and equation (4) is no longer valid.

The magnitude range over which the rate of

decay-type echoes could reliably be determined

was thus +8.3>Mr > + 6 for this equipment.

The tape-recording system was supplemented

by a camera, which photographed an intensitymodulated range display on a film moving

continuously in a direction normal to that of

the trace sweep, so that the distribution of

echoes in range and time was automatically

plotted on the film (range-time photograph).

Examples taken during the activity of the

Quadrantid shower are shown in plates 2 a

and b. It should be noted that the range-time

motion associated with a particular shower will

usually appear distinct from the mean-range

distribution of the sporadic background only

if the value of « for the shower meteors is

substantially less than for the sporadic meteors

(for which «=2.16 ±0.04; Baldwin and Kaiser,

1965).

In addition to the 17 Mc/sec equipment

another radar with a similar tape-recording and

calibration system, and used with a rotating

dipole antenna, was operated at a frequency

near 30 Mc/sec. The faintest observable

meteor on this equipment had M,= + 7.0.

3. Results

The shower-radiant coordinates given in this

section have been provided by Evans (1960):

R.A.=right ascension, Dec.=declination, o =

solar longitude. Where more detailed descriptions of the various experiments are to be

published, the appropriate references are given.

A. PERSEIDS.—(Kaiser, Poole, and Webster,

1966)

R.A. = (48.5 ±0.3)°+(1.21 ±0.2) (o-138)°,

Dec. = (52.9±0.2)°+(0.13 ±0.2) (©-138)°.

The main series of observations on this stream

was carried out in 1962 between August 1

(O = 128?2) and August 21 (o=147?6) with

the 17 Mc/sec equipment. Certain aspects of

these results were checked by a more limited

set of observations carried out in 1963.

The expected rate curve for Perseid meteors

occurring within the range limits 250 to 450 km

(fig. 1), determined as outlined in section 1 for

August 13 (when Perseid activity was at a

maximum in 1962), is shown in figure 2,

together with the observed rate curves for the

same date in 1962 and 1963. The experimental

peak in activity is significantly wider than the

theoretical one, and this has been attributed to

an overall diffuseness in the Perseid radiant.

A comparison of the expected range-time motion

with that observed on August 13, 1962 (not reproduced here; see Kaiser, Poole, and Webster,

1966), indicates a fairly sharp radiant, and it

was consequently assumed that meteors associated with the Perseid shower emanate from a

complex radiant comprising a discrete central

component surrounded by a more diffuse

"halo." This is in broad agreement with the

result of Hawkins and Almond (1952).

The activity of the radiant as a whole was

assessed by determining the hourly rates of

meteors brighter than Aff=+8.3, +7.5, and

+6.8 over a half-hour period centered at

04.05 UT, and that of the diffuse component by

determining the corresponding rates over a

similar period centered at 05.15 UT (see fig. 2).

To allow for the contribution of sporadic

meteors to the observed rates, the hourly rates

over the corresponding half-hour intervals on
160 SYMPOSIUM ON METEOR ORBITS AND DUST

1

 V '- -

0300 0400

UT

FIGURE 2.—Hourly echo rate vs time for different dates:

. . . August 13, 1963

August 13, 1962

August 1, 1962

Theoretical rate curve (on an arbitrary scale) for a point radiant,

R.A.=49.°5, Dec.= 53°, assuming

140

SOLAH LONGITUD I

M .•• 8 3

ISO

dates between August 1 and August 5 (inclusive) were averaged and subtracted from

the observed rates. This could not be done for

dates following Perseid activity since a study

of range-time photographs indicated that the

enhanced rate persisting until August 21 (the

latest date on which records were obtained in

1962) was due to shower meteors, and this was

again apparent in 1963. The shower rates

thus obtained for the Perseid radiant as a

whole aDd for the diffuse component are shown

in figures 3 a and b, respectively, as functions

of solar longitude. It was found that over a

more limited range of solar longitude, the

contribution of the discrete radiant to the

total Perseid rate could be estimated with

sufficient accuracy by subtracting the rates in

figure 3b from the corresponding ones in

figure 3a, to give figure 3c.

The value of the exponent s was determined as

a function of 0 for the curves in figures 3a-c

from equations (1) to (5). The results are

shown in figures 4a, b. The value of 0 obtained

from equation (4) for the discrete radiant on

August 13, 1962, is shown in figure 5 as a

function of Mr.

The most striking feature of these results is

the rapid decrease of s with o for the discrete

radiant in figure 4c, which suggests that the

distribution of meteoroid masses changes as

the earth moves through the stream. The

low value of s at o = 139?9 in figure 4c supports previous suggestions (e.g., Hawkins and

ui2000

1500

5 1000

5 0 0

130 >f^,140—~

^"-~--.Mr«+83

SOLAR LONGITUDE

130 uo

SOLAR LONGITUDE

FIGURE 3.—Mean hourly echo rates for meteors associated

with: a, the Perseid radiant as a whole vs solar longitude

(1962); b, the diffuse component of the Perseid radiant vs

solar longitude (1962); c, the discrete component of the

Perseid radiant vs solar longitude (1962).
2 0

1 5

STRUCTURE OF MAJOR NORTHERN-HEMISPHERE METEOR STREAMS POOLE

-lO.Or

-10.2

-10.4

-10.6

-10.8

-11.0

161

135 140 145

" SOLAR LONGITUDE

2 0

135 140

SOLAR LONGITUDE

145

135 136 137 138

SOLAR LONGITUDE

140

FIGURE 4.—Variation of the exponent / with solar longitude

(1962) for: a, the Perseid radiant as a whole; b, the diffuse

component of the Perseid radiant; c, the discrete component

of the Perseid radiant.

+6.5 +7.0 +7.5 +8.0 +8.5

FIGURE 5.—Absolute incident flux 0 (m~* sec"1) of meteors

brighter than absolute radio magnitude Mr:

0 0 0 Perseid maximum 1962, discrete

radiant

X X X Geminid maximum 1962, main radiant

+ Quadrantid maximum 1965

Almond, 1952) that this stream contains a

core of large meteors. This is discussed

further in section 4.

B. GEMINIDS.—(Webster, Kaiser, and Poole,

1966)

R.A. = (112.5 ± 0.4) °+(0.80± 0.2) (o-259.9)° ,

Dec. = ( 33.3±0.5)°+(0.18±0.2)(o-259.9)°.

The equipment and the methods of analysis

and data reduction for this experiment are

essentially the same as were used for the

Perseids. The main series of observations on

this stream were conducted in 1962 between

November 23 (o=240°) and December 22

(O=269?5), with auxiliary observations in

1963 and 1964. The expected and observed

rate curves for December 13, 1962 (Geminid

maximum) are shown in figure 6, again with

the range gate 250 to 450 km. An unexpected

feature of these results is the peak in activity

approximately an hour before the expected

peak on this date. This early peak was less

pronounced, but nevertheless present, on other

dates near the Geminid maximum in 1962,
162 SYMPOSIUM ON METEOR ORBITS AND DUST

0100

UT

33 OO

FIGURE 6.—Hourly echo rate* vs time for different dates:

X X0 0

t •

December 13. 1962

December 13, 1963

December 12, 1964

Mean of rates on November 26 and

December 22, 1962

Theoretical rate curve (on an arbitrary scale) for a point radiant,

R.A.-112!6, Dec.-33?3, assuming /3> 1.6

and has been tentatively ascribed to the

activity of a secondary radiant (the "early

radiant") with a similar declination to that

of the main radiant, but with R.A. ~15°

smaller. On the range-time photograph for

December 13 (Webster, Kaiser, and Poole,

1966), the activity of such a radiant can

be detected, but it is less noticeable than

that of the main radiant. Observations during

the 1963 (December 13) and 1964 (December

12) encounters have shown only a slight suggestion of enhanced activity before the expected peak (see fig. 6). The earlier date in

1964 is in order to make the results for the

different years correspond as closely as possible

in solar longitude.

The hourly rates associated with the early

and main radiants in 1962 were determined for

each day of observation over 20-min intervals

centered at 23.55 UT and 00.55 UT, respectively, and appear in figures 7a, b as functions

of o . In this case the sporadic contribution

was determined on November 26 and December

22. The plots of « vs o for the two radiants

are shown in figures 8a, b. As for the Perseids,

a gradient in «is apparent for the main Geminid

1000

500

250 260

SOLAR LONCITUOC

5

= 1000

500

250 260

SOLAR LONGITUDE

FIGURE 7.—Mean hourly echo rates tor meteors associated

with: a, the early Geminid radiant vs solar longitude (1962);

b, the main Geminid radiant vs solar longitude (1962).

radiant, while the early radiant appears to be

associated with a more complex structure with

a minimum for « at o=256°.3. It will be

noticed that on December 13 (o=260°.5), «

is significantly higher for the early radiant than

for the main one, and this could explain the

comparatively poor experimental range-time

plot obtained for the former radiant (see section

2). We have obtained 9 for the maxim""*

activity of the main radiant in 1962 (December

13), as shown in figure 5.
STRUCTURE OF MAJOR NORTHERN-HEMISPHERE METEOR STREAMS—POOLE 163

2 ?

I 2

24

22

20

» 18

1.6

12

( 0 )

255 260

SOLAR LONGITUDE

(b)

250 255

SOLAR LONGITUDE

FIGURE 8.—Variation of the exponent s with solar longitude

(1962) for: a, the early Geminid radiant; b, the main Geminid radiant.

The fact that the early peak has not thus far

reappeared since 1962 has led to the surmise

that it might be connected with the periodic

Sextanid stream, which has an orbit similar

to that of the Geminids (Nilsson, 1964). The

Sextanids appear in September every 4 or 5

years, so that if the "early Geminids" exhibit a

similar periodicity we might expect their return

in 1966 or 1967.

C. QUADRANTIDB.—(Poole, Webster, and Kaiser

in preparation)

R.A.=233°±2

Dec.=50°.5±0

J at o =283C

This shower does not endure over a sufficient

range of solar longitude to permit a study of

structure as described in sections 3.A and

3.B. The main activity extends over <1°

in o, and Bullough (1954) has reported an

intense subcenter that extends over a mere

O.°l in o. Observations of Quadrantid activity

have been considerably hampered at Sheffield

by the severe weather conditions prevalent at

the time of year. In January 1963 attempts to

make recordings completely failed, and in 1964

only limited success was achieved. Every

effort was made to ensure satisfactory results

in 1965, especially since the 17 Mc/sec aerial

geometry was favorably disposed to observe

Bullough's (1954) subcenter during this

encounter. On this occasion, however, the

sporadic control days before the date of maximum activity were lost.

The expected and observed range-time plots

for January 4, 1964, are shown in plate 2a.

The well-defined experimental plot is indicative

of a narrow shower radiant and low s value, and

on January 3, 1965, an estimate of the radiant

coordinates was made by switching the antenna

so that it was directed eastward after transit in

order to obtain the "mirror image" range-time

photograph shown in plate 2b (the interference

evident after the switchover is from European

stations). This facilitated the more exact determination of the time of transit, and hence of

R.A.; declination was estimated by comparing

the theoretical range-time envelopes for various

declinations with the experimental plots. The

radiant found was R.A.=231°±0.1, Dec.=

+50° ± 2 for o=282?65. This agrees well

with Evans' mean radiant, although the latter

appears to be more diffuse.

The theoretical rate curve derived for the

above radiant predicts a peak in activity at

06.55 UT, and figure 9 (comprising 2 years'
164

SYMPOSIUM ON METEOR ORBITS AND DUST

1000-

500-

tr a.

£x

o at

x m

279 280 281 282 283 284

SOLAR LONGITUDE

2 85 286

FIGURE 9.—Mean hourly echo rates determined over a half-hour period centered at 06.55 UT vi solar longitude. Full circlet:

results obtained in 1964; open circles: results obtained in 1965. The accuracy of the point marked X is in doubt.

results) shows the variation with o of total

hourly rate of meteors brighter than M,= -(-6.8

determined over a half-hour interval centered

at this time. The high rate at o=282?7 was

obtained on January 3, 1965, and the corresponding value of 0 for Mr= +6.8 is shown in

figure 5. The rate of persistent echoes during

this encounter was too high to allow a meaningful determination of the echo rate for fainter

meteors, and this has rendered the determination of s for this shower difficult. The best

estimate from the available data is s= 1.55±0.2.

The point marked X in figure 9 was obtained

on January 4, 1964, when heavy icing of the

antenna occurred, and its accuracy is consequently in doubt.

D. ARIETIDS.—(J. Jones, unpublished)

R.A. = (45.1 ±0.2) °+(0.69±0.11)(o -78.3)°,

Dec. = (23.8 ± 0.5) °+ (0.43 ± 0.25) ( O - 78.3) °.

For these observations the 30 Mc/sec rotating

dipole equipment was used in an experiment

designed to examine the effect of changing zenith

angle (x) on shower meteor rates. The observations were conducted between June 1 and

June 20, 1964. Every effort was made, through

suitable adjustment of aerial azimuth and of the

range gate, to avoid observing echoes associated

with the f-Perseid stream (R.A.« 59°, Deo. »

22°), but for imxlerate values of x contamination by the latter stream appears to have been

unavoidable. The observed daily rates for the

(contaminated) Arietid meteors determined

over successive 24-hour intervals centered on

the time of radiant transit (thus encompassing a

range of values of x) are shown in figure 10

against solar longitude, and the corresponding

values of s in figure 11. These agree well with

the mean value of 2.14 ±0.02, obtained by

Brooks (1963) at Sheffield, for a mixture of

Arietid and f-Perseid meteors observed between June 3-8 (inclusive), 1959.

E. ORIONIDS, LEONIDS, AND LYRIDS.—The

Orionid shower occurs over a few days in

October with a maximum around October 21.

This shower has produced a noticeable rangetime plot on a continuous slow-film recording

being conducted at Sheffield, but the overall

activity has not been investigated in detail.

Tape recordings were taken with the 17 Me/

sec equipment on November 16-18, 1964, to

investigate the activity of the Leonid stream,

since the period 1964 to 1966 coincides roughly

with the 33-year cycle characteristic of this

shower. However, no significant activity associated with the shower could be detected.

Further observations were planned for 1965.
STRUCTURE OF MAJOR NORTHERN-HEMISPHERE METEOR STREAMS POOLE 165

75 SO

SOLAR LONGITUDE

FIGURE 10.—Daily echo rates for meteors associated with the

Arieiid stream vs solar longitude (1964).

76 77 78 79

SOLAR LONGITUDE

80 81

FIGURE 11.—Variation of the exepnont s with solar longitude

(1964) for meteors associated with the Arietid stream.

Observations have also been carried out on

the Lyrid shower during April 1964 with the 30

Mc/sec equipment, but again no significant

shower activity was detected.

4. Conclusion

The present results, where they cover aspects

already examined by other workers, are in

general agreement with the previous work.

Points of difference worth noting are: (1) activity associated with the Perseid stream persists until a later date than is suggested by

other results (and appears to be associated

with the diffuse component of the radiant);

(2) a double radiant associated with the

Geminid stream has not previously been

detected by radar methods, although complexities in this radiant have been found from visual

observations (King, 1926); and (3) the Quadrantid radiant is apparently well defined according to the present evidence, whereas

Evans (1960) finds a comparatively large

radiant diameter.

For many of the various radiants studied

significant variations in s with o are revealed.

Of the various processes acting throughout the

lifetime of a stream that might produce changes

and gradients in the distribution of masses

among members of the streams, three appear

to be of prime importance: (1) the PoyntingRobertson effect, discussed by Wyatt and

Whipple (1950); (2) the drag induced by the

solar wind; and (3) the sputtering of meteoroids

by the solar wind (Kresak, 1960). The effect

of these mechanisms is difficult to assess

quantitatively, but each acts within the orbital

plane of the stream; any resulting gradients

will thus be detected by the earthbound observer only if the inclination of the stream to

the ecliptic is sufficiently low. Processes

(1) and (2) will preferentially shorten the major

axes of orbits of the smaller particles in the

stream so that in time an increase of s among

meteors with shorter orbits may be expected;

on the other hand, (3) tends to decrease s,

preferentially among the shorter orbit meteors.

The trend in s with o observed will thus

depend on which of these mechanisms is predominant and on the direction of the earth's

motion through the stream.

Of the streams under consideration here the

Geminids and Arietids have the lowest inclinations (<20°). As the earth traverses the

Geminid stream, it intersects orbits of increasing major axis, and the value of s (for the main

radiant, fig. 8b) is found to decrease. In the

case of the Arietids the situation is reversed,

and we would expect the trend in s to be opposite to that for the Geminids. No such

trend is immediately apparent in figure 11 (if
166 SYMPOSIUM ON METEOR ORBITS AND DUST

anything, s again tends to fall). The orbit of

the Perseid stream is steeply inclined to the

ecliptic, and the rapid variation of s in figure

4c for the discrete radiant is again unexpected.

These results thus do not generally support an

evolutionary theory of stream structure (at

least in terms of the above selective processes),

and imply that the observed gradients are more

probably dependent on the mode of a stream's

formation than on its subsequent history.

Southworth (1963) has shown that the present

width of the Perseid stream can be explained

in terms of an explosion of the parent comet

some 1000 years ago, and it is thought that

most streams are likewise formed by the disintegration of cometary-type bodies, although

this is probably a gradual process in many

cases. The velocities imparted to meteoroids

leaving the parent body might well be size

dependent, and this could in principle explain

the existence of cores and discontinuities within

streams. The structure of a stream would thus

depend on such factors as the nature of the

comet, the distribution of particle sizes within

the nucleus, and the mode of disintegration.

It is well known that the values of 8 for

shower meteors are generally lower than those

for the meteors comprising the sporadic background, and this is confirmed by the present results (with the exception of the Arietid shower).

This low value of s has again been ascribed

(Wyatt and Whipple, 1950; Kresak, 1960) to

the processes discussed above, which will selectively remove smaller particles from the

streams. The time scales involved are, however, still uncertain, and it is doubtful whether

any streams are sufficiently long lived for the

effect of these processes to become apparent

(Kresak, 1960). It is conceivable that the

increased value of 8 for sporadic meteors is due

to fragmentation through mutual collisions of

meteoroids over a period of time long compared

to the average age of a meteor stream. This

might also account for their relative lack of

abundance (to which attention has also been

drawn by Kresak, 1960) in the solar system.

Acknowledgments

The author i> indebted to his colleagues,

Drs. T. R. Kaiser, A. R. Webster, and J. Jones,

on whose work he has drawn in the preparation

of this communication. The work lias been

supported by the Scientific Research Council.

References

BALDWIN, J. P., and KAIHEK, T. It.

1965. Radio observations of tiporadir meteors at

17 MC/B. Monthly Notice* Roy.

Ajjtron. Soc., vol. 129, pp. 85-102.

BROOKS, I).

1963. Radar echoea from the aurora and meteors

and their aiwociation with other phenomena. Phi) Tlumix, Sheffield Univ.,

Sheffield, England

Hi I.I.IH I.II, K .

I'.i.Vl Radio echo <>}•-< r\ .it mm of the day- and

night-time meteor stream* 1951 October

to 1953 December. Jodrell Bank Ann.,

vol. 1, pp. OH 97.

EVANS, O. C.

1960. Itadio echo olxw-rvations of meteor activity

between 1954 December and 1958

December. Jodrell Bank Ann., vol. 1,

pp. 280-337.

HAWKINS, G. S., and ALMOND, M.

1952. Radio echo observations of the major night'

time meteor streams. Monthly Notice*

Roy. Astron. Soc., vol. 112, pp. 219-233.

KAISER, T. R.

1960. The determination of the incident flux of

radio meteors. Monthly Notices Roy.

Astron. Soc., vol. 121, pp. 284-298.

KAISER, T. R.; POOLE, L. M. G.;and WEBSTER, A. R.

1966 Radio-echo observations of the major

night-time meteor streams, I: Pereeids.

Monthly Notices Roy. Aatron. Soc.,

vol. 132, pp. 225-237.

KINO, A.

1926. An emphemeris of the Geminid radiantpoint. Monthly Notices Roy. Astron.

Soc., vol. 86, pp. 638-641.

KRESAK. L.

1960. The effect of solar corpuscular emission on

the magnitude distribution of meteors.

Bull. Astron. Inst. Czechoslovakia, vol.

11, pp. 1-9.

NlLSSON, C. S.

1964. Short communications. The Sextanid

meteor stream. Australian Journ. Phys.,

vol. 17, pp. 158-160.
STRUCTURE OF MAJOR NORTHERN-HEMISPHERE METEOR STREAMS—POOLE 167

SOUTHWORTH, R. B. night-time meteor streams, II: Geminids.

1963. Dynamical evolution of the Perseids and Monthly Notices Roy. Astron. Soc.,

Orionids. In Proceedings of the Sym- vo l 13 3 p p 309-319.

posium on the Astronomv and Physics of w Q n T , „. _, T

», . o ... . „

 J

. _ WYATT, S. P., Jr., and WHIPPLE, F. L.

Meteors. Smithsonian Contr. Astrophys vol 7 PD 299-303 1950. The Poynting-Robertson effect on meteor

WEBSTER, A. R., KAISER, T. R., and POOLE, L. M. G. orbits. Astrophys. Journ., vol. Ill,

1966. Radio-echo observations of the major pp. 134-141.

Abstract

Systematic radar observations on the major northern meteor streams have been carried out at Sheffield since

1962 in order to study the variation of the total incident flux and magnitude distribution exponent (s) of shower

meteors with solar longitude (G). Significant gradients in » with O have been found for the Perseid, Geminid, and

Arietid showers, which are not generally easy to explain in terms of known selective processes acting during the

lifetime of the streams. Information has also been obtained concerning the radiant structure of some of the showers.

The Perwid radiant is found to consist of a discrete center of activity surrounded by a more diffuse "halo." The

main Geminid radiant was accompanied in 1962 by a less active radiant that transited an hour earlier than the main

one, but which has not since reappeared, and is possibly connected with the periodic Sextanid stream. In 1965 the

Quadrantid stream provided a higher meteor rate than any other stream observed, but the high level of activity

was maintained over a range of G of less than 1°, and appears to be associated with a well-defined radiant.
168

SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 1

Photograph of two decay-type echoes as displayed on the large-screen oscilloscope.
09 00

z

<

0-1—

05.00 06.00 07.00 08.00 09.00 10.00 11.00 12.00

UT -*-

PLATE 2

Range-time photographs: a, January 4, 1964. For comparison the theoretical range-time envelope is shown for the point radiant,

R.A.= 233°, Dec.= 5O.°5, and for echoes received from the segment of the echo time where p>0.1 . Aerial is directed westward, b, January 3,1965. Aerial is directed westward before the time marked by the arrow, and eastward afterward. (Meteor

echoes appear as white dots.) CO

Luminosity Function of Sporadic Meteors and Extrapolation

of Influx Rate to Micrometeorite Region

B.-A. LlNDBLAD

The statistics of meteor magnitudes form the

basis for the derivation of the distribution of

meteor masses. To determine the mass influx

rate of meteors we must study the characteristics of the luminosity function of meteors.

Experimental investigations suggest that the

luminosity function is of the form

F(m)=F(0)Xrm, (1)

where F(m) is the number of meteors equal to

or brighter than a given magnitude m. The

parameter r, which is assumed to be constant

over a fairly wide range of magnitudes, determines the increase in meteor numbers as we

go to fainter meteors. Taking logarithms to

the base 10 and differentiating equation (1),

we get

dlog

dm (2)

If the ratio of increase r is independent of

magnitude, the logarithms of the accumulated

meteor numbers lie on a straight line of slope

log r. It follows that the ratio r may be determined directly from an experimental plot of

log F(m) against m, provided a sufficiently large

meteor sample is available.

A number of experimental investigations of

the luminosity function of meteors have been

published. The vast majority of these studies

are based on naked-eye observations. It is

difficult to assess the significance of many of

these studies since information about the area

of sky searched for meteors, the sky conditions,

Land Observatory, Sweden.

the date and length of the observational periods,

etc., is missing. In addition, the investigators

usually analyze the luminosity function of apparent magnitudes, which may differ considerably from that of the absolute magnitudes. It

is hence not surprising that there is considerable

divergence in the experimental determinations

of the ratio of increase r. For sporadic or nonshower meteors, published values of r vary between 2.3 and 4.0. Shower meteors tend to

show some individual peculiarities, but values

of r generally lie in the range 3.0 to 4.0. For

complete references as well as a general discussion of the visual investigations see, for example, the monographs by McKinley (1961), Millman and McKinley (1963), and Hawkins (1964).

Previous investigations

In the following, reference will be given only to

a few representative investigations that were

based on carefully supervised group observations or where the circumstances of the observations were otherwise carefully controlled.

One of the first large-scale attempts to study

meteor phenomena was the Arizona expedition.

As part of this project, Watson (1937) analyzed

a small number of naked-eye and telescopic

magnitudes collected by Opik and Boothroyd.

Independent, naked-eye data published by

Hoffmeister (1931) were also analyzed. The

study gave r=4.0 for naked-eye meteors. In a

later summarizing discussion of all the available

Arizona data, Opik (1958) found an average

value of r=3.3. This ratio he found to be

constant over the apparent magnitude range

-fl to -f5 mag.

171
172 SYMPOSIUM ON METEOR ORBITS AND DUST

The most extensive investigations in recent

years of the luminosity function of naked-eye

meteors have been carried out by Millman and

collaborators. In an analysis of Canadian

meteor observations, Millman and Burland

(1956) deduced from a study of the apparent

magnitudes that r=3.7 for a mixture of shower

and nonshower meteors. This ratio is constant

over the absolute magnitude range —6 to +1

mag. For fainter meteors the authors suggest

that the ratio decreases, possibly reaching a

value as low as 2.5 for meteors of absolute

magnitude +5 mag. It is noted, however, that

there is considerable uncertainty involved in

determining the ratio for faint meteors, since it

is very dependent on the corrections made for

objects missed by the observers.

A detailed investigation of photographic

meteor magnitudes has been published by

Hawkins and Upton (1958). This study differs

from the previous ones in that it analyzes the

luminosity function of absolute magnitudes.

The authors studied the magnitudes of randomly selected meteors photographed with

Super-Schmidt cameras, and found a constant

ratio r=3.4 over the photographic absolute

magnitude interval from —2.5 to +3.4 mag.

No tendency was found for r to decrease as

fainter meteors were studied.

The conversion of photographic meteor magnitudes to visual magnitudes (or vice versa) presents certain scale problems that are not yet

completely solved, and that may influence the

magnitude statistics. Hawkins and Upton in

their discussion corrected for a variable color

index and found that the gradient of the luminosity function of sporadic meteors on the visual

magnitude scale was not entirely constant over

the magnitude range studied; however, this effect was not very pronounced in their study, and

they apparently accepted r=3.4 as the best estimate of the ratio of increase on the visual magnitude scale as well.

Several attempts have been made to deduce

the luminosity function of meteors from telescopic observations. If the observing instrument is directed to high elevations, the inclusion

of telescopic meteors considerably extends the

magnitude range of a study; however, the telescopic data are as a rule quantitatively small

and the telescopic magnitudes are extremely

difficult to evaluate on the naked-eye magnitude

scale. Further large magnitude-dependent corrections for the effective field of view of the

instrument must be applied to the observed

frequencies of magnitudes.

Watson (1939) made a study of the luminosity function of meteors in the telescopic magnitude range +4.5 to +9.5 mag. The difficulties

involved in a telescopic study are well illustrated

by Watson's paper. The original apparent

telescopic magnitudes were first corrected to the

naked-eye scale by means of a nonlinear relation

between apparent telescopic magnitude and true

magnitude. After a correction of the observed

frequencies for variation of effective telescopic

field with meteor magnitude, Watson concluded

that the ratio of increase was r~2.7. Very similar results have been obtained by other investigators such as Williams (1939) and Kresakova

and Kresak (1955).

A model distribution of meteor magnitudes

was published in tabular form by Watson

(1941). This in..del distribution, which is

based on an assumed ratio of increase r — 2.5

over the magnitude range —3 to +10 mag, has

been used extensively in the literature. The

observational basis for this table is not stated,

but presumably it is based on Watson's 1939

paper. It can be shown that a ratio r = 2.5 produces the mathematically convenient result

that there is constant mass per magnitude interval in the meteor population. This result,

sometimes referred to as Watson's law of constant mass, has formed the basis of a number

of theoretical discussions about meteors and

interplanetary dust.

Present investigation

The purpose of the present investigation is

to obtain the luminosity function of meteors

from a study of the absolute magnitudes of

naked-eye meteors. The data were collected

in the years 1953 to 1964 as part of a more

general study of meteors, which is being carried

out by the Lund and Onsala Observatories in

Sweden by both radar and visual techniques.

Details of the radar equipment and of the

general program are given elsewhere (Lindblad, 1963).

OBSERVATIONAL PROCEDURE.—The same basic

observational procedure has been followed ever
LUMINOSITY FUNCTION OF SPORADIC METEORS LINDBLAD 173

since the inauguration of these studies in 1953.

Visual recording is made by a standard team of

three observers. The observers estimate meteor magnitudes and also plot the meteors on

star charts. Meteor brightness is estimated to

the nearest half-magnitude by direct comparison with standard magnitudes within the field

of observation. The probable error of a magnitude estimate is 0.3 mag.

The detailed arrangement of our visual program differs in certain respects from that of

other workers. In radar-visual studies the

total field of the observers is determined by the

obvious condition that adequate sky coverage

must be obtained over the beamed sky area of

the meteor radar. Since we are using a moderately directive antenna, the observed sky area

is limited to a field of approximate radius 40°.

This field in turn is subdivided into three

standard regions, which are assigned to the

individual observers. These regions, each of

approximate radius 25°, are kept fixed with

respect to the horizon. Two adjacent fields

are centered at an elevation of 40° to 50°, and

the third field corresponds to the adjacent zone

in zenith.

A meteor is always entered in the records as

having been seen by only one observer. The

responsibility of recording and plotting a

meteor trail normally rests on the observer in

whose field the meteor appears. If the circumstances of observation are unfavorable,

which may be the case if the meteor rate is

high, the responsibility may by mutual agreement be transferred to another member of the

team.

The position of a meteor in the observer's

field of view is of importance for the following

discussion. For future reference we therefore

note that a meteor recorded within the observer's regular field will have an angular distance from the fixation point of the observer of

less than 25°, and a meteor recorded in the

field of another observer will have a value larger

than 25°.

OBSERVATIONAL DATA.—The observational material used comprised 4000 meteors recorded

during the month of August in the years 1953

to 1964. Of these meteors, 2865 belonged to

the Perseid shower, 238 to the 6-Aquarid

shower; 859 were sporadic meteors, and 38 were

identified members of various other showers.

REDUCTION OF MAGNITUDE DATA.—The recorded

apparent magnitudes were reduced to a zenithal

or absolute value by adding a correction Am=

10—5 log d, where d is the distance in kilometers

to the meteor. The zenithal correction was

computed to 0.1 mag. Visual absolute magnitudes of the present paper are therefore

nominally given to 0.1 mag.

Computation of Am demands a knowledge of

the distance to the meteor. For about onethird of the meteors recorded by us a direct

radar range determination of d was available

and Am was computed directly from the above

formula. To obtain Am for the remaining

objects we prepared nomograms that directly

on a curved earth basis gave Am as a function

of elevation angle and mean meteor height.

The mean height adopted in our investigation

was 95 km for sporadic and 5-Aquarid meteors

and 100 km for Perseid meteors.

As a check upon the consistency of the

reduction procedure, a random sample of

meteors with radar data was chosen and the

absolute magnitude was computed by both

procedures. The standard deviation of the

difference between absolute magnitudes computed from range data and from elevation data

turned out to be 0.2 mag. This error was thus

the additional magnitude error appearing in the

no-radar data group when we reduced the

apparent magnitudes to absolute magnitudes

using elevation information only. It should

be noted that if one neglects the zenith correction Am one introduces a far larger error—in

exceptional cases it may amount to several

magnitudes. A study of the luminosity function of meteors should therefore always be

based on absolute magnitudes computed for

each single meteor in the investigation. The

sole reason these studies in the past were based

on apparent magnitudes is that no range or

elevation information had been recorded.

For each meteor in our study, the absolute

magnitude, the code number of the observer,

and the position in the sky were collected on a

punched card together with other relevant

information. Luminosity functions of absolute

magnitudes were then studied for various

groupings of the data.
174

SYMPOSIUM ON METEOR ORBITS AND DUST

Luminosity function of absolute magnitudes

In figure 1 the log accumulated numbers of

absolute magnitudes are plotted for every tenth

of a magnitude for the total meteor sample. In

figures 2, 3, and 4 cumulative curves are drawn

for nonshower, Perseid, and 6-Aquarid meteors,

respectively. Inspection of the cumulative

curves shows that the slope of log F(m) against

m in each case may be represented by a straight

line over a fairly wide magnitude range. From

the slope of this line we deduce the values of

r listed in table 1.

COMPLETENESS OF SURVEY.—For magnitudes

fainter than approximately + 2 mag the nonshower and fl-Aquarid curves become nonlinear.

It is unlikely that this is a real effect; more

probably the departure from linearity at +2

mag represents a decrease in efficiency of the

eye, which is associated with the apparent

speed of the meteors. Support for this conclusion may be found if the departure values of

all three samples as listed in the fourth column

of table 1 are compared with the estimated

mean angular velocities. The departure points

given in table 1 thus indicate the faintest

absolute magnitude at which the particular

survey is complete.

RATIO OF INCREASE r.—Inspection of table 1

shows that the two showers studied by us

exhibit significantly higher values of r than the

sporadic meteor background. In particular,

the high r value obtained for the 5-Aquarid

shower is interesting, since it indicates that this

shower is very rich in faint meteors and thus

of recent origin.

For the purpose of the present paper interest

is focused mainly on the ratio r for sporadic

meteors. From the straight line slope we deduce that r=3.2. This result applies to an

absolute magnitude range —3 to -f 2 mag and

to an analysis in which no corrections for losses

or for observational errors have been applied.

The observed cumulative curve of absolute

magnitudes is distorted by two main factors:

(1) the selectivity depending upon magnitude

leading to a progressive loss of meteors as the

study is carried to fainter objects, and (2) the

accidental errors of individual magnitude estimates. Both these factors operate to lower the

observed slope, and thus also the experimental

value of r. In careful meteor studies based on

counts by trained observers the distort!ve effect

of the accidental magnitude errors is of minor

importance, and the progressive loss of meteors

with decreasing luminosity is the main dUtortive

factor. This factor may be ascribed to a dependence of the diameter of the field of vision

upon the brightness of a meteor.

VARIATION OF r WITH SIZE OF OBSERVED

FIELD.—We investigated how the experimental

ratio r varied with the radius of the field of

vision of an observer. This study was facilitated by the observational procedure used in

the present program, which implies that the

same three carefully delineated regions of sky

are observed each year. Although in consecutive years different individuals may be responsible for any one region, the center of the field

is consistently well defined. It is thus possible

to compute for each meteor the angular distance

to the appropriate center of field or fixation

point. From this information cumulative

curves of absolute magnitudes can be studied

for selected intervals of angular distance.

The data were first split into 3 angular zones

or rings with the limits 0°-19°, 20°-39°, and

40°-59°. Figure 5 depicts the value of log r for

TABLE 1.—Ratio of increase r

Sporadics

S Aquarids

Pereeids

All meteors

Slope of

line

(log"*)

0.51

0.68

0.56

0.56

Ratio of

increase (r)

3.2

4.8

3.6

3.6

Completeness

of survey

(magnitudes)

2.0

2.0

0.0

—

Linear

velocity

(km/sec)

40

40

60

—

Angular

velocity

(deg/sec)

15

16

20

—
LUMINOSITY FUNCTION OF SPORADIC METEORS—LINDBLAD 175

ALL METEORS

-4 -4 -3 -2 -t 0 •! ^2 »3 • * . 5

ABSOLUTE VISUAL MAGNITUDE

ABSOLUTE VISUAL MAGNITUDE ABSOLUTE VISUAL MAGNITUDE

FIGURES 1-4.—Log accumulated numbers versus absolute visual magnitude.
176 SYMPOSIUM ON METEOR ORBITS AND DUST

SfOHADIC MUtOBS

. r . f . f .

«IM€CO Mtuao

OS.

FIGURE 5.—Slope log r as determined for three separate angular zones.

these zones as deduced from plots of log F(m)

against m. It is convenient to treat the sporadic and Perseid data separately. This division corresponds'roughly to a classification into

a low-velocity and a high-velocity group. Both

diagrams exhibit the same general trend, the

value of log r rapidly decreasing when only

meteors in the outer rings are studied. Extrapolation of the sporadic meteor data to zero

angular distance gives log r=0.63. Incidentally, the same value of log r is obtained if the

study is restricted only to meteors appearing

within the limits 0°-19°, i.e., to meteors appearing within 20° of the fixation point of the

observer. It is thus concluded that the true

ratio of increase for nonshower meteors is 4.3.

The datum points in figure 5 that refer to the

Perseid shower should probably be treated with

some caution, since shower meteors are not uniformly distributed over the sky. Figure 5 suggests that the variation of r with angular distance is more pronounced for objects of high

angular velocity. This result indicates that the

observers have difficulty in ascertaining whether

fast luminous streaks seen in the outskirts of

their fields are real phenomena or not.

The dependence of the ratio r on the radius

of the total field of vision is shown in figure 6.

The datum points refer to sporadic meteors

only and correspond to radii 20°, 40°, and 60°,

respectively. The decrease in the ratio r, as

the observer extends his field, is very clearly

brought out.

The datum points of figures 5 and 6 are

deduced from a group count in which the recording procedure is arranged to minimize the

FIGURE 6.—Variation of log r with lize of observed field.

loss of meteors. Hence, there is reason to

believe that the general trend shown in the

diagrams will be more pronounced in studies

of data collected by a single observer. In the

case of a single observer the ratio r may also

be strongly dependent on individual peculiarities in the magnitude scale of the observer.

It therefore does not appear unreasonable that

these two factors alone may explain the discrepancy found between the results of various

investigators, thus causing an experimental

spread over the range 2.5 to 4.0 in determinations of r.

Mean influx rate of sporadic meteors

A mean value of the influx rate of sporadic

meteors may be determined from our data if

the collecting area of the atmospheric layer at

a height of 95 km is computed. It is a good

approximation to assume that the collecting

area was an ellipse with the major axis located

between zenith distances —50° and +65°.

A value of 33,000 km2 is then computed and

adopted as the total collecting area of the team.

The relation between influx rate, luminosity

function, and time-area product may be

written

log AT=log F(m) — log AXt, (3)

where N is the accumulated influx rate, F(m)

the luminosity function, A the collecting area,

and / the observing time. Let m be the faintest

absolute magnitude at which the survey is

complete. The total number of sporadic meteors recorded down to the magnitude of

completeness of the survey is, in our data, 255.

The total observing time is 212 hours and the
LUMINOSITY FUNCTION OF SPORADIC METEORS—LINDBLAD 177

time-area product is 7 X10* hrs km2. Inserting

numerical values in equation (3) we find that

the mean influx rate of meteors of +2.0 absolute

magnitude or brighter is 1.0X10"14 meteors

m~2 sec"1 (2T sterad)"1. If we adopt the slope

log r=0.51, as deduced from our total sporadic

sample, we find the influx of sporadic meteors

of zero visual magnitude or brighter to be

1.0X10"16 meteors m~2 sec"1 (2* sterad)"1.

The above influx rate is deduced from nighttime observations made during the month of

August at a northern latitude (</> = 57?4). It

should therefore be corrected for diurnal, seasonal, and latitude effects. From a study of

radar rates, Hawkins (1956) has predicted the

diurnal and seasonal variations in meteor influx

rate to be expected at various latitudes. Inspection of his tabular data indicates that the

mean rate over the hours of darkness agrees to

within 5 percent with the mean rate over a 24-

hour period. Further, it is found that latitude

effects are negligible. The conversion of our

August rate to a mean yearly rate introduces a

correction factor of approximately 0.6. Hence

we conclude that the influx rate of sporadic

meteors of zero magnitude or brighter averaged

over the entire year is 0.6X10""18 meteors m~2

sec"1 (2T sterad)"1.

It is interesting to compare our mean influx

rate with that obtained by Hawkins and Upton

(1958) for photographic meteors. Their influx

rate of 1.26X10"14 meteors m~2 sec"1 at zero

photographic magnitude corresponds to 2.5 X

10"16 meteors m~2 sec"1 at zero visual magnitude, if a meteor color index of —1.3 mag is

assumed. Our influx rate is, therefore, lower

than that of Hawkins and Upton by a factor

of four.

EXTRAPOLATION TO MICROMETEORITE REGION.—

For comparison with results obtained by other

meteor-counting techniques it is tempting to

extrapolate the log accumulated numbers curve

of naked-eye meteors to the micrometeorite

region. On the basis of the above influx rate

and the observed (unconnected) slope of the

luminosity function, an extrapolation through

the 30th magnitude produces the linear relationship marked log r=0.51 in figure 7. A similar

extrapolation based on the corrected slope

produces the relationship marked log r=0.63.

In order to obtain conformity with similar diagrams published elsewhere, the results are

shown in figure 7 on a mass scale. This scale

is based on the assumption that meteor velocities are independent of magnitude and that

log mass is proportional to log luminosity. A

mass of 1 g has been adopted for a zero-magnitude sporadic meteor.

The line marked log r=0.40 is an extrapolation of the tabular data given by Watson (1941).

The photographic data of Hawkins and Upton

are not plotted in figure 7, but they would not

deviate much from our curve marked log r=

0.51. The same conclusion applies to the data

of Millman and Burland (1956) if the extrapolation is based on the r value obtained for the

magnitude range over which their study is complete (m< + l mag).

Inspection of figure 7 shows that extrapolated

micrometeorite fluxes based on precise studies

of visual or photographic meteors are several

orders of magnitude higher than the values

obtained from Watson's model. Either this

large discrepancy may be due to some systematic error in the telescopic magnitude estimates

on which the Watson model is based, or one

must postulate a change in the ratio r somewhere below the limiting magnitude of the visual and photographic studies.

Extrapolations of naked-eye or telescopic

data may be in error for several reasons. The

observational data determining the slope of the

luminosity function in the naked-eye meteor

region had a range of error that is considerably

magnified in the extension into the micrometeorite region. The range of uncertainty involved

is well illustrated by our two experimental

relationships shown in figure 7. Further, the

adopted mass-magnitude relation may be in

error. Additional, but less important, errors

are associated with the assumed collection area

of the visual observers on which the influx rate

of visual meteors is based.

COMPARISON WITH SPACE-PROBE RESULTS.—

Direct studies of micrometeorite particles in

the upper atmosphere and in interplanetary

space are possible by means of rocket and

satellite-borne instruments. Statistically, the

most significant data to date have been obtained with piezoelectric microphone detectors.

A number of micrometeorite influx rates as

determined by these sensors have been pub-
178 SYMPOSIUM ON METEOR ORBITS AND DU8T

(30)

VISUAL ABSOLUTE MAGNITUDE

(20) 16 14 12 10 8 6 4 *2 0 -2

•5.0

0.0

-50

-10.0

-15.0

- 20.0

log r = 0.40

Wotson

-12.0 -10.0 -8.0 -6.0 -4.0 0.0

- • 5.0

0.0

- 5.0

10.0

15.0

-20.0

LOG ME TEOR MASS (g)

FIGURE 7.—Log cumulative influx rate versus log mass.

- - - - -Flux based on Watson's meteor model.

— Extrapolated flux based on visual observations by Lindblad; all meteors.

Extrapolated flux based on visual observations by Lindblad; meteors within 20° of the center of field of observation.

lished. In figure 7 we inserted datum points

from investigations by LaGow and Alexander

(1960), Dubin (1960), Soberman and Delia

Lucca (1963), and McCracken and Alexander

(1963). In this compilation the threshold

masses are standardized to an assumed velocity

of 30 km/sec. With the exception of 1960 fl,

the datum points represent influx rates uncorrected for earth shielding.

Inspection of figure 7 indicates that the spaceprobe impact counts are several orders of

magnitude higher than the influx values deduced

by extrapolation of Watson's meteor model.

Agreement between the space-probe measurements and our extrapolated meteor counts

based on an observed ratio of increase r=3.6

(curve marked log r=0.51), however, is satisfactory. The agreement between our data

and the space-probe results is further improved

if we base the extrapolation on the corrected

experimental ratio r=4.3 (curve marked log

r=0.63). Superficially at least, the micrometeorite impact data thus support the conclusions of the present paper, indicating that

the slope of the luminosity function of meteors

is considerably steeper than the slope assumed

in the Watson model.

Distribution law of meteor masses

The relation between magnitude and mass may

be written Tn—m0—2.5 log ffl, where Tfl is

meteor mass and m0 is a constant assumed

independent of m and 77?- Inserting into

equation (1) we get

F{Ut)=constantXr" lotm,
LUMINOSITY FUNCTION OF SPORADIC METEORS LINDBLAD 179

where F07t) — F(m) is the number of meteors

of mass equal to or greater than 777- Applying

an elementary law of logarithms, we obtain the

cumulative mass law

(4)

where F(l) is the number of meteors of mass

equal to or greater than unit mass, and r is the

ratio of increase per unit magnitude interval.

The distribution law of meteor masses may

thus be inferred from studies of the luminosity

function of meteors, since the exponent in the

mass law is directly determined by the slope

log r. Experimental values of log r lie in the

range 0.4 to 0.7, and these studies thus suggest

an exponent in the cumulative mass law in the

range —1.0 to —1.8. Inserting experimental

values as obtained in the present study, we find

that the exponent in the mass law is — 1.28 or

— 1.58, depending on whether or not the data

are weighted as a function of the angular

distance of the meteor from the center of field

of the observer.

Acknowledgments

The author is indebted to the directors of the

Lund Observatory and the Onsala Observatory,

Professors C. Schal&i and O. Rydbeck, respectively, for their constant interest in the work.

Among those who assisted at various times in

the reduction of the data, the author would

like to express his thanks particularly to Miss

I. Olsson.

Financial support for the investigation was

received from the Swedish Natural Science

Research Council.

References

DUBIN, M.

1960. IGY micrometeorite measurements. In

Space Research, ed. by H. Kallmann-Bijl,

pp. 1042-1058, North-Holland Publ. Co.,

Amsterdam.

HAWKINS, G. S.

1956. Variation in the occurrence rate of meteors.

Astron. Journ., vol. 61, pp. 386-391.

1964. Meteors, Comets and Meteorites. McGraw-Hill Book Co., New York, 134 pp.

HAWKINS, G. S., and UPTON, E. K. L.

1958. The influx rate of meteors in the earth's

atmosphere. Astrophys. Journ., vol.128,

pp. 727-735.

IIOFFMEISTER, C.

1931. Zur Theorie der Variation der Sternschnuppenhaufigkeit. Veroff. Universitatsstemwarte Berlin-Babelsberg, vol.

9, no. 1.

KBBSAKOVA, M., and KRESAK, L.

1955. On the activity of telescopic meteors and

some related problems. Contr. Astron.

Obs. SkalnatS Pleso, vol. 1, pp. 40-77.

LAGOW, H. E., and ALEXANDER, W. M.

1960. Recent direct measurements of cosmic dust

in the vicinity of the earth using satellites.

In Space Research, ed. by H. KallmannBijl, pp. 1033-1041, North-Holland Publ.

Co., Amsterdam.

LINDBLAD, B.-A.

1963. The relation between visual magnitudes of

meteors and the durations of radar

echoes. In Proceedings of the Symposium on the Astronomy and Physics

of Meteors. Smithsonian Contr. Astrophys., vol. 7, pp. 27-39.

MCCRACKEN, C. W., and ALEXANDER, W. M.

1963. The distribution of small interplanetary

dust particles in the vicinity of earth.

In Proceedings of the Symposium on the

Astronomy and Physics of Meteors.

Smithsonian Contr. Astrophys., vol. 7,

pp. 71-83.

MCKINLET, D. W. R.

1961. Meteor Science and Engineering. McGraw-Hill Book Co., New York, 309 pp.

MILLMAN, P. M., and BURLAND, M. S.

1956. The magnitude distribution of visual

meteors. (See Millman, Journ. Roy.

Astron. Soc. Canada, vol. 51, pp.

113-115, 1957.) Presented at 96th

Amer. Astron. Soc. Meeting, New York,

December.

MILLMAN, P. M., and MCKINLET, D. W. R.

1963. Meteors. In The Solar System, vol. IV,

ed. by B. M. Middlehurst and G. P.

Kuiper, Univ. of Chicago Press, Chicago,

pp. 674-773.

OPIK, E. J.

1958. Statistical results from the Arizona Expedition for the study of meteors. Contr.

Armagh Obs., no. 26, pp. 1-82.

SOBERMAN, R. K., and DELLA LUCCA, L.

1963. Micrometeorite measurements from Midas

II (Satellite 1960 fl). In Proceedings

of the Symposium on the Astronomy and

Physics of Meteors. Smithsonian Contr.

Astrophys., vol. 7, pp. 85-88.
180 SYMPOSIUM ON METEOR ORBITS AND DUST

WATSON, F. G. 1941. Between the Planets. Blakiston Press,

1937. Distribution of meteoric masses in inter- Philadelphia, Pa.

stellar space. Ann. Astron. Obs. Har- WILLIAMS, J. O.

vard, vol. 105, pp. 623-632. 1939. Relative frequencies of meteor magnitudes.

1939. A study of telescopic meteors. Proc. Astron. Journ., vol. 48, pp. 100-103.

Amer. Phil. Soc, vol. 81, no. 4, pp.

493-504.

Abstract

Data for visual meteors, observed under carefully controlled conditions, are used to determine the luminosity

function and mean influx rate of sporadic meteors. The log cumulative distribution curve of absolute meteor magnitudes is studied. It is deduced that the observed number of sporadic meteors increases by a factor of 3.6 per absolute

visual magnitude. The mean influx rate of sporadic meteors brighter than or equal to zero absolute magnitude in

0.6X 10-'4 meteors m~2 sec"1 (2x sterad)-'.

Analysis of the visual data shows that the observed ratio of increase r systematically varies with the size of the

field of an individual observer. A correction for this effect indicates that the true number of sporadic meteors increases by a factor of 4.3 per absolute visual magnitude.

The resulting slope for log cumulative flux versus log mass is —1.28 or -1.58, depending on whether or not

the data are weighted as a function of tin* angular distance of the meteor from the center of field of tin- observer.

Conversion of the observed meteor counts to a mass influx rate and linear extrapolation of the influx data to

the micrometeorite region on the basis of the observed r values produce influx rates in good agreement with recent

influx data from satellites and space probes.
Duration Distribution of Radio Echoes Obtained from

Underdense Shower Meteor Trains

L. M. G. POOLE

Radio echo theory predicts that the amplitude

of an echo obtained from an underdense

meteor train (with electron line density a«;lO~12

cm"1) at time t is given by

(— t/r), (1)

where Ao is the peak amplitude at time t=0.

The decay constant T is given by (Herlofson,

1948)

(2)

where X is the wavelength and D the ambipolar

diffusion coefficient in the meteor train. Various theoretical expressions for D (Kaiser, 1953;

Weiss, 1955) predict that for an isothermal

atmosphere D is inversely proportional to the

atmospheric density p, which at a height h is

given by

p=Po exp

where po is the density at height Ao and H the

atmospheric scale height. The distribution in

lnr (duration distribution) for a sample of such

meteor echoes should thus give a direct measure

of their distribution in height.

Duration distributions have been obtained

(Poole and Kaiser, in preparation) for underdense echoes recorded on a 17 Mc/sec radar

during the activity of the Perseid, Geminid,

and Quadrantid meteor showers, and compared

with the theoretical height distributions of

Kaiser (1954). In every case the r.m.s. deviation of the measured distributions was consider1

 Department of Physics, The University, Sheffield, England; now

with Department of Physics, Rhodes University, Grahamstown, South

Africa.

ably smaller than expected. Basically two

interpretations can be placed on this: (1) the

distribution in lnr does not reflect the true

height distribution, or (2) the actual height

distribution is not as predicted by Kaiser (1954).

Let us consider these possibilities separately.

1. Even assuming that equations (1) to

(3) are valid, there are several reasons why

D might not be inversely proportional to p,

and the duration distribution in this case will

not correspond to the height distribution.

There are certain high-altitude selection effects

(Greenhow, 1963) that could result in the

formation of an apparent echo "ceiling," and

it can be shown that the geomagnetic field is,

in principle, capable of affecting diffusion

(Kaiser, 1953). In either case, the observed

value of D is likely to increase less rapidly with

height than expected, but provided the variation remains essentially exponential we can

define an apparent scale height H'^>H. If

this inequality exists for the present results,

the geomagnetic field is most probably responsible since the effect of the ceiling is not thought

to be important here owing to the comparatively

low frequency used (see Greenhow, 1963).

2. If meteoric ionization is not correctly

described by the classical evaporation theory

(Herlofson, 1948), deviations from Kaiser's

theory (1954) may be expected. This theory

has been adapted by Weiss (1960) to allow for

variations in effective train length, and by

Poole and Kaiser (in preparation) to allow for

variations of the exponent n in the relation

Pi oca?,

(4a)

181
182

SYMPOSIUM ON METEOR ORBITS AND DUST

where ax is the maximum electron line density

of a meteor and occurs at the height where

p=P l . The classical theory predicts n—%.

When dealing with duration results we are

more fundamentally concerned with the analogous relation

Aocaf"', (4b)

where Dx is the value of D at the height where

a=c*i, and n' is given by

n'=nH/H'. (4c)

We can measure n' directly by comparison of

the mean Inr for meteors occurring within

different ranges of magnitude, and for the

present data values obtained range between

~0.3 and ~0.4.

It has been shown (Jones and Kaiser, 1966)

through consideration of the effect of the

thermal capacity of particles capable of producing radio meteors that the onset of ablation

can be sufficiently delayed to cause significant

foreshortening of the train and consequent

enhancement of maximum line density. If we

use reasonable values for the boiling point,

specific heat, and latent heat (of vaporization)

of stony meteor material, the ail density at the

height of ablation commencement (p0) is found

to be Po = 0.3pi for meteors in the size range

under consideration. With this result, and if

we assume initially that H'=H and n=n' =

0.33, the expected r.m.s. deviation of the duration distribution is calculated from the equations of Weiss (1960), and the agreement with

observation is fairly good. However, external

evidence (e.g., Greenhow and Hall, 1960a)

indicates that H' could be greater than H by a

factor of as much as 1.4, and from equation

(4c) we see that the upper limit of n is thus

~0.5. The expected r.m.s. deviation calculated, if we assume H'=\.±H and n=0.5, also

agrees well with observation, and other values

of the ratio H'/H in the range 1<H'/H<IA,

and of n in the range 0.33<n<0.5, can likewise be shown to be consistent with the present

results. It seems reasonable to conclude that

the quantities H'/H and n lie within these limits.

Other height (Evans, 1954) and duration

(Greenhow and Hall, 1960b) distribution results tend to support this conclusion if train

lengths are as predicted by Jones and Kaiser

(1966); the results in Evans (1954) imply that

n~0.5, and the results in Greenhow and Hall

(1960b) indicate that //'/// > 1 for all values of

n between 0.33 and 0.5.

The conclusions to be drawn from the present evidence can thus be summarized: (1)

meteor trains are considerably shorter than

predicted by the classical evaporation theory;

(2) the geomagnetic field appears to have a

noticeable height-dependent effect on diffusion

in meteor trains; and (3) the exponent n>K

(Weiss, 1960, suggests n<%).

References

KVANH, H.

1054. Scale heightn and prenmiren in the upper

at inn-,phi-i v fro m ruili n . i !u i otiMTValtotl B

of meteors. Monthly Notice* Koy. Aatron. Hoc., vol. 114, pp. 63 73.

OKEENHOW, J. S.

1963. Limitation* of radar technique a for the

Htudy of meteor*. In Proceeding* of the

Symposium on the Antronomy and

Physio* of Meteors. Smithsonian Contr.

Astrophys., vol. 7, pp. 5-17.

(JKEENHOW, J. S., and HALL, J. E.

196()a. Diurnal variations of density and «cale

height in the upper atmonphere. Journ.

Atmos. Terr. Phys., vol. IS, pp. 203-214.

1960b. The importance of initial train radius on

the apparent height and number distributions of meteor echoes. Monthly

Notices Roy. Astron. Soc., vol. 121,

pp. 183-196.

HERLOFSON, N.

1948. The theory of meteor ionization. Phys.

Soc., Rep. Prog. Phys., vol. 11, pp.

444-454.

JONES, J., and KAISER, T. R.

1966. The effects of thermal radiation, conduction

and meteoroid heat capacity on meteoric

ablation. Monthly Notices Roy. Astron.

Soc., vol. 133, pp. 411-420.

KAISER, T. R.

1953. Radio echo studies of meteor ionization.

Adv. Phys., Phil. Mag. Suppl., vol. 2,

pp. 495-544.

1954. Theory of the meteor height distribution

obtained from radio echo observations,

I: Shower meteors. Monthly Notices

Roy. Astron. Soc., vol. 114, pp. 39-51.

WEISS, A. A.

1955. Diffusion coefficients from the rate of decay

of meteor trails. Australian Journ.

Phys., vol. 8, pp. 279-288.

1960. Meteor height distribution and the fragmentation hypothesis. Australian Journ.

Phys., vol. 13, pp. 532-549.
Radar Studies of Meteors

B. L. KASHCHEYEV and V. N. LEBEDINETS

Introduction

Kudui studies of meteors, together with photographic observations and direct rocket- and

satellite-borne measurements, are at present the

main sources of information on meteoritic

matter in the vicinity of the earth's orbit as

well as on the physical processes associated

with meteors in the upper atmosphere.

Compared with the photographic method,

the radar method has a number of advantages:

the possibility of carrying out 24-hour measurements in any weather, high sensitivity of apparatus, which permits the study of very weak

meteors, etc. A basic shortcoming of this

method is the somewhat lower accuracy of the

measurements. It is impossible to interpret

correctly the results of any observations without first solving the main problems of the

physical theory of meteors. Because of the

specific character of radio observations, the

physical theory of radio meteors is more complicated than that of optical meteors.

In this paper we shall present results of radar

measurements of meteors carried out at the

Kharkov Polytechnical Institute according to

the IGY program, and also of theoretical

studies on the physical theory of meteors.

Particular attention was paid to the analysis

of the data on radiants and velocities of individual meteors.

Apparatus and methods of measurements

In our complex studies of meteors and their

associations we included radar measurements of

velocities and radiant coordinates of individual

meteors. Velocities were determined by the

pulse-diffraction method (Ellyett and Davies,

1

 Kharkov I'olytechnical Institute, USSR.

1948). The coordinates of the radiant were

determined by using three stations for the reception of radio waves scattered by a meteor

trail in the process of formation (Gill and

Davies, 1956).

A description of the radar station (RS) used

for the measurements has been published

(Kashcheyev et al., 1960). The basic RS

parameters are: wavelength X=8 m, peak

power Pt=75 kw, pulse frequency F= 500/sec,

pulse duration T=1 0 usec, gain coefficients of

transmitting antennas and receiving antennas

Ot—Or—16, threshold sensitivity of the receiver « = 2X10"-14

 watts.

One of the receivers was located near the

transmitter at the main receiving point. Two

outside receiving points were located at distances di=4.3 km northeast and d2 = 7.1 km

northwest from the principal point. The angle

between the base lines is 85°. For each meteor

the following were measured: time of the occurrence T, velocity v, and time displacements

ti and t2 between the corresponding extremes

of diffraction patterns of signals received in

three points. If the lengths of the base lines

are much less than the distance R to the point

of specular reflection on the trail, the angles

0! and 02 between the base lines and the trail

may be deduced from

. 2vti a 2vt2

COS 0i=—T

1

' COS 02 = -j —

« U

(1)

If the trail orientation in space and the meteor

velocity are known, it is possible to calculate

the orbit of the meteor body. Coordinates of

the corrected radiant and orbital elements were

calculated according to a somewhat modified

183
184

SYMPOSIUM ON METEOR ORBITS AND DUST

Kleiber scheme (1891) adjusted to the "Ural"

electronic computer. Four quantities, T, v, tu

and U, were assumed as incoming data. The

remaining values, which are usually taken from

the astronomical almanac, were expressed as

analytical time functions. The calculations

were carried out in the following order:

A, 2=horizontal coordinates of visible radiants;

a, 5=equatorial coordinates of corrected radiants; v0, vt=extra-atmospheric and geocentric

velocities; X, /3=ecliptic coordinates of corrected

radiants; X', /3' = ecliptic coordinates of true

radiants; vh=heliocentric velocity; E, E' =

elongation of corrected and true radiants of

apex; a, e, q, i, fi, « = orbital elements.

Measurement errors

The accuracy "of the measurements was determined from an analysis of different sources of

errors and also from the inner consistency of the

results of measurements for known meteor

showers.

From December 9 to 14, 1959, velocities and

radiants of 298 meteors of Geminid showers

were obtained (Kashcheyev, Lebedinets, and

Lagutin, 1961). The distribution of deviations

of individual values of velocity and radiant

coordinates from the average values appeared

to be close to the gaussian. The root-meansquare errors are AP O =±2.O km/sec, Aa=2?7,

and A5=±2?4.

The main sources of errors when measuring

the velocity are inaccurate consideration of the

atmospheric deceleration, the effect of diffusion

and atmospheric turbulent winds, the effect of

resonance during the reflection of radio waves

from the train, and inaccuracy of pulse counting

in the Fresnel zones. For meteors with velocities of 20 to°50 km/sec, the root-mean-square

error in the determination of extra-atmospheric

velocity of an individual meteor is Ayo~±2.O

km/sec. In the case of very slow meteors, the

errors of velocity measurements increase owing

to the inaccurate consideration of deceleration

and the effect of turbulent winds. When »0> 50

km/sec, the errors increase because of the diffusion effect and an inexact consideration of

deceleration. When »0<20 km/sec and ro>5O

km/sec, the root-mean-square error of one

measurement of velocity is Aro« ±3 km/sec.

From (1) we shall obtain

<

2

>

Errors in velocity determinations and in

measurements of time delays contribute nearly

equally to errors in the determination of radiant

coordinates. Errors in time deluys are due

mainly to turbulent winds in the atmosphere

(Lebedinets, Lagutin, and Lysenko, I960).

The role played by the other factors (resonance

effect, inaccuracy of pulse counting, diffusion

effect) is relatively small. For meteors with

velocities ro>30 km/sec, the root-mean-square

errors in the determination of radiant declination and right ascension are A4«±2?f> and

Aa«2?5 sec 6. With ro<30 km/sec, the errors

increase as the velocity decreases, and at

t\,<20 km/sec they may reach ±5°.

Results of measurements

During an annual cycle of measurements from

November 1959 to December 1960, the necessary data were obtained for the calculation of

velocities and radiants of several tens of thousands of meteors brighter than +7 mag. The

best records were selected from these observational data and the orbits of 12,500 meteor

bodies were obtained.

Radio-technical measurements of individual

radiants and velocities of meteors were made

by Davies and Gill (1960) at Jodrell Bank and

by Nilsson (1964) at Adelaide. According to

measurements carried out from May 1954 to

April 1955, Davies and Gill obtained 2474

orbits for meteors ranging from + 5 to -f 7 mag,

the catalog of which was not published. From

the results of measurements in 1961, Nilsson

obtained 2200 orbits for meteors brighter than

+6 mag. The catalog of orbits was not published, and the results of researches on sporadic

meteor orbits were not reported.

The orbits of small meteor bodies derived at

Jodrell Bank (Davies and Gill, 1960) and at

Kharkov (Kashcheyev and Lebedinets, 1961)

differ essentially from the orbits of larger bodies

generating photographic meteors (Whipple,

1954; McCrosky and Posen, 1961; Babadzhanov

and Kramer, 1963). These discrepancies may
RADAR STUDIES OF METEORS—KASHCHEYEV AND LEBEDINETS 185

be caused both by a real difference in the orbits

along which the particles of different size are

moving and by selective differences between

radar and photographic methods with respect

to velocity and radiant coordinates. While

reducing the obtained observational material,

we paid particular attention to these selection

effects.

l)ctc< tability of radio meteors

The selectivity of radio observations of meteors

was considered by LebedineLs (1963). To transfer from a measured to a real orbit distribution

we must take into account the following factors:

(1) a geometrical factor, l/l\, which characterizes a relative detection probability of meteors

with different radiant declinations, determined

by the geometry of radio-wave reflection from

meteor trails and by the sensitivity diagram of

the antennas; (2) a physical factor, I/P2, which

characterizes a relative detectability of meteors

with different velocities and zenith distances of

radiants, defined by a dependence of the ionization coefficient 0, evaporation height A, and distribution of linear electron density a along the

trail on v0, z, and on the initial mass of the

meteor body Mo, and also by a dependence of

an initial radius of ionized trail r0 on v0 and A;

and (3) an astronomical factor, 1/P3, which

characterizes the dependence of the probability

of an encounter with the earth on the parameters

of the particle orbit.

The astronomical factor affects to the same

extent the results of ground observations, irrespective of the method used. The value P3

was calculated by Opik (1951):

v. sin

(3)

The method of calculating the geometrical

factor was described by Lebedinets (1963). In

this study the method was generalized by considering the dependence of Pi on 5 as well as

a weaker dependence of Pj on v0. Table 1 gives

5

I/Pl

-20 °

0.3

0°

0.6

TABLE

+ 20°

0.9

1

+ 40°

1.6

+ 60°

2.5

+80°

3.4

the values of P, (6, v0) for RS as used in Kharkov,

the antennas being oriented eastward for

meteors with 00=40 km/sec.

The maximum value for power of a signal

scattered by the meteor train with a<1012

electron/cm is

where

V2A

(5)

e and m are charge and mass of the electron,

respectively, c is the light velocity, and D is

the coefficient of ambipolar diffusion.

The value and dependence on the velocity

of the ionization coefficient, determining the

scale of radio-meteor masses, have been considered (Kashcheyev and Lebedinets, 1961; Opik,

1958). The most thorough measurements of

the coefficient of ambipolar diffusion were

carried out by Kashcheyev (1963).

We discussed (1963) the theory of an initial

expansion of ionized meteor trails. We deduced

that r0 is proportional to v0 and inversely proportional to the atmospheric density. Measurements of r0 by parallel radar observations

of meteors on two wavelengths were carried out

at Jodrell Bank (Greenhow and Hall, 1960),

Kharkov (Kashcheyev and Lebedinets, 1961,

1963), and Kiev (Bairachenko, 1963). From

our 1963 paper it is evident that the results of

measurements are in satisfactory agreement

with theory. At the height of 95 km with

i;0=40 km/sec, r0otl m.

The effective sensitivity of RS is characterized by a minimum value of the effective linear

electron density, a$ia, of meteor trails, which

may be determined in the direction of maximum

radiation. When due account is taken of some

random position of the point of specular reflection on the trail, the probability of the detection

of the trail formed by the meteor body with the

given Mo, v0, and z is proportional to the length

of the trail path l(M0, vQ, z, X, aS"), where

aef>a3in. Here, arf=a*>(A)<T(2'

r

o

A

>2.

240-022 O—87- -13
186 SYMPOSIUM ON METEOR ORBITS AND DUST

Relative detectability of meteors with different v0 and z is

Pa(Vo, z, X, a*")

= f l(MOt Po, z, X, o^n)n(M0)dM0. (6)

Jo

Here n(M0) is the differential distribution of

meteor bodies by masses, which are usually

given in the form

n (j/) = J L. (7)

Generally speaking, c and * coefficients may be

somewhat different for different intervals of

meteor-body masses.

To calculate the physical factor we must know

the height of maximum evaporation of meteor

bodies with different masses, velocities, and

zenith distances of radiants, and distributions

of ionization along the meteor trails.

Greenhow (1963) used the simplest physical

theory of meteors (Herlofson, 1948) to calculate

the height of maximum evaporation km for

meteor bodies of any mass. He obtained

hm= 128 km for meteors of brightness +15 mag

with po=4O km/sec. At this height the initial

radius of the trail is so large that the observations of such meteors are for the most part

possible only with X>30 m no matter how great

the RS power. Hence Greenhow concluded

that radar studies of very weak meteors are

impossible.

Lebedinets (1963, 1964) deduced more precise formulas for hm, and also gave the luminous

intensity and ionization curves with different

masses and velocities of meteor bodies. With

PO=40 km/sec for meteors of brightness +15

and +20 mag, the heights of maximum evaporation are practically the same and equal to

102 km. With sufficiently high RS power, observations of such meteors are quite possible

at X> 12 m.

The physical factor was calculated with different values of the parameters z, X, s, and a$*.

Table 2 gives the values of Pt calculated with

cos z=%, X=8 m, s=2, and a5ia=2X1010

electron/cm.

Ascribing the statistical weight P,P» to every

meteor, we correct the results of continuous

t>o km/sec

I/Pi

15

0.06

TABLE

20

0.40

30

1. 10

2

40

1.00

50

0.68

60

0.36

70

0.20

24-hour measurements due to the selectivity of

the radar method in relation to the velocities

and radiant coordinates of meteors. We can

thus transfer from the measured distribution

of different parameters of meteor bodies to the

true distribution for a complex of meteor bodies

encountered by the earth, with masses larger

than a certain minimum value. Similarly,

assuming the weight of meteors /*=• /VVi , we

can change over from the measured orbit distribution to that for the whole complex of

meteor bodies with masses larger than a certain

minimum value, whose orbit* have perihelion

distances q< 1 a.u. and aphelion distances

q'> 1 a.u.

Orbits of meteor streams and associations

The term "meteor association" was introduced

by Jacchia and Whipple (1961) to designate

groups of orbits whose reality was established

with less certainty than that of streams. The

authors themselves point out, however, that

there is no clear boundary between these two

types of orbit groups.

Since the accuracy of the radar method of

measurements of individual radiants and meteor

velocities is comparatively low, the scatter of

the obtained orbital elements of meteor bodies

of the given stream is caused mainly by measurement errors. Hence we could not use the

methods elaborated by South worth and Hawkins (1963) for selecting the stream orbits from

the results of photographic measurements.

The values T, v, a, and 6 are defined from

observations. The accuracy of the measurements of AP, Aa, and A5 is known, and the

assumed scatter of T can be evaluated by the

duration of the effect of known meteor streams.

Hence the simplest way to detect meteor associations in four-dimensional space would be from

the T, v, a, and & coordinates. Application of

such a method, however, is hampered by the

variation of the radiant coordinates of the

stream during the period of its visibility.
RADAR STUDIES OF METEORS—KA8HCHETEV AND LEBEDINETS 187

Hence our selection of orbits of meteor streams

and association*, was divided into stages.

All meteors for every month were divided into

overlapping groups according to their velocities:

10-20, 15-25, . . .,60-70, 65-75 km/sec. Meteor radiants of each of the groups were roughly

reduced to the middle of the observational

intervals and were marked on individual charts.

The meteor velocity was written down next to

the appropriate radiant. Since the measurements were carried out for 5 to 10 days during

each month, the inaccuracy of reducing the

radiants to the middle of the interval did not

lead to an appreciable scattering of stream

radiants, if there were any in the given group.

Meteor associations were marked on the charts.

A mean velocity 0 was roughly determined

for each of these associations. Meteor radiants,

with velocities from 0—2.5AP to 5-}-2.5AP, were

then marked on a corresponding part of the

chart several tens of degrees on a and b in size.

In the process of such repeated markings on the

charts, some of the associations recorded earlier

stood out more clearly against the background

of sporadic meteors. Some of the associations,

on the contrary, practically coincided with the

background of sporadic meteors. Such groups

of radiants were ignored in the following investigation.

Preliminary mean orbital elements S, q, i, w,

and their theoretical deviations from the mean

Ae, &q, At, and Aw, corresponding to mean measurement errors Av, Ad, A5, were calculated for

each association. A further selection was carried out by consideration of orbital elements e,

q, i, and w. A meteor was referred to a given

association if the following conditions were

satisfied:

\e-e\<2Ae; \i-i\<2Ai,

\q—g|<2Ag; |«—w|<2A«. (8)

When the mean orbital elements were obtained,

a search for meteors belonging to the given association observed in the adjacent months was

carried out.

By applying the method described above to

the obtained catalog of orbits, we found that

3529 orbits can be related to 194 meteor streams

and associations. In table 3 we included

streams and associations for which we obtained

iV>15 orbits, as well as a number of known

streams whose orbits are known from radar and

photographic observations. The following data

are given for each association: the number, day,

and month of the beginning and the end of observations, the number of orbits obtained, mean

radiant coordinates, velocity, and orbital elements. The names of the streams, whose orbits

were obtained earlier by photographic or radar

measurements, are given in the last column.

The highest number of orbits was obtained

for Geminid (401) and Arietid (380) streams.

A large number of orbits was also obtained for

certain known streams: Southern 6 Aquarids

(151), Southern Taurids (73), Orionids (61), f

Perseids (60), 17 Aquarids (51), and Northern 5

Aquarids (50). A total of 1227 meteors belong

to these 8 streams.

For 104 streams and associations the number

of measured orbits is N> 10. Most of them are

apparently real streams where meteor bodies

have a common origin. Some of them may be

random groups of bodies with similar orbits.

Ninty-three meteors are referred to 21 small

streams and associations with N<5. A considerable number of such small groups may be

random. Among them, however, Lyrids and

a Leonids are known. The orbits of some of

the others are similar to orbits of associations

discovered by other observers.

For the Perseids, the most active stream in

photographic and visual observations, 10 orbits

in all were obtained. During our measurements of meteor activity, Perseids were practically indistinguishable against the background

of sporadic meteors. The small number of

recorded radio meteors in a stream cannot be

explained by poor detectability by radio observations of fast meteors, since a great number

of radio meteors is observed in streams having

still higher velocities, e.g., Orionids and r\

Aquarids. Evidently in the Perseids stream

there are comparatively few small meteor

bodies.

A comparison with other results

From the results of basic radar and photographic measurements, several authors obtained

more than 150 meteor streams and associations.

The orbits of 24 of them are close to the orbits

of streams and associations obtained from our

catalog. Tables 4 to 16 give for several streams
188

SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 3.—Catalog of meteor streams and associations

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

Days of

observations

14.3-15.3

14.3-23. 3

15. 4-26. 5

15. 4-25. 4

15. 4-22. 4

15. 4-25. 4

15. 4-26. 4

15. 4-25. 4

3. 5-24. 5

4. 5-27. 5

4. 5-27. 5

4.5-19.6

4. 5-27. 5

4. 5-20. 6

4. 5-27. 5

4. 5-27. 5

5. 5-27. 5

6. 5-27. 5

6. 6-20. 6

6.6-10.6

4. 7-30. 7

4. 7-29. 7

4. 7-28. 7

6. 7-31. 7

6. 7-29. 7

6. 7-14. 8

4. 7-13. 8

4. 7-13. 8

15. 7-12. 8

14. 7-14. 8

14. 7-28.7

16. 7-13. 8

3. 8-14. 8

3.8-14.8

4. 8-14. 8

21. 9-28. 9

20. 9-22. 10

21. 9-27.9

21. 9-27. 9

10. 10-21. 10

10.10-27. 10

10. 10-22. 10

10. 10-22. 10

10. 10-21. 10

10. 10-21. 10

10. 10-22. 10

10. 10-21. 10

11. 10-27. 10

11. 10-22. 10

11. 10-23. 10

9. 12-14. 12

N

5

9

86

34

16

16

18

16

30

16

43

60

17

380

16

17

51

18

33

15

17

23

41

17

23

50

13

13

34

151

23

32

18

10

15

83

73

16

21

21

13

20

17

18

15

28

24

61

18

13

401

a

172°

188

356

7

343

12

288

18

291

41

33

52

17

43

293

276

338

20

44

53

6

98

13

330

20

337

328

321

340

341

0

340

53

41

38

42

27

86

162

108

104

81

88

40

34

44

52

93

141

34

111

5

+ 3°

+ 1

+8

+ 3

+ 20

+ 10

+ 10

+ 4

+ 29

+ 23

+ 9

+ 23

+ 19

+ 23

+ 22

+ 13

+ 0.5

+ 21

+ 12

+ 7

+ 27

+ 16

+ 66

+ 2

+ 75

- 5

- 1 8

- 8

O

o

- 1 6

+ 56

- 2 6

+ 33

+57

+37

+ 20

+ 9

+ 9

+ 16

+ 15

+ 25

+ 29

+ 12

+ 15

+ 20

+ 14

+ 15

+ 16

+ 23

+ 18

+ 33

km/sec

23

30

37

31

40

29

58

27

34

27

31

30

39

39

33

33

64

33

39

37

60

40

42

35

42

42

33

35

39

41

41

42

60

60

61

43

31

63

45

66

69

58

58

33

38

42

42

66

59

30

36

a

1.95

1.94

1.27

1.32

1.42

1.55

1.92

1.66

0.89

1.94

1.68

1.61

1.64

1.66

0.78

0. 96

3.34

1.09

1.34

1.84

1.59

5. 18

1.72

0.93

3.65

2. 16

2. 12

1.92

1.38

2.04

1.09

4.31

1.45

11.0

1.52

2.98

2.07

1.52

48.0

1.90

3.58

1.69

1.48

1.74

4.05

4.46

1.74

4.76

1.36

2. 19

1.31

e

0.67

0.82

0.92

0.32

0.85

0.78

0.50

0.77

0.27

0.77

0.84

0.80

0.93

0.94

0.47

0.64

0.84

0.86

0. 95

0. 90

0.45

0.97

0.49

0.90

0.76

0.97

0.88

0.89

0.96

0.96

0.18

0.96

0.54

0.91

0.35

0.98

0.84

0.40

1.00

0.51

0.75

0.84

0.74

0.86

0.95

0.98

0.97

0.83

0.71

0.84

0.89

q

0.64

0.36

0. 10

0.22

0.21

0.34

0.95

0.39

0.65

0.44

0.27

0.31

0. 11

0. 10

0.41

0.35

0.54

0. 15

0.06

0. 18

0.88

0. 18

0.87

0.09

0.87

0.06

0.26

0.20

0.05

0.08

0.90

0. 17

0.67

0.95

0.98

0.07

0.33

0.91

0. 11

0.94

0.88

0.27

0.38

0.24

0.22

0. 11

0.05

0.57

0.39

0.36

0. 14

0?l

6

27

0.5

61

6

120

3

67

6

5

6

30

19

68

56

161

23

20

26

138

16

77

41

71

18

8

12

1.4

28

83

45

152

113

141

16

2.2

152

26

166

175

163

152

1.2

112

7

17

164

161

6

24

U

175°

356

32

30

29

30

28

210

48

54

232

71

52

77

55

55

47

57

258

257

116

297

115

115

116

128

307

120

126

307

114

303

132

136

137

198

15

2

0

23

203

201

23

22

201

22

21

25

203

205

260

83°

297

28

45

44

5'J

211

246

309

74

233

57

32

30

327

312

90

34

202

223

234

228

126

336

133

334

126

313

339

151

107

114

92

151

173

332

118

47

39

3

223

307

119

131

307

145

158

86

62

295

326

Name of

stream

a Leonids

Virginids

f 1'inwidn

AriHidn

if A(|U:in.l -

Northcrn >

Aquarids

Southern t

Aquarids

Southern 6

Aquarids

Perseids

Southern

Taurids

c Geminids

Southern

Arietids

Orionids

Northern

Taurids

Geminids
RADAR STUDIES OF METEORS KASHCHEYEV AND LEBEDINETS

TABLE 4.—Radiant and orbit of Geminids

189

Source

Authors

Whipple (1954)

McCrosky and Poeon (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Habadzhanov and Kramer (1963)

Niljwon (1964)

N

401

13

72

20

16

12

22

a

111?4

112.7

111.3

111.4

112.6

111.2

109.4

S

+32

+32.

+32.

+32.

+ 32.

+32.

+ 30.

G

4

5

5

3

4

4

i'o

36.

36.

36.

36.

36.

36.

34.

0

4

3

2

3

9

2

I/a

0.76

0.73

0.71

0.74

0.73

0.76

0.79

e

0.89

0.90

0.90

0.90

0.90

0.90

0.88

0.

0.

0.

0.

0.

0.

0.

q

14

14

14

14

14

13

15

i

23 ?7

23.9

23. 1

23.3

23.3

24.8

17.4

259 ?6

261.2

260.2

260.2

261.4

258.7

259.8

u

325 ?8

324.4

324.2

324.3

324. 1

326.2

325. 1

Mean dally motion of th« radiant according to our measurements: Aa«0*83 and M- -0T28.

Source

Autho rJ

mea n

Authors |Jun e 1?2 0

Da vies and Gill (1960)

NiUson 0964) {jjj

» ii ,.,.,... (1950 observations

Lovell (1954){,..., . (1951 observations

TABLE 5.-

N

380

18

6

8

7

—

-Radiant and orbit of Arielids

a

43 ?3

52. 1

50.0

46.1

46.6

43.8

43.4

6

+ 22?9

+ 25.1

+ 26.0

+ 26.1

+ 25.0

+ 21.9

+ 23.9

t'o

38.6

39.8

41.0

39.6

43.6

37.7

38.7

I/a

0.60

0.60

0.75

0.67

0.44

0.67

0.62

e

0.94

0.96

0.97

0.96

0.98

0.94

0.94

0.10

0.08

0.04

0.06

0.04

0. 10

0.09

i

18?7

22.8

46.0

33.4

38.9

18.0

21.0

il

76 ?6

87.4

89.0

84.8

84.6

77.0

76.8

(0

29 ?9

25.4

19.0

23.0

20.3

29.0

29.0

Mean daily motion of the radiant: ia - ? u°7 mid AJ- -rO°l.

TABLE 6.—Radiant and orbit of Northerns Aquarids

Authors

McCrosky and

Source

Posen (1961)

Southworth and Hawkins (1963)

Ceplecha et al. (1964)

N

50

2

3

1

a

336 ".8

346.0

346.7

345.4

S

-4? 9

0.0

+2.6

+ 0.8

t'o

41.8

42.2

39.8

40.9

I/a

0.46

0.38

0.41

0.30

e

0.97

0.98

0.95

0.96

q

0.06

0.08

0. 12

0. 12

i

18

14

21.

18.

'0

0

2

3

n

127

142.

143.

142.

'7

0

2

4

338e

332.

324

323.

8

5

4

4

Mean daily motion of the radiant according to our measurements: Aa= +0?9 and Ai=+0?3.

TABLE 7

Source

Authors

Katasev (1964)

McCrosky and Posen (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Babadzhanov and Kramer (1963)

Ceplecha et al. (1964)

Gill and Davies (1960)

Nilsson (1964)

.—Radiant and orbit of Southern S Aquarids

N

151

1

17

11

3

8

1

35

48

a

341?2

339.5

341.6

341. 3

338. 6

341. 6

350. 7

339.0

339. 4

&

-16! 4

-15. 2

-14 6

-14. 4

-16.7

-15.9

-13.8

-19.0

-17.3

t'o

41.2

44.3

42. 4

42.2

42. 6

40.8

40. 1

43.0

41.2

I/a

0.49

0. 18

0.35

0.36

0.40

0.37

0.32

0.44

0.43

e

0.96

0.99

0.97

0.97

0.97

0.96

0.96

0.96

0.97

q

0.08

0.07

0.08

0.08

0.07

0. 11

0. 14

0.09

0.07

i

28?4

24 0

25.0

22. 7

28.9

23.7

22.8

30.0

32.5

n

306?7

308.5

309. 2

309. 2

304 6

311.0

322. 5

304 0

305.8

w

151?1

150.6

151. 1

151. 1

153. 5

145.4

139.4

150.0

152.4

Mean daily motion of the radiant according to our measurements: Aa=0?85 and AS=+0?35.
190

SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 8.—Radiant and orbit of Southern Taurida

Source N v, l/o

Authors

Whipple (1954)

McCrosky and Posen (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Babadzhanov and Kramer (1963)

Ceplecha et al. (1964)

Nilsson (1964)

73

8

17

13

11

8

27 ?2

52.8

42.6

37.5

28.0

24.2

+ 8?6

+ 13.9

4-10.7

+ 9.6

+ 7.5

+ 6.2

30.9

30. 1

28.8

29.8

30.4

31.5

0.48

0.43

0.53

0.55

0.56

0.54

0.84

0.84

0.80

0.81

0.82

0.83

0.33

0.38

0.37

0.34

0. 32

0.33

1 28.2 +7.0 33.3 0.45 0.88 0.26

17 59.0 +16.6 25.8 0.48 0.76 0.50

5. .'»

5. 3

5. 1

5. ii

3. 4

«). 4

4 . 2

14°6

43. 3

31.2

24. 5

13.7

9.5

11.9

56. 1

118?2

111.2

114.6

117.8

122. 7

118.9

125.2

99.0

TABLE 9.—Radiant and orbit of Orionida

Source

Authors

Whipple (1954)

McCrosky and Posen (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Babadzhanov and Kramer (1963)

Ceplecha et al. (1964)

Nilsson (1964)

N

61

2

48

5

12

5

4

8

a

93? 1

95.4

94.9

95.2

95.6

95.9

90.0

96.7

S

+ 16?0

+ 15.5

+ 15.4

+ 16.0

+ 16.2

+ 20.2

+ 15.4

+ 14.4

65.9

66.3

68.2

67.6

67.6

70.7

69.4

65.3

I/a

0.21

0. 16

0. 02

0.06

0.05

0.25

0.05

0. 16

r

0.88

0. 92

1.01

0.96

0.97

1. 16

1.03

0.92

'/

0. 57

0. 54

0.58

0. 57

0.57

0.63

0.66

0.50

i

164 °2

162.9

162. 8

164.4

164.9

161.6

164.0

160.3

a

25*4

29.3

30. 9

28.6

29.2

28.7

21.2

32.3

M

86*1

87.8

80. 3

82. 3

82.8

72. 5

70.6

90.9

TABLE 10.—Radiant and orbit of f Peraeida

Source N v0 I/a

Authors

Nilsson (1964)

60

27

51 ?5

50.7

+22?9 29.8 0.62 0.80 0.31

+21. 5 29. 9 0. 59 0. 82 0. 31

5°7

4.8

70?6

70.5

57 ?0

56.3

TABLE 11.—Radiant and orbit of Southern Arietids

Source N I/a

Authors

McCrosky and Posen (1961)

Nilsson (1964)

18

13

30

39 ?6

38.8

44.8

+ 14?7

+ 10.5

+ 12.4

32.7

30.0

30.2

0.57

0.57

0.50

0.86

0.83

0.83

0.24

0.30

0.34

I'.

5.

5.

'2

8

9

22

24

33

°5

. 2

. 0

130?

122.

118.

7

5

3

TABLE 12.—Radiant and orbit of Southern i Aquarida

Source N v0 I/a

Authors

McCrosky and Posen (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

13

10

6

4

327 ?8

330.9

322.4

323.8

-17 ?

-12 .

— 14.

-14 .

8

9

8

6

33.

35.

34.

35.

4

7

4

5

0.47

0.36

0.40

0.50

0.88

0.92

0.90

0.88

0.26

0.22

0.25

0.23

7?6

4.2

3.6

1.2

306?6

310. 3

3033

301. 1

125!

129.

126.

133.

•9

6

3

5
RADAR STUDIES OF METEORS KASHCHEYEV AND LEBEDINETS

TABLE 13.—Radiant and orbit of Northern t Aquarids

191

Source

Authors

McCrosky and Posen (1961)

Jacchia and Whipplc (1961)

South worth and Hawkins (1963)

Nilason (1964)

N

13

2

2

1

3

a

320?7

332.5

332.6

323.8

326.2

6

-8?2

-5. 5

-4. 2

-6. 8

-12. 3

34.8

33.2

35.9

38.5

31.5

I/a

0.52

0.49

0.52

0.29

0.64

«

0.89

0.88

0.91

0.95

0.85

q

0.20

0.25

0. 17

0. 18

0.23

i

12 ?0

7.5

15.9

15.0

6.9

0

119T6

134.5

129.4

124 1

125.3

a

313?4

308.0

318.8

312.8

312.5

TABLE 14.—Radiant and orbit of Perteids

Souroe

Authors

Whipplc (1954)

Katascv (1964)

McCrosky and Poaen (1961)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Babadshanov and Kramer (1963)

Ceplecha et al. (1964)

N

10

12

25

44

10

9

94

15

a

4l!0

45.2

46.1

45.6

46.1

45.2

45.1

44.2

i

+ 56?6

+ 56.9

+ 57.8

+ 58.8

+ 57.8

+ 57. 1

+ 57.6

+ 57.8

00

59.9

60.7

60.3

60.2

60.2

60.6

61.1

61.2

I/O

0.09

0.05

0.12

0.02

0.05

0.04

0.04

0.01

e

0.91

0.91

0.88

0.98

0.95

0.96

1.04

0.99

q

0.95

0.95

0.96

0.94

0.95

0.95

0.95

0.96

»

113?1

114.2

113.0

112.3

112.8

113.8

112.5

112.7

0

136!5

138.5

138.7

138.5

138.5

138.0

137.8

137.5

«

150!9

152.9

150.0

151.1

150.5

150.9

150.5

151.9

TABLE 15.—Radiant and orbit of Northern Taurids

Source

Authors

Whipple (1954)

McCrosky and Poaen (1961)

Kataaev (1964)

Jacchia and Whipple (1961)

Southworth and Hawkins (1963)

Babadzhanov and Kramer (1963)

N

13

7

15

1

6

8

1

a

33 ?5

46.0

53.8

5 4 2

53.2

47.9

62.8

a

+ 18?2

+20.9

+21.6

+20.0

+21. 1

+20.5

+23.2

«o

30.5

30.6

30.9

30.7

31.2

31.9

29.2

I/a

0.46

0.42

0.43

0.45

0.42

0.48

0.48

e

0.84

0.85

0.85

0.83

0.86

0.85

a 8i

q

0.36

0.36

0.35

0.39

0.34

0.31

a 39

*

5?5

3.8

2.9

0.8

2.6

3.8

2.2

a

205?4

218.1

224 6

226.9

223.6

216. 1

234 8

u

294?6

293.1

294 6

29a 3

295.3

300.9

290.6

TABLE 16.—Radiant and orbit of Virginids

Souroe

Authors

Whipple (1954)

McCrosky and Posen (1961)

Jacchia and Whipple (1961)

Nilsson (1964)

N

9

4

5

3

3

a

188 ?2

182.3

179.4

175.6

188.5

i

+ 1?2

+ 4 4

+1.0

+0.1

-3.8

»o

30.5

31.6

28.7

29.4

34 3

Ha

0.51

0.25

0.46

a 37

0.42

e

0.82

0.90

0.80

0.83

0.89

q

0.36

0.42

0.44

0.45

0.26

»'

5?7

5.5

0.8

1.7

2.9

0

355 °.5

353.5

351.4

170.0

354 5

0)

296?9

284 0

285.4

101.9

304 3

the number of observations, radiants, velocities,

and orbital elements according to the measurements of the various authors.

We showed (1961) that, for the period of

visibility of the Geminids, a systematic variation of the velocity of the meteor stream as

well as of the eccentricity and semimajor axis

of the orbit occurs. Taking into account the

differences in the mean solar longitudes of

different observers, our measurements agree
192 SYMPOSIUM ON METEOR ORBITS AND DUST

well with photographic observations. The radiant and orbit of Geminids, obtained by

Nilsson, differ somewhat from the results of

the other authors. This is explained by Nilsson

(1964) to be the result of relatively large errors

in his measurements due to a low position of

the stream radiant above the horizon in

Adelaide.

The Arietids radiant is close to the sun;

hence the stream orbit is determined only from

radio observations. Nilsson detects two stream

branches with very close radiants but with

different velocities. Since the measurements

of Davies and Gill (1960) and also those of

Nilsson refer to the end of the period of stream

visibility (June 15 to 21), table 5 gives separately the results of our measurements from

June 17 to 20. Since measurements of individual Arietids orbits are few in number, table

5 also gives, for purposes of comparison, the

results of statistical measurements by the Clegg

method, carried out at Jodrell Bank in 1950

and 1951 (Lovell, 1954).

The radiant and the orbit of Arietids (table 5)

obtained by us are in good agreement with the

results of statistical measurements. Radiant

location obtained by Davies and Gill differs

from ours by 3°; the velocity differs by 1

km/sec, which is evidently caused by the small

number of orbits determined by Davies and

Gill, and by the comparatively low accuracy

of measurements of individual radiants and

meteor velocities by the radar method. Nilsson

overestimates the accuracy of his measurements. With such a low number of measurements (Nilsson, 1964) two simultaneously active streams, whose radiants are separated by

1° and whose velocities differ by 4 km/sec,

can hardly be distinguished.

The obtained radiant and orbit of the

Northern 8 Aquarids (table 6) agree satisfactorily with the results of quite scanty

photographic measurements.

Within the limits of scatter of the results

obtained by different authors, the radiant and

orbit of the Southern S Aquarids (table 7)

obtained by us are in satisfactory agreement

with data of photographic and radar measurements.

For the Southern Taurids a good agreement

of our results with the data of photographic

measurements is observed (table 8). The

difference of orbits obtained by Ceplecha et al.

(1964) and by Nilsson from the results of the

other authors is evidently due to the fact that

their measurements refer to the very beginning

and the end of the stream visibility, respectively.

The great scatter of data obtained by different

authors is associated apparently with the

diffusivity of the stream whose visibility period

exceeds 2 months.

Except for Badadzhanov and Kramer, all the

other authors obtained very close position* of

the radiatit of the Orionids (table 9). In spite

of a large number of measurements, the mean

velocity of the stream obtained by different

authors from photographic observations varies

within the rather wide limits of 66.3 to 70.7 km/

sec. Correspondingly, the scatter of mean a

and e values is also great. The values of v0, a,

and < for individual meteors in each of the

catalogs change within wide limits. This

scatter greatly exceeds measurement errors and

can be explained by a complex stream structure

associated with great disturbances of the parent

of the Orionids stream—Comet Halley.

Our results for the daytime stream of the f

Perseids are practically identical with those of

Nilsson (table 10). For the Southern Arietids,

the results obtained by different authors are in

satisfactory agreement (table 11).

In spite of the scantiness of photographic and

radar measurements, the results of different

authors for the streams of both Southern and

Northern t Aquarids agree satisfactorily (tables

12 and 13).

Though some of the photographic catalogs

include a large number of orbits of Perseids,

quite a large scatter of mean radiant positions

and orbital elements is observed, which apparently exceeds the errors due to the photographic

method of measurements. The scatter is very

great for individual meteors in each of the catalogs. This indicates a higher diffusivity of the

stream. Our results, within the limits of measurement accuracy, agree with the data of photographic observations (table 14).

The results of all the measurements for the

Northern Taurids are in good agreement (table

15). Within the limits of real precision of the
RADAR STUDIES OF METEORS—KA8HCHEYEV AND LEBEDINETS 193

measurements for the Virginids the results of

the different authors are in good agreement

(table 16).

Connection of meteor streams with comets

To carry out a comparison with our measurements we shall make use of the catalog (Kramer,

1953) of 280 comet radiants, computed for

comets whose orbits approach the earth's orbit

by a distance of not more than 0.3 a.u.

Out of 194 meteor streams and associations

observed by us, 14 have orbits similar to those

of 11 comets from Kramer's catalog. Table 17

presents for each of them: (1) mean radiant

coordinates, velocity, and orbital elements obtained by us; (2) comet radiant coordinates,

velocity, and comet orbital elements; and (3)

solar longitude Xo at the moment of the earth's

encounter with the comet orbit for which radiant and velocity are calculated.

Table 18 gives the orbits of Comets Giacobini-Zinner, Biela, and 1866 I, and of their

associated meteor streams, Draconids, Andromedids, and Leonids, which were not observed

by us. The orbits of streams are taken from

photographic measurements.

The data given in Tables 8, 9, 14, 15, 17,

and 18 show good agreement of orbital eleStream/comet

AquaridB

Orionlds

Comet Halley (1835 III)

Taurids

Southern Taurids

Northern Taurids

Comet Encke (1937 VI)

Lyrid8

Comet 1961 I

Perseids

Comet 1861 III

Association 45

Comet 1948 IV

Association 66

Comet 1698

Association 108

Comet 1764

Association 124

Comet 1946

Association 182

Comet 1366

Association 193

Comet 1798 II

Association 195

Comet Tootle (1926 IV)

TABLE

a

338°

93

337

94

64

27

34

85

56

272

270

41

44

34

45

338

338

57

51

41

26

124

149

163

158

190

210

17.—Data for streams and associated comets

5

0°

+ 16

0

+ 19

+ 15

+9

+ 18

+ 13

+8

+31

+34

+57

+57

+ 20

+ 28

- 9

- 8

+ 49

+45

+ 9

+4

+ 29

+31

+30

+34

+75

+ 76

64

66

67

31

31

30

32

32

48

48

60

61

38

41

66

68

59

60

67

71

68

70

64

66

34

36

e

0.84

0.88

0.97

0.85

0.84

0.84

0.85

0.84

0.98

0.91

0.96

0.95

1

0.85

1

0.77

1

0.59

1

0.60

0.90

0.81

1

0.66

0.82

7

0.54

0.57

0.59

0.34

0.33

0.36

0.33

0.92

0.92

0.95

0.95

0.22

0.21

0.65

0.73

0.70

0.56

0.98

1.02

0.98

0.98

0.81

0.78

0.89

1.02

t

161°

164

162

7

2

6

12

82

80

113

114

12

23

179

169

123

127

168

170

164

150

138

138

52

55

H

90°

86

111

243

118

295

185

216

213

151

153

307

317

104

151

108

105

22

22

164

165

249

215

224

207

n

47°

25

55

258

15

205

205

28

30

136

137

201

203

46

66

134

120

314

301

205

227

249

250

270

270

XO

43°

98

221

139

40

123

121

227

249

270
194 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 18.—Data for streams and associated comets (not observed at Kharkov)

Stream/comet

Draconidsl

Draconids *

Comet Giacobini-Zinner 1926 VI

Andromedids '

Andromcdids *

Comet Biela 1852 III

Leonids*

Leonids '

Comet 1866 I

a

271°

271

264

26

19

24

153

152

150

6

+ 47°

+ 47

+ 54

+ 32

+ 5

+ 43

+22

+ 23

+ 23

to

20

20

—

21

22

—

72

72

—

e

0.70

0.70

0.72

0.71

0.70

0.76

0.93

0.92

0.91

</

1.00

1.00

0.99

0.74

0.70

0.86

0.99

0.98

0.98

»

25°

25

31

It

0. 4

13

163

162

103

M

177°

177

172

247

74

246

174

171

171

Q

196°

IM

225

26

223

233

233

231

i Jscchia and Whippie (1901).

* South worth and Hawkins (1963).

< Whlpple (10M).

ments of comets and of their associated meteor

streams only in 4 instances: Comet 1862 III

and Perseids, Comet Giacobini-Zinner and

Draconids, Comet 1866 I and Leonids, and

Comet 1861 I and Lyrids. In all the other

cases the orbits of comets and of meteor streams

differ noticeably.

These results are quite natural if we consider

the magnitude of the encounter between comet

orbits and the earth. The earth passes close

to the orbits of the four enumerated comets.

The minimum distances between them are

0.009, 0.003, 0.007, and 0.002 a.u., respectively.

For other comets, these distances are much

larger. If the comet's orbit passes at a large

distance from the earth's orbit, the orbit of the

related stream, to be observed at the earth,

should differ noticeably from the comet's orbit.

Since a relation between a number of streams

(Andromedids, Northern and Southern Taurids,

etc.) and comets that do not suffer very close

encounters with the earth's orbit has been quite

reliably established, there are indeed differences between the orbits of comets and the

streams generated by them.

These differences may be explained by two

reasons:

1. The present orbit of a comet due to

planetary perturbations may differ appreciably

from the orbit along which the comet moved

during the generation of the stream. A partial

disruption of the comet nucleus, which caused

a stream to be generated, may also lead to a

change of the orbit.

2. Immediately after formation of the

stream it begins to be disrupted by differential

planetary perturbations, deceleration of meteor

bodies due to the Poynting-Robertson effect,

resistance of interplanetary media, etc. From

the very beginning the stream may have a complicated structure if the nucleus disruption

occurs during several returns of the comet in different orbits. All these factors lead to a considerable broadening of streams. The width

of known meteor streams, such as Perseids,

Taurids, etc., near the earth's orbit is measured

by many tens of millions of kilometers. The

earth meets only a small part of such an extensive stream of meteor bodies. In connection

with this the orbit of the stream obtained by

observation of meteors from the earth may

differ essentially from the mean orbit along

which the parent comet of the stream moved

during the process of its formation.

Distribution of orbits of meteor bodies

Figures 1 to 4 give the distribution of orbital

elements of small meteor bodies obtained by the

various authors: (a) measured distribution; (b)

distribution corrected for selectivity of radio

observations (for geometrical and physical

factors); (c) distribution corrected for geometrical, physical, and astronomical factors.

For a comparison, figures 5 to 8 give the distribution of orbital elements of larger meteor

bodies (McCrosky and Posen, 1961) generating

meteors brighter than approximately +-3 mag:

(a) measured distribution; (b) distribution of
RADAR 6TUDIE8 OF METEORS KASHCHETEV AND LEBEDINET8 195

8OO

z 400

(a)

<0.0 0.5 1.0

800

- 400

1.5 20

(b)

<0.0 0.5 1.0

•Q

1.5 20

800

.«o CL

aTM 400

E

(C)

<0.0 0 5 1.0 1.5 2.0

FICURE 1.—Distribution of orbits of small meteor bodies in

reciprocal semimajor axis.

orbital elements corrected for the dependence of

luminosity coefficient on the velocity and for

the astronomical factors. Figure 9 gives the

distribution obtained by Whipple (1954) of

semimajor axes of orbits of large meteor bodies,

generating meteors brighter than approximately

0 mag.

Let us consider the distribution of each of the

orbital elements separately.

SEMIMAJOB AXIS.—Consideration of the selectivity of the radar method of measurements and

also of the astronomical factor does not affect

practically the obtained orbit distribution in

I/a. Large meteor bodies generating meteors

brighter than 0 mag usually have a values of

the order of 5 a.u. A large number of orbits

are nearly parabolic. Smaller particles generating meteors of brightness 0 to + 3 mag usually

have orbits with a« 3 a.u. The nearly

parabolic orbits occur more rarely than in the

case of meteors brighter than 0 mag. About

6 percent of orbits have o< l a.u., and for

several a<0.56 a.u.

In the case of still smaller meteor bodies

generating meteors of brightness + 5 to +7

mag, the maximum of distribution is displaced

tooo

5 0 0

1000

o- 500

aT

0.5

q(o.u.)

(b)

IJO 1500

1000

5 0 0

-i (c)

0.5

q(o.u.)

1-0

0.5

q (a.u.)

IJO

FIGURE 3.—Distribution of orbits of small meteor bodies in

perihelion distance.

2000

Z 1000

(a)

2000

a.TM_ 1000

Q.

(b)

2000

1000

(c)

0.5

e

l.0>l 0 0.5 I.O»I 0

e

FIGURE 2.—Distribution of orbits of small meteor bodies in eccentricity.

0.5

e
196

SYMP08IUM ON METEOR ORBITS AND DUST

1000

5 0 0

(a)

1

0° 30° 60° 90° 120° 150° 180°

i

1000

500-

0° 30° 60° 90° 120° 150° 180°

1000

500

(c)

M'\

0° 30° 60° 90° 120° 150° 180°

FIGURE 4.—Distribution of orbits of small meteor bodies in

inclination.

15-

<0.0 0.5

FIGURE 5.—Distribution of orbits of large meteor bodies in

reciprocal semimajor axis.

to the region of still lower values, a«2 a.u.

About 20 percent of orbits have a<l a.u., and

several tens of orbits, a<0.56 a.u. The number

of nearly parabolic orbits is considerably less

than in the case of photographic meteors.

zoo

0 0 9 I 0>l

FICURE 6.—Distribution of orbit* of Urge meteor bodies in

eccentricity.

6OO

400

200

0

( 0 )

1

1T 1

6O0

4OO

20O

09

q(au>

0 5

FIGURE 7.—Distribution of orbits of Urge meteor bodies in

perihelion distance.

Thus, with the decrease of mass of meteor

bodies there is a systematic decrease of the

average sizes of the orbits along which they

move.

ECCENTRICITY.—Radar and photographic measurements give a nearly similar distribution of

eccentricities of meteor orbits. With a variation of e from 0 to 1, a monotonic increase of the

distribution function is observed. Correcting

for the selectivity of observations and the

astronomical factor leads to still higher increases

of the number of orbits with eccentricities of

0.9 to 1.0.

PERIHELION DISTANCE.—-The astronomical factor produces the highest effect on the measured

distribution of meteor orbits in q and i. From

radio observations we obtain a nearly even

distribution of orbits in q within the interval of

0.2<g<0.9 a.u., and two maxima occurring at

0.05<?<0.2 and 0.9<g<1.0 a.u. After consideration of selectivity of measurements and

of astronomical factor the second maximum

disappears. The distribution function increases

almost monotonically with the decrease of q

from 1.0 to 0.05 a.u.
RADAR STUDIES OF METEORS—KA6HCHBYEV AND LEBEDINETS 197

800

400

( Q )

0° 30° 60° 90° 120° 150° 180°

i

8 0 0

4 0 0

(b)

0° 30° 60° 90° 120° 150° 180°

FIGURE 8.—Distribution of orbits of large meteor bodies in

inclination.

The distribution of perihelion distances of

orbits of larger meteor bodies appears to be

essentially different. With a decrease of q from

1 to 0, a nearly monotonic decrease of distribution function occurs. The sharp maximum at

0.1<g<0.15 a.u. is caused by meteors of the

Geminids stream. The mean perihelion distance of orbits of small meteor bodies generating

meteors of brightness +5 to +7 mag appears

to be almost twice as small as for larger particles

generating meteors of brightness 0 to +3 mag.

ORBIT INCLINATION.—Radar measurements give

an almost even distribution of meteor orbits in i.

A certain increase of the number of orbits takes

place with i<30°, and a decrease within the

interval of 80°<i<105°. With the consideration of selectivity of radio observations the

number of orbits increases with small inclinations to the ecliptic plane. After consideration

of the astronomical factor the number of orbits

with i<15° sharply decreases. There are two

2 0 -

15

10-

< 0

(a.u.)

0.5 1.0

FIGUKE 9.—Distribution of orbits of large meteor bodies

(approx. 0 mag) in reciprocal semimajor axis (Whipple, 1954).

wide maxima at 15°<i<65° and 120°<i<160°.

The minimum at i«90° remains nearly the

same as with directly measured distribution.

In the case of photographic meteors the orbits

with small inclinations i<30° prevail. The

values of 5°<i<25° occur most often. The

minimum of distribution function occurs at

t«=90°, and a certain increase with

In the case of large meteor bodies the distribution in i is different for orbits with small

and large eccentricities. With e>0.8, distribution in i is almost even within the interval of

30°<i<180°. A comparatively small increase

of orbit concentration within the region of

small inclinations is observed. With e<C0.7

nearly all the orbits have small inclinations

i<30°. Such an increase of concentration to

the ecliptic plane with the decrease of eccentricity is especially typical of the orbits of the

largest meteor bodies, generating meteors

brighter than 0 mag. Out of 144 orbits given

by Whipple (1954), only 1 is in the region of

30°<i<150° and e<0.7. Meteors brighter

than +3 mag have less than 10 percent of such

orbits. At the same time about 30 percent of

radio meteors have orbits of the same type.

After consideration of the selectivity of radio

observations and astronomical factor, a con-
198

SYMPOSIUM ON METEOR ORBITS AND DUST

centration of orbits with e<0.7 is found within

the interval of inclinations of 30°<t<80° and

A comparison of orbits obtained by photographic and radar measurements permits us to

deduce a number of generalizations on the

nature of movement in the solar system of

meteor bodies of different size. From photographic observations of several hundred meteors

brighter than 0 mag, two basic types of orbits

of large meteor bodies can be distinguished:

(1) Orbits similar to those of long-period

comets; for these, high values of a, as well as

arbitrary inclinations to the ecliptic plane, are

typical. (2) Orbits similar to those of shortperiod comets; these are characterized by their

comparatively small sizes (a^5 a.u.) and

small inclinations to the ecliptic plane. A

small number of meteor bodies had an asteroidal-type orbit (low values of e and t).

When 2500 orbits of smaller meteor bodies

generating meteors brighter than -f 3 mag were

obtained, a much greater variety of orbits was

discovered. There were orbits with a< l a.u.,

nearly circular orbits, and also a small number

of orbits with low eccentricities and great

inclinations; however, the vast majority of the

orbits belonged to the above-mentioned types

(1) and (2).

Basic radar measurements carried out at

Jodrell Bank and at Kharkov revealed a third

basic type (3) of orbits characteristic of meteors

weaker than about + 5 mag. Orbits of type

(3) have small eccentricities (e<0.7) and large

inclinations (30°<i<165°). About 30 percent

of orbits obtained by radio observations belong

to this type.

An analysis of 12,500 orbits, obtained by us,

shows that the majority of small meteor bodies

moves along the orbits of a fourth type (4),

which by their shape and inclination to the

ecliptic plane are close to the orbits of shortperiod comets, but differ from them by having

considerably less perihelion distances and still

smaller sizes (a<3 a.u.). From photographic

observations such orbits were obtained for

several meteor streams (Geminids, S Aquarids,

etc.), the parent comets of which were not

discovered. In the case of small meteor bodies

orbits of type (4) are characteristic for a great

number of meteor streams and for sporadic

meteors.

The discovery of the two new types (3) and

(4) of orbits of small meteor bodies is very

important for the study of the origin and evolution of meteor matter. Two groups of comet

orbits are connected with each other since the

perturbations of Jupiter can transfer the comets

from orbits of type (1) to type (2). Orbits of

types (2) and (4) hardly ever occur among the

known greater bodies of the solar system and

are not derivatives of orbita of type (2) or

asteroid orbits.

As Da vies and Gill (1960) showed, the discovery of the basic type (3) of orbits indicates

that a considerable part of small meteor bodies

is formed on the orbits of large sizes. Under

the influence of the Poynting-Robertson effect

the sizes of their orbits gradually decrease as

the mass of meteor body decreases. During

a certain interval of time the orbit appears to

be close to that of Jupiter, and the meteor body

may suffer close encounters with Jupiter. For

large bodies this interval is longer and the

probability is great that the body will be affected

by Jupiter and thrown into the orbit of type

(2) or thrown out of the solar system. Opik

(1951) has shown that with small orbit inclination to the ecliptic plane, the "Jupiter barrier"

may be overcome only by very small meteor

bodies, generating meteors weaker than about

+ 9 mag. With large inclinations, the "Jupiter

barrier" may be overcome by some larger

particles.

The discovery of a great number of meteors

with orbits of type (4) shows that in the solar

system a great number of short-period comets

with orbits of such a type must appear. Due

to their closeness to the sun in perihelion, the

lifetime of comets in orbits of type (4) is very

short; it is evidently much shorter than the

lifetime of meteor streams generated by such

comets.

References

BABADZHANOV, P. B., and KRAMER, E. N.

1963. Methods and some results of the photographic researches of meteors. Ionosphere and Meteors, Sec. V of IGY

Program, no. 12, Publ. House Ac ad.

Sci. USSR, Moscow.
RADAR STUDIES OF METEORS KASHCHETEV AND LEBEDINETS 199

BAIRACHENKO, I. V.

1963. Physics of interaction of radio waves with

meteor trails. IGY Reports, Univ. of

Kiev, Kiev.

CEPLBCHA, Z.; JEZKOVA, M.; NOVAK, M.; RAJCHL, J.;

SEHNAL, L.; and DAVIES, J. G.

1964. Ondfejov double-station meteors during

the IGY and IGC. Bull. Astron. Inst.

Csechoslovakia, vol. 15, pp. 144-155.

DAVIES, J. G., and GILL, J. C.

1960. Radio echo measurements of the orbits of

faint sporadic meteors. Monthly Notices

Roy. Astron. Soc., vol. 121, pp. 437-462.

ELLYETT, C. l». and DAVIES, J. G.

1948. Velocity of meteors measured by diffraction

of radio waves from tails during formation. Nature, vol. 161, pp. 596-597.

GILL, J. C, and DAVIBS, J. G.

1956. A radio echo method of meteor orbit

determination. Monthly Notices Roy.

Astron. Soc., vol. 116, pp. 105-113.

GBEENHOW, J. 8.

1963. Limitations of radar techniques for the

study of meteors. In Proceedings of

the Symposium on the Astronomy and

Physics of Meteors. Smithsonian

Contr. Astrophys., vol. 7, pp. 5-17.

GREENHOW, J. S , and HALL, J. E.

1960. The importance of initial trail radius on

the apparent height and number distributions of meteor echoes. Monthly

Notices Roy. Astron. Soc., vol. 121, pp.

183-196.

HERLOFSON, N.

1948. The theory of meteor ionization. Phys.

Soc., Rep. Prog. Phys., vol. 11, pp.

444-454.

JACCHIA. L. (I., and WHIPPLE, F. L.

1961. Precision orbits of 413 photographic meteors. Smithsonian Contr. Astrophys.,

vol. 4, no. 4, pp. 97-129.

KASHCHETEV, B. L.

1963. On studies of properties of the upper

atmosphere by radar observations of

meteors. "Meteory," no. 2, Kharkov

Univ., Kharkov.

KASHCHEYEV, B. L.; DUDNIK, B. 8.; LAGUTIN, M. P.;

and LTSENKO, I. A.

1960. Instrumentation for radar observations of

meteors. "Meteory," no. 1, Kharkov

Univ., Kharkov.

KASHCHEYEV, B. L., and LEBEDINETS, V. N.

1961. Radar studies of meteor phenomena. Izd.

Akad. Nauk SSSR.

1963. The initial radius of ionized meteor trails.

In Proceedings of the Symposium on the

Astronomy and Physics of Meteors.

Smithsonian Contr. Astrophys., vol. 7,

pp. 19-22.

KASHCHETEV, B. L.; LEBEDINETS, V. N.; and LAGUTIN,

M. F.

1961. Radar determination of the orbits of individual meteors. Astron. Journ. USSR,

vol. 38, pp. 681-691.

KATASEV, L. A.

1964. Photographic Methods in Meteor Astronomy. Trans, from Russian by Israel

Program for Scientific Translations,

Jerusalem, 114 pp.

KLEIBER, I. A.

1891. Determination of Orbits of Meteor Streams.

St. Petersburg, 330 pp.

KRAMER, E. N.

1953. Cometary radiants and the association of

meteor streams with comets. Izv.

Astron. Obs. Odessa, vol. 3, pp. 163-247.

LEBEDINETS, V. N.

1963. Density of meteoric matter in the vicinity of

the earth's orbit, from radar observations

of meteors. Astron. Journ. USSR, vol.

40, pp. 719-732.

1964. On the mechanism of formation of a region

of higher atomic density with atoms of

meteoric origin at 100-110 km. In

Space Research IV, ed. by P. Muller,

North-Holland Publ. Co., Amsterdam,

pp. 553-560.

LEBEDINETS, V. N.; LAGUTIN, M. P.; and LTSENKO,

I. A.

1960. The effect of atmosphere turbulent wind

on measurements of radiants and meteor

velocities. "Meteory," no. 1, Kharkov

Univ., Kharkov.

LOVELL, A. C. B.

1954. Meteor Astronomy. Clarendon Press,

Oxford, 463 pp.

MCCROSKT, R. E., and POSEN, A.

1961. Orbital elements of photographic meteors.

Smithsonian Contr. Astrophys., vol. 4,

no. 2, pp. 15-84.

NILSSON, C. S.

1964. A southern hemisphere radio survey of

meteor streams. Australian Journ.

Phys., vol. 17, pp. 205-256.

OPIK, E. J.

1951. Collision probabilities with the planets and

the distribution of interplanetary matter. Proc. Roy. Irish Acad., vol. 54,

Ser. A, pp. 165-199.

1958. Physics of Meteor Flight in the Atmosphere,

Interscience Publ., New York, 174 pp.

SOUTHWORTH, R. B., and HAWKINS, G. S.

1963. Statistics of meteor streams. In Proceedings of the Symposium on the Astronomy

and Physics of Meteors. Smithsonian

Contr. Astrophys., vol. 7, pp. 261-285.

WHIPPLE, F. L.

1954. Photographic meteor orbits and their distribution in space. Astron. Journ., vol.

59, pp. 201-217.

Further Data Concerning the 1963 Anomalous Increase in

Radar Meteor Rates

B. A. MCINTOSH

 1

An increase in radar meteor rates during the

middle months of 1963 was observed in the

Northern Hemisphere (McIntosh and Millman, 1964) and in the Southern Hemisphere

(EUyett and Keay, 1964). The worldwide

nature of the event, the extended period of

time over which it occurred, and the fact that

the rates were proportionally higher throughout

the day make an explanation difficult.

Figure 1 shows the monthly mean diurnal

variations for May and June 1963 compared

with those of the average of 5 years (1958

through 1962). The bars indicate the standard deviation of a single year in the 5-year

average. The excess counts in 1963 exceed

the standard deviation by a factor that averages 7 times in May and 4 times in June.

Ellyett and Keay (1964) reject an extraterrestrial or an atmospheric cause and tend

to favor a man-made agency. In considering

atmospheric effects, one thinks immediately

of the "height ceiling," which is presumed to

restrict stringently the fraction of incoming

particles that can be observed by radar.

Since short-duration echoes from underdense

trails are more severely affected by the height

ceiling than long-duration echoes, a raising of

the height ceiling would explain the observation

that the increase in rates was restricted to

short-duration echoes.

Although the Ottawa radar provides no

height information, an increase in average

height should appear as an increase in average

range. From a preliminary examination of

the range data it may be said that there appears

to be a tendency for the average range of the

echoes to be higher during the middle months of

1963, as illustrated in figure 2. Each point

represents an average of 7 hours of the monthly

mean day, and the standard deviations are

those of the average of the 7-hour values. It

should be emphasized that the differences in

20 00 04 06 12 16 20 00 04 08

EASTERN STANDARD TIME

FIGURE 1.—Comparison of 1963 radar meteor counts (dashed

curve) with 5-year average rates (solid curve) for 2 typical

months during the anomalous period. Vertical bars indicate

the standard deviation of a single value in the 5-year average.

1

 National Research Council, Ottawa, Canada.

FIGURE 2.—Difference between monthly mean average range

of meteor echoes for 1963 and for combined 5-year data (1958

through 1962). Vertical bars indicate standard deviation

in the average of 7 hours in the monthly mean day.

201

24O-022 O—67- -14
202 SYMPOSIUM ON METEOR ORBITS AND DUST

average range are of the order of 3 km in 160

km, and that the statistical significance of the

values in figure 2 has not yet been determined

quantitatively. We do not have figures for

the dispersion in the 5-year mean values of

average range.

The results of Greenhow and Hall (1960)

indicate that, of the total population of meteors,

the fraction n that can be observed with a

radar of wavelength X is approximately

The attenuation of reflected power, which gives

rise to the height-ceiling effect, is

exp [-

where r0 is the initial radius of the ionized

meteor trail. If we take

where p is the atmospheric density at the height

in question, then the effect of atmospheric density on the fraction of meteors that can be observed goes approximately as p2

.

It must be noted, however, that if there is a

uniform increase in atmospheric density down

to meteor heights (such as occurs at the minimum of the sunspot cycle), there would be no

increase in the number of meteor echoes since

the entire meteor population rises in height and

the relative position of the height ceiling remains the same. Only an unusual increase in

atmospheric density in a localized height region

could contribute to an increase in rateH.

Ackno wledgmen t

A portion of the data reduction for this paper

was carried out under Duke University Contract No. DA-31-124-AROD-59.

References

ELLIOTT, C. D., and KBAY, C. 8. L.

1964. Meteors: an unexpected increase in 1963.

Science, vol. 146, p. 14&8.

GREENHOW, J. 8., and HALL, J. E.

1960. The importance of initial trail radius on the

apparent height and number distributions

of meteor echoes. Monthly Notices Roy.

Astron. Soc., vol. 121, pp. 183-196.

MCINTOSH, B. A., and MILLMAN, P. M.

1964. Radar meteor counts: anomalous increase

during 1963. Science, vol. 146, p. 1457.
Zodiacal Light as an Indicator of the Nature of the Interplanetary Matter—Past, Present, and Prospective Results

J. L. WEINBERC *

Introduction

Considerable use has been made of zodiacal

light observations over the past two decades in

an attempt to infer something of the characteristics of gas and dust in the interplanetary

space. The degree of success has been only

slightly more discouraging than that of attempts

to rationalize widely discordant zodiacal light

observations.

A number of models of the interplanetary

matter have been constructed on the basis of

families of solutions to the integral equations

describing the brightness and polarization of

the zodiacal light (e.g., Whippie and Gossner,

1949; Bohr and Siedentopf, 1953; Siedentopf,

Behr, and Elsasser, 1953). In most of the

models the degree of polarization was used

only to estimate the number density of free

electrons that contributed to the observed

brightness of the zodiacal light. The fact that

the observed polarization is considerably less

than that expected for a component of free

electrons was erroneously explained on the

grounds that the dust component is probably

unpolarized and therefore dilutes the polarization field of the electron component. On the

basis of this method one could obtain an electron

density of the order of 103 cm' 3 at the earth's

distance. The situation remained much the

same for a number of years, with principal

effort being given to redetermining, by various

techniques, the number density of free electrons

at 1 a.u.

1

 Hawaii Institute of Geophysics. Haleakala Observatory, Kula,

Hawaii.

Subsequent laboratory polarization measurements (Kloverstrom and Rense, 1952; Richter,

1962a; Borngen and Richter, 1962; Richter,

Oberender, and Wallis, 1956) and theoretical

studies (van de Hulst, 1955) suggested that

dust particles could probably account for at

least part of the polarization of the zodiacal

light, since the degree of polarization was found

to be quite large for some size distributions

and classes of particles.

Recent developments in instrumental techniques for both laboratory and field studies,

coupled with new methods of observing the

zodiacal light and the use of large computers

in problems associated with scattering theory,

have led to a new picture of the gas and dust

in the solar system, namely, relatively few

electrons (~10 cm"3 at 1 a.u.) and metallic

particles and large numbers of small dielectric

particles.

Comparison of theory and observations

The experimentally determined scattering phase

functions of Richter are in fairly good agreement with Giese's (1961) calculations of theoretical (Mie) scattering phase functions for

mixtures of spherical particles of diameter of

the order of 1 n (Borngen and Richter, 1962);

and as a follow-up to Giese's work, Giese and

Siedentopf (1962) calculated the brightness

(/J + TJ) and polarization (p) to be expected

from 4 different groups of models of the interplanetary matter in the plane of the ecliptic.

The size-distribution law was chosen to be of

the form n(a)=n(ofo)(a/ato)"k, where a is the

size parameter (circumference/wavelength), a0

203
204

SYMPOSIUM ON METEOR ORBITS AND DUST

corresponds to the smallest particles present,

and A: is a constant. The resultant distributions were compared with the observations

of Elsasser (1958) and Blackwell and Ingham

(1961a) (see fig. 1).

The first group of models consisted of six

single-component models of spherical particles

and free electrons. The metallic, dielectric,

and free-electron models of this group are shown

in figure 2. The maximum polarizations for

the dielectric component models (see figs. 2a,

2b) are associated with the Nebelbogeneffektt?

(haze bow) in the brightness and are followed

by a sharp decrease to negative polarizations

at large elongations (angular distance from the

sun). Note, also, the negative polarizations

at small elongations. The other two singlecomponent models consisted of a hypothetical

isotropically reflecting material giving no polarization and a hypothetical metal giving a low

brightness. Although our observational results

from Haleakala (see figs. 4, 5, and 6 and

Weinberg, 1964c) differ from those used by

Giese and Siedentopf, we support their conclusion that none of these single-component

models can quantitatively produce the observed

brightness and polarization of the zodiacal light.

The second and third groups consisted of

mixtures of dielectric particles and electrons,

and of mixtures of dielectric and metallic

particles and electrons, respectively. All three

models in each group had the same spatial

2511

,o2

20* 40* 60"

Elongation

FIGURE 1.—Giese and Siedentopf (1962) observational model

for the brightness (in lOth-mag stars/deg2 in Si0 (vis) units)

and polarization of the zodiacal light (Giese, 1962, fig. 7).

El.= Elsasser (1958), Bl.= Blackwell and Ingham (1961a).

density distribution law for electrons and electron densities of about 1000 and 300 cm' 1

 at

I a.u. for the second and third groups, respectively. The composite distributions of brightness and polarization are very similar for the

models in each of these groups, and we therefore show only one representative model for

each group (models I and II of fig. 3). Apart

from the strong evidence (e.g., Blackwell and

Ingham, 1961b; Gringauz et al., 1961; Bridge

et al., 1962; Beggs et al., 1964) against the

existence of an electron component of density

103 cm"8 at 1 a.u., model I predicts a degree

of polarization considerably larger than that

which we observe. We do not observe the

large degree of polarization predicted by model

II in the region 40° < « < 60° (from the inclusion of metallic dust particles), and the magnitude of the brightness distribution is too small

for all elongations. We therefore conclude that

models I and II do not satisfactorily represent

our observations.

The fourth group (one model) consisted of a

mixture of an isotropically reflecting dielectric

and a hypothetical metal. This model is the

result of a variation of parameters to reproduce

as closely as possible the observational model of

figure 1. Our results (especially at large

elongations) rule out any serious consideration

of this model.

The "Venus Flytrap" observations ot Hemenway and Soberman (1962) led Giese (1962) to

suggest another group of models, that involves

the presence of large numbers of small particles

and no electrons. Model III (see fig. 3) is an

example of one of these models. The degree

of polarization for this model is very similar

to that of model I (i.e., too large), and the

magnitude of the brightness distribution is

unquestionably too small, but it demonstrates

again that electrons are not required to produce

a significant degree of polarization.

Giese (1962) justifiably concluded that none

of their single-component models quantitatively approximate their limited (in elongation)

observational model. The lower polarization

of our observational model, however, makes it

unnecessary to postulate the existence of large

numbers of electrons or metallic particles, and

we find that one of Giese's single-component

models agrees reasonably well with the magni-
ZODIACAL LIGHT AND INTERPLANETARY MATTER—WETNBERO

Si02m=l.5

k=2.5 6*a*120

40° 80° 120°

Elongation

40c 80° I2OC

Elongation

160*

cvj I04

•

\

E 3

2 io

o

V) 9

CVJ ic r

+

IO1

1

I

i

F

k =

n

o

o^!

€m» 1.27-1.3*

2.5 2*ai|20

5xldl4Partic k S

cm3

O5m_

H S H J

15

icr CVJ

T3

'40* 80c

120° 160*

0.5

0.25

0

I01

l \ \

V

s

>

Electrons

LMJU

/3*o 0 5

1.5 I.Q.--_--i

Z-r-i -f**v .

0.5 0 *

1.6 1.5

—

Elongation

40° 80° 120° 160°

Elongation

p

0.5

0.25

0

FIGURE 2.—Surface brightness (upper curves) and degree of polarization for single-component models of the interplanetary matter

(Giese and Siedentopf, 1962; Giese, 1962, figs. 9a, b, c, e). Here no is the number density of particles at 1 a.u., m the refractive

index, a the size parameter, /5 the power dependence on the distance from the sun (~r-0), and k the slope of the distribution

of particle sizes.

tude and distribution of our results. This

model, which is compared with our observations

in figure 4, is characterized by a very steep

particle-size distribution and contains a large

number (n0=1.5X10~n particles cm"3) of

small, Rayleigh-like dielectric particles. The

size parameter for this model extends from 1 to

26, which corresponds to a range of particle

diameters of 0.17 n to 4.4 jx for 5300 A radiation.

The lack of a large haze bow in the zodiacal

light radiation indicates that large spherical

particles do not play a dominant role. A small
206 SYMPOSIUM ON METEOR ORBITS AND DUST

. o4

.o3

io2

IO1

MODEL COMPOSITION nQ

jl I IOOO Electrons, I5>

~~*\ H 305 Electrons, 3x

\ ' 5 "

\ HI No Electrons, 6xlC

V 1.8x1

'**•• .

Particles

L cm3 J

IO"15 H2 0

IO"15 H2 0

id' 3 Fe

~

12

 H2 0

D"'2 Fe

- . -

p

05

0 25

40° 80° 1204

Elongatio n

160"

FIGURE 3.—Surface brightness and degree of polarization

for multiple-component models of the interplanetary

matter (Giese, 1962, fig. 10).

!04

CM

0

to

a

»—i

IO1

\

0

L

H20

k = 4 1

os:^.

m«l.32

cm3

.05.

I -

i.6

•s

1 • '

15

^|0.50

0.25

40* 80° 120° 160°

Elongation

FIGURE 4.—Surface brightness and degree of polarization

for a model composed of a large number of small dielectric

particles (Giese, 1962, fig. 9d). The dots correspond to

the observations of Weinberg (1964c).

haze bow is associated with the small-particle

model (see fig. 4), but it could easily escape

detection. This comparison suggests that small

dielectric particles can account for the major

fraction of both the brightness and the polariza10*

10'

I • 5220 A

MSO

5300

5425

5430

5430

VISUAL

• VOUAL

1 1 1 T I

OtVARI AND A3AA0 (IMO) ,

NOM.EY (IM2)

WCINK M 0M4c)

KTCKSONIIMI*)

K M ANO SICOCNTOPf (ItOS)

OIVAMl ANO KRYLOVA (IMS)

CLSlsSCItOtS*)

FCSCNKOV 0M4 )

1 I I 1 I

1—

\

\

I

»O* »0« 40*

FIGURE 5.—Representative poct-1950 results for the surface

brightness of the zodiacal light in the plane of the ecliptic.

tion of the zodiacal light that we observe. A

more definitive test for the presence of small

particles would be the demonstration that there

exists a wavelength dependence of the polarized

component.

From this comparison of theory and observation we see the following: (1) only dielectriccomponent models produce a gegenschein effect

(see also Walter, 1958); (2) only dielectriccomponent models produce an irregular decrease

of polarization such as we observe at large

elongations; (3) for those models discussed here

only dielectric- or electron-component models

(or combinations of these) give a maximum

polarization at 6 = 70° such as we observe;

(4) metallic-component models cannot alone

account for the observed brightness and polarization ; and (5) to include more than some tens *

of electrons cm"3 at 1 a.u., we must postulate

the existence of a hypothetical nonpolarizing

dust component.

The theoretical results are based on spherical

particles because we do not yet have enough

1

 A closer estimate cannot yet be made since electrons and very small

particles are nearly equivalent in their polarisation properties.
ZODIACAL LIGHT AND INTERPLANETARY MATTER—WEINBERG 207

0.4S

04 0

ass

| 0 23

2

&0.20

| 0,5

0.10

0.05

o DUFAYCI925)

0 HURUHATA (1951)

* BEHR AND SIEDENTOPF (1953)

° ELSASSER (1958)

O DIVARI AND ASAAD (I960)

4 PETERSON (1961a) green

* PETERSON (1961a) blue

* BLACK WELL AND IN6HAM (19610)

" ROBLEY (1962)

WEINBERG (1964c)

20» 30* 40* 5 0#

6 0 70* 80 110* 120* I3O» I4O«

#

 90* 100*

ELONGATION,6 (deg)

FIGURE 6.—The degree of polarization of the zodiacal light in the plane of the ecliptic.

160*

information on the scattering properties of

mixtures of differently shaped particles. While

there appears to be some evidence (Donn and

Powell, 1963) that irregular particles, in general,

are somewhat larger than the so-called equivalent spheres for indices of refraction greater

than or equal to those of the spherical particles,

such inferences regarding the kind of particle

(i.e., dielectric versus metallic) will probably

be unaffected. In an attempt to assess whether

one is justified in applying the Mie theory

for crushed nonspherical aggregates, Little,

0'Mara, and Aller (1964) performed calculations (as per Giese and Siedentopf, 1962) using

Richter's particle-size distributions in the Mie

theory. Their findings concur with our results

on the importance of dielectric particles to the

observed zodiacal light.

Choice of an observational model

Clearly, the aforementioned method of analysis

depends most critically on the reliability of

the observations. A meaningful comparison of

theoretical scattering calculations with zodiacal

light observations can be accomplished only if

observational uncertainties are recognized.

These uncertainties, which are reflected in the

widely divergent results of zodiacal light observers, arise primarily from (1) the lack of a

rigorous method for separating the individual

components of the night-sky radiation field,

(2) the lack of a satisfactory formulation for

the effects of tropospheric scattering, (3) difficulties associated with the absolute calibration

of low light-level extended sources, and (4)

limited observational coverage in time and

over the sky. To illustrate the divergence of

zodiacal light results and the resultant difficulty in specifying the nature of the interplanetary matter, we have collected all known

zodiacal light results as of 1964 (Weinberg,

1964a).

In figure 5 representative post-1950 results

for the surface brightness of the zodiacal light

are plotted as a function of elongation in the

plane of the ecliptic. To indicate more clearly

the extent of the divergence of results, we have

chosen results only in the visible spectral region
208 SYMPOSIUM ON METEOR ORBITS AND DUST

and only in the more easily observed bright

portions. If results are included for other

wavelengths and for regions far from the sun,

the disagreement becomes worse. There are

no observations of the zodiacal light in the

ultraviolet or infrared. Of particular interest

in figure 5 are (1) the generally lower results of

the Russian observers and of Elsasser (1958),

and (2) the sharp decrease of brightness at

large elongations found by Divari and Asaad

(1960). If we forced our brightness determinations to agree with the results of Divari

and Asaad, we would find that the degree of

polarization approaches unity in some parts of

the sky. This is untenable. Furthermore,

contrary to the findings of the Russian observers, we now have conclusive evidence

(Weinberg, 1965) that the zodiacal light does

indeed extend to high ecliptic latitudes. There

is some evidence (Roach and Smith, 1964) of a

calibration error in the work of Elsasser.

In figure 6 we have plotted all known distributions of polarization in the plane of the

ecliptic. Of particular interest are the large

polarizations found by Blackwell and Ingham

(1961a) and by Elsasser (1958). Unpublished

results by Ney (1964) indicate general agreement with our polarization results from Haleakala (Weinberg, 1964c). Since inferences from

the aforementioned scattering calculations are

very sensitive to the magnitude and distribution

of the polarization, the nature of these polarization discrepancies is particularly important.

In an attempt to rationalize these differences,

we have made polarization measurements by

various techniques using different sources of

laboratory and field calibrations, and the common difficulty is always that of the separation

of the zodiacal light from the total radiation

field. The importance of wavelength discrimination (i.e., avoiding the principal airglow emission lines) is magnified by our recent finding at

Haleakala that there are nonzodiacal light

sources of polarization (both astronomical and

atmospheric) in the night-sky radiation. In

particular, we have found small polarizations

(several percent and less) associated with the

5577-A and 6300-A airglow lines. It does not

concern us here (nor does it concern the instrument) whether the polarization arises from the

process of line formation or from atmospheric

scattering (or from both). The salient fact is

that although the degree of polarization is

small, these lines are "bright," and a significant

amount of polarized light will be measured by

instruments whose bandpasses admit (and this

includes many instruments) these airglow line

radiations.

In view of this result, of the inherent difficulty

in measuring low light levels, and of the number

of factors involved in each set of measurements

(instrument bandpass, time, place and duration

of observation, measurement and analysis

technique, calibration, etc.), it is (>erhaps

remarkable that the disagreement is as small as

it is.

Recent results

ZODIACAL LIGHT AT LARGE ELONGATIONS.—A

year ago (Weinberg, 1964b), I reported that

while we had found in our observations through

1962 some cases of negative polarization at large

distances from the sun in the plane of the

ecliptic, the low polarization in this region made

it extremely difficult to obtain accurate quantitative results. Its importance for interpretation of the nature of the zodiacal material led

us to modify our observing techniques and to

conduct a concentrated study of this region in

an effort to obtain accurate observational

results.

Measurements were made on top of Haleakala

during 17 nights between October 1963 and

October 1964 with the instrument (Weinberg,

1964c) fixed in the zenith.3 The detailed results are still being analyzed, but we are able to

present preliminary results on the observed

brightness (#obi), the orientation of the plane

of polarization (x*) for the E vector, and the

degree of polarization (Pt©t) for one night's

study (October 4-5, 1964) as observed at the

base of the atmosphere (fig. 7). Of particular

interest are the fluctuations of x* and the nature

of the distribution of Ptot . The enhancement

starting at approximately 0510 is associated

with astronomical dawn.

There are two principal sources of the variation of x*: statistical fluctuation noise associated

1

 Contrary to recent remarks In the literature, accurate measurements

of the Stokes' parameters of the lodiacal light at large elongations ecu be

made from the ground if these regions are observed far from the Milky

Way when they are at or near the zenith where the airglow Is ftint(er)

and extinction and scattering are much reduced.
ZODIACAL LIGHT AND INTERPLANETARY MATTER—WEINBERG 209

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160

140

120

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1900 2000 2100 2200 2300 0000 0100 0200

LOCAL TIME (HST)

0300 0400 0500

FIGURE 7.—Brightness and polarization parameters as measured at the zenith October 4-5, 1964.

with uncertainties resulting from the nearness to

zero polarization where x* is not defined (note,

especially, the region between 2230 and 0200);

and as yet unexplained structure near the

plane of the ecliptic (as seen in the zenith at

approximately 0300). In the interval 2230 to

0200 HST the ecliptic latitude and elongation

(0, «) vary from 26°, 150° to 6°, 148°. At 0330

the coordinates are 0°,128°.

The small and slowly varying degree of

polarization is characteristic of this region of

the sky, and, while we (and R. D. Wolstencroft,

1965, private communication) have again found

some cases of negative polarization, it was

always of small magnitude. These results and

the fact that it is difficult to determine the

polarization at large elongations provide further

evidence that relatively few large dielectric

particles contribute to the observed zodiacal

light.

ZODIACAL LIGHT AT HIGH ECLIPTIC LATITUDES.—

Preliminary results and some description of

the difficulties associated with both the measurement and analysis of the night-sky radiation at

high ecliptic latitudes have been given by

Beggs et al. (1964), Weinberg (1964c), Divari,

Krylova, and Moroz (1964), and Smith, Roach,
210 SYMPOSIUM ON METEOR ORBITS AND DUST

and Owen (1965). As we would expect, the

divergence of results increases rapidly as we

move toward high ecliptic latitudes.

Contrary to the results of most Russian

observers, there is now considerable evidence

for an appreciable polarization in regions far

from the ecliptic. Recent broad-band studies

of the zodiacal light at high latitudes by Beggs

et al. (1964) are in agreement with our findings

on the measured polarization of the nightsky, but in disagreement with the inferred

polarization of the zodiacal light in these

regions.

In a recent result (Weinberg, 1965) we have

shown that the principal component of the

polarization far from the ecliptic is associated

with the zodiacal light. This is not at all

an obvious conclusion, since, as previously

mentioned, we have found nonzodiacal light

sources of polarization in the night-sky radiation. One of these components, which is

associated with the starlight at low galactic

latitudes, manifests itself as a rotation of the

plane of polarization as we scan through these

regions. R. D. Wolstencroft (1965, private

communication) reports that he has recently

found similar results at low galactic latitudes.

This component of polarization in conjunction

with the distribution of starlight at low galactic

latitudes (Weinberg, in preparation) offers

some hope of separating the starlight into its

components: integrated starlight and galactic

light.

Smith, Roach, and Owen (1965) have recently

given an isophotal map of the brightness of

the zodiacal light over the sky. Their results

are discussed by one of the authors (Roach,

see pp. 225-226), and we only remark here

that we (Wolstencroft and I) do not confirm

some of the details in the map—in particular, the so-called photometric perturbation

at 65° from the sun at high ecliptic latitudes.

Conclusion

Investigations of the zodiacal light have dealt

primarily with the brightness and polarization

averaged over the period during which observations were obtained. There has not been a

detailed analysis of fluctuations in the zodiacal

light radiation field. This is due, in part, to

the lack of accurate polarimetric observations

until recent years, and, of more importance,

to the lack of a method for separating diurnal

variations of the airglow from zodiacal light

fluctuations. Simultaneous, long-term studies

of the zodiacal light and of the principal airglow

radiations are now being carried out at the

Haleakala Observatory in an attempt to analyze

fluctuations in the night-sky radiation.

The apparent concentration of dust about

the earth (de Jager, 1955; Beard, 1959; Singer,

1961; Whipple, 1961; Hibbs, 1961; and others)

is based on a comparison of zodiacal light

results and direct measurements. It is interesting to note that if submicron dielectric particles

exist in the quantity predicted by Giese's

(1963) model (fig. 4), the geocentric concentration for these particles may be only a factor

of 10.

As we have shown, it is meaningless to use an

average of zodiacal light observations for comparison with results of theoretical and laboratory studies of the scattering by microscopic

particles. Recent findings on some of the

reasons for the wide divergence in zodiacal light

results should soon lead to better agreement on

results in the ecliptic and at high ecliptic

latitudes, and to preliminary results on the

wavelength dependence of the polarized component. The night-sky radiation field is dominated by terrestrial radiations (atomic and

molecular) to the extent that observations have

been made of the zodiacal light only in a small

number of narrow wavelength intervals in the

visible part of the spectrum. This fact, in

conjunction with the wide divergence in existing

observations and the lack of ultraviolet and

infrared observations, necessarily precludes our

finding the wavelength dependence on the basis

of existing observations.

We do not share the current widespread

belief that observations from a satellite will

reduce to insignificance those difficulties associated with ground-based observations of the

zodiacal light. There are, however, a number

of observations that can be accomplished only

from a satellite, e.g., ultraviolet and infrared

studies, and observations close to the sun using

an external system, not the earth, to occult

the solar disk. The first satellite observations

of the zodiacal light are now being processed at
ZODIACAL LIGHT AND INTERPLANETARY MATTER—WEINBERO 211

the University of Minnesota by Ney and his

associates.

Further information on the small, solid

particles in the solar system should be forthcoming from studies of doppler shifts of Fraunhofer absorption lines in the spectrum of

zodiacal light (Ring et al . 1964), of thermal

radiation by interplanetary dust (Peterson,

1961b, 1963a, 1964; Harwit, 1964; and others),

and, we hope, of further scattering calculations

as a function of wavelength for spherical and

irregular particles.

Acknowledgment

This research was supported by the National

Aeronautics and Space Administration under

grant NsG-676.

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1964. Further observations of the zodiacal light

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Abstract

A brief summary is given of the current status of zodiacal light research with emphasis on the interpretation in

terms of small solid particles in the solar system. Recent observations are presented which provide further evidence

di aT1St6nC e ° f larg G nUmber s ° f sma1 1 dielectri c Particles as the principal constituents responsible for the observed
Conditions of Encounter between Dust and the Planets

C. W. MCCRACKEN *

Introduction

Dust-particle sensors on spacecraft for direct

measurements of the speeds and directions of

motion of small dust particles with masses

m > 10 " " g have been developed during the

past few years. These sensors were designed

for the study of interplanetary dust particles

for which the force of solar radiation is not

negligible in comparison with the force of solar

gravity. The range of sensitivity of the sensors

extends into the region of particle size where

dust particles can be blown out of the solar

system by sunlight.

The effects of solar-radiation pressure must

therefore be included when the measured

speeds and radiants of small dust particles are

used in computing the orbits. Evaluation of

these effects requires an investigation of the

conditions of encounter between a planet and

interplanetary dust particles for which radiation

pressure modifies the heliocentric orbital speeds.

These conditions also have an important bearing

on the problem of the enhanced flux of small

dust particles measured in the vicinity of the

earth and possibly existing also near the other

planets.

Earth's dust belt

The flux of small dust particles measured in

the vicinity of the earth from rockets and

satellites is higher than would be expected if

radiation pressure were neglected and the

orbits of small interplanetary dust particles

were assumed to be similar to those of larger,

meteor-producing meteoroids. This enhancement of the flux of small dust particles has been

called a dust blanket by Beard (1959), a dust

1

 Goddard Space Flight Center, National Aeronautics and Space

Administration, Oreenbelt, Md.

belt by Whipple (1961), and a dust shell by

Singer (1961). From existing data we are

unable to distinguish the various models envisioned by these and other investigators. A

knowledge of the geocentric trajectories is

critical in discussions of the nature and origin

of the earth's dust belt. Referring to the

phenomenon as an enhancement of the flux

of small dust particles in the vicinity of the

earth carries few implications about the currently unknown geocentric trajectories of the

dust particles and, more importantly, permits

close contact with the available observational

data.

The rate at which information can be

obtained with a satellite-borne dust-particle

sensor is increased by the enhancement of the

flux of small dust particles near the earth. At

the same time, the complicated geocentric

trajectories responsible for this phenomenon

make the experimental determination of the

orbits of the small dust particles more difficult

than for meteoroids.

The geocentric enhancement of the flux of

small dust particles is shown in figure 1,

which is a cumulative flux distribution expressed in terms of the particle mass. The

numerical data in figure 1 are given in table 1.

The data selected are considered to be representative of the available data, although

figure 1 is a corrected version of a rather outdated figure that was presented in an earlier

paper (McCracken and Dubin, 1964).

The geocentric enhancement of the flux of

small dust particles is revealed by plotting in

figure 1 the cumulative flux distributions for

two different regions of space. The data from

studies of the zodiacal light, meteors, and the

213
214 8YMPO8IUM ON METEOR ORBITS AND DUST

-14 -12 -10 -• -6 -4 -7 0 7 4

LOG PARTICLE MASS (g)

FIGURE 1.—Cumulative flux distribution compiled from the

data in table 1 to show the enhancement of the flux of small

dust particles in the vicinity of the earth.

frequency of meteorite falls are used to represent the flux of dust particles and meteoroids

at the earth's distance from the sun but in

regions removed from the earth. The direct

measurements made in the vicinity of the earth

are used to represent the flux near the earth.

The flux of meteoroids is essentially the same

for both regions of space, since the known distributions of orbits and the high speeds of

encounter (20 to 40 km/sec, on the average, as

determined by radar and photographic studies

of meteors) preclude any appreciable geocentric

enhancement of the flux of meteoroids. The

flux of 10"8 particles/m2/sec/2T ster for meteoroids with masses m~1.3X10~6

 g, observed by

Elford, Hawkins, and Southworth (1964) by

means of radar, indicates that no measurable

geocentric enhancement of the flux occurs for

the faint radar meteors.

Comparison of the flux in interplanetary

space with the higher flux measured in the

vicinity of the earth leads to the conclusion

that a geocentric enhancement of the flux of

small dust particles exists. The degree of this

enhancement and the particle mass at which

the flux begins to increase both depend on

which of the various size distributions derived

from studies of the zodiacal light and solar F

corona is used to represent the flux of small

dust particles in interplanetary space. The

size distribution derived by Ingham (1961) and

shown in figure 1 represents the best fit to the

distribution of surface brightness of the zodiacal

light that was observed by Ingham and Blackwell. This size distribution, if extended to

smaller sizes of dust particles, is in good agreement with the size distribution of small dielectric spheres (water ice) used by Giese (1962)

in calculating models for the zodiacal light.

The photoelectric observations of the surface

brightness and polarization of the zodiacal light

reported by Weinberg (1964) are fitted more

closely by the size distribution given by Giese

than by any of the other size distributions that

have been suggested. The size distribution

given by Elsfisser (1954) has subsequently been

altered and was included in figure 1 only to

indicate the desirability of a smooth transition

between the cumulative flux distribution for

the zodiacal dust particles and the one for the

radar meteors.

The geocentric enhancement of the flux of

small dust particles, as shown in figure 1, begins to appear at a particle mass between 10"e

and 10~7 g and reaches a maximum (~10* enhancement) for dust particles with masses in

the neighborhood of m~10~u g. This suggests that some nongravitational force, such

as that of solar-radiation pressure, may play

an important role in this phenomenon. If so,

similar enhancements of flux can be expected

to exist in the vicinity of other planets. Investigation of this possibility again requires

that radiation pressure be included in the conditions of encounter between small interplanetary dust particles and the planets.

The following sections are devoted to an

approximate treatment of the conditions of

encounter between the planets and small interplanetary dust particles. Solar-radiation pressure is included in the treatment, but other
ENCOUNTER BETWEEN DUST AND THE PLANETS—M'CRACKEN

TABLE 1.—Selected observational data on the mass distribution of interplanetary dust particles

215

Type of observation

Meteor observations

Meteorite collections

Zodiacal light studies

Direct measurements

Source

Watson (1956)

Millman and Burland (1956) [in

McKinley (1961,

p. 110)1

Hawkins and Upton

(1958)

Hawkins (1959)

Kaiser (1961)

Brown (1960, 1961)

Elsasser (1954)

Ingham (1961)

McCrackcn, Alexandcr, and Dubin

(1961)

Equation of distribution41

log N(M.) =

logJV(M.) =

log N(M,) =

log N{M.) =

logAr(M,) =

logAT(M.) =

log N(Mr) =

log N(m) -

log /(«)

log /(«)

log /(m) - -

5. 88+0. 4M,

6.3 +0. 4Af,

6.0 +0. 50M,

6.0 +0. 57M,

4. 93+0. 538M,

4 52+0. 4Af,

4.86+0. 468Mr

3. 5 - 0. 8 log TO

-14. 32-2. 5 log a

-16. 38-3. Ologa

- 17. 30-1. 70 log m

Range of validity

-3<M,<10

3<M,<10

0<M,<3

-10<M,<0

0<M,<4 1

-10<M,<- 3

8<Mr<10. 8

10*<TO<10»g

2M<«<0 . 2 cm

0. 4M<«

10->»<TO<10-«g

*N( > -cumulative accretion raU In part teles/ear th/d*y, /( )-cumulative flux in particles/m>/sec/2r ster, M,

tude, A/r=A/., m»particle maa» In t. »-partlcle radius in cm.

. visual magnitude, M, = radar raagninongravitational forces such as corpuscular

drag, coulomb drag, and Lorentz forces are

neglected in this first-order approximation.

Any force that eflFectively reduces the central

gravitational force exerted by the sun can produce effects on the motion of a small dust particle similar to the effect of radiation pressure.

Equations of motion and Poynting-Robertson effect

The equations used here provide a convenient

means for introducing parameters needed in the

discussion. The scalar equations of motion

given by Robertson (1937) or by Wyatt and

Whipple (1950) form a convenient starting point.

Expressed in polar coordinates (r, 8), the

equations fgr the heliocentric motion of a dust

particle of mass m moving in the combined

gravitational and radiation fields of the sun of

mass

and

where

are

0 is the constant of gravity, Lo is the luminosity

of the sun, c is the speed, of light, 6 is the mass

density of the dust particle, and 8 is the particle

radius (all measured in cgs units). The parameter Qpr is the radiation-pressure efficiency

factor defined by

where Cpr is the cross-sectional area of the dust

particle effective in intercepting sunlight to produce radiation pressure on the dust particle.

The magnitude of the force of radiation is

FT=u(r)CpT, where u(r) is the energy density of

sunlight at a heliocentric distance r. The magnitude of the force of gravity is

„ _nm

t— ^ •

A dimensionless parameter 0, defined as

IF-GH*-* * *•*•»

p

 Ft os

UK-3MS <-—>

- v , -• j 3X« Q Vpr

c, ti=6MQ, and «=jg^-^- '

will be used extensively throughout the following discussions. The parameter 0 is simply the

magnitude of the force of radiation measured in

units of the force of gravity. Both the flux of

sunlight and the force of solar gravity vary inversely as the square of the distance from the
216

SYMPOSIUM ON METEOR ORBITS AND DUST

sun; hence, the parameter 0 is independent of

the heliocentric distance. Other nongravitational forces could be introduced at this point

by using an additional parameter /3' that would

not (in general) be independent of the heliocentric distance. By substituting the appropriate numerical values for the various constants, we obtain

0=5.78X10-i^ ,

The equations of motion may also be written

in terms of the dimensionless parameter /3 as

<Pr (dff\* M.M/3/ , ldr\ M 0 1 dr

dt*~r \dt) ~ ~?+^ V ~~c Itrl* ~c Jt

and

1 ^ / _^§f

rdt\ dt)~ r2

dt)~ c dt

since 0 and a are related by the expression

in the radiation pressure exerted on the dust

particle. The terms

vfi 1 dr A nfirde

-=• - -j-. and -r - -r. r* c dt r c dt

represent the radial and tangential components,

respectively, of the acceleration produced by

this drag force. The equations of motion

given previously are correct to the first order

in the ratio of the speed of the dust particle to

the speed of light. The problem was first

formulated correctly by Robertson (1937), who

used a relativistic treatment in order to derive

the generalized equations of motion. The action of sunlight, which effectively reduces the

central gravitational force of attraction by the

sun and gives rise to the nonconservative drag

force, is called the Poynting-Robertson effect.

The energy and angular momentum no

longer constitute constants of motion because

of the presence of the nonconservative drag

force introduced by radiation pressure. Integration of the angular equation of motion

yields

Radiation pressure produces several effects

on the motion of a small dust particle. A dust

particle moving in a heliocentric orbit receives

sunlight from a source that is moving relative to

the dust particle, so the incident sunlight

undergoes aberration through a small angle

r dO

v

 c dt

which can be neglected in a first approximation.

The component of motion of the dust particle

along the position vector of the dust particle

causes sunlight of frequency v to be shifted

through the doppler effect to a new frequency

v' given by

' (i 1

—v dr\ I 1 -j )•

\ c dt)

The radial motion of the dust particle and the

shift in frequency of the incident sunlight produce a corresponding change in the energy

density of the intercepted radiation and, hence,

at

where h is the angular momentum (per unit

mass) of the dust particle and /<,, is the value

of h at some epoch, t=U. As time t (or 6)

increases, the angular momentum decreases.

Since the dust particle loses angular momentum

and energy of motion, it spirals toward the sun.

The dynamical evolution of the orbits of

meteoroids under the Poynting-Robertson effect

has been considered by Wyatt and Whipple

(1950) for elliptic orbits as well as for the circular orbits considered by Robertson (1937).

By dropping the small terms in

Idr .rdd

- -j-. and - jc dt c dt

from the equations of motion, we obtain

and

df 4

dt
ENCOUNTER BETWEEN DUST AND THE PLANETS M'CRACKEN 217

The radial equation of motion now displays

only the action of solar-radiation pressure in

effectively reducing the central force of gravity.

A value 0 > 1 makes the right-hand side of this

equation positive and causes the central force to

become one of repulsion. A dust particle for

which 0 > 1 will be blown out of the solar system

by radiation pressure, while one for which 0= 1

will not be subject to any acceleration by

the sun.

Integration of these approximate equations

of motion yields the orbital speed v of the dust

particle as

log PARTICLE MASS.I g (8«2.5g/cm9)

-8 -6 -4 -2

where a is the semimajor axis of the orbit of the

dust particle. Comparison with the analogous

equation

for a dust particle sufficiently large so that 0 = 0

shows that radiation pressure reduces the orbital

speed of a small dust particle below that for the

purely gravitational case. A small dust particle

moving in a planet-like orbit moves more slowly

than the planet and therefore has a nonzero

speed relative to the planet. This effect was

noted by Poynting in 1912, soon after the

existence of radiation pressure had been experimentally verified.

An assumption commonly used in simplified

treatments of this type is that a dust particle is

perfectly absorbing and absorbs sunlight over

an area equal to the geometric cross-sectional

area of the particle. Values of 0 computed

under this assumption (Qpr=l) are shown

graphically in figure 2 for various values of the

mass density 5 and particle radius s. As was

noted previously, a value 0>1 means that the

dust particle will be blown out of the solar

system by radiation pressure. The values

0= 1 occur in figure 2 for particle radii 8~1 n,

which are comparable to the wavelength of

sunlight (~0.55 n). The assumption that

classical optics could be used to compute 0

fails. The radiation-pressure efficiency factor

Qpr (and hence 0) is one of the parameters that

can be computed through use of the Mie theory

of light scattering by spherical particles of

0.001

-5 -4 -3

log PARTICLE RADIUS,

-2 -I

FIGURE 2.—Dependence of the ratio (0) of the force of radiation to the force of gravity on the »ize and mass density of a

dust particle.

arbitrary size and known index of refraction.

It is unlikely that interplanetary dust particles

are isotropic homogeneous spheres, but at

present we have no alternative in computing the

values of 0 but to assume a composition for

which the index of refraction is known and to

use the Mie theory for computing Qpr.

Further treatment of the rather complicated

relations among particle mass or size, mass

density, composition, structure, shape, and the

parameter 0 is beyond the scope of this work.

An extensive treatment of the Mie theory can

be found in van de Hulst (1957). The important points in the present discussion can be

adequately illustrated if we take QpT=\ and

use figure 2 to relate 0 to the physical parameters of the dust particles. A scale of particle

mass computed for a mass density of 5=2.5

g/cm3 has been added along the top border in

figure 2 for this purpose.

The direct measurements apply for dust particles with masses m<10~7

 g. Figure 2 shows

that such dust particles have values of 0>O.l

for any of the values of mass density 6 that are

represented. A value 0=0.01 might be considered to be negligible in comparison with

unity, but such a value applies only for the

upper end of the range of particle mass encompassed by the direct measurements. The majority of the direct measurements apply for

dust particles with masses between about 10~n

and 10"8 g. A dust particle with a mass m=

240-022 O—67- -15
218

SYMPOSIUM ON METEOR ORBITS AND DUST

10-" g and a mass density 5=2.5 g/cm3 has a

radius of about 1 M and, from figure 2, a value

of 0 = 0.23, which is hardly negligible compared

to unity.

The dependence of the speed at encounter

(entry of the dust particle into the sphere of

influence of a planet) on the value of 0 as the

mass of the dust particle is varied from m~lO~7

g down to any limits (0=1) set by radiation

pressure must be emphasized. The treatment

is approximate because of the simplifying

assumptions made in relating 0 to the particle

mass or the particle size. It is also approximate to the extent that we follow the heliocentric motion of a dust particle by using the twobody equations of motion presented earlier with

radiation pressure included. As the dust particle enters the planet's sphere of influence,

gravitational control is transferred to the planet,

and the motion of the dust particle in the region

of the planet is treated as a two-body problem.

The small tangential drag force produced by

radiation pressure can be neglected during an

encounter but should be included in the motion

of a dust particle between encounters.

The orbital speed of a dust particle at encounter is given by

in which the semimajor axis a of the heliocentric

orbit of the dust particle is measured in units of

the semimajor axis a0 of the planet's orbit

(assumed to be circular), and

The notation used here is that employed by

Opik (1951). The relative speed can then be

found by vector addition of the velocity of the

dust particle and the velocity of the planet.

Alternatively, and much more simply, the

problem can be formulated as a Jacobi threebody problem with radiation pressure included.

The speed U of the dust particle at encounter

(measured relative to the planet and expressed

in units of the circular speed vt of the planet)

is given by

U*=(jy=l -2(1 -fi)l/1A(l-f)]in cost

where e is the eccentricity of the heliocentric

orbit of the dust particle, and t is the inclination

of the heliocentric orbit of the dust particle

measured relative to the plane of the planet's

orbit. If we set t=0° and replace A by Q,

where

Q=A(l-e), q=a(l-e), and $=£»

we obtain

U*=l-2(l-0)x/>lQ(l+e)Yn

This expression reduces to the quadratic equation

U*=l-2(l-0y»(l+ey»+(l-(JHl+e)

for encounter at the perihelion passage (Q=l)

of the dust particle, and has the root

Now, U=0 for 0=0o, where 0o and e are related

by the expression

1

0o=l -

1+e

The ranges of ft, and e for which U=0 can

occur, when radiation pressure is included, are

0<&,<0.5, 0<e<l, (elliptic orbits)

/So=O.5, e=l, (parabolic orbits)

O.5<0O< 1, e> 1 • (hyperbolic orbits)

Circular heliocentric orbits (<=0) give U=0

only for 0=0, which applies to dust particles

considerably larger than those studied through

the direct-measurement technique. Figure 3

shows U (or v/ve) as a function of 0 for circular

orbits and for several values of the inclination.
ENCOUNTER BETWEEN DUST AND THE PLANETS—M'CRACKEN 210

The ordinate on the right will be explained and

used later. It should be noted that small dust

particles with ,J ><).<) 1 and planet-like orbits do

not have particularly low speeds of encounter

(even for zero inclination) when the effect of

radiation pressure on the orbital speed of a dust

particle is included.

Figure 4 gives U (or v/ve) as a function of

0 for two values of eccentricity t arbitrarily

chosen such that ,*„ falls in the range of particle size (0>O.O1) encompassed by the direct

measurements. Figures 3 and 4 show that very

low speeds of encounter between planets and

small dust particles can occur for dust particles

with noncircular heliocentric orbits of fairly

low inclination. Further calculations show

that the singular solutions illustrated in figure

4 are but two of an entire class of orbits for

which small dust particles can have low speeds

at encounter. Figure 5 shows the (A~l

f

 e)

domain in which the clear areas contain values

of A and e for which planetary encounters are

possible. Representative values of 0O are noted

along the line for perihelion intercepts. The

class of singular solutions that gives U=0 for

t = 0° forms a line singularity. An eccentricity

£^0.01 is required for &> to fall in the range

(0>O.O1, m^l0~7g) encompassed by the direct

measurements. The entire class of orbits for

which t^5° and e^O.Ol provides small dust

particles that have low speeds at encounter near

the perihelion passage of a dust particle. The

action of radiation pressure in reducing the perihelion distance of a dust particle through the

OOOOI 1.0

0 001

FIGURE 3.—Dependence on particle size (or 0) of the speed at

encounter for dust particles and a planet when both are

moving in circular heliocentric orbits.

FIGURE 4a,b.—Two examples of the dependence on particle

size (or 0) of the speed at encounter for a planet moving in a

circular orbit and dust particles moving in elliptic heliocentric orbits.

Poynting-Robertson effect further serves to

move orbits of low inclination continuously into

position for the low-speed encounters to occur.

The line singularity appearing at Q=l in the

(.A"1, e) domain for i=0° presents no problem

regarding an "infinite" enhancement of the flux

in the vicinity of a planet, because the number

of dust particles with such orbits is finite. The

orbits of primary interest in the problem of the

enhanced flux near a planet are those in the

neighborhood of the line Q=l in the (A~l, e)

domain for i=0 ° and having 0.1<e<l.

The component of U normal to the plane of

the planetary orbit is given by

Ut=±(l-0)1/i[A(l-e*)]m sin i;

hence, as i increases from 0° a nonvanishing

component is added to U fairly rapidly through

the dependence of Ut on sin i. The factor

(1—0)1/2 broadens the range of i over which
220 SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 5.—The (A~x, e) domain showing the orbits for which

planetary encounters are possible and the line singularity

next to which are clustered the orbits that yield very low

speeds of encounter for small dust particles in orbits of low

inclination.

a given small value of Uz can be obtained.

The component of U along the heliocentric

position vector of a dust particle is

Uz= ± (1-

A nonvanishing component is added to U fairly

rapidly as Q is reduced below 1. Again, the

factor (1— 0)1/2 reduces the magnitude of the

nonvanishing component. Evaluation of the

degree of enhancement of the flux of small dust

particles that will occur near a planet therefore

requires an integration over the orbital elements

a, e, and i as well as over a size distribution or a

distribution of the values of 0 for the dust

particles encountered by the planet. I have

not yet succeeded in performing this integration.

The action of radiation pressure in reducing

the orbital speed of a small dust particle also

affects the apparent radiant of the dust particle.

If the size of a dust particle is varied so that the

value of 0 crosses a singularity of the type

shown for i 0° in figure 4, the radiant of the

dust particle is shifted by 180°. Dust particles

having orbits with e>0, i = 0°, and 0</3o appear

to overtake the planet, while those in similar

orbits but having 0>0o appear to be overtaken

by the planet. If a planet encounters a cloud

of dust particles all with similar orbits of low

inclination and a distribution of values of 0

encompassing the value of #, appropriate for the

eccentricity of the orbits, the dust particles can

appear to enter the planet's sphere of influence

from all directions. Such a cloud of dust

particles would, of course, be in the process of

dispersing because of the differential effects of

radiation pressure on the heliocentric orbits

of the dust particles.

The effects of radiation pressure on the

conditions of encounter described in the preceding paragraphs apply also to the small dust

particles detected by a dust-particle sensor

mounted on an interplanetary probe such as

Mariner 4. The effects of radiation pressure

on the speeds and radiants of the dust particles

detected by such an instrument need to be

investigated in greater detail.

The effect of radiation pressure on the accretion process has some implications (the importance of which has not yet been investigated)

regarding the formation of planetesiraals in a

rotating circumstellar nebula out of which a

star forms. As a newly formed star becomes

luminous and clears away the gas in the nebula,

the small dust particles that are not blown away

by radiation pressure assume Keplerian orbits

about the star. The accretion process may

then change because of the differential effects of

radiation pressure on the planetesimals and the

smaller dust particles being accreted by the

planetesimals. The solar system is in a stage

somewhat analogous to the latter. The nebular

gas is gone, so the planets are now accreting

small dust particles that have their heliocentric

motion modified by radiation pressure and the

radial flow of the solar wind.

Gravitational enhancement of the flux of

interplanetary dust particles

The geocentric enhancement of the flux of small

dust particles has been the subject of considerable discussion both before and after its exist-
ENCOUNTER BETWEEN DUST AND THE PLANETS—M'CRACKEN 221

ence was recognized in the results obtained with

dust-particle sensors flown on rockets and satellites. Whipple (1961) suggested that the dust

particles were the product of meteoroidal impacts on the moon. The majority of the remaining proposed explanations for the existence

of the enhanced flux basically depend on the

gravitational concentration of interplanetary

dust particles streaming at low speed into the

vicinity of the earth. No attempt is made here

to review the numerous variations on this theme,

because the effects of radiation pressure on the

conditions of encounter have been neglected.

The gravitational enhancement of the flux of

interplanetary dust particles entering the vicinity of the earth has been treated through the

use of Liouville's theorem by Singer (1956, 1961)

and by Shelton, Stern, and Hale (1964). The

three-body problem (consisting of the sun, the

earth, and a dust particle) was treated as a

succession of two-body approximations. Singer

(1961) assumed that the velocities of the dust

particles were isotropic at infinity (entry into

the earth's gravitational field).

The degree of enhancement of the flux depends on the average speed at which dust

particles enter the vicinity of a planet. The

requirements on the speed of encounter can be

illustrated by a very brief treatment using

Liouville's theorem and following closely the expositions given by Singer (1961) and by Shelton,

Stern, and Hale (1964). The general treatment

applies for any planet, with the degree of enhancement of the flux depending rather sensitively on the distributions of a, i, and 0 for the

dust particles encountered by the planet.

The densities at two points (r,, v,) and (r^

v^) on a dynamic trajectory in a six-dimensional

phase space composed of the geocentric position and velocity vectors r, and vf

 are related

through Liouville's theorem by

The scalar flux of dust particles at a geocentric

distance rt is

where r't v't pm, and * . are taken to apply

when the particles enter the earth's gravitational

field. This leads to the density enhancement

and the flux enhancement

at a geocentric distance rf. The factor/ allows

for those dust particles that are absent from

the receding flux because they collided with the

earth. The algebraic expression for the factor

/ is given by Shelton, Stern, and Hale (1964).

The numerical values of / range between 0.5

and 1. The speed at infinity p. corresponds

to the speed at encounter v used earlier in the

discussion of the conditions of encounter.

The conservation of energy of geocentric motion yields

1/2

where

is the speed of escape from the earth at a distance rf

. At the altitudes of the near-earth satellites (r4~7000 km), the speed of escape is

km/sec.

For speeds at encounter

we have

km/sec,

if no particles are lost. The density of dust

particles in real space at a geocentric distance

rg is obtained by integrating n(rf, vf) over velocity space, giving

f

J

= f n(rf, vf)dvf.

so that the density and flux enhancements

reduce to

p

 J 0

and

*

» ~J «2
222 SYMPOSIUM ON METEOR ORBITS AND DUST

An enhancement of the flux by a factor ~10*

therefore requires vw ~0.1 km/sec. The concept of the sphere of influence inherent in the

simplified treatment using Liouville's theorem

causes trouble, for 0.1 km/sec is not small compared to the speed of escape at the distance of

the boundary of the sphere of influence for the

earth. A realistic treatment of the problem

therefore requires numerical integration of the

three-body equations of motion with radiation

pressure included.

The orbits for which very low speeds at

encounter are possible for dust particles of

various sizes were discussed earlier and are

represented in figures 3, 4, and 5. The speed

at encounter v measured in units of the speed

of escape ve at the altitudes of the near-earth

satellites is given as the ordinate on the right

in figures 3 and 4.

Singer (1961) assumed that relatively large

dust particles (s~200 M) have almost circular

heliocentric orbits of very low inclination

(e —0, i = 0°) in order to justify taking c . = l

km/sec, which leads to a flux enhancement

^lO2. A subclass of these orbits was investigated by Dole (1962), who numerically integrated the geocentric trajectories of dust

particles with initial circular heliocentric orbits

of zero inclination (e=0, i=Q°). Southworth

(1963) has criticized the two-dimensional model

used by Dole and argued that the fraction of

zodiacal dust particles with such heliocentric

orbits must be quite small.

A dust particle of radius s^'200 n and mass

density 1 g/cm3 has a value of 0~2.4X1O~3,

which justifies the neglect of radiation pressure

by Singer (1961). But the same dust particle

has a mass m~3.3X10~5 g, which removes it

from the region of particle mass covered by the

direct measurements and places it in the region

of radar meteors. The available direct measurements apply for dust particles with masses

w<10~7 g, with the maximum enhancement of

the flux occurring for dust particles with masses

in the neighborhood of TO~10~U g. A dust

particle of mass m=10" u g and mass density

5=2.5 g/cm3 has a radius s = 1 \i. The value of

0 is about 0.23, according to figure 2. The

speed of encounter for such a dust particle with

an earth-like orbit is about 3.6 km/sec. If we

take this as an" average speed we obtain a flux

enhancement of only 8, which is very much less

than the factor ~10* given by the direct

measurements.

The shortcomings of the treatments by

Singer (1961) and Dole (1962) are shared by

numerous other proposed explanations for the

geocentric enhancement of the flux of small dust

particles in which radiation pressure was

neglected. The work of Dole was mentioned

here because such numerical integrations should

be extended to a three-dimensional model and

to the case in which radiation pressure is not

neglected. The formulation of the problem of

the gravitational enhancement of flux in terms

of Liouville's theorem as given by Singer (1961)

is useful, provided two important changes are

made, namely, (1) radiation pressure should be

included so that the discussion can be directed

to the range of particle size for which the measured geocentric enhancement of the flux occurs,

and (2) the assumption that the small dust

particles that produce the zodiacal light have

predominantly circular heliocentric orbita of

very low inclination should be avoided. The

assumption that small dust particles with orbits

of fairly low inclination contribute most to the

enhancement of the flux near a planet cannot

be avoided, but the restriction on the range of

the inclination can be relaxed slightly because

of the presence of the term (1— 0)l/1 in the

expression for Ut. The low-speed encounters

occur only for noncircular orbits of fairly low

inclination when dust particles of the sizes

involved in the measured enhancement of the

flux are considered.

The remaining unsolved problem consists of

integrating over the unknown distribution of

orbits and the rather poorly determined size

distribution for the small interplanetary dust

particles in an attempt to ascertain whether

appreciable planetocentric enhancements of the

flux can occur directly. The boundary conditions that must be met by any distributions of

orbits and size distributions assumed for use in

such an integration include the observed distribution of surface brightness and polarization

of the zodiacal light over the celestial sphere.

Summary

The conditions of encounter between planets

and small interplanetary dust particles have
ENCOUNTER BETWEEN DD8T AND THE PLANETS—M'CRACKEN 223

been investigated in an approximate manner.

Solar-radiation pressure has been included in

the conditions of encounter, and the dependence

of the speed at encounter on the size of a dust

particle has been emphasized.

The low speeds of encounter, which occur near

perihelion passage, encompass an entire class of

noncircular heliocentric orbits of fairly low

inclination when dust particles of the sizes

studied with the use of spacecraft are considered.

This class of orbits provides dust particles that

can encounter the planets at the very low speeds

necessary for a gravitational enhancement of the

flux to occur. Evaluation of the effectiveness

of this class of orbits in directly producing the

enhanced flux of small dust particles measured

in the vicinity of the earth is made difficult by

the present lack of knowledge about the orbits

of small dust particles both in the vicinity of the

earth and in interplanetary space. The source

of the small dust particles and the mechanism

for the enhancement of the flux measured in the

vicinity of the earth with the use of spacecraft

are not yet satisfactorily explained.

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the earth." Planet. Space Sci., voL 11,

pp. 499-503.
2 2 4 SYMPOSIUM ON METEOR ORBITS AND DUST

VAN DE HULST, H. D. WlUPPLE, F. L.

1957. Light Scattering by Small Particles. John 1961. The dust cloud about the earth. Nature,

Wiley and Sons, Inc., New York, 470 pp. vol. 189. pp. 127-128.

WATSON, F. G. WYATT, S. P., Jr., and WHIPPLE, F. L.

1956. Between the Planets. Rev. ed., Harvard 195(). The Poynting- Robertson effect on meteor

Univ. Press, Cambridge, Mass., 188 pp. orbits. Astrophys. Journ., vol. HI,

WEINBERO, J. L. pp. 134-141.

1964. The zodiacal light at 5300 A. Ann.

d'Astrophys., vol. 27, pp. 718-738.

Abstract

The conditions of encounter between interplanetary dust particles and the planets are investigated for the range

of particle size where the force of solar radiation is not negligible in comparison with the force of solar gravity. The

action of solar-radiation pressure in reducing the heliocentric orbital speed of a small dust particle make* possible

very low planetocentric speeds at encounter for an entire class of heliocentric orbits of nonzero eccentrioity and

fairly low inclination. The speed at encounter and the apparent radiant depend on the site of the dust particle for a

given heliocentric orbit throughout the range of particle size investigated by means of dust-particle Mcnsoni mounted

on spacecraft.
The Brightness of the Zodiacal Light at the Ecliptic Pole

 l

F. E. ROACH

 2

The brightness of the zodiacal light at the pole

of the ecliptic is pertinent to an understanding

of the nature of the zodiacal cloud. A trivial

polar brightness resulting from low integrated

scattered sunlight from particles normal to the

plane of the ecliptic would imply that the

zodiacal cloud is highly concentrated toward

the ecliptic plane in agreement with the historical conception based on visual observations.

The fact that many observers have been able to

distinguish the zodiacal band over the full

sweep from its bright region some 25° from the

sun to the gegenschein opposite the sun shows

that the ecliptic concentration is a general

property of the phenomenon. However, the

visual observations should not be trusted as a

guide in the matter of the polar brightness,

which must be based on a careful resolution of

the observed brightness near the ecliptic pole

into the three major competing components:

airglow, integrated starlight, and zodiacal light.

This review is based on a recent study by

Smith, Roach, and Owen (1965). The principal

results of the study are given in their tables 4

and 5, from which two plots are here given

(figs. 1 and 2).

Two general statements can be made:

1. For an elongation of 90° the brightness

in the ecliptic is equivalent to 250 lOth-magnitude visual stars per deg

 2 (Si0 (vis)); the brightness at the pole is 110 Sl0 (vis); the ratio of

brightness is thus 250/110=2.3.

2. The ratio of brightnesses goes to a

maximum value of 4.9 at an elongation of about

35°.

1

 Kfcsume of paper presented at the Symposium.

!

 Institute for Telecommunication Sciences and Aeronomy, Environmental Science Services Administration, Boulder, Colo.; formerly at

Central Radio Propagation Laboratory, National Bureau of Standards,

Boulder, Colorado.

10 20 30 40 SO 60 70 80

ECLIPTIC LATITUDE

FIGURE 1.—Brightness of the zodiacal light as a function of

ecliptic latitude for an elongation of 90°.

i i i i

i i i i i i i i i i i I i i

0 90 180

ELONGATION IN DEGREES

FIGURE 2.—Ratio of brightness in the plane of the ecliptic to that in a plane perpendicular to the ecliptic as a

function of elongation.

225
2 2 6 SYMPOSIUM ON METEOR ORBITS AND DUST

The indication is that the ecliptic concentra- tance. The distribution of particles with distion of the zodiacal light (and therefore the tance in the two directions will differ and affect

zodiacal cloud) is significant but smaller than tn e integrated brightness observed photogenerally thought. In particular, it is noted metrically

that figure 1 calls for 2.3 times as much light

looking tangentially along the earth's orbit as at References

right angles. This does not imply exactly . , _ _ _ _ _

nZ, L- - . . i • .i SMITH, L. L.; ROACH, F. E.; and OWBN, R. W.

2.3 times as many scattering particles in the 1965 Th e ab8O,ute photometr y ^ th e iodicftl

line of sight, since the scattering angle will vary Ught. pumet. Space Sci., vol. 13, pp.

as a function of the individual particle's dis- 207-217.
Interplanetary Dust-Particle Flux Measurements between 1.0

and 1.56 a.u. from Mariner 4 Cosmic-Dust Experiment

W. M. ALEXANDER,1 O. E. BERG,2 C. W. MCCRACKEN,2 L. SECRETAN,2 and J. L. BOHN

 3

Abatract

A cosmic-dust detector on the Mariner 4 spacecraft has measured the flux and mass distribution of dust particles in interplanetary space

between 1.0 and 1.56 a.u. During the 228-day

interval starting a few hours after launch

(OO^OO-UT, November 29, 1964) and ending

with Mare encounter (01h00mUT, July 15,

1965), 215 particles were detected by the experiment sensor. The threshold sensitivity of the

detector transducer was (6 ±0.7) X10"5 dyne sec.

The salient features of the measurement are:

1. Between 1.0 and 1.25 a. u., a mean flux

of 7.3 X10"4 particles/m1 sec/irster was determined for particles of mass 6X 10~"g (assuming

a mean impact velocity of 10 km/sec). From

1.25 to 1.36 a.u., the mean flux was 2.1 X10"4

part ides nr sec/vster, and the flux continued to

increase, reaching a peak between 1.36 and

1.43 a.u. where the mean value was 3.3X10"4

particles/m2 sec/irster. The interval from 1.43

to 1.49 a.u. showed a mean flux of 2.2X10"4

particles/m2 sec/»ster; the last interval, which

• Temple University, Philadelphia, Pa.; formerly at Uoddard Space

Flight Center, National Aeronautics and Space Administration,

Oreenbelt, Md.

'Ooddard Space Flight Center, National Aeronautic? and Space

Administration, Oreenbelt, Md.

s

 Temple University, Philadelphia. Pa.

ended at Mars encounter, 1.49 to 1.56 a.u., re

vealed a flux of 1.8X 10~* particles/m2 sec/*ster.

2. The cumulative flux-mass distributions

near the orbits of the earth and Mars were proportional to m~

ll2

y while the distribution between 1.25 and 1.36 a.u. appears to be proportional to TO"09

. These values indicate a variation between the distributions of dust particles

(10-ng<TO<10"'g) (a) in the vicinity of the

orbits of large planetary bodies, and (b) in deep

space.

3. No statistically significant evidence of

any well-defined dust-particle streams has been

revealed from the measurement.

4. The flux indicated by the Mariner 2

cosmic-dust experiment is in good agreement

with the Mariner 4 measurement between 1.0

and 1.26 a.u.

5. There was no measurable enhancement

of the flux in the vicinity of Mars (closest

approach to Mars was about 3 Mars radii).

The data from the Mariner 4 cosmic-dust

experiment have been obtained from "quick

look" telemetry records, and, therefore, the

measurement results presented above are preliminary. However, the gross variations in the

flux and mass distributions, which indicate

perturbations by the two large planetary bodies,

earth and Mars, are not expected to change

significantly.

227

A New Solar-Terrestrial EflFect

C. HOFFMEISTER

 1

The neutral point of atmospheric polarization,

named after Arago, can be observed in the sky

opposite the sun before and after sunset and

sunrise above the antisolar point. The variable

distance of the neutral point from the antisolar

point has been extensively investigated as an

indicator of atmospheric turbidity. During my

three temporary visits in South Africa (1937-38,

1952-53, and 1959), 2% years in all, I measured

the Arago point not only for meteorological purposes but also in order to ascertain how it is

affected by upper-atmospheric conditions. This

required reaching the highest possible negative

values of the solar elevation. Surprisingly, I

noticed that the strong increase of the Arago

distance in the evening, after A©~ —2°, does

not continue up to the time of invisibility due to

the darkening of the sky, but attains a maximum at about hQ=— 7?8, after which the

distance decreases again by several degrees until

the end of the observation. Most previous

observations were discontinued at about ho=

— 7?5; only those made by Neuberger show an

indication of this effect.

Early in 1965 I compared my 1959 measurements with those previously obtained and

noticed large differences in the mean maximal

Arago distances far exceeding the scatter of the

individual values. I found that these variations were clearly related to solar activity.

Values of 30° and 31° were associated with the

period of maximum solar activity, and values of

23° and 24° with minimum solar activity. Of

all the series of observations made in the past

I could find only a few that could confirm this

phenomenon; many had to be rejected because

> Deutache Akademie der Wissenschaften tu Berlin, Sternwarte Sonneberg in Thuringen, East Germany.

of too large scatter. The most reliable observations, however, such as those of Dorno, Menze,

and Neuberger, confirmed this relation to solar

activity. I repeated my observations in the

spring of 1965 at the Sonneberg Observatory

and obtained a value that further substantiates

this dependency on solar activity.

I examined my 1959 observations, made at

the Boyden Observatory near Bloemfontein,

to see whether there is a connection with the

actual rapid changes in solar activity; only a

very slight interrelation, if any, was found.

This is significant in the explanation that I

propose below.

The theory of the Arago neutral point depends

on the fact that in the sunlit atmosphere the

plane of polarization passes through the sun

and the zenith, while in the region of indirect

illumination, i.e., the earth's shadow, the plane

is at right angles to the vertical through the

sun. Arago uses the concept of "positive"

and "negative" polarization, the interaction

of which causes a line of neutral light. The

rise in the neutral point is explained as an effect

of direct sunlight fading, and the decrease that

occurs after the maximum distance might be

understood if we assume that, at KQ= —8°, the

lower regions of the atmosphere are practically

dark, while at higher altitudes, near 80 to 100

km, there is a source of reflected light strong

enough to produce a relative increase of the

"positive" polarization.

We may ask: What polarizes the scattered

sunlight in the region above 80 km? There

are several possible contributing factors: atmospheric molecules and atoms, free electrons of

the ionosphere and possibly of the Van Allen

belts, dust particles in the layer near 100 km

22!)
230 SYMPOSIUM ON METEOR ORBITS AND DUST

and those suspended in higher layers of the

atmosphere or gravitating in outer space near

the earth. It is difficult to estimate the extent

to which each of the above factors contributes,

but there are indications that dust plays a

considerable, if not decisive, part. At the

International Astronomical Union meeting in

Hamburg in 1964, F. Link stated that at Ao =

—10° the light from the zenith is 10 to 100 times

stronger than if only atmospheric particles

were involved. He attributes this effect to the

dust layer at 100 km, but from my measurements it is most probable that dust at higher

layers is also involved.

Our next question is: What kind of polarization is responsible for the greater Arago distances at times of maximum solar activity?

The immediate cause must be a decrease of the

''positive" or an increase of the "negative"

polarization. This means that the phenomenon

cannot be explained as due to changes in air

density, in which case the opposite effect would

be expected. In addition, the air density is

so strongly affected by solar events that a

much greater scatter of the measured values

would occur. But there is another phenomenon

that, according to my investigations, behaves

in a similar fashion, i.e., shows practically no

correlation with the instantaneous solar activity,

but exhibits a well-established correlation with

the 11-year and probably also with the 80-year

period. This phenomenon is the enhanced

airglow. I explain the phenomenon as caused

by the interaction of interplanetary dust

particles and the atoms and molecules of the

atmosphere, which results in an increased

release of stored solar energy. The maxima

coincide with the minima of solar activity.

This explanation is supported by an interrelation between the annual variations of solar

activity and the short-period meteor streams,

especially the ecliptical streams. In this case

the long-period variation is caused by the

change of radiative pressure, which at the times

of strong solar activity acts like a weakening

of the sun's gravitational field, thus increasing

the semimajor axes of the orbits of the dust

particles and changing them into ellipses of

long periods, or even into hyperbolic orbits.

Dust particles will follow their orbits through

perihelion, but afterward will move to large

distances and not return, if ever, for a long

time. The effect is a decrease in the density

of dust near the earth. This explanation holds

good for the rather slow reaction of the observable secondary phenomena and for the

absence of an immediate effect. The decrease

in dust density explains both the weakness of

the increased airglow and the decrease of

"positive" polarization, which results in large

values of Arago point distances.

From this explanation and from the fact that

the minimum of solar activity did not occur

prior to late 1964, the 1965 value appears to be

a little too high when compared with the 1952

and 1953 values. An interesting interpretation

of this is that, as a result of the extremely high

maxima of solar activity in 1947 and 1957, a

continuous decrease in the airglow phenomena

is observed, and the low density of the dust also

weakens the "positive" polarization. We

might, therefore, expect a very high mean

maximum of Arago distances in 1968.

The results set out in this paper follow my

earlier works on enhanced airglow, noctilucent

clouds, and interplanetary dust, published in

1951 and 1960.

References

H0FFMEI8TER, C.

1951. Spezifische Leuchtvorgange im Bereich der

mittlercn Ionosphare. Ergebnissc der

cxaktcn Naturwissenschaften, vol. 24,

pp. 1-53.

I960. Interplanetare Materie und vcretarktes

Nachthimmelleuchten. Zeite. f. Astro ph vs., vol. 49, pp. 233-242.
Rocket and Satellite Studies of Meteoric Dust

T. N. NAZAROVA

 l

For some time now meteoric particles have

been studied by optical and radar techniques,

as well as by the collection and analysis of

meteoric bodies that have fallen onto the earth.

These investigations have contributed to a

thorough study of meteoric matter.

From observations of meteoric bodies at the

moment of their encounter with the earth, the

vector velocity, mass, density, composition, and

spatial density of particles with mass /n> 10

 4

g have been determined. From an analysis of

these data we can obtain information of meteoric

matter in interplanetary space.

As far as particles with smaller mass are

concerned, until recently it has been possible

from photometric observations of the zodiacal

light and solar F corona to obtain only integral

characteristics of particles and their spatial

density in interplanetary space. Extrapolation

of data characteristic of particles with mass

/w>10~4 g to particles of smaller mass is not

always accurate—in particular, the type of

change in spatial density with decrease in mass.

With the advent of rockets and artificial

earth satellites it became possible to record

individual particles with mass of up to about

10"13 g in the neighborhood of the earth and in

interplanetary space.

When a meteoric particle moving with a

velocity of >~ 5 km/sec (with respect to the

satellite) strikes the surface of the detector

(mounted on the satellite), the particle bursts

and the momentum of the ejected material in

the explosion impact is considerably greater

than the momentum of the particle itself.

Measurement of this "reactive" momentum

> Institute of Geochemistry and Analytical Chemistry of the USSR

Academy of Sciences, Moscow.

will not yield the momentum of the particle,

but a function of its mass and velocity.

The theoretical calculation performed by

Stanyukovich (1960) has shown that for high

velocities the recorded momentum / is proportional to the particle energy E. This relation

I~E is not universally accepted. Lavrent'ev

(1959) assumes I~mv1*, where m and v are

the mass and velocity of the particle, respectively. In our reduction of experimental data

we assumed I~E.

To record a reactive momentum Izakovich

and Roy (1958) used a ballistic piezoelectric

detector with separate mass and elastic elements. Deflection of the elastic elements

caused a deformation of the piezo elements and

the latter produced an electric potential. Absolute calibration of the detector can be achieved

by observing the height to which a small ball

of known mass rebounds after falling from a

known height. In fact, for the actual values

of the "collision" times obtained in the case of

the impact of the ball, the detector operates as

a ballistic device in the same way as it does

during meteoric impact.

When meteoric particles strike the detector,

a voltage output in the form of transient

damped oscillations develops in the piezo elements; these voltages enter the amplifiertransformer, provide resonance amplification of

the signals, their distribution into ranges according to amplitude, the memorizing of the

number of impacts on the trigger elements, and

the yield of the remembered information to the

telemetry device from each element of the

memory system. Thus the piezoelectric detectors of different design that we used made

it possible to record both the number of impacts

231
232 SYMPOSIUM ON METEOR ORBITS AND DUST

of particles per unit area per unit time and

some function of the particle mass and velocity

that is apparently close to its energy.

An estimate of the mass of the recorded

particle depends, of course, on the velocity

assumed. When we reduced the results of our

first measurements we assumed the particle

velocity to be 40 km/sec. Whipple's conclusion

(1961a) that the speed of encounter of the

meteor particles and the satellite is about 15

km/sec appears to us to be well founded.

Hence, for the first experiments recalculations

were made, and from 1961 onward we assumed

the speed to be 15 km/sec.

Table 1 summarizes the results of investigations of meteoric particles from Soviet rockets

and satellites (Nazarova, 1962; Nazarova,

Bektabegov, and Komissarov, 1963). For all

the experiments the table gives the area of the

working surface S (the effective surface area is

listed for the geophysical rockets), the operating

time t of the instrument, the impact rate, and

the height ranges. In the geophysical rocket

experiments the equipment was tested in the

process. The impact rates of the meteoric

particles recorded in these experiments contain

an uncertainty (of the order of about three).

Table 1 does not include unprocessed observational results from the satellite Elektron 4

and the space probe Zond 2. These results

contain data of sporadic meteoric matter and

meteoric bodies of some streams. According

to preliminary data they do not contradict the

results given in this paper.

The increased density of meteoric particles

near the earth observed with the USA rockets,

in the experiments known to us, at altitudes of

100 to 150 km, was recorded in the USSR

during our experiments conducted at heights of

100 to 300 km.

Recent studies of the brightness of the atmosphere at heights of 120 to 450 km by means

of instruments carried by rockets (Mikirov,

1965) made it possible to estimate the density

of scattering matter at those heights. According to Mikirov, at a height of 450 to 500 km

the aerosol matter has a density of 10~20 g/cm3.

This estimate is the lowest limit. Thus the

density of the dust particles is greater, by not

less than an order of magnitude, at a height of

500 km than in interplanetary space.

Independent confirmation of the presence of

a high density of dust particles in the neighborhood of the earth is given by observations of the

twilight glow (Divari, 1957, 1964). From

photometric observations of twilight glow,

Divari has determined the dust concentration

at a height of 100 km to be 2X10"4 cm"3,

which exceeds by 6 to 7 orders of magnitude

the concentration obtained experimentally from

rockets and satellites. Divari explains this

discrepancy by the presence in this region of

fine dust not recorded by means of rockets and

satellites, but which scatters solar radiation.

This concentration of fine dust responsible for

twilight scattering of solar radiation decreases

with increasing height much more rapidly than

does the concentration of larger particles recorded by the satellites (Divari, 1964). This

fact may be regarded as a proof that the height

range from 100 to at least 300 km is the region

where fine dust particles are formed as a result

of fragmentation of the circ urn terrestrial cloud,

or the region of their accumulation.

Several hypotheses have been advanced to

explain the presence of a dust cloud around the

earth. According to Moroz (1962) there is a

special class of interplanetary particles that are

relatively unstable and possibly consist of ice.

He suggests that these particles separate into

fragments at heights of a few hundred kilometers above the earth and cause an increase in

the dust concentration in the earth's vicinity;

however, it seems that none of the hypotheses

so far advanced to explain the enhanced density

of meteoric particles near the earth can be

finally accepted.

Investigations of meteoric matter from rockets and satellites have shown that its spatial

density decreases with increase of distance

from the earth.

For particles with mass 10~8 g at heights 100

to 300 km, the number of impacts N is 3X10"2

to 7X10"1 m"2 sec"1. At heights 400 to 2000

km, iV=10-8 m~2 sec"1. At distances of tens

and hundreds of thousands of kilometers from

the earth, according to measurements obtained

from Lunik 2 and Lunik 3, AT=9X10"4 to

10~3 m~2 sec"1. During the time interval of

3.6X104 sec, no impacts were recorded from

Lunik 1. Measurements obtained from Explorer 6 and Pioneer 1 give iV=5X10~6

 to
ROCKET AND SATELLITE STUDIES OF METEORIC DUST—NAZAROVA

TABLE 1.—Rocket and satellite meteoric dust data

233

Satellite or rocket

Geophysical

rocket

Geophysical

rocket

Geophysical

rocket

Sputnik 3

First Cosmic

rocket

Second Cosmic

rocket

Automatic interplanetary station (third Cosmic rocket)

Interplanetary

station Mars 1

Satellite Elektron

2

Date

May 24,

1957

Aug. 25,

1957

Feb. 22,

1958

May 15,

1958

May 16-17,

1958

May 18-25,

1958

Jan. 2, 1959

Sept. 12,

1959

Oct. 4-18,

1959

Nov. 1, 1962

Nov. 31,

1962-Jan.

30, 1963

Jan. 30-31,

1964

Feb. 11-13,

1964

Feb. 23-25,

1964

Feb. 29,

1964

Mar. 5, 1964

Area

S

(m»)

4

4

4

0.34

0.2

0.2

0. 1

1.5

1.5

0.03

0.03

0.03

0.03

0.03

Time*

(sec)

134

148

85

1.8X10*

3.6X10*

1. 1X10*

2.3X1O»

6X10*

1.5X104

5.4X10*

Area X time

(m1 sec)

536

592

340

6X10»

7.2X10»

2. 2X 10»

2.3X104

9X10*

2. 3X104

1.6X10*

Altitude

range h

(km)

100—200

100—210

126—297

400—1880

400—700

400—700

2000—

360,000

2000—

360,000

102, 000—

470, 000

6.6X10*-

42X10*

23X106-

45X10*

7130—400

Mass of recorded

particle m (g)

io-«

10-"

io-»

6X10-»-2X10-7

2X 10-"- 10-7

io-7-io-«

>io-«

10-8-4X10-«

4X10-'-4X10-7

>io-7

7Xl0-»-2X10- 8

2X.10-8-6X10-8

>6X10~8

>io-7

>10~7

1.3X10-*

4. 4X10-»-l. 3X1O"»

10- 8-4. 4X10-*

3.3X10-»-10-8

>3.3X1O"8

6.5X10"8-2X10-8

6. 5X1O"8-2X1O-8

6. 5X10-8-2X10"8

6. 5X10- 8-2X10- 8

Influx rate

(m~*

sec-1)

0.06

0.05

0.75

7

5X10-*

<io-<

<2X1O"»

<5X10"«

<io-4

<5X10~s

<5X10"s

9X10-5

4X10~<

2X10-*

4X 10-*

7X10-*

5X10-*

1.1 XI©"1

io-»

6X10"3

4X 10-3

io-J

2.4X10-*

5. 8X 10-»

io-3

1.5X10-3

4X10"5. The large scatter of the data obtained possibly indicates fluctuations of the

density of meteor matter in interplanetary

space. Extreme estimates of matter in the

zodiacal cloud obtained by a photoelectric

method give N= 10~8 to 10"* m"2 sec"1.

As pointed out by Whipple (1961b), there is

a strong N(h) dependence. However, the

240-022 O—67 16

change in N \vith increase of distance from the

earth up to heights of about 104 km is difficult

to explain by one type of N(h) dependence.

In the height range 100 to 200 km, N falls more

steeply than in the range from 2000 km and

above.

An average cumulative mass distribution

curve of the influx rates of sporadic meteoric
234 SYMPOSIUM ON METEOR ORBITS AND DUST

particles with mass 10"7 to 10"" g plotted by

Alexander et al. (1963) (fig. 1) shows good consistency of the experimental data,2

 although, as

mentioned earlier in this paper, Soviet and

United States workers made different assumptions. The former assumed I~A(mt?/2), while

the latter assumed I~mv. Apparently the

differences in the numerical values of the coefficient and in the velocity values assumed for

calculations compensate each other, and the

results agree within the accuracy of the measurements.

10

-I

•0-

lO"3

10"5

lO"6

< •

\ •

\

•

-

1

1

%

V

(

1

1 1 1

<•> EXPLORER 8 (PRELIMINARY)

®

•

9

w

a

t

\

t

1

VANGUARDS

EXPLORER 1

OSU ROCKETS

SPUTNIK 3

SPACE ROCKET I

SPACE ROCKET 2

INTERPLANETARY STATION

PIONEER 1

ELEKTRON 2

\

\

10' 10

PARTICLE MASS (g)

FIGURE 1.—Average cumulative mass distribution curve

for the vicinity of the earth (Alexander et al., 1962, fig. 2).

The data based on recording meteoric particles that penetrated the screens of satellites

Explorer 16 (D'Auitolo, 1964) and Ariel 2

(Jennison and McDonnell, 1966) for the mass

range of about 5X10"8 to 10~n g do not lie on

the curve of figure 1. This confirms the suggestion made by Whipple (1963), on the basis

of observing meteors from the earth, of the

presence of meteoric bodies with densities of

about 0.5 g/cm3.

Measurements taken from rockets and satellites have demonstrated that the density of

meteoric particles is subjected to spatial and

1

 This graph shows, in addition, results pertaining to the satellite Elektron2.

time fluctuations. Apart from the streams,

individual collections of meteoric particles

were observed to have unequal spatial density

of particles in them. The linear dimensions of

these aggregations varied within wide limits

reaching millions of kilometers.

There exist, evidently, very rarefied formations that are difficult to detect because of

their small spatial density.

Aggregations of micrometeoric particles unobserved on the earth and not belonging to the

known meteor streams have been discovered by

means of satellites. From Elektron 2 (Nazarova and Rybakov, 1966), for the exposure

time of approximately 479 hours from January

30 to March 10, three aggregations of meteoric

particles were recorded. The aggregations

were observed during the time period from 14 to

49 hours (the distance between them by time

was 147-177 hours) when not a single impact

was recorded.

The linear dimensions of these aggregations

reached 3 to 5X10* km. The first of them,

recorded on January 30-31, 1964, was sufficiently dense to enable us to determine the

direction of its motion.

During approximately 15 hours, 1S5 impacts

were recorded. The distribution of the impacts

over the orbit enabled us to separate a part of it

for which out of 185 impacts only 3 impacts

took place (fig. 2). Such a distribution of

impacts is possible when the earth passes the

aggregation of meteoric particles (similar to

crossing the stream). In this case, for an appropriate angle between the satellite orbit plane

and the aggregation vector velocity, a greater

or smaller portion of the satellite orbits turns

out to be shielded by the earth.

A geometric consideration of the problem has

shown that in the above case this angle is

~36°, and the angle between the direction of

the aggregation vector and the earth's velocity

vector is ~42°.

If we assume that the aggregation had the

velocity of 42 km/sec, which is the maximum

for the distance of the earth from the sun, the

average relative velocity of the encounter of

meteroric particles with the sensors was ~61

km. In this case the average impact rate was

1.1X10"1 m"2 sec"1. To estimate the mass of

recorded particles, we used, as in our previous
ROCKET AKD SATELLITE STUDIES OF METEORIC DUST—NAZAROVA 235

c; uu*

FIGURE 2.—Concentration of meteoric particles recorded by

the satellite Elektron 2, January 30-31, 1964.

papers, the relation /~mr*/2, and assumed that

©==61 km/sec.

As is evident from table 2, the distribution of

particles by mass for this aggregation cannot be

characterized by one law. In the formula

F(M)~1/Mn, n> 2 for mi and m2, n< 2 for

mj and m3, and n< 2 for m8 and m4.

TABLE 2.—Particle distribution by mass in the aggregation of January 80-31

Mass of particles (g)

4. 4X10-* >m, > 1. 3X 10-»

1 Xl0-»>m,>4.4X10-»

3.3X10-»>mi>l XlO-«

m4>3. 3X10-1

Number of particles

166

10

7

2

During the time up to March 10, 1964, while

the equipment was functioning, two more

aggregations of meteoric particles were observed

on February 11-13 and on February 23-25.

Since only a small number of impacts were

recorded (in one case 10, and in another, 24),

we were unable to determine the direction of

motion of these aggregations; when we estimated

the mass of the particles we assumed the

velocity to be 15 km/sec, which is the value we

usually take for sporadic meteoric particles.

The number of recorded impacts of particles

with mass 6.5 X10"8 g>ro>2X10"8g in these

cases was AT,=2.4X10"3 and #3=5.8X10"'

m"2 sec"1.

From February 29 to March 10, 4 impacts of

meteoric particles were recorded, among them

2 during approximately 22 hours from February

29 to March 1, and 2 on March 5 during

approximately 14 hours.

It should be noted that the average impact

rate for particles with mass 6.5X10"8>m>2X

10"

 8g from February 3 to March 10 during a

period of ~460 hours was 7.5X10~*m"2 sec"1,

which fits well on the curve plotted by Alexander

et al. (1963) (fig. 1).

Aggregations of micrometeoric particles that

do not coincide with the known streams were

observed earlier. Near the earth, on May 15,

1958, Sputnik 3 recorded an aggregation of

particles with mass 2X10~7g>m>6X10~8g

(with ©=15 km/sec); N rose from 4 to 11

impacts m~2 sec"1, i.e., approximately by 3.5

orders of magnitude higher than was observed

during subsequent days. The mass of particles

in this aggregation may have been 5X10~10g

with an assumed velocity of 70 km/sec.

The interplanetary probe Mars 1 permitted

us to investigate meteoric matter beyond the

earth's orbit at large distances from the sun.

On the day of launching, September 1, 1962,

both the earth and Mars 1 crossed the Taurids.

At a distance 6600 to 42,000 km from the earth

during 100 minutes of the flight, 60 impacts of

meteoric particles with mass >10~7 g were

recorded. The average impact rate was 7 X10~3

m~2 sec"1. Since for sporadic meteoric bodies

the number of impacts of the particles of mass

>10"7 g is approximately 10"s m~* sec"1, we

may infer that all the recorded particles

belonged to the stream (Taurids).

The spatial density of the meteoric bodies in

the stream was extremely uneven (fig. 3). The

particles moved in space in individual condensations, observed at distances of 4000 to 45,000

km from each other. The measured spatial

density of the meteoric bodies averaged over

the time during which the impacts were

recorded (2 min) varied within the limits (5.4

to 0.35) X10"' m"8, i.e., one meteoric body in

a cube of side 60 to 140 m.
236 SYMPOSIUM ON METEOR ORBITS AND DUST

N j

30

25

20

15

10

5

20 40 60 80 100 t min

FIGURE 3.—Observation of the Taurid stream. Data from

the 100-min period of November 1, 1962.

In the second half of November and December, at a distance of up to 23 X106

 km from the

earth, during a total observation time of

approximately 7.5 hours, no impact was

recorded. Hence, we may infer that the data

on the number of sporadic meteoric bodies

with mass >10~7 g obtained for the vicinity of

the earth's orbit (according to observations at

a distance of thousands of kilometers from the

earth) apparently remain correct for distances

from the sun, i.e., for m> 10~7 g, N^IO'5 m~2

sec"1.

From December 31, 1962, to January 30,

1963, at a distance 23 to 45X10* km from the

earth, Mars 1 again recorded an increased

density of meteoric matter in interplanetary

space. This aggregation could not be identified

with any known meteor stream. During the

total recording time of ~ 4 hours, 104 impacts

were recorded, the average impact rate being

4.5X10-3m-2sec-1.

The spatial density of meteoric bodies in this

formation was uneven, as in the Taurid stream.

The densities of some of the condensations

varied within the limits 1.7X10"6 to 6.7X10"4

m~3 and the distances from 8000 to 190,000 km.

After January 30, 1963, the instrumentation

for recording meteoric particles ceased to function. Therefore, it is not known how long Mars

1 continued to move in the region of enhanced

spatial density. Using Explorer 1, American

investigators (Dubin, I960) also observed a

"stream of sporadic meteors" that was not

recorded on the earth.

According to preliminary reports (1965), the

spacecraft Mariner 4 recorded on some portion

of its trajectory an enhanced density of meteoric

particles belonging perhaps to a condensation

similar to the one recorded by Mars 1.

Apparently meteoric matter is mostly associated in space into more or less dense formations

with linear dimensions varying within wide

limits.

In interplanetary space there are many

meteoric streams and aggregations unknown on

the earth, and so far it is impossible to predict

them.

Regular observations from artificial earth

satellites will enable us to reveal those streams

encountered by the earth during its motion

along the orbit and those inaccessible to

observations from its surface.

Further investigations of different regions of

interplanetary space by means of space vehicles

will increase our knowledge of the solid components of interplanetary matter, extend the

number of the known meteoric streams, and

perhaps in the future enable us to predict the

probability of meteor particle encounter with

spaceships.

References

ALEXANDER, W. M.; MCCRACKEN, C. W.; SECRETAN, L.;

and BERG, O. E.

1963. Review of direct measurements of interplanetary dust from satellites and probes.

In Space Research III, ed. by W.

Priester, North-Holland Publ. Co., Amsterdam, pp. 891-917.

D'AIUTOLO, C. T.

1964. Satellite measurements of the meteoroid

environment. Ann. New York Acad.

Sci., vol. 119, pp. 82-97.

DIVARI, N. B.

1957. Cbor die Polarisation des D&mmerung8himmellicht8 im Zenit. Doklady Acad.

Sci., USSR, vol. 112, pp. 217-220.

1964. The dust concentration in the upper layers

of the earth's atmosphere. Geomagnetism and Aeronomy, USSR Acad. Sci.,

vol. 4, no. 5, pp. 886-892.

DUBIN, M.

1960. Meteoritic dust measured from Explorer I.

Planet. Space Sci., vol. 2, pp. 121-125).

IZAKOVICH, M. A., and Roi, N. A.

1958. An accoustical method for the measurement of the mechanical parameters of

meteorites. Artificial Earth Satellites,

USSR Acad. Sci., vol. 2, pp. 105-107.
ROCKET AND SATELLITE STUDIES OF METEORIC DUST—NAZAROVA 237

JENNISON, I; C , and MCDONNELL, J. A. M.

1966. Interpretation of the interplanetary duBt

measurements in the Ariel II Satellite.

In Space Research VI, cd. by R. L.

Smith-Rose, Macmillan Co., New York,

pp. 937-944.

LAVRENT'EV, M. A.

1959. The problem of piercing at cosmic velocities. Artificial Earth Satellites, USSR

Acad. Sci., no. 3, pp. 85-91.

MIKIHOV, A. E.

1965. Investigations of atmospheric brightness ut

heights of 120-450 km. Cosmic Studies,

USSR Acad. Sci., vol. 3, no. 2, pp. 201-

210.

MoROf, V. I.

1962. On the "dust envelope" of the eurth.

Artificial Earth Satellites, USSR Acad.

Sci., no. 12, pp. 166-174.

NAIAKOVA, T. N.

1962. Rocket and satellite studies of meteor

dust. Artificial Earth Satellite**, USSR

Acad. Sci., no. 12, pp. 154-158.

NAXAROVA, T. N.; BEKTABEGOV, A. K and KOMIRHAHOV, O. 1).

196.'}. Preliminary results of a study of meteoric

matter along the trajectory of the interplanetary stationary "Mars 1." Cosmic

Studies, USSR Acad. Sci., vol. 1, no. 1,

pp. 137-139.

NAZAROVA, T. N., and RYBAKOV, A. K.

1966. Meteoric dust measured by the satellite

Elektron II . In Space Research VI, ed.

by R. L. Smith-Rose, Macmillan Co.,

New York, pp. 946-951.

STANYUKOVICH, K. P.

1960. Elements of the theory of the impact of

solid bodies with high (cosmic) velocities.

Artificial Earth Satellites, USSR Acad.

Sci., no. 4, pp. 292-333.

WHIPPLB. F. L.

1061a. The participate contents of space. In

Medical and Biological Aspects of the

Energies of Space, ed. by P. Campbell,

Columbia Univ. Press, New York,

pp. 49-79.

1961b. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

1963. On meteoroids and penetration. Journ.

Geophys. Res., vol. 68, pp. 4929-4939.

Recent NASA Meteoroid Penetration Results from Satellites

C. T. D'AIUTOLO, 1 W. H. KINARD, 2 and R. J. NAUMANN

 3

Introduction

One of the principal parameters to be considered

in the design of space vehicles is the possibility

of damage resulting from impacts with extraterrestrial debris. Depending upon their kinetic

energy, the impingement of high-velocity particles on spacecraft structures may result in

surface erosion, puncture, or catastrophic rupture of sensitive spacecraft structures.

The problem of the spacecraft designer is to

provide protection for vital parts of the spacecraft and for the occupants, if any. He must

be able to estimate the likelihood of damage, in

flight, of structures of various configurations

and materials.

Early knowledge of the hazard resulting from

the meteoroid environment was based on information obtained from two broad fields of

inquiry—astronomy, the foremost source of

information, and laboratory hypervelocity impact studies. Combined information from these

two sources was used to estimate the magnitude

and character of the meteoroid hazard to

spacecraft.

Two early estimates of the meteoroid-penetration frequency, based on data from these

sources, are shown in figure 1. The estimated

number of penetrations/m2/day is plotted as a

function of thickness for the penetration of

aluminum sheets. The upper curve combines

an early estimate by Whipple (1958) of the

meteoroid flux with the penetration criteria

io"V

• National Aeronautics and Space Administration Headquarters,

Washington, D.C.

- Langley Research Center, National Aeronautics and Space Administration, Hampton, Va.

1

 Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, Ala.

WHIPPLE (1958) DISTRIBUTION

CHARTERS AND SUMMERS

PENETRATION

WATSON (1941) DISTRIBUTION

BJORK PENETRATION

10

10 10 10

THICKNESS OF ALUMINUM, cm

FIGURE 1.—Estimated meteoroid penetration frequency.

determined experimentally by Charters and

Summers at the Ames Research Center, reported by Summers (1959), and represents a

23U
240 SYMPOSIUM ON METEOR ORBITS AND DUST

pessimistic limit for the hazard. The lower

curve combining Watson's (1956) estimate of

the meteoroid flux with the theoretical penetration criteria derived by Bjork (1961) represents an optimistic limit for the hazard. For

a given material thickness, an uncertainty of

over three orders of magnitude existed in the

estimated penetration frequency. The following example illustrates what such an uncertainty

means in the design of space vehicles. In

design studies for one particular spacecraft we

found, from the upper curve of figure 1, that

for adequate meteoroid protection an additional

weight of about 12,500 pounds would be required. This weight would entail a severe

performance penalty. Use of the lower curve

resulted in no additional weight for meteoroid

protection. The dilemma of the designer is

readily apparent.

In order to narrow the uncertainties that

have existed in predicting the probabilities of

meteoroid penetrations in spacecraft structures,

the Office of Advanced Research and Technology of the National Aeronautics and Space

Administration has formulated a comprehensive

program of investigation, which includes flight

experiments to measure meteoroid penetrations

over a range of material thicknesses in the

near-earth environment.

This paper will summarize the results to

date from two series of spacecraft in this program. First, we shall present the results from

the Explorer 16 and Explorer 23 satellites,

each of which exposed to the meteoroid environment a total area of about 2.0 m2

 of very

thin materials and used pressurized cells as

the prime experiment. Next, we shall describe

preliminary results from the large satellites,

Pegasus 1 and 2, each of which exposed more

than 200 m2 of material thicknesses up to 0.040

cm and used electrical capacitor-type detectors

that discharge when penetrated. Finally, we shall

make a comparison of the preliminary results

from these satellite penetration measurements

with the latest estimates based on observations

of meteors.

Spacecraft and experiments

EXPLORER 16

Spacecraft.—Two Explorer-series micrometeoroid satellites have been launched to date

with the primary objective of obtaining meteoroid penetration rates in relatively thin target

materials. The first of these two satellites,

designated Explorer 16 (1962 Beta Chi 1),

was launched December 16, 1962, from the

NASA Wallops Station onboard a Scout launch

vehicle. It was placed in an earth orbit

having an apogee of 1180 km, a perigee of 750

km, and an inclination to the earth's equator

of 52°. The weight of the spacecraft, including

the spent last-stage rocket motor, which remained as part of the orbiting satellite, was

233 pounds (106 kg).

Explorer 16 continued to transmit useful

data for approximately 7% months, failing on

July 22, 1963. Several NASA Technical Memorandums (Hastings, 1963a, b, c, 1964) describing this satellite and the data obtained

have been published. The data have also been

presented at various symposia (D'Aiutolo,

1964a, b).

Figure 2 is a schematic of the Explorer 16

spacecraft, cylindrical in shape, 58.5 cm in

SOLAR-CELL TEST TRAYS

SOLAR CELLS

IMPACT DETECTOR

CADMIUM SULFIDE CELL

SOLAR CELLS

- -

, 1 ,

-

x

PRESSURE CELLS

58.5-cm DIAMETER

GRID DETECTOR

WIRE CARDS

FIGURE 2.—Explorer 16 (1962 Beta Chi 1) satellite.
NASA METEORO1D PENETRATION RESULTS FROM SATELLITES—D'AIUTOLO ET AL. 241

diameter, and 193 cm long. The primary

penetration detectors onboard consisted of

pressurized cells mounted around the periphery

of the last-stage rocket motor.

Other penetration-type detectors placed on

the spacecraft were stainless steel-covered grid

detectors mounted in a ring just aft of the

pressure cells, copper wire card detectors

mounted in a ring just aft of the steel-covered

grid detectors, and two cadmium-suliide cell

detectors mounted on the spacecraft nose section. Sounding-board-type impact detectors

were also mounted on the spacecraft nose

section.

Experiments.—Figure 3 is a drawing of the

pressurized-cell penetration detector. The cell

consisted of a thin exposed surface in which

penetrations were detected, a base plate, a

pressure-sensitive capsule, and a microswitch.

Each cell, approximately 5.0 cm in diameter

and 18.8 cm long, was filled with helium.

When the cell was punctured the gas leaked

out and the resulting pressure loss actuated the

switch, which signaled the telemeter of the

penetration. Each cell can detect only one

penetration. Beryllium copper was selected as

the cell material because of previous experience

in fabricating pressure diaphragms.

At the time Explorer 16 was launched, no

direct measurements of meteoroid penetration

PRESSURE

DIAPHRAGM

rates existed, and, as shown previously, estimates of expected rates varied by orders of

magnitude. To ensure that some useful penetration data would be obtained, the number of

cells of each thickness was varied inversely as

the cell skin thickness. The exact cell and

thickness distributions were as follows: 100

0.0025-cm cells for a total exposed area of

1.0 m2, forty 0.0051-cm cells for a total exposed

area of 0.4 m2, and twenty 0.0127-cm cells for

a total exposed area of 0.20 m2.

The stainless steel-covered grid detector

(Davison and Winslow, 1964) is shown in figure

4. These detectors were made in triangular

segments with each side about 11.6 cm long.

The stainless steel covers were 0.0025, 0.0076,

and 0.0152 cm thick. They were bonded to

12.7-/1 mylar, which had a thin continuous grid

circuit. A break in this continuous grid indicated when the stainless steel cover plate was

penetrated. The area distribution for these

detectors was as follows: 0.14 m2 of 0.0025-cm,

0.19 m2 of 0.0076-cm, and 0.023 m2 of 0.0152-

cm thick materials.

STAINLESS

STEEL COVER

PLATE

0.0025, 0.0076, OR 0.0152-cm THICK STAINLESS

STEEL COVER PANELS

. / 12.7-/1 THICK MYLAR INSULATOR

FIGURE 3.—Pressurized cell detector.

1.52-/1 THICK GOLD GRID

635-c m THICK SILICONS RUBBER

FIGURE 4.—Stainless steel-covered grid detector.
242 SYMPOSIUM ON METEOR ORBITS AND DUST

EXPLORER 23

Spacecraft.—The primary mission of the second

Explorer meteoroid satellite, Explorer 23 (1964

74A), was to define more accurately the penetration flux in the 0.0051-cm material and obtain

additional data on the 0.0025-cm material, thus

establishing at a higher confidence level the

slope of the penetration flux curve in the region

of 0.0025-cm and 0.0051-cm thick materials.

This spacecraft was launched on November 6,

1964, from the NASA Wallops Station on board

a Scout launch vehicle. It was placeq1 *n a n

earth orbit having an apogee of 979 km, a perigee of 464 km, and an inclination to the earth's

equator of 52°. The weight of the spacecraft,

including the spent last-stage rocket motor,

which remained as part of the orbiting satellite,

was 296 pounds (135 kg).

A schematic of Explorer 23 is shown in figure

5. It is basically very similar to Explorer 16.

The primary penetration detectors were of the

pressurized-cell type flown on Explorer 16; however, the Explorer 23 detectors were made of

stainless steel rather than beryllium copper.

Since fabrication techniques had advanced so

far as to permit the use of stainless steel, this

material was selected because it is a more typical spacecraft structural material.

Explorer 23 had 70 cells of 0.0025-cm stainless steel for a total area of 0.69 m2

, and 140

cells of 0.0051-cm stainless steel for a total area

of 1.38 m2. The area thickness distribution was

selected to provide approximately the same

number of events in the 0.0025-cm and 0.0051-

cm cells based on the penetration-rate data obtained by Explorer 16.

Explorer 23 also had on board two capacitortype penetration detectors with a combined

total area oi 0.073 m2.

Experiments.—The primary penetration detectors (pressurized cells) are described above.

Figures 6a and b show the details of the capacitor-type detectors on board. Each detector

was approximately 16.8 cmX21.1 cm. The

outer target material was 0.002-cm stainless

steel. A dielectric consisting of a bilaminate

of 4-M mylar was bonded together and to the

stainless steel, with the thickness of each adhesive bond approximately 0.76 p. Approximately 0.3 M of copper was deposited on the

rear surface of the dielectric to serve as the rear

capacitor electrode.

OOOD-cm STAINUSS Still

4> MVIAR

0 76> AOWSIVt

FIGURE 6a.—Typical crow section of Explorer 23 capacitor

detector.

FtlHTCD CKCUIT

FIGURE 5.—Schematic of Explorer 23 (1964 74A).

FIGURE 6b.—Explorer 23 capacitor penetration detector.

The capacitors were charged to approximately

14 volts. The operation of the detector depended on ionization being created by the

energy dissipated by a penetrating meteoroid.

This ionization, which is very short-lived, provided a conducting path through which the

capacitor was partially discharged. The discharging of the capacitor thus provided the

signal of the penetration event. Since the
NASA METEORO1D PENETRATION RESULTS FROM SATELLITES—D'AIUTOLO ET AL. 243

shorting mechanism is temporary, the detector

can recharge and be used repeatedly for detecting meteoroid penetrations.

PEGASUS 1 AND 2

Spacecraft.—The primary mission of the Pegasus

spacecraft was the measurement of meteoroid

penetration rates in materials up to 0.040 cm in

thickness. The first spacecraft, Pegasus 1

(1065 09A), was launched on February 16, 1965,

from Cape Kennedy on board the SA-9, Saturn

1 launch vehicle. It was placed in an earth

orbit having an apogee of 740 km, a perigee of

495 km, and an inclination to the earth's

equator of 32°. The second spacecraft, Pegasus

2 (1965 39A), was launched from Cape Kennedy

on May 25, 1965, on board the SA-8, Saturn 1

launch vehicle, and was placed in an almost

identical orbit: apogee, 745 km; perigee, 510

km; and inclination, 32°. A third spacecraft,

Pegasus 3 (1965 60A), was launched on July 30,

1965, from Cape Kennedy on board the SA-10,

Saturn 1 launch vehicle, and placed into a nearcircular earth orbit: apogee, 541 km; perigee,

520 km; and inclination, 29°. Since at the

time of this writing Pegasus 3 has been in orbit

only a few weeks, the results obtained from it

will not be reported here, but will be published

later when more data are available.

Each spacecraft was identical in configuration. Plate 1 is an artist's concept of the

Pegasus spacecraft in orbit. During launch the

spacecraft was folded and when inserted into

orbit was extended in an accordion-like manner.

To provide a lifetime of at least one year, the

spacecraft remained attached to the spent

second stage of the launch vehicle. In the

fully extended condition, the spacecraft has a

span of about 29.2 m. Exclusive of the

attached spent second stage, the weight is

about 3200 pounds (1455 kg).

Experiments.—The penetration detectors on

board consist of parallel plate capacitors. The

erectile winglike structure of the Pegasus spacecraft supports 208 such detectors, each of

which measures 50 cmXIOO cm, attached to

both sides of the wings. As shown in figure 7,

the parallel plate capacitor penetration detectors are formed by backing target sheets with a

12-fi mylar trilaminate, which in turn is backed

by a vapor-deposited copper layer. The caMETEOROID DETECTOR PANEL

EXPLOOE0 VIEW

TAROET SHEET

CAP»crcw»-[

ALODINE THERMAL CONTROL COATING

400,20 0 OR 40-/1 ALUMINUM

12-/1 MYLAR DIELECTRIC

0.07-/i. VftPOR DEPOSITED COPPER

0.639-em FLEXIBLE OPEN CELL FOAM

1.27-« RIGID CLOSED CELL FOAM

O 635-cm FLEXIBLE OPEN CELL FOAM

0 07-fj. VAPOR DEPOSITED COPPER

12-/1 MYLAR DCLECTRtC

400,200 OR 40-/1 ALUMINUM

FIGURE 7.—Pegasus capacitor detector.

pacitors were bonded to each side of a 2.54-cm

foam core, which acts as a structural support as

well as a barrier to prevent the meteoroid and

debris resulting from the penetration of one

capacitor from impinging on the opposite

capacitor. An Alodine coating was placed on

the target sheets for thermal control. Thicknesses of the target sheets are: 40 p-1100-0

aluminum, 200 M-2024 T-3 aluminum, and

400 M-2024 T-3 aluminum. The winglike structure provides 194.5 m2

 of instrumented area, of

which 171 m2 is allocated to the 400-M thickness,

16 m2 to the 200-M thickness, and 7.5 m2 to the

40-M thickness.

The 400-M area is subdivided into 48 identifiable logic groups, each containing 5 to 8 individual detector sheets; the 200-M area has 6

logic groups, each containing 3 to 8 individual

detectors; the 40-M area has 8 logic groups, each

with 2 detectors. Figure 8 shows the location

of the various panel logic groups; the number

without a letter represents the 400-M thickness,

the letter B the 200-M thickness, and the letter C

the 40-M thickness.

A penetration through the detector target

sheet and mylar dielectric momentarily shorts

the capacitor detector, which is normally
244 SYMPOSIUM ON METEOR ORBITS AND DUST

PEGASUS DETECTOR PANELS

+ Y

...

- -

-

R

-

-

-

m

. -

«

r

-—-

m -

-

. . .

H

...

-Y

...

"•

•Y L

...

R

u

... ...

...

- ... ...

- ... ...

,. ...

.... ...

H

-Y

...

FIGURE 8.—Pegasus wing-panel schematic showing location of

various logic groups.

maintained at a 40-volt potential by a network

of current-recharge amplifiers (CRA). The

energy stored in the capacitor is dumped into

the shorted area, which burns away the coppervapor deposit and clears the detector in approximately 1 sec. The initial voltage drop

across the capacitor starts an integrator in the

hit detector, which integrates the voltage

variation across the detector panel for 250 /xsec.

If the integrated voltage-time product is

greater than a certain predetermined value, a

hit word is written in the memory and a

cumulative counter is incremented.

The recharge of the panel is accomplished

by three CRA's, which are selected by a dioderesistor logic matrix in a unique pattern for

each logic group. This pattern is also written

into the hit word.

In laboratory testing of the detectors, it

was found that the discharge voltage produced

by a high-velocity particle ranged from fractions

of a volt to full discharge. No direct correlation

between discharge level and any projectile

property could be found, although there was

some indication that the signal levels increased

somewhat at higher velocities. The voltagetime product required to record a hit word was

selected so that a typical discharge of 4 volts

would be registered on Pegasus 2 and 3, 3 volts

on the 40-M panels on Pegasus 1, and 5 volts

on the remainder of the Pegasus 1 panels.

Laboratory tests indicated that these settings

would accept 80 to 90 percent of the signals

resulting from meteoroid penetrations.

Rate of meteroroid penetrations

EXPLORER 16

Accumulative Penetrations.—Explorer 16 has

provided the first significant data on the

penetrating capability of meteoroids in thin

structural materials. Figure 9 shows the

accumulated punctures as a function of time

for the 0.0025-cm and 0.0051-cm berylliumcopper pressurized cells as well as for the

0.0025-cm and 0.0076-cm stainless steel-covered

grid detectors. The data presented extend

from December 16, 1962 (launch), through

July 22, 1963, at which time the spacecraft

ceased to transmit data. During the 7#

months in orbit, forty-four 0.0025-cm and

eleven 0.0051-cm beryllium-copper penetrations

were recorded. Six 0.0025-cm and one 0.0076-

cm stainless steel penetrations were also recorded in t his time period. As discussed by

Secret mi (see pp. 307-315), several penetrations

of the cadmium-sulfide cell were recorded. Although not reported, two penetrations were

recorded in copper wire card detectors. No

penetrations were recorded in the 0.0127-cm

beryllium-copper pressurized cells or in the

0.0152-cm stainless steel wire grid.

i -

mi m. »u MM. ni AH. IW wt

FIGURE 9.—Explorer 16 history of accumulated penetrations.

Penetration Rates.—The penetration data obtained from the pressure cells and the stainless

steel-covered grid detectors are shown in

figure 10; the thickness of the detector target

is plotted against the puncture rate.

Some preliminary impact tests performed at

Langley Research Center and at Ames have

indicated that equal thicknesses of the stainless

steel and of the beryllium copper used have approximately the same resistance to penetration.
NASA METEOROID PENETRATION RESULTS FROM SATELLITES—D'AIUTOLO ET AL. 245

-'• I

4 >

1

O PRESSURIZED CELLS "

O GRIDS

THICKNISS Of MATERIAL.cm

FIGURE 10.—Explorer 16 penetration rate*.

It can be seen that a flux of 3.86X10"*

punctures/m2/sec was observed in the 0.0025-cm

pressure cells. This flux is based on the 44

penetration events. The flux measured in

the 0.0051-cm cells was 1.99X10'* punctures/

m

2

/sec based on the 11 events. No penetration

was observed in the 0.0127-cm cells, and the

point shown in figure 10 represents an upper

limit of the flux.

Because of their small exposed area, the

stainless steel-covered detectors received only

a small number of penetrations. The six

0.0025-cm penetrations gave a flux rate of

1.329X10"* punctures/m2/sec, while the one

0.0076-cm penetration gave a flux rate of

8.68X10~7 punctures/mVsec.

In summary, Explorer 16 established with a

reasonable level of confidence the penetration

flux in 0.0025-cm beryllium copper and, to a

reduced confidence level, the flux in 0.0051-cm

beryllium copper. The stainless steel data

seem to agree with the beryllium results.

EXPLORER 23

Accumulative Penetrations.—Figure 11 illustrates the accumulated punctures as a function

of time for the 0.0025-cm and 0.0051-cm stainless steel pressurized cells. The data presented

extend from November 6, 1964 (launch),

through July 22, 1965. During this period,

forty-three 0.0025-cm and fifty-four 0.0051-cm

FIGURE 11.—Explorer 23 history of accumulative penetrations.

pressurized cells were penetrated. Two penetrations were also recorded in the capacitor

detectors during the same period.

Penetration Rates.—The penetration data obtained by Explorer 23 prior to July 22, 1965, are

presented in figure 12, which is a plot of the

penetration rate on the ordinate and the material thickness on the abscissa. The penetration rates for the 0.0025-cm and 0.0051-cm

materials were 3.74X10~* and 1.87X10"* penetrations/m2

/sec, respectively.

- \

_

\

\

o

x \\

1 1

O PRESSURIZED CELL

O CAPACITOR

-

1

THICKNESS OF MATERIAL cm

FIGURE 12.—Explorer 23 penetration rates.

As of July 22, 1965, the capacitor detectors

had been penetrated only twice, and, as a result,

calculated penetration rates for these detectors

have little statistical significance. The calculated rate for the capacitors does seem to be in

reasonable agreement with the 1-mil pressure

cells. The fact that the capacitor-detector rate
246 SYMPOSIUM ON METEOR ORBITS AND DUST

\

O

\

EXPLORER 16

A PRESSURIZED CELLS

O GRIDS

EXPLORER 23

O PRESSURIZED CELLS

O CAPACITOR

\

THICKNESS OF MATIHIAl.c m

FIGURE 13.—Comparison of Explorer 16 and Explorer 23

penetration rates.

is low, compared to the pressure-cell rate, could

result from either or both of two factors: the

first, as already mentioned, is the small data

sample of only two events; the second, which

would cause the capacitor-detector rates to be

lower than the cell rates, results from a difference in the threshold detection for each detector.

The pressure-cell detectors will indicate as a

penetration any impact that penetrates into the

material to a sufficient depth to allow small

cracks to develop between the crater bottom

and the rear of the plate. The actual penetration depth in these cases may be only % the

thickness of the plate. The capacitor detectors,

on the other hand, require a complete penetration of the target and the dielectric forming the

capacitor before an impact is detected; consequently, even though both types of detectors

have 0.0025-cm plates, the capacitor will require

a little larger particle under the same impact

velocities to detect a penetration.

Figure 13 compares the results of Explorer 16

and Explorer 23. It can be seen that the data

from the beryllium-copper pressure cells of

Explorer 16 fall almost on top of the data

obtained by the stainless steel cells of Explorer

23. This fact supports the finding from ground

tests, which indicated that both the stainless

steel and beryllium-copper material used have

about the same resistance to penetrations.

There is also good agreement in the data

obtained from the 0.0025-cm pressurized cells

and the 0.0025-cm stainless steel grid detector.

The 0.0076-cm stainless steel grid data and the

0.0127-cm beryllium-copper-cell data have little

significance, since only one penetration was

recorded in the grid detector and no penetration

was recorded in the beryllium-copper-cell detector.

With the large total data sample obtained by

both satellites, the rates at the 0.0025-cm and

0.0051 -cm materials based on the pressure-cell

measurements are established with very good

confidence, as evidenced by the confidence

limits shown on the data points.

PEGABUH 1 AND 2

Minor instrumentation difficulties in Pegasus 1

prevented panel identification and recharge

times from being recorded for the 200-M and

400-M panels. Also, it was found that these

panels had a tendency to become intermittent;

that is, a single panel may suddenly generate

many hit words in the space of a few orbits. It

is believed that such a condition is caused by

debris or ragged edges around a meteoroid

perforation that produce point physical shorting. The energy stored in the capacitor would

burn away such a short, but thermal expansion

and contraction could cause the process to

repeat many times. Laboratory tests to investigate this phenomenon will be conducted in

the near future.

Pegasus 1 received four hit indications on the

400-M panels in the first 11 days. However,

several panels became intermittent at that time,

and the lack of panel identity precluded separating valid hits from the intermittent events

after that time. Based on four events in 1925

m

2

 day, the penetration frequency is 0.0021/m*

day.

For Pegasus 1, a very high fraction of the

penetrations on the 200-M panels resulted in

shorts, and since there were only six logic

groups, the 200-M area very quickly became lost.

There were nine hit indications in 248 m1 day

exposure, which resulted in a penetration frequency of 0.036/m2

 day. Again it should be

pointed out that the 200-M and 400-M hit words

did not contain panel identity or recharge time

unless a short resulted. Therefore, some of the

tests for validity could not be made.
NASA METEOROH) PENETRATION RESULTS FROM SATELLITES—D'AIUTOLO ET AL. 247

The 40-M panels gave panel identification

about 70 percent of the time for Pegasus 1 and

are still functioning extremely well. A total

of 104 penetrations have been recorded in 858

in2 day for u flux of 0.121/nr day. A time

history of the cumulative events is shown in

figure 14.

j

1 y • •

• *i • •V *0 • ( at «• i

• •«

B •

. - •

• ia

•-

c

FIGURE 14.—Time history of accumulated penetrations for

40-ji panels on Pegasus 1.

The number of penetrations, area-time exposure, and puncture frequency observed by

Pegasus 1 and 2 (as of July 20, 1965) are summurized in table 1. Note that the few punctures observed in the 200-M and 400-M Pegasus 1

detectors are in reasonably good agreement with

Pegasus 2 results. The total 40-M events

give a somewhat higher puncture rate for

Pegasus 2 than for Pegasus 1.

TABLE 1.—Pegasus 1 and ii penetration rates

Pegasus 1

400 n

2 0 0 M

4 0 M

Pegasus 2

4 0 0 M

2 0 0 M

40 M (total)

4()M (shtworpeak)

4 0 M (sporadic)

Number of

penetrations

4

0

104

30

14

Cl

12

40

Area-time

(m1 day)

1925

248

858

S457

734

357

26

290

Frequency of

penetrations

(number/m*

sec)

2. 4X 10-»

4. 2X 10-7

1.4X10-'

4. OX 10-"

2.2X10-*

2. OX 10-«

5. 3X 10-*

1.5X10-*

One possible explanation may be seen by

comparing the time history of the 40-M cumulative counts on Pegasus 2 (fig. 15) with figure 14.

There appears to be a significant increase in

counts during the period June 6 to June 12.

It is interesting to note that this period corresponds with times of known meteor-shower

activity, i.e., the Arietids and the f Perseids.

If the shower events are subtracted from the

Pegasus 2 counts, a sporadic background that

is very close to the Pegasus 1 data is obtained.

Of course, a reasonable explanation must be

found for the nonobservation of the showers by

Pegasus 1.

FIGURE 15.—Time history of accumulated penetrations for

40-M panels on Pegasus 2.

One plausible explanation may be found in

the difference of the rotational behavior of the

two satellites. Angular momentum in the form

of rotation about the x axis was imparted to

both spacecraft when the residual propellants

were vented. Since the x axis is a principal

axis of least moment of inertia, such a rotational

state is quasistable for a semirigid body.

Pegasus 1 underwent a transition to the minimum rotational energy state (i.e., rotation

about the z axis, which is the axis of maximum

moment of inertia) in 15 days. This rotation

stabilized the sensor plane in space. Gravity

gradient torque causes a precession of the

rotational axis, which provides a relatively slow

scanning of the celestial sphere.

The result of this motion may be seen in

terms of the angle the sun makes with the sensor

plane shown in figure 16. Preliminary analysis

indicates that the normal to the sensor plane

made angles of 50° and 65° with the radiants
248

SYMP08IUM ON METEOR ORBITS AND DUST

K

3

l u

i?:

5 °

_

3

I "**

.'

•

PI

•

'•

—J

•

•

•

FIGURE 16.—Angle sun makes with Pegasus 1 sensor plane as a

function of time.

I:

-i r

j i

aara oriw<i«.M

J L

SU A

of the Arietids and f Perseids, respectively, during the times of peak activity. Since the area

presented to the shower direction is reduced by

the cosine of the angle of incidence, and since

the penetrating ability of an impacting meteoroid falls roughly as the % power of the cosine of

the angle of incidence, it is understandable that

these showers may be missed by Pegasus I. Of

course, the deviation that was attributed Jo

shower events in Pegasus 2 data is small and

may very well be nothing more than a coincidental statistical fluctuation.

Pegasus 2, for reasons that are not yet completely clear, retained its rotation about the

x axis. This rotational configuration, together

with the lower angular momentum imparted to

it, results in a more rapid precession of the

rotational axis as is evident in figure 17, which

shows the angle between the sun and the rotational axis. The motion is such that the entire

celestial sphere is swept with the sensor axis in

a period of a single day. Therefore, the observation of showers having a population of detectable particles sufficiently above the sporadic

background is virtually assured.

The time histories of the 200-M and 400-M

cumulative counts are shown in figures 18 and

t

H

f

—r

-h \

—i

-V

*v

• •—H

FIGURE 17.—Angle sun makes with Pegasus 2 rotational axis

as a function of time.

FIGURE 18.—Time history of accumulated penetration* for

200-/1 panels on Pegasus 2.

FIGURE 19.—Time history of accumulated penetrations for

400-/1 panels on Pegasus 2.

a PEGASUS t

t ) PEGASUS 2

SHOWER PEAK

TOTAL

SPORADIC

THICKNESS OF ALUMINUM, cm

FIGURE 20.—Pegasus 1 and 2 penetration rates.
NASA METEOKOID PENETRATION' RESULTS FROM SATELLITES—D*AIUTOLO ET AL. 249

19. The sampling rates for these thicknesses

are too low to see any shower effects.

The penetration rates in the various thicknesses for Pegasus 1 and 2 are shown in relation

to one another in figure 20. The error bars

indicate 95 percent confidence limits.

Comparison of meteoroid penetration rates

In figure 21 the direct near-earth meteoroid

penetration measurements obtained from Explorer 16 and Explorer 23, as well as from

Pegasus 1 and 2, are compared with a current

estimate (Whipple, 1963) of the expectation of

frequency of meteoroid ]>enetrations. The

number of penetrations/m2 day is plotted as a

function of thickness for the j>enetration of

aluminum sheet*. The0.0025-cm and 0.0051-cm

A EXPLORER 16

O EXPLORER 2 3

D PEGASUS I

t l PEGASUS 2

WHIPPLE (1963)

BEST ESTIMATE

10 10 10

THICKNESS OF ALUMINUM, em

FIGURE 21.—Comparison of meteoroid penetration rates.

240-022 O—67 17

Explorer 16 beryllium-copper-cell data, as well

as the 0.0025-cm and 0.0051-cm Explorer 23

stainless steel-cell data, are plotted at equivalent thicknesses of aluminum based on laboratory impact tests wherein it was determined that

the resistance to penetration of the beryllium

copper and stainless steel is about twice that for

aluminum. The bars on the satellite data

indicate the statistical uncertainty in the direct

measurements. With a 95 percent confidence,

the actual value lies between the bars shown.

There is reasonably good agreement between

measurements obtained from the several spacecraft in spite of the fact that a number of refinements, as pointed out previously, have not yet

been applied to the data. For the thinner

materials, the rate of decrease of the frequency

of penetration with thickness is seen to be considerably less than that previously estimated.

Also, for the thin materials, there are approximately two orders of magnitude difference

between the measured and the estimated penetration rates. On the other hand, the penetration frequency and the rate of change in thick

materials are in better agreement with the

estimates.

Concluding remarks

The direct meteoroid-penetration measurements

by spacecraft have significantly narrowed the

uncertainty in predicting the penetration frequency in materials approaching actual spacecraft skin thicknesses. Although the data

obtained are extremely useful to spacecraft

designers, measurements of penetration rates

in thicker materials, which will correlate with

ground-based observations, must be determined

before a complete appraisal of the near-earth

meteoroid hazard to space flight can be ascertained.

References

BJORK, B. L,

1961. Meteoroids vs. space vehicles. Amer.

Rocket Soc. Journ., vol. 21, pp. 803-807.

D'AUTOLO, C. T.

1964a. Review of meteoroid environment l>ased on

results from Explorer XIII and Explorer

XVI Satellites. In Space Research IV,

wl by P. Muller, North-Holhnd Piibl.

Co., Amsterdam, pp. 858-874.

19641). Satellite measurements of the mcteoroid

environment. Ann. New York Acad

Sci., vol. 119, pp. 82-97.
250 SYMPOSIUM ON METEOR ORBITS AND DUST

DAVISON, E. H., and WINSLOW, P. C . Jr.

1964. Micrometeoroid satellite (Explorer XVI)

stainless steel penetration rate experiment. NASA Tech. Note D-2445,

August.

HASTINGS, E. C, compiler

1963a. The Explorer XVI micrometeoroid satellite: Description and preliminary result*

for the period December 16, 1962 through

January 13, 1963. NASA Tech. Memo.

X-810, February.

1963b. The Explorer XVI micrometeoroid satellite, Supplement I: Preliminary results

for the period January 14, 1963 through

March 2, 1963. NASA Tech. Memo.

X-824, April.

1963c. The Explorer XVI raicrometeoroid satellite, Supplement II: Preliminary results

for the period March 3, 1963 through

May 26, 1963. NASA Tech. Memo. X899, September.

1964. The Explorer XVI micrometeoroid ?atellite, Supplement III: Preliminary results

for the period May 27, 1963 through

July 22, 1963. NASA Tech. Memo. X949, March.

SECRETAN, L.

1967. Measurements of interplanetary dust-particle flux from Explorer XVI CdiS and

wire grid dust-part icle detectors. Smithsonian Contr. Astrophys., vol 11, pp.

307-315.

SUMMERS, J. L.

1959. Investigation of high-speed impact: Regions of impact and impact at oblique

angles. NASA Tech. Note D-94,

October.

WATSON, F. G.

1956. Between the Planets. Harvard Univ.

Press, Cambridge, Mass., 188 pp.

WHIHPLB, F. L.

I'.t.-.x The mcteoritic risk to spaa' vehicles. In

Vistas in Astronautics, vol. I, ed. by

M. Alju-rui and M. Stern, lYrgamoM

Prom, Iiondon, pp. 115-124.

I'"..; On meteoroklit and penetration. Jouru.

(icophys. Ites., vol. 68, pp. 4920-4930.

Abstract

The need for direct measurements in the space environment to determine metcoroid penetration rates for application to spacecraft design is discussed. Recent penetration measurements by the Explorer 16 and the Explorer 23

satellites and the Pegasus series of satellites an; presented. The primary experiment on the Explorer satellites

utilized thin-wall pressurized cells. These cells, covering an aggregate area of about 2 m1 on each spacecraft, gave

indication of meteoroid puncture by loss of internal gas pressure. Each of the large-winged Pegasus satellites

measured meteoroid penetrations over a surface area of more than 200 m1 by means of electrical capacitor-type detectors that discharge when penetrated. The large detector area on these spacecraft permitted the use of target

materials up to 0.040 cm in thickness. The penetration statistics obtained to date from the satellites arc presented

and compared with estimates of expected penetration rates.

The satellite measurements appear to have reduced significantly the uncertainty in predicting the penetration

frequency in materials approaching actual spacecraft-skin thicknesses. Further measurements are required, however,

before an accurate mass-frequency distribution of penetrating metcoroids can be established.
NASA METEOROID PENETRATION RESULTS FROM SATTELLITES—D'AIUTOLO ET AL. 25 1

Pegasus satellite configuration with body-fixed coordinate axes indicated.

Some Penetration and Charge-Detection Techniques

R. C. JENNISON

 i

Between 1960 and 1964 the Space Research

Group at the Nuffield Radio Astronomy Laboratories of the University of Manchester developed a number of techniques for the investigation of the dust particles in space. The first

of the techniques to be flown were rocket-borne

penetration detectors mounted on Skylark

rockets launched at Woomera, Australia. The

first series of launchings were not successful as a

result of failures of the rockets, but the technique is of interest and has not been described

in previous publications.

The Skylark rocket was fitted with a split

nose cone, which could be separated and discarded at a height of about 60 km. Within the

nose cone four roller blinds of aluminum foil

about 1 m long and 10 cm wide were erected so

as to be exposed to the space environment.

The foils were supported by a pulley system,

which was locked while the rocket was in the

upper part of its trajectory but which could

release the blinds so that they were withdrawn

onto the rollers in armored cassettes when the

vehicle descended to a height of 60 km. The

cassettes were then sealed by the simple process

of feeding an electrical current into a small

resistor, which heated a loop of nylon thread

and released a spring-controlled lid that locked

into place over each cassette.

In the first rocket shots the roller blinds were

double, spaced apart by about 1 cm over the

whole of their length in the erected position but

retracting together onto the same rollers when

withdrawn into the cassettes. The reason for

this arrangement was that it was hoped that if

a particle penetrated the outer foil the second

1

 The Electronics Laboratories, The University of Kent, Canterbury,

England; formerly at the Physical Laboratories, The University,

Manchester. England.

foil could also be examined for a coincident hole

or signs of debris from the first impact; this

would provide information on the impacting of

the particles, help in the analysis of true punctures, and possibly provide information for the

development of future techniques. Unfortunately, these early experiments were mounted

on an ill-fated series of rockets that came to

grief for a variety of reasons.

Similar equipment was later successfully

launched, but on this occasion it was designed

to study the impacts in aluminum foil bonded

to mylar and no secondary foils were incorporated. In this experiment six holes were found

in the foils when they were recovered and removed from the sealed cassettes. These holes

were extensively analyzed and examined with

high-powered microscopes. None of them was

of the type that had been anticipated from

hypervelocity impacts, for the holes were of

various shapes, ragged and elongated, and it

could not definitely be established that they

were formed through the impact of the dust

particles in space. Nevertheless, the holes

were not there on the foils before launching and

identical control foils, which were subject to

similar treatment at Woomera but were not

flown in the rocket, did not show any holes. It

appeared that the holes in the flight foils must

have been formed during the flight but might

have resulted from fatigue of the aluminum.

The foils were exposed in space for less than 10

min, so that if the holes were true dust-particle

punctures the impact rate would be very high,

commensurate with that claimed for the Venus

Flytrap experiment. The research group had

to be disbanded and it was not possible to follow up this result with a further series of rocket

253
254 SYMPOSIUM ON METEOR ORBITS AND DUST

shots, though it was highly desirable to sample

the penetration rate, if it were real, at a number

of heights in the atmosphere, as there was a

possibility that the rocket penetrated a dust

layer at about 80 km. A continuously moving

roller blind would form the basis of a simple

future experiment.

Ariel 2 experiments

An experiment to determine the distribution of

particle sizes that could puncture thin aluminum foils was incorporated in the Ariel 2 satellite, which was launched on March 27, 1964.

This experiment incorporated four sensor units,

two of which were designated Instaneous-ReadOut Detectors (IRODs) and two were called

Delayed-Read-Out Detectors (DRODs). All

four units were arranged around the equator of

the satellite and utilized the light from the sun,

combined with the spin of the satellite, to scan

the holes in the foil. The satellite had an initial

spin rate of 5.5 rpm falling to 0 after 6 months.

The apogee and perigee were 1358 and 289 km,

respectively; the inclination of the orbit was

51?7.

Instantaneous-Read-Out Detectors

These detectors were wedge-shaped, with the

apex of the wedge parallel to the axis of the

satellite and the base of the wedge mating to

the cylindrical outer surface of the satellite.

The base carried an aperture or slot 10% by 2

inches and the aluminum foil was wound very

slowly from a full spool at one end to a take-up

spool at the other end, behind the aperture.

The foil width was approximately 4 inches, the

extra 2 inches being taken up in light-tight,

slotted guides at the edges of the aperture, and

the wind-on occurred in discrete movements of

about }{t inch every other time the satellite

passed into the earth's shadow. A 7-inch strip

of silicon solar cells approximately Ke inch wide

was mounted in the apex of the detector parallel

to the satellite spin axis. In contact with this

strip, on the sensitive side nearest the aluminum

foil, a molded epoxy resin cylindrical lens % inch

in diameter served to enlarge the apparent

width of the solar cells and reduce the resolving

power of the system without appreciably reducing the electrical sensitivity. The triangular end covers of the wedge-shaped detectors

were of aluminum alloy sheet, polished on the

inner side to serve as mirrors so that the image

of a hole in the foil could scan across the cylindrical lens and silicon cells when the sun was

inclined at angles of up to 35° to the plane

normal to the spin axis of the satellite.

The 10# by 2-inch aperture in the base of

each detector had two struts on the inner surface between the foil and the cylindrical lens.

These struts were 1 inch wide and were inset

approximately %t inch behind the foil. From

the inside of the detector the struts appeared

to divide the foil into three equal sections.

They served to strengthen the detector while

suppressing readout of the micrometeorite holes

during the readout of calibration holes, which

were mounted in line with the strut* about 1

inch from the two mirror surfaces. The foils

installed in the two detectors were 12-M and 15-M

aluminum, respectively.

Both detectors used a Ledex solenoid-type

actuator to wind on the foil in discrete steps of

approximately K« inch at a time. The Ledex

had an angular movement of 25°, which was

limited by a ratchet mechanism to about 15°,

thus imparting the requisite motion to the takeup spool, which was J4-inch diameter before the

foil was taken up. The gradually increasing

effective diameter of the take-up spool resulted

in an increase in the rate of wind-on, but this

was not significant during the lifetime of the

satellite.

The output of each silicon solar cell strip was

amplified and then telemetered at a rate of 26

samples per second. Repeated scans of one

foil could be combined later when analyzing

the data to obtain a higher resolution. The

detectors were scanned throughout alternate

orbits, their outputs being switched in turn to

the telemetry orbit by orbit.

Delayed-Read-Out Detectors

These units were designed to detect finer micrometeorite particles but could also record impacts by larger particles. They were much less

sensitive to satellite spin than the Instantaneous-Read-Out Detectors but incurred an appreciable delay between the formation of the

holes and the telemetering of the information

concerning them.
PENETRATION AND CHARGE-DETECTION TECHNIQUES—JENNISON 255

The detectors employed an exposed area of

aluminum foil bonded to mylar, which was

wound on in discrete movements of approximately }{« inch across a rectangular aperture.

The film in this case was wound on in a direction

parallel to a spin axis so that holes in the main

part of the foil were brought over strips of

silicon cells by the wind-on action. Thus,

resolution was achieved primarily by the windon action, while the problem of diffraction from

the smallest holes was removed. Two flaps on

either side of the aperture restricted the

illumination onto the foil so that the sun swept

across the strip of foil in front of the silicon

strip and would, if there were a large flux of

small penetrating particles, give rise to a

triangular pulse lasting for 90° of the rotation

of the satellite and having a height dependent

upon the integrated flux of the smallest particles

capable of penetrating the metal surface.

Larger particles would cause rectangular pulses

whose phases in relation to the calibration holes

would determine their position across the width

of the strip. Thus, larger holes could be resolved by the system in both the longitudinal

and lateral directions.

The foils used in the DROD sensors were 5-

and 9-M thick. The foils in their virgin state

were not free from pinholes, and for this reason

two strips of silicon cells were employed in each

detector, one on each end of the aperture, so

that the foil was examined immediately before

and after exposure to micrometeorites.

Calibration of the system was automatically

performed by pinholes at the base of a slot

immediately to one side of the detectors. These

pinholes covered a section of the silicon cells

and produced pulses immediately before the

sun illuminated the foil.

The width of the strip of solar cells was 2.5

times the wind-on stepping distance, i.e.,

approximately 0.2 inch.

The outputs of the detectors were amplified

and telemetered, each output being sampled

three times a second. The before-exposure

outputs of two detectors were transmitted

concurrently on separate telemetry channels

for one orbit, and the after-exposure outputs

were transmitted for the next orbit, and so on.

A full account of the equipment has been

published elsewhere (Jennison et al., 1965).

Performance in orbit

All four sensor units operated satisfactorily

from the time of injection into orbit until the

present. The spin rate of the vehicle fell to

zero after 6 months and, although occasional

readouts are still obtained, the analysis of data

is confined to the first half year, and in particular

to those periods when the attitude of the

satellite was such that the sun was within

±35° of the normal to the spin axis. The

calibration holes of all the units gave clear and

easily recognized signals, while a sequence of

holes, preformed with a laser in the actual

foils, also gave clear signals, which moved on in

the correct manner relative to the calibration

holes as the foils were transported across the

sensors. Computer processing of the data will

enable a very much higher sensitivity to be

obtained than that apparent in figure 1, which

was recorded directly from two successive

spins of the telemetered data.

The analysis of the DROD data is not yet

complete, but that for the IRODs covers most

of the 6-month period. No holes have been

detected that can be attributed to micrometeorites. A single hole appeared after 2

months exactly at the point where the foil

enters the exposed aperture, and it was transported across the aperture during the succeeding days. This hole was almost certainly a

defect in the virgin foil that had either escaped

observation on the preflight examination, or from

which the small blob of black paint, applied to

such defects, had become detached. Nevertheless,

there is a slight possibility that this hole could

have been formed by a micrometeorite that

impacted at the extreme end of the exposed

surface.

Upper limits for the penetration rates of the

foils are shown in figure 2, with the abscissa

marked in microns. The IROD limits shown

CALIBRATION

FIGURE 1.—Telemetry output.
256 SYMPOSIUM ON METEOR ORBITS AND DUST

3-,

"*""O

• EXPLORER 8 (PHOTOMULTIPUERl

-( RANOCR1 (PHOTOMULTIPUER)

O EXPLORER • (MICROPHONE)

< MIDAS 2 (MICROPHONE)

t> SAMOS 2 (MICROPHONE)

<} SPUTNIK 3 (MICROPHONE I

"••O VENUS FLTTRAP (COLLECTION)

T—»S% I ARIEL 2 (UPPER LIMITS

• — SO%[ FOR CONFIDENCI

• ' LEVELS SHOWN

5 » 13 IS JO SO 100 '

LOO PARTICLE MASS (9)

FIGURE 2.—Cumulative flux of particles.

are those for 15-/x aluminum, and the PROD

limits correspond to the incomplete analysis of

the 9-M foil. The thick bars across the vertical

arrows indicate 50 percent confidence limits,

and the dotted vertical extensions give the

limits for 95 percent confidence.

The most definitive result of the experiment

concerns the hazard from the micrometeorite

particles in space. The penetrating power of

the smaller particles appears to be such that

the lifetime for the survival of thin surfaces is

many orders of magnitude greater than that

anticipated when the experiment was designed.

Not only is the penetrating power of the average

particle very low but less than one in a thousand

of those detected by microphones within the

range of sensitivity of the Ariel 2 detectors could

have a mass commensurate with a solid particle

of iron or stone. The results indicate that

the density of the particles is probably very

small and the radiation pressure limit for the

particle size is probably considerably higher

than most earlier estimates.

Charge-detection techniques

A technique was developed some years ago that

lias considerable possibilities for determining a

number of parameters associated with the dust

particles. Unfortunately, although a rocket

payload was prepared, the closing down of the

group's activities in space research resulted in

the premature abandonment of the project.

The technique detects the dust particle by

virtue of any electrostatic charge it may have.

The charge qm is related to the potential of the

surface of the micrometeorite Vm by the micrometeorite self-capacity, which in electrostatic

units equals the radius of the particle rm:

In an ionized medium the currents formed by

the processes of emission and capture of ions

are both proportional to the area of surface

considered, and thus the potential of particles

in space remains largely independent of the

particle dimensions. It is the potential, and

not the charge, that remains the common parameter of bodies in space of differing dimensions but of similar surface properties.

The ion-capture current is a function of the

potential of the micrometeorite; if the micrometeorite is negatively charged up to a voltage

of, say, V volts, it will repel all electrons up to

an energy of eV electron volts. If it is positively charged it will attract electrons, constituting an effective area of capture very much

greater than its physical area. Estimates of

the micrometeorite potential differ by a small

factor and are dependent on environmental

conditions that have not been fully established.

The processes affecting the variation of micrometeorite potential in differing environmental

conditions are, however, reasonably veil understood quantitatively. In the Van Allen belts,

capture of the flux of energetic electrons causes

a negative micrometeorite potential. In the

F2 regions, where there is a high concentration

of thermal energy electrons, the potential may

again assume a negative value, but of lower

magnitude.

If the dust particle is illuminated by the sun,

a certain fraction of the absorbed photons will

create photoelectrons over a wide range of

energies. The photoelectrons of low energy

may return to the micrometeorite under the

influence of its potential if this is positive, but

those of energy greater than the micrometeorite

potential will escape completely from the micrometeorite, the effect of which is to cause the

equilibrium potential to become less negative.

This photoelectric current is insufficient to

cause the potential of the dust particle to
PENETRATION AND CHARGE-DETECTION TECHNIQUES—JENNISON 257

become positive in the Van Allen and F2

regions, but may do so at greater distances

from the earth where the concentration of electrons is less than a value of the order of 100/cm3

.

As the potential increases beyond a value of

+ 6 V, corresponding to the energy of the

Lyman emission, there is a reduction of one

order of magnitude in the photoelectric current.

These considerations render it unlikely that

at all distances from the earth the environmental conditions will be so well balanced as

to maintain a micrometeorite potential of lower

than several volts. A potential of 5 V on a

spherical dust particle of radius 1 n corresponds

to a charge of 3X 103 electrons. The charged

particle may be detected in a passive system in

which it is allowed to pass through a hollow

cylindrical detector that is suitably screened

from various sources of interference. The induced signal is independent of the satellite

potential; it is probable that the satellite and

micrometeorite will be at similar potentials, but

even if the two potentials are identical the

micrometeorite charge will still be detected.

If the micrometeorite radius is rn, the potential is Vm volts, and the total input capacity of

the detecting system is Ct picofarads, then the

signal voltage is given by

V.= lllrmVm

It has been shown (Jennison and McDonnell,

1964) that this voltage may be clearly detected

against the background noise in a transistor

amplifier using a high-impedance field-effect

transistor in the input stage.

A single detector in the form of a hollow

cylinder mil provide a pulse from which the

micrometeorite charge may be obtained. A

second detecting cylinder makes it possible to

determine the time separation of the two pukes

and thus to derive the micrometeorite velocity.

The particle is not affected in passing through

the cylinders, and the two detectors may be

followed by a microphone sensor that is sensitive to a function closely related to the micrometeorite momentum. By combining this

measurement with the measurement of velocity

from the two detecting elements, the velocity

and mass of each micrometeorite may be

obtained. The complete system is sensitive to

particles in a relatively small solid angle and

may be used to determine the radiants of the

detected particles, but the price paid for this

is a considerable reduction of the flux of

detectable particles.

The original technique was capable, in

principle, of detecting micrometeorites greater

than 3-/t diameter (3X10~12 g for a density of

0.3 g/cm3), and even more sensitive if potentials of greater than 5 V exist on micrometeorites

in space. Greater sensitivity may be obtained

by the use of improved components.

References

JENNISON, R. C, and MCDONNELL, J. A. M.

1964. A technique for the detection and determination of the velocity, mass, radiant,

charge and flux of micrometeorite particles in space. Planet. Space Sci., vol.

12, pp. 627-635.

JENNISON, R. C; MCDONNELL, J. A. M.; RODGER, I.;

and SMITH, M.

1965. Proc. Inst. Electronics, vol. 8, no. 1.

Direct Measurements of the Mass Distribution and Time

Variations in the Flux of Small Dust Particles

C. W. MCCRACKEN, 1 W. M. ALEXANDER,2 and M. DUBIN

 3

Introduction

Dust-particle sensors mounted on rockets,

satellites, and space probes have been used

extensively during the past decade for studying

small dust particles outside the atmosphere of

the earth. The sensitivities of the sensors

ranged from about 10~* to 10~u g, and most of

the data were obtained in the range of dustparticle mass 10"' to 10~M

 g. These studies

yielded information concerning (1) the flux of

small dust particles, both in the vicinity of the

earth and in interplanetary space, (2) the mass

distribution for dust particles in the vicinity

of the earth, and (3) the time variations in the

flux near the earth. Most of the data relating

to the mass distribution and the time variations

in the flux were obtained with the microphone

type of dust-particle sensor flown on near-earth

satellites.

A summary and analysis of the available

direct measurements of small dust particles

were given earlier (Alexander et al., 1963). The

direct measurements obtained by various investigators with several types of dust-particle

sensors were found to be in good agreement with

the mass distribution that was measured with

the microphone system on Explorer 8. An

obvious lack of statistically valid data, which

could be used for investigating a possible

decrease in the flux of small dust particles with

increasing geocentric distance, was noted. The

1

 Goddard Space Flight Center, National Aeronautics and Space

Administration, Oreenbelt, Md.

•Temple University, Philadelphia, Pa.; formerly at Ooddard Space

Flight Center, National Aeronautics and Space Administration,

Greenbelt, Md.

• National Aeronautics and Space Administration, Headquarters,

Washington, D.C.

somewhat lower flux measured with the microphone system on Pioneer 1 was considered to be

indicative of a radial decrease in the flux, but

the data sample was limited (17 impacts at

geocentric distances ranging between 2 and 19

earth radii). If we allow for a possible decrease

in the mean relative speed of the particles with

increasing geocentric distance, the flux measured with Pioneer 1 comes within the range of the

time variations in the flux measured with the

microphone system on Vanguard 3. An indirect

(but quite sound) argument for the existence of

a geocentric enhancement of the flux of small

dust particles was provided by Whipple, who

pointed out that the flux measured in the

vicinity of the earth was several powers of 10

higher than the flux expected in interplanetary

space on the basis of studies of the zodiacal

light and solar F corona.

Additional data on the flux of small particles

near the earth were obtained with a set of

penetration-type dust-particle sensors flown on

Explorer 16 (D'Auitolo, 1964). These data

indicated that the penetrating flux was 10 to

100 times lower than had been expected on the

basis of the flux measured with microphone

systems. This discrepancy, if real, might be

interpreted in terms of a low penetrating power

for particles of the sizes measured by the two

different types of sensors. It could occur if

dust particles with radii between about 10

and 100 M have irregular shapes and a fluffy or

dendroidal structure and are therefore less

effective in penetrating a target than is a dense

particle of comparable mass. Another possible

explanation is that a size-dependent parameter

259
260 SYMPOSIUM ON METEOR ORBITS AND DUST

is present in the hypervelocity cratering formulas used in calculating the sensitivity for

penetration-type sensors. These penetration

criteria are, for the most part, based on laboratory studies of craters formed by larger

particles than those registered in space by

penetration-type dust-particle sensors. The

apparent discrepancy that has arisen between

the results obtained with the microphone

systems and the penetration-type sensors requires further investigation.

This paper was to have been a review of the

data obtained with the microphone type of

dust-particle sensor. With the exception of

the new data from the microphone systems on

Mars 1, Elektron 2, Mariner 4, and OGO-1

being presented at this symposium, only the

data from Mariner 2 are to be added to the information summarized in the earlier review.

We shall discuss anew some aspects of the older

data obtained with microphone systems and of

the bearing of these data on the problems of

the mass Ustribution and time variations in the

flux of small dust particles. In addition, we

shall include the latest available readout of the

data obtained with the microphone systems on

Vanguard 3 and Mariner 2.

Neither the Soviet nor the U.S. investigators

have succeeded in obtaining statistically valid

measures of the flux in cislunar space that

could be used in establishing the radial dependence of the geocentric enhancement of "the

flux of small dust particles. The data included in this review clearly limit our discussions

to the immediate vicinity of the earth.

Time variations

The first evidence for large time variations

in the flux«of small dust particles was obtained

with the microphone system flown on Explorer 1

(Dubin, 1960a). The impacts of 145 dust

particles were registered on a real-time telemetry basis during a 12-day interval following

launch on February 1, 1958. An interval of

enhanced flux occurred approximately 38 hours

after launch and persisted for about 15 hours.

This interval accounted for 67 of the 145

recorded impacts; thus, 46 percent of the

impacts occurred during only 6 percent of

the time for which telemetered data were

received.

The maximum number of impacts recorded

during any one pass over a telemetry station

was 12. These 12 impacts occurred during

an interval of 261 sec beginning at 0141 UT,

February 3. The corresponding impact rate

(2.8 impacts/min) was the highest recorded

during the interval of enhanced flux and was

higher by a factor of 25 than the average

impact rate (0.11 impacts/min) for the entire

12-day interval.

Although the sample time and the number

of impacts recorded for any one given telemetry

pass are small, the interval of enhanced flux

actually can be traced for a 23-hour interval

between the two passes beginning at 1512

UT, February 2, and 1405 UT, February 3.

The systematic dependence of the impact rate

on the position of the satellite during this

interval is shown in figure 1. The apparent

shielding of the satellite during the early

morning passes and the dependence of impact

rate on position suggest that the swarm of dust

particles in this sporadic shower may have

overtaken the earth in the manner that would

occur if the dust particles had noncircular

heliocentric orbits of fairly low inclination.

FIGURE 1.—Dependence of impact rate on the position of

Explorer 1 during the dust-particle shower on February 2

and 3, 1958.

Nazarova (1960) reported that the microphone system on Sputnik 3 recorded a flux of 4

to 11 particles/m2/sec on May 15, 1958, which

was the day of launch. The flux subsequently

decreased by a factor of 10* to a level of 5X10~4

particles/m2/sec for May 16 to 17. The flux

during the remainder of the sampling interval

(May 18 to 26) was less than 10"4 particles/m2/
MASS DISTRIBUTION AND TIME VARIATIONS IN FLUX OF PARTICLES—M'CRACKEN ET AL. 261

sec. The exact number of impacts recorded by

Sputnik 3 is not available to us.

A microphone system on Vanguard 3,

launched on September 18, 1959, recorded the

impacts of 6307 dust particles during 80 days

of continuous operation. The experiment included a cumulative counter, which was read

out during passes over telemetry stations

(Alexander and LaGow, 1960). The known

time history for the cumulative counter defines

both the number of real-time impacts recorded

during each telemetry pass and the total number of impacts recorded between successive

telemetry passes.

Of the numerous experiments performed by

us, only two are known to have been subject to

interference problems. The data from OSO-1

obtained with a combination microphone and

photomultiplier type of dust-particle sensor

(like the one flown successfully on Ranger 1)

have never been presented, because interference

appeared during the flight. The other system

for which interference occurred was the microphone system on Vanguard 3. Interrogation

of the magnetometer sometimes caused the

cumulative counter in this microphone system

to advance by one or more counts.

Almost complete recovery of the data from

the microphone system on Vanguard 3 was accomplished by Messrs. C. M. Stout and R. D.

Carper, whose painstaking and time-consuming

work is gratefully acknowledged. Corrections

were applied for the false counts observed to be

caused by interrogations of the magnetometer,

leaving 6307 indicated impacts of dust particles.

There were some interrogations of the magnetometer that could not be monitored because of

loss of signal, poor signal-to-noise ratio, lack of

telemetry coverage, etc. Some of the unmonitored interrogations, like many of the monitored

interrogations, are known to have caused no

false counts because the settings of the cumulative counter were identical before and after

the interrogations.

An estimated 5 percent of the 6307 indicated

impacts may have been caused by the unmonitored interrogations. It may therefore

be said, with reasonable confidence, that the

microphone system on Vanguard 3 registered

the impacts of approximately 6000 dust particles

during the 80 days of continuous operation extending from 0735 UT, September 18, to 2321

UT, December 6, 1959. Impact rates and

fluxes for intervals of less than 80 days are, for

lack of complete restoration of the data, computed on the basis of the 6307 impacts listed

in the processed data, which had been corrected

for the false counts caused by monitored interrogations of the magnetometer. The data

presented here are based on the best available

processed data from Vanguard 3 and, as such,

supersede the data presented in earlier papers

(Alexander and LaGow, 1960; Alexander,

McCracken, and LaGow, 1961). A more detailed discussion of the time variations is therefore possible.

The recovered data from Vanguard 3 established the time dependence of the flux of dust

particles during the mid-November 1959 dustparticle event (Alexander, McCracken, and

LaGow, 1961), which was the most spectacular

dust-particle shower observed through the use

of satellites. During the 3-day interval extending from 0122 UT, November 16, to 0054

UT, November 19, 2436 of the 6307 impacts

occurred. This interval constitutes only 3.8

percent of the sampling time but accounts for

~40 percent of the recorded impacts. The

impact rates during this interval are shown in

figure 2. The data for November 16, 17, and

18 are shown on an expanded time scale and

have been filtered to the extent that sampling

intervals of less than 30 min are combined with

NOVEMK* 1939

INTEKKANCTMY DUST PMTKZLE

EVE NT

VANGUAID 3 (I959IJ)

* Nov. 16-IS

I No«. 10-20

C S«pt.18-0ct9

I I I I I I I I I I I I I

0 6 12 18 0 6 12 18 0 6 12 ;8 24

10 II 12 II 14 IS

FIGURE 2.—Time variations in the impact rate during the

dust-particle shower observed with Vanguard 3 in midNovember 1959.
262 SYMPOSIUM ON METEOR ORBITS AND DUST

adjacent intervals. The daily average impact

rates are shown for the remainder of the rather

arbitrarily chosen 10-day interval extending

from November 10 through November 20.

The highest impact rate occurred during a

real-time pass at 0336 UT, November 17,

when 190±5 impacts were recorded in 7m19i.

This interval does not appear in figure 2 because

of filtering, but the impact rate (1560 impacts/hour) lies outside the range of the

logarithmic ordinate that is used. The highest

impact rate shown in figure 2 is based on 363

impacts recorded in 2h3

m

 on November 16,

while the next highest is based on 351 impacts

recorded in 2b30m on November 17. At the

opposite extreme is an interval of 2h18m on

November 18 during which no impacts were

recorded, although the impact rate on this day

was 249 impacts/day or about 10 impacts/hour.

The number of impacts recorded on each day

during the 80 days of operation of the microphone system on Vanguard 3 is shown in figure

3. Day-to-day variations in the daily count

are considerably larger than the variations

expected on the basis of the counted numbers

of impacts. The lowest count was 8 impacts

on October 22, and the highest was 1354

impacts on November 17. The daily counts

do not apply for sampling intervals of exactly

24-hour duration, since the sampling intervals

were set by the location of the telemetry

stations. The daily counts are therefore converted to daily impact rates, which are presented in figure 4.

Figure 4 also shows the 80-day mean and the

10-day means of the daily rate*. Error flags

denoting one standard deviation of the daily

impact rates from the 80-day mean and each

VANGUARD 3

DAILY COUNTS OF IMPACTS

ERROR BARS AT LIFT DENOTE

EXPECTED VARIATION ^

FOR COUNT OF N IMPACTS

DAY 1

DATE IS

SEPTEMBER OCTOBER

•

16

NOVEMBER OECEMSiR

FIGURE 3.—Daily counts of dust particles recorded with the microphone system on Vanguard 3.
MASS DISTRIBUTION AND TIME VARIATIONS IN FLUX OF PARTICLES—M'CRACKEN ET AL. 263

_

3

i *

i

5

1

f t

-

—

•

-

•

•

•

VANGUARD 3 (1959 V •

AVERAGE IMPACT RATES

OVER

1 • DAY INTERVALS

10 - DAY INTERVALS

AND 80 - DAY LIFETIME

ERROR BARS DENOTE R.MS . DEVIATION

OF DAI, v AVERAGES FROM

AVERAGE FOR THE INTERVAL

* _ lt__ .

1 •

•* •

. ... ^

•

' '• • •

• •

•

•

•

•

•

• •

• •

• •

• •

• •

I I I I I I I I I I I I I I I I I I I I I I I 1

1

s

5 10

SEPTEMBER

15

2

20

7

25

1?

»

17

OCTOBER

35

22

4'1

27

45

1

50

6

55

11

a

lb

NOVEMBER

65

21

Is

26

75 SO

1 6

DECEMBER

FIGURE 4.—Daily impact rates and means over various intervals for the dust particles recorded by Vanguard 3.

of the 10-day means are included. The

standard deviation from the 80-day mean is

larger than the 80-day mean of the daily impact

rates, so the lower end of the error flag cannot

be shown on the logarithmic ordinate used in

figure 4. Similarly, the standard deviations

for two of the 10-day intervals are larger than

the 10-day means of the daily impact rate.

In figure 4 numerous cases are apparent where

the daily impact rate easily changes by

a factor of 2 from one day to the next.

The logarithmic ordinate and linear abscissa

used in figure 4 are reminiscent of the decay

curves used in determining the half-life of a

radioactive element. The half-life for the

mid-November 1959 dust-particle shower can

be read directly from figure 4 and is about 2

days. The rapid decay rate for the flux does

not at all suggest that the dust particles were

trapped into closed geocentric orbits with long

lifetimes.

It has been suggested that the mid-November

1959 dust-particle shower might have been

associated with the Leonid meteor stream

(Alexander, McCracken, and LaGow, 1961).

Leonid meteors show high speeds (~70 km/sec)

because the meteoroids meet the earth almost

head on. Neither gravitational concentration

nor the action of radiation pressure is effective

for such high speeds in increasing the accretion

cross section of the earth above the geometric

cross section. Any geocentric enhancement

of the flux of small dust particles associated with

the Leonid stream must have proceeded from

the level of the flux in the stream rather than

from the higher level of the average flux near

the earth. Such an association seems to be

very doubtful when the incremental mass
264 SYMPOSIUM ON METEOR ORBITS AND DUST

influx (which emphasizes the amount of material

rather than the number of dust particles) is

considered.

During the 80 days of operation, there were

112 cases where Vanguard 3 completed one or

more orbits (a period of 130 min) without registering the impact of a single dust particle. The

longest interval showing zero impacts was

15b15m in duration (7 orbits) and occurred on

October 20. The durations of the intervals

generally appear to exceed those expected statistically for random variations in the impact

rate. The complete interval distribution cannot be established, because the intervals

between individual impacts are not known.

The existence of the long intervals (1 to 7

orbits) that showed no impacts provides considerable assurance to the experimenters that

the microphone system on Vanguard 3 was not

subject to environmental interference (thermal,

electrical, and energetic-particle radiation) beyond the previously discussed interference from

the magnetometer.

Only 417 of the 6307 impacts registered by

Vanguard 3 were recorded while real-time telemetry was being received. Of these, 190 ± 5

impacts occurred in 439 sec during the previously mentioned pass at 0336 UT on November

17, 27 ± 5 occurred in 492 sec during a pass at

2026 UT on November 16, and 31 occurred

during a pass at 0414 UT on December 6. The

remaining 169 impacts were distributed

throughout the remainder of the 80 days to

yield an average of 2 impacts/day. This low

rate precludes determining the dependence of

the flux on the position of the satellite from the

impacts recorded during telemetry passes. Attempts to use the numbers of impacts recorded

between successive telemetry passes in lieu of

real-time impacts for investigating the dependence of the flux on position of the satellite,

altitude of the satellite, phase of the moon, etc.,

have also failed to yield any results of statistical

significance because of the effect of the terrestrial distribution of telemetry stations on the

sampling intervals. Further investigations will

have to wait until more definitive data can be

obtained.

The microphone system on Explorer 8 included a cumulative counter that was read out

in the same manner as for Vanguard 3. All

impacts registered by the microphone system

on Explorer 8 were stored in the cumulative

counter, but alternate impacts were included in

the telemetered data. Recovery of the data

from Explorer 8 to the extent accomplished for

Vanguard 3 is not feasible. Although the

data obtained on Explorer 8 were insufficient

for studying time variations in the flux, it was

possible to determine the total number of

impacts recorded for each of the three levels of

sensitivity during the 40 days of continuous

operation. No evidence for the occurrence of

intervals of enhanced flux like those observed

with Explorer 1 and Vanguard 3 appears in

the data from the microphone system on

Explorer 8.

Mass distribution

Establishing a mass distribution for the small

dust particles studied through the use of spacecraft involves measuring the flux as a function of

some observable parameter for the dust particles. Microphone systems employing piezoelectric crystals respond very accurately to the

momentum for spherical glass beads dropped

at normal incidence and low speeds during

laboratory calibrations of the systems. If we

assume that microphone systems respond also

to the momentum for dust particles impacting

at high speeds, we can express the measured

flux as a function of the particle momentum.

The transformation from momentum to mass

is then accomplished by assuming an average

speed for the dust particles registered by a

microphone system. The small uncertainties

introduced by these assumptions will be discussed after a brief review of the available

data.

The spacecraft, which carried microphone

systems, and the number of dust particles recorded by each are listed in table 1. Other

numerical data pertinent to the various systems (except for Mariner 2) were given in the

earlier summary (Alexander et al., 1963).

The microphone system on Mariner 2 recorded

the impacts of two dust particles between the

orbits of the earth and Venus. Telemetry

was available for approximately 75 days out of

the 90-day flight. The area of the sensor was

350 cm2, and the sensitivity of the system was

7.4 X10"4 dyne sec (Alexander, 1962). The
MASS DISTRIBUTION AND TIME VARIATIONS IN FLUX OF PARTICLES—M'CRACKEN ET AL. 265

omnidirectional flux computed on the basis of

the two impacts is 2.1 X10"5 particles/m2/sec.

The power for the instrument was applied when

the spacecraft was approximately two lunar

distances from the earth, so the flux indicated

by Mariner 2 applies strictly to interplanetary

space. The small number of impacts was

roughly what was expected on the basis of

studies of the solar F corona. Technological

limitations and the time schedule simply prevented the building of a more sensitive instrument at the time the design for the system was

set.

Table 1 shows that more than 10,000 impacts

of dust particles have been recorded with

microphone systems. (The data given by

Nazarova (1963) can be used to calculate that

a few hundred dust-particle impacts were

recorded by Sputnik 3 and the three Soviet

Geophysical Rockets.) The impacts registered by the microphone systems on Mars 1

and Elektron 2 (Nazarova, see pp. 231-237) and

those on Mariner 4 and OGO-1 (Alexander et

al., see p. 227) will bring the total to more

than 11,000 dust particles. Since almost 10,-

000 impacts were recorded on Explorer 8 and

Vanguard 3, we depend very heavily on these

results of continuous operation (~3700 impacts

TABLE 1.—The numbers of dust-particle impacts recorded

on microphone systems mounted on various vehicles

Vehicle

Explorer 8

Vanguard 3

Explorer 1

Pioneer 1

Ranger 1

Midas 2

Samoa 2

SLV-I

OSU Rockets

Sputnik 3

Lunik 1

Lunik 2

Interplanetary Station

Soviet Geophysical Rockets

Mariner 2

Total

Number of dust

particles

3726

~6000

145

17

64

67

157

10

287

(?)

<16

7

2

(?)

2

~10, 500

during 40 days and ~6000 impacts during 80

days, respectively).

The data obtained with microphone systems

are shown in figure 5 as a cumulative flux distribution expressed in terms of the particle

mass. This figure (which is figure 2 in Alexander et al. (1963) with the data from the

photomultiplier type of dust-particle sensors

deleted and the data from Mariner 2 added)

should be revised after further information has

been obtained regarding (1) the geocentric

trajectories of the small dust particles, (2) the

average speed for small dust particles at various

geocentric distances, and (3) the response of

microphone systems for dust particles having

speeds of at least 15 km/sec. The revisions

have a tendency to counteract one another, and

when the necessary information becomes available, corrections will probably leave the cumulative mass distribution shown in figure 5

relatively unchanged. Hence revision of figure

5 through the use of assumed values for the

correction factors hardly seems worth while at

the present time. A discussion of the magnitudes of the corrections, as they are currently

5

4

1

1

\

0

-1

-J

-3

-4

-5

- a

-7

V

V

• \ &

•ft

o o 9

^ T •

^ «.e «.'

RADIATION PRESSURE LIMITS

1 L , 1 1 1

<S>

©

a

.

*

\

1

Eiplntr 8

Vanavard 3

Espt«r«r 1

Pion..r 1

H,,,,,!

Midai 2

liM 2

SIV-I

OSU RackaH

Sputnik 3

lunik 1

L.nik 2

Sovi»t tackali

Mariaar 2

\

\

\

\

\

\

\

\

FIGURE 5.—Cumulative flux distribution showing the data

obtained with microphone systems.

240-022 O—«7- -18
266 SYMPOSIUM ON METEOR ORBITS AND DUST

known, should serve equally well until experimentally determined values for the corrections become available for use in a realistic

revision of the cumulative mass distribution.

The corrections applied for shielding of a

sensor by the earth and for the effective solid

angle of a sensor depend on the distribution of

orbits for the dust particles. The present lack of

knowledge concerning the geocentric trajectories

of small dust particles leaves the omnidirectional flux uncertain by a factor of about 2,

which is much smaller than the time variations

in the observed flux. The ordinate used in

figure 5 refers to the omnidirectional flux (reduced to 4x ster). A flux expressed in units of 2T

ster is physically more meaningful because of

both the general lack of omnidirectionality for

dust-particle sensors and the presence of

shielding by the earth for sensors mounted on

rockets and near-earth satellites. Revision

of figure 5 would therefore be accompanied by a

change from omnidirectional flux to a flux

expressed in units of 2x ster.

In the original version of figure 5 we assumed

that the average speed of dust particles detected

by an omnidirectional microphone on a nearearth satellite was 30 km/sec. We assigned

different values for an average speed for the

various spacecraft because some of the sensors

did not scan the whole celestial sphere. The

existence of the geocentric enhancement of the

flux of small dust particles now requires the

assumed average speed to be reduced from 30

km/sec to about 15 km/sec, which changes the

mass sensitivity of the microphone systems

only by a factor of 2. Reduction of the

assumed average speed used in converting

from momentum sensitivity to mass sensitivity

for the microphone systems will shift the results

shown in figure 5 toward slightly larger values

of particle mass by factors ranging from about

1.5 to 4, depending on the particular set of data.

This small correction and the correction that

may be required if the average speed varies

appreciably with geocentric distance are better

left until information about the geocentric

trajectories of the dust particles can be obtained so that the revision will be more realistic

and more accurate than one based on assumed

values for the average speed.

The magnitude of the small correction required by the reduction of the assumed average

speed depends on the assumption that microphone systems respond to the momentum of an

impacting dust particle. Opik's (1958) theory

of hypervelocity impact predicts that the

impulse delivered to a target will be about

three times the momentum of the projectile.

The effective coefficient of restitution for

high-speed impacts would therefore be about 2,

provided the microphone systems respond to

the impulse delivered by an impacting dust

particle. The effective coefficient was purposely set equal to zero in stating the sensitivities for several of the microphone systems,

pending a determination of the correct value.

The sensitivities given for other microphone

systems were based on the assumption that

the effective coefficient of restitution is unity,

while the effective coefficients of restitution

that apply for the Soviet results are unknown to

us. Despite attempts to handle all the data

shown in figure 5 in a consistent manner,

inconsistencies have unfortunately appeared

through the use of different values for the

effective coefficient of restitution. Use of an

effective coefficient of 2, as predicted by Opik

(1958), rather than the values of zero and unity

that were used, serves to shift the results

shown in figure 5 toward smaller values of

particle mass by factors as large as 2. The

required corrections for the most part cancel

one another.

The assumption that microphone systems

respond to the momentum of a high-speed

particle has been the subject of considerable

controversy. There is a lack of hypervelocity

particle accelerators that could be used for

realistically calibrating microphone systems

(like those on the spacecraft listed in table 1)

with particles having accurately known masses

and speeds. The Soviet investigators have

assumed, on the basis of the hypervelocity

cratering theory of Stanyukovich, that their

microphone systems respond to the kinetic

energy of a dust particle impacting at high

speed. The U.S. investigators have assumed

that their microphone systems respond to the

momentum of an impacting dust particle. This

assumption is supported by the hypervelocity
MASS DISTRIBUTION AND TIME VARIATIONS IN FLUX OP PARTICLES—M'CRACKEN ET AL. 267

cratering theory of Opik. Despite the different

assumptions, the results reported by the two

groups are in fair agreement concerning the

flux of dust particles of any given mass.

There are some experimental data that support the assumption that microphone systems

respond to the momentum of a dust particle

impacting at high speed. Calibrations performed at the Stanford Research Institute

showed that systems using crystal microphones

constructed by Professor J. L. Bohn of Temple

University responded (within a factor of 2) to

the particle momentum for steel spheres accelerated by shaped charges to speeds as high as

4 km/sec (I)ubin, 1960b). The microphones

used in the systems on Explorer 1, Pioneer 1,

and the U.S. rockets were all constructed by

Professor Bohn.

A converted 2-Mev van de Graff machine is

now being used routinely in calibrating microphone systems with iron carbonyl particles

having speeds that range up to 3 km/sec.

These calibrations show that microphone systems somewhat more sensitive than those with

which the data in figure 5 were obtained respond

(within a factor of 2) to the momentum of a

high-speed particle. Preliminary results for

particles having speeds as high as 8 km/sec

indicate that the effective coefficient of restitution is appreciably larger than unity.

We assume that the microphone systems

represented in figure 5 responded to the momenta of impacting dust particles. The cumulative flux distribution shown is uncertain by

the small factors previously discussed in connection with the revision known to be required

for figure 5. The results could shift considerably in particle mass if the effective coefficient

of restitution should prove to be markedly

greater than unity. It is unlikely that any

such shift would alter the slope of the distribution curve. A small change in slope could

conceivably occur if the average speed is a

function of the particle mass, but such an

effect surely must be negligible for the range

of particle mass encompassed by the direct

measurements shown in figure 5. The presence of a size-dependent parameter in the

hypervelocity cratering process might also

cause a small change in the slope of the distribution. The suspected (or demonstrated) presence of such a size-dependent parameter would

require further evaluation of the apparent discrepancy between the results obtained with the

microphone type and the penetration type of

dust-particle sensor.

It is evident from figure 5 that there are two

basic ways in which to establish the mass distribution of small dust particles. The first

involves the use of a microphone system having

several levels of sensitivity that encompass a

range of several powers of 10 in the particle

mass. The second involves the use of a system

with a single level of sensitivity or one with two

or more levels of sensitivity that are limited in

effectiveness by either close spacing or a limited

data sample. The latter approach requires accumulated data from several flights of systems

with different sensitivities; it is also necessary

to assume that the flux remains fairly constant

from one flight to the next. This assumption

has been in question since the first flight of a

microphone system on a satellite (Explorer 1),

which gave evidence for large time variations

in the flux.

The first approach is exemplified by the

microphone system flown on Explorer 8, and

the second by all the other microphone systems

flown on rockets and near-earth satellites. The

validity of both methods is well illustrated in

figure 5, which shows the good agreement among

the various data obtained in the vicinity of the

earth. Due allowance should be made for the

fact that Pioneer 1, Luniks 1 and 2, the Interplanetary Station, and SLV-1 operated at

somewhat greater geocentric distances where

the flux is undoubtedly intermediate between

that near the earth and that in interplanetary

space where Mariner 2 operated. The small

number of impacts recorded at geocentric distances greater than about 2 earth radii currently limits a discussion of the mass distribution to the immediate "vicinity of the earth.

The cumulative flux distribution shown in

figure 5 is combined in figure 6 with other data

on the flux of meteoroids and small dust particles. (The numerical data used in figure 6

are given in McCracken, see pp. 213-224.) The

distribution curves refer to the average flux

and do not show the effects of meteor showers

and dust-particle showers. The flux of meteoroids is essentially the same near the earth as
268 SYMPOSIUM ON METEOR ORBITS AND DUST

HAWKINS and UPTON (1958)

HAWKINS .1959

BROWN (1961)

FIGURE 6.—Cumulative flux distribution based on data from

various sources and showing the enhanced flux of small dust

particles (m < 10"6 g) in the vicinity of the earth.

in interplanetary space near the orbit of the

earth, but the flux of small dust particles having

masses m<O0~* g shows a geocentric enhancement of the flux. This enhancement appears

as the difference between the flux measured in

the vicinity of the earth and the flux inferred

from studies of the zodiacal light for. interplanetary space. The degree of enhancement

of the flux depends on the particle mass and

appears to reach a maximum of about 104 for

a particle massw~10"n g. The interpolation

between the flux distribution measured with

microphone systems and that for radar meteors

has reeently been verified by the results of

Elford, Hawkins, and Southworth (1964), who

used radar to obtain a flux of 10~8 particles/m2/

sec/2*- ster for meteoroids having masses

m~1.3X10-6g.

Several points regarding the validity of the

direct measurements obtained with the microphone type of sensor deserve special comment.

The open literature contains statements that

these data are highly uncertain and that the

flux measured with satellites decreases during

the first day or so following launch. The

known uncertainties in the calibration of the

systems were discussed in the preceding paragraphs. The alleged uncertainty possibly refers

to the large decrease in the flux measured with

Sputnik 3 on the day of launch. This decrease represents a large variation in the flux

rather than an uncertainty, if the data are to

be accepted. Such large variations in the flux

are not representative of the data obtained with

the remaining microphone systems. Large

time variations in the flux were recorded by

the microphone systems on Explorer 1 and

Vanguard 3, but these showers of dust particles

occurred after these satellites had completed

a considerable number of orbits. The system

on Explorer 1 indicated eight impacts while

the satellite was being injected into orbit,

but there is nothing peculiar about the numbers

of impacts recorded after injection was completed. These K impacts were questionable

and were subtracted from the 153 nonredundant indicated impacts in order to obtain

the 145 impacts reported for Explorer 1. The

first available readout of the cumulative

counter for the system on Vanguard 3 was

obtained about 2 hours (almost 1 orbit) after

launch. The detailed time history of the

cumulative counter during the first day of

operation shows no cause for alarm. The

impact rate on the day after launch was

lower than on the day of launch, but the impact rate on the second day after launch was

higher than on either of the two preceding

days (see fig. 4). Likewise, the time history of

the cumulative counter for the microphone

system on Explorer 8 shows no systematic

trend in the impact rate following launch that

would arouse suspicion concerning the validity

of the data. The microphone system on

Pioneer 1 did show an impact rate that decreased with time during the outbound portion

of the trajectory. A probe that was meant to

go to the moon should show such a decrease in

the impact rate if the geocentric enhancement

of the flux exists and the flux decreases with

increasing geocentric distance. The data from

Explorer 6 have not been published because

instrumental difficulties occurred after the

satellite was launched. The microphone system on Vanguard 3 was definitely subject to

interference from interrogations of the magne-
MASS DISTRIBUTION AND TIME VARIATIONS IN FLUX OF PARTICLES M'CRACKEN ET AL. 260

tometer, but the effects of this interference have

been largely removed from the latest data presented earlier in this paper. The data presented

by us as valid are not characterized by a flux

that decreases systematically following launch.

There is an acute need for data from composite dust-particle sensors for which a sequence of

events absolutely unique to the impact of a dust

particle is required before the system will register an impact. The data from the combination

of microphone and photomultiplier flown on the

short-lived Ranger 1 represent limited success in

this direction. Further progress toward obtaining data that unquestionably apply for impacting dust particles has been realized with

the development of the composite dust-particle

sensor being flown on the Orbiting Geophysical

Observatories. The data obtained with the

microphone type of dust-particle sensor have

been most essential in the development of the

more complex sensors that are now being flown

in order to obtain additional information about

the speeds, directions of motion, momenta, and

kinetic energies of small dust particles.

Summary

The microphone type of dust-particle sensors

flown on rockets, satellites, and interplanetary

probes has given information concerning the

average flux and time variations in the flux for

dust particles with masses between about 10~7

and 10~u g. The flux is known as a function

of particle mass for the vicinity of the earth, so

the cumulative mass distribution for this region

of space has been fairly well established. The

cumulative flux distribution, if slightly extended

toward larger dust particles, is in very good

agreement with the flux of radar meteors.

The flux of small dust particles observed in

the vicinity of the earth sometimes undergoes

large systematic variations with time. On one

occasion, the flux rose by a factor of 170 above

the average value. The measured flux also

shows variations by a factor of 10 within intervals of a few hours' duration. None of the

intervals of enhanced flux can be positively

associated with the known meteoroid streams.

Further investigation of the small-particle

content of meteoroid streams and of the mechanism by which the flux of small particles is

enhanced near the earth will have to await

definitive data regarding the orbits of these

particles.

References

ALEXANDER, W. M.

1962. The mission of Mariner II: Preliminary

observations: Cosmic dust. Science, vol.

138, pp. 1098-1099.

ALEXANDER, W. M.; BERG, O. E.; MCCRACKEN, C. W.;

SECRETAN, L.; and BOHN, J. L.

1967. Interplanetary dust particle flux measurements between 1.0 and 1.56 a.u. from

Mariner IV cosmic dust experiment.

Smithsonian Contr. Astrophys., vol. 11,

p. 227.

ALEXANDER, W. M., and LAGOW, H. E.

1960. Recent direct measurements of cosmic dust

in the vicinity of the earth using satellites. In Space Research, ed. by H.

Kallmann-Bijl, North-Holland Publ. Co.,

Amsterdam, pp. 1033-1041.

ALEXANDER, W. M.; MCCRACKEN, C. W.; and LAGOW,

H. E.

1961. Interplanetary dust particles of micron-size

probably associated with the Leonid

meteoroid stream. Journ. Geophys.

Res., vol. 66, pp. 3970-3973.

ALEXANDER, W. M.; MCCRACKEN, C. W.; SECRETAN, L.;

and HE it<;, O. E.

1963. Review of direct measurements of interplanetary dust from satellites and probes.

In Space Research III, ed. by W.

Priester, North-Holland Publ. Co., Amsterdam, pp. 891-917.

BROWN, H.

1960. The density and mass distribution of

meteoritic bodies in the neighborhood of

the earth's orbit. Journ. Geophys. Res.,

vol. 65, pp. 1679-1683.

1961. The density and mass distribution of

meteoritic bodies in the neighborhood of

the earth's orbit: Addendum. Journ.

Geophys. Res., vol. 66, pp. 1316-1317.

D'AUITOLO, C. T.

1964. Review of meteoroid environment based on

results from Explorer XIII and Explorer

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Co., Amsterdam, pp. 858-874.

DUBIN, M.

1960a. Meteoritic dust measured from Explorer I.

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1960b. IGY micrometeorite measurements. In

Space Research, ed. by H. KallmannBijl, North-Holland Publ. Co., Amsterdam, pp. 1042-1058.

ELFORD, W. G.; HAWKINS, G. S.; and SOUTHWORTH,

R. B.

1964. The distribution of sporadic meteor radiants.

Harvard Radio Meteor Project Res. Rep.,

no. 11, December.
270 SYMPOSIUM ON METEOR ORBITS AND DUST

ELS ASS EH, H.

1954. Die raumliche Yerteilung der zodiakallichtmaterie. Zeits. f. Astrophys., vol. 33,

pp. 274-285.

HAWKINS, G. S.

1959. The relation between asteroids, fireballs,

and meteorites. Astrophys. Journ., vol.

64, pp. 450-454.

HAWKINS, G. S., and UPTON, E. K. L.

1958. The influx rate of meteors in the earth's

atmosphere. Astrophys. Journ., vol. 128,

pp. 727-735.

INGHAM, M. F.

1961. Observations of the zodiacal light from a

very high altitude station, IV: The

nature and distribution of the interplanetary dust. Monthly Notices Roy.

Astron. Soc, vol. 122, pp. 157-175.

KAISER, T. R.

1961. The determination of the incident flux of

radio-meteors, II: Sporadic meteors.

Monthly Notices Roy. Astron. Soc, vol.

123, pp. 265-271.

MCCRACKEN, C. W.

1967. Conditions of encounter between dust and

the planets. Smithsonian Contr. Astrophys., vol. 11, pp. 213-224.

MCCRACKEN, C. W.; ALEXANDER, W. M.; and

DUBIN, M.

1961. Direct measurements of interplanetary dust

particles in the vicinity of earth.

Nature, vol. 192, pp. 441-443.

MH.I.M \N. P. M., and BURLAND, M. S.

1956. The magnitude distribution of visual

meteors. Presented at 96th Amer.

Astron. Soc. Meeting, New York, December. (See Millman, Joum. Roy.

Astron. Soc., Canada, vol. 51, pp. 113-

115, 1957.)

NAZAROVA, T. N.

1960. The results of studies of meteoric dust by

means of Sputnik III and space rockets.

In Space Research, ed., by H. KallmannBijl, North-Holland Publ. Co., Amsterdam, pp. 1059-1062.

1963. Rocket and satellite studies of meteoric

dust. In Proceeding* of the Symposium on the Astronomy and Physics

of Meteors. Smithsonian Contr. Astrophys., vol. 7, pp. 105-108.

1967. Rocket and -ai.IIit.- Mtudien of meU*orir

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vol. II, pp. 231-237.

<ink. E. J.

1958. Mri.-or impact on nolid surface. Iriih

Aatron. Journ., vol. 5, pp. 14-33.

WATSON, F. G.

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vol. 189, pp. 127-128.

Abstract

Information concerning the mass distribution and the time variations in the flux of small dust particles has

been obtained with dust-particle sensors flown outside the atmosphere of the earth. The relevant data have been

obtained primarily with the microphone type of dust-particle sensor flown on near-earth satellites. These measurements are in good agreement with the mass distribution measured with the microphone system on Explorer 8. The

measured flux of dust particles often shows temporal variations of a factor of 10 within intervals of several hours,

as well as larger, systematic enhancements of flux or sporadic showers which persist for intervals ranging from several

hours to a few days.
Physical Parameters of Cosmic Dust Obtained from Rocket

Collections

0 . E. BERG

 l and L. SECRETAN

An Aerobee rocket specifically instrumented to

measure and record various parameters of the

earth's cosmic dust environment was launched

at 0700 MST on December 17, 1964, at the

White Sands Missile Range. The principal

experiment aboard the rocket was designed to

register and recover physical evidence of impacts by extraterrestrial particles.

Development

One of the major problems in the evaluation of

the meteoroid environment hazard is the absence of definitive measurements and data regarding the character and effects of the hypervelocity microparticle impact as they apply to

true meteoric bodies at meteoric velocities.

The state of the art of laboratory microparticle accelerators is limited to low meteoric

velocities and to solid, high-density, essentially

spherical microparticles. There is little or no

justification for assuming that the physical

characteristics of cosmic dust are generally

similar to those of the hypervelocity laboratory

particles. Donn (1964) has recently published

the results of a study of the various sources of

cosmic dust, which indicate that the particle

geometries range from high-density spherules

to fluffy particles or whiskery aggregates.

Several attempts made in the past to collect

physical evidence of micrometeoric impacts,

such as craters, have failed, partially or totally,

because of technological difficulties readily

recognized by investigators engaged in micro1

 Qoddard Space Flight Center, National Aeronautics and Space

Administration, Oreenbelt, Md.

analytical techniques. The major technological

difficulties can be expressed as follows:

1. The size of the hypervelocity microparticle impact crater is near the limits of

resolution of the finest optical microscopes.

2. Even the finest optically polished surfaces contain inherent surface defects having

dimensions and characteristics similar to those

of the craters sought for study. Two striking

examples of such "craters" are shown in plate

1. Both "craters" appeared on the surface of

an aluminized lucite block, which had been

optically polished and coated with an opaque

layer of aluminum in preparation for an exposure to micrometeoritic impacts. The experiment was abandoned when numerous craterlike irregularities of a similar nature were discovered in the preflight surfaces.

In view of the existence of these surface defects, it is obvious that the finest prepared

surfaces available remain inadequate, per se, as

a medium for the registration of meteoric impacts. One stringent criterion must be observed for the surface medium: that every

square micron of that surface be scanned before

and after cosmic-dust exposure with a precision

that will categorically single out cosmic-dust

impacts from inherent surface defects.

It is believed that this criterion has been fulfilled by instruments and techniques that were

developed for and are described in this experiment.

The exposure substrate selected for this

experiment was in the form of a glass cylinder

11.4 cm in diameter and 10.2 cm long, with a

total impact area of 0.037 m2. The exterior

271
272 SYMPOSIUM ON METEOR ORBITS AND DUST

surface of each cylinder was optically polished

and coated with an opaque layer of evaporated

metal 2500 A in thickness. The entire surface

of each cylinder was photometrically mapped

for preflight pinholes or similar surface transparencies in a precision photometric scanner

shown schematically in figure 1.

/ EYE OR CAMERA

PHOTOMULTIPLIER \ ,

6199 PM PWSM

W

LIGHT

SOURCE

OlASS CYLINDER

WITH EVAPORATED

OPAOUE

METALLIC COATING

FIGURE 1.—Precision photometric scanner.

The exposure cylinder is rotated in the scanner at 2 sec/rev. The evaporated metal layer

normally presents an opaque barrier between

the light source and the photomultiplier. If,

during the scanning procedure, a pinhole in the

opaque layer appears in the light-source photomultiplier axis, it will transmit an amount of

light relatively proportional to its area. The

momentary light transmission is detected by a

6199 photomultiplier, amplified, and recorded

on Sanborn tape. Recorded simultaneously

with the light pulse and on the same tape is the

precise position of the pinhole in the cylinder

to an accuracy of ±0.005 cm laterally and

±2?0 circumferentially.

A slit in the optical system of the microscope

limits its lateral field of view to approximately

0.008 cm of the surface. Thus, any particular

pinhole will record its relative amplitude and

its position for each of several consecutive

revolutions of the cylinder, since the field of

view of the microscope (0.008 cm) is greater

than the cylinder's lateral travel per revolution

(0.0025 cm).

Plate 2 shows a section of Sanborn tape that

has recorded the registration of a typical pinhole

during a scan. Each of the spacings between

the five positive pulses represents one revolution of the cylinder in the scanner. This

particular registration is that of a pinhole

approximately 1M in diameter.

The resolution capability of the experiment

to detect perforations produced in thin coatings

by high-density, hypervelocity dust particles

has been determined with the GSFC Dust

Particle Accelerator. Impacts by carbonyl

iron spheres having masses ranging from 10"10

to 10~12 g and velocities from 2 to 8 km/sec

exhibited perforations in the opaque layer

sometimes only a fraction of a micron in

diameter but readily detectable in the scanning

system.

Unfortunately, we cannot determine from

this calibration a practical detection capability

for cosmic-dust-particle impacts because: 1 (as

stated earlier, the physical characteristics of

cosmic dust may vary widely from those of the

iron spheres used in the laboratory; and 2)

accordingly, the crater and penetration characteristics of low-density particles are not well

known. In a recent theoretical study, Bjork

(1962) concluded that for craters produced by

impacts between unlike materials (target and

projectile) we might expect substantial deviations from the generally accepted crater characteristics. He concluded further that the crater

characteristics do deviate from an idealized

pattern as a function of particle velocity and

may vary widely as a function of particle

geometry.

All flight cylinders were photometrically

scanned twice previous to installation in their

individually sealed flight containers. A timer

in the payload was used to extend the three

cylinders at 73 sec and retract them at 410 sec,

providing an exposure of 337 sec. These times

correspond to rocket altitudes of 73.6 km and

92.7 km and to rocket velocities of 1.6 km/sec

and 1.4 km/sec, respectively.

After recovery of the payload, each cylinder

was removed and scanned again. A comparison of the postflight record with the preflight

record revealed the location and relative magnitude of new perforations. Only new perforations were considered and accepted for further

analysis.

A total number of 14 "probable impacts" was

discovered on the surface of the three exposed

cylinders. "Probable impacts" refer to all new
PHYSICAL PARAMETERS OF COSMIC DUST FROM ROCKETS—BERG AND SECRETAN 273

pinholes or transparent areas that were definitely not present in the preflight scanning

records.

The "control cylinder," prepared and flown

under the same conditions as the three exposed

cylinders but not extended to the cosmic-dust

environment, showed no new pinholes nor transparent areas.

It is customary and sometimes advantageous

to separate collections into groups or classes

and proceed to discuss each group or class separately. The impacts discussed in this paper,

however, are not readily divided into groups,

but tend to show gradual transitions over a

wide range of densities, velocities, sizes, and

shapes. For this reason, only 6 of the 14 impacts will be illustrated and discussed as representative samples of the collection.

Plate 3 shows the largest of the impact areas

recovered. The shallow, large-area character

of this crater suggests an irregularly shaped,

low-density, hypervelocity projectile. The refracting areas in the bottom of the crater denote

physical damage to the substrate—the glass—

possibly inflicted by smaller inclusions of higher

density in the impacting particle.

Another representative impact area, shown

in plate 4, was produced by a projectile, probably similar to the previous one but possibly

more filamentary and having a lower velocity.

The streaks emanating from only one side of

the crater suggest a low-angle impact favoring

nonsymmetrical ejecta.

One of the more significant features generally

observed in the 14 impacts is the relatively

shallow crater. This impact, as an example,

shows a large area affected by the impact,

while only the relatively small areas at either

end of the crater show penetration through the

very thin layer.

The next impact shown in plate 5 exhibits

an interesting extrorse effect, which is evident in

several other impacts in the collection. The

dark-shaded parallel streaks emanating from

the impact proper are most assuredly associated

with the plastic surface deformation imparted

by the impact. Similar extrorse effects are commonly observed in impacts produced by the

Goddard Dust Particle Accelerator. We believe this is the first time this type of surface

deformation due to microparticle impacts has

been visually detected. Its appearance is inconsistent with normal shock-wave effects, which

exhibit essentially symmetrical, concentric patterns annexed to the impact proper. That this

effect is truly plastic deformation is substantiated by the hypervelocity impact shown in

plate 6. This impact crater, recorded by J. F.

Friichtenicht of the Space Technology Labs,

was produced upon a solid aluminum block by

a 1-M iron sphere accelerated to a few km/sec

in an Electrostatic Dust Particle Accelerator.

The magnification is indicated in the lower left

corner by the two marks separated by 1 p. The

plastic surface deformation as revealed by distortions of the surface polishing marks extends

from the center of the impact outward to several crater diameters, and is markedly asymmetrical. This extrorse effect is at present the

subject of a separate study, the results of which

will be published later.

The next two impact areas are most informative when considered together, since they are

remarkably similar in appearance although

created by two completely dissimilar means

on similar targets. One of the two impacts

shown in plate 7a was produced in the laboratory

by a l-fx iron sphere having a velocity of a

few km/sec. Notice the total asymmetry of the

impact proper as well as the plastic deformation.

The other impact shown in plate 7b was created

by a cosmic-dust particle. The general similarities of the impacts and their associated effects

lead us to believe that both impacts were produced by similar projectiles, i.e., high density

and high speed.

Two of the 14 impacts recovered were of the

type shown in plate 8. Although the interesting

feature of this impact is the deposit of material

on the surface, its impact had produced a

detectable perforation in the opaque film, by

which it was registered as a postlaunch event.

These two impacts will be further studied by

an electron microprobe and microchemical

analysis.

It is interesting, but not particularly practicable, to compare the cosmic-dust influx rates

as indicated by this experiment with established

influx rates as measured by a variety of realtime sensors in rockets, probes, and satellites.

The impracticability of such a comparison is a

consequence of the conditions of exposure
274 SYMPOSIUM ON METEOR ORBITS AND DUST

under which this experiment was performed.

During the early phase of the exposure, the

surfaces were traversing an atmosphere laden

with extraterrestrial dust particles that are

decelerated and "slowly settling to earth."

At that time the rocket velocity relative to

"stationary" particles was sufficient to inflict

detectable perforations in the opaque film,

at least for solid, high-density particles. Hence,

any concentration of cosmic dust in the 80-

to 90-km layer (Fiocco and Smullin, 1963;

Fiocco and Colombo, 1964) should have contributed appreciably to the integrated impact

rate measured in this flight.

The data composing the general cumulative

meteoric influx curve reported by Alexander

et al. (1962) and shown in figure 2 for comparison were obtained, in general, from impacts by cosmic dust essentially outside the

earth's atmosphere and with an assumed average

velocity of 25 km/sec.

The exposure area of 0.11 m* (for three

cylinders), corrected for earth shielding (50

percent) and rocket shielding (30 percent),

yields a correction factor of 65 percent or an

FIGURE 2.—Average cumulative mass distribution curve.

effective exposure area of 0.033 m1, and an

area-time factor of 11.1 m2 sec. The impact

rate then becomes 14/11.1 m2 sec or 1.2 impacts/m2

/sec, which is plotted as a point on

the ordinate with the absicssa variation representing the present existing uncertainties in

computing particle masses from studies of

hypervelocity craters.

The relatively low influx rates exhibited by

the new measurement on the well-established

plot are somewhat surprising inasmuch as the

impact detectability of the latter experiment

has been shown to be sensitive to craters

produced by 10~12 g iron carbonyl particles

having a speed of only a few km/sec.

There are two possible explanations for the

low influx rates: (1) the real-time sensors are

capable of and have been recording impacts

by particles that by virtue of their fragile,

low-density structure are not capable of penetrating the opaque metallic layer; and (2) the

penetration characteristics of low-density projectiles are not well known. Accordingly,

there may be for this system a detectability

cutoff for low-density particles that may differ

by a factor of 10 or more from that of solid

particles.

The following conclusions are based on the

results of this experiment: (1) cosmic dust encompasses a wide range of particle densities and

shapes as well as sizes and velocities; (2) penetration parameters for low-density, hypervelocity microparticles may vary widely from

accepted values derived from dissimilar laboratory-produced particles; and (3) as indicated by

this experiment, the large area of the impact

proper, coupled with the evidence of plastic

surface deformation, strongly suggests that

surface damage rather than penetration presents

the greater hazard to space material.

References

ALEXANDER, W. M.; MCCRACKEN, C. W.; SECRETAN,

L.; and BE KG, (). E.

1962. Review of direct measurements of interplanetary dust from satellite and probes.

In Space Research III, ed. W. Priester,

North-Holland Publ. Co., Amsterdam,

pp. 891-917.

BJORK, R. L.

1963. Review of physical processes in hypervelocity impacts and penetration. Sixth

Hypervelocity Symp., vol. 2, pp. 1-58.
PHYSICAL PARAMETERS OF COSMIC DUST FROM ROCKETS BEKG AND SECRETAN 275

DONN, B.

1964. The origin and nature of solid particles in

space. Ann. New York Acad. Sci.,

vol. 119, pp. 5-16.

Fiocco, G., and COLOMBO, G.

1964. Optical radar results and meteoric fragmentation. Journ. Geophys. Res., vol.

69, pp. 1795-1803.

Fiocco, G., and SMULLIN, L. D.

1963. Detection of scattering layers in the upper

atmosphere (60-140 km) by optical

radar. Nature, vol. 199, pp. 1275-1276.
276 SYMPOSIUM ON METEOR ORBITS AND DUST

t

/ 4

PLATE 1

Inherent surface defects (SOOX).
PHYSICAL PARAMETERS OF COSMIC DUST FROM ROCKETS BERG AND SECRETAN 277

•a

• • •

I

•

•

, ]1

1

I

1

1

-ALL

* • ••

-

,..

i

I

1 I 1 ii r i

• ?» f i

V

• fi i

L.MI^I -I.-.H.II . •••»•.• |.

• * !•••'•• > 1

•

•

— ONE REVOLUT1OI

I I OF CYUNDER

i ; .

• : "

•" ; ' '

M . . a

' • - •

PLATE 2

A typical photometric scan recording.
278 SYMPOSIUM ON METEOR ORBITS AND DUST

10 u

I. .1

PLATE 3

Cosmic-dust-particle impact crater.
PHYSICAL PARAMETERS OP COSMIC DUST FROM ROCKETS—BERG AND SECRETAX 279

PLATE 4

Cosmic-dust-particle impact crater.
280 SYMPOSIUM ON METEOR ORBITS AND DUST

'

PLATE 5

Cosmic-dust-particle impact area showing plastic surface deformation.
PHYSICAL PARAMETERS OF COSMIC DUST FROM ROCKETS—BERG AND SECRETAN 281

PLATE 6

Simulated micrometeoritic impact crater showing plastic surface deformation.
282 SYMPOSIUM ON METEOR ORBITS AND DU8T

!

:

:-- -

PLATE 7A

Simulated micrometeoritic impact crater.
PHYSICAL PARAMETERS OF COSMIC DUST FROM ROCKETS—BERG AND 8ECRETAN 283

PLATE 7B

Cosmic-dust impact crater.
284 SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 8

Cosmic-dust impact area containing debris.
Electron Diffraction Control Studies of Venus Flytrap

Particles

N. N. GREENMAN and C. B. GILPIN

 l

Introduction

The first successful collection of particles from

high altitudes for direct study was provided by

the Venus Flytrap rocket launched on June 6,

1961, at White Sands Proving Grounds, New

Mexico. The nose cone carried particle collectors of the impact variety mounted on extendible and retractable leaves. Collection was

made between altitudes of 88 and 168 km for

about 4 min, the entire flight lasting about 8

min. The project was carried out by R. K.

Soberman and his group at the Meteor Physics

Branch of the Air Force Cambridge Research

Laboratories (AFCRL), Bedford, Mass., and

they very kindly provided us with samples for

study.

One of the findings reported by Soberman

et al. (1963) in their initial studies was that the

possible extraterrestrial particles generally

showed no selected area diffraction patterns in

the electron microscope, a circumstance they

suggested may be due to crystalline damage by

cosmic radiation. Our first studies, which confirmed this observation, were based on this

feature and were an attempt to determine

whether the apparent lack of crystallinity was

in fact due to radiation damage. The reason

for this approach was that terrestrial sources

of contaminants in micrometeorite collections

are either crystalline or amorphous, not radiation-damaged. Extraterrestrial particles, on

the other hand, could suffer such damage to the

crystalline lattice, according to Ryan's (1964)

calculations. Moreover, that damage could

survive in small particles that fall through the

• Space Sciences Department and Astropower Laboratory, Douglas

Missile and Space Systems Division, Santa Monica, Calif.

atmosphere too slowly to undergo appreciable

frictional heating. Therefore, radiation damage, if demonstrated to exist, would be a valuable criterion for distinguishing extraterrestrial

from terrestrial particles.

Venus Flytrap studies

Because radiation damage is known to anneal

out at temperatures well below the melting

point, the Venus Flytrap particles were heated

in stages of increasingly higher temperature and

examined in the electron microscope after each

stage for evidence of newly produced crystalUnity. The substrates, as a result of their poor

heat resistance, suffered enough destruction

during the tests to make it almost impossible

to follow the same particle through every

heating stage. For this reason a statistical

approach was used in which as many particles

as possible were examined after each stage.

The results of heating to 250° C, 400° C, and

500° C were that in general the percentage of

particles showing evidence of crystallinity increased with increasing temperature. The diffraction spots were small in number and included both symmetrical pairs or groups and

single, unpaired spots (pi. la, b). Only the

symmetrical spots, however, were considered

evidence of crystallinity because of the possibility that individual spots might be due to

spurious effects, such as film defects, rather than

to diffraction by the particle. Statistical

analysis indicated that the crystallinity was

probably produced by the heating, although

the differences in percentages were not great

enough to be certain on this point. The d

spacings of the diffraction spots were found to

285
286 SYMPOSIUM ON METEOR ORBITS AND DUST

correspond rather well with those of olivine and

enstatite, the major minerals of the most

abundant meteorite type, thus indicating that

annealing of radiation damage could have

occurred. On the other hand, similar correspondence was found with other materials, such

as mica and aluminum oxides and hydroxides,

that could be contaminants or reaction products

formed in the course of the heating tests. The

results of these first tests, described in detail

by Greenman (1964), were thus suggestive but

inconclusive.

Two factors were chiefly responsible for the

failure to achieve conclusive results. The

first was the inadequate heat resistance of the

available substrates, which not only limited

the maximum temperature of the test but also

made it impossible to follow a particular particle

through every heating stage so as to be certain

that changes had or had not occurred. The

second was the scarcity of information on the

electron diffraction characteristics of silicate

particles, both normal and radiation-damaged,

in the same size range as the Venus Flytrap

particles—about 0.1 to 1 MTo overcome the first of these difficulties,

we have developed a heat-resistant substrate

of good collection efficiency, which is now being

flown on a second series of Venus Flytrap

flights. To overcome the second, we have

begun control studies of submicron particles of

olivine, (Mg,Fe)iSiO4, and enstatite, (Mg,Fe)

SiO3. These are the two most common minerals

of the stony meteorites, the most abundant

type of meteorite, and may therefore well

represent the micrometeorites. One of the

objectives of the control studies is to determine

the type and quality of the electron diffraction

patterns and how the patterns are affected by

size, shape, crystallographic orientation, substrate thickness, radiation damage and annealing, and other variables. Another objective is

to determine from irradiation and annealing

tests of the olivine and enstatite whether likely

micrometeorite minerals can be damaged by

space radiation to the extent that they appear

amorphous by electron diffraction and, if so,

whether annealing well below the melting point

can restore the crystallinity. The purpose of

this paper is to describe some of the first results

of these control studies with olivine and

enstatite.

Control studies

Samples of olivine and enstatite were pulverized

by placing them in a hardened steel tube with

hardened steel balls and vibrating the tube in a

Crescent Wiggly Bug apparatus for 4 hours.

Tests had shown that such treatment produced

particles of these minerals from about 0.08 to

10/x in size. To prepare the samples for viewing

in the electron microscope, we shook the powder

and, after allowing a short period of time for

the coarsest particles to settle, inserted a freshly

prepared carbon substrate into the residual

cloud of fine material. No shadowing was used

with this series of observations. A tilting stage

that allowed the particle to be tilted up to 15°

in any direction from the axis of the electron

beam was used to obtain for each particle the

orientation that produced the most diffraction

spots and the best symmetry of the spot pattern.

Olivine particles and their diffraction patterns

are shown in plates lc to 26. The smallest

particle of plate lc, about 0.5 n in its longest

dimension, yielded the pattern shown in

plate Id, the best pattern observed. The main

rectangular and diagonal dimensions give d

spacings of 4.82, 3.82, and 3.07 A, which agree

rather well with the X-ray measurements of

this same material of 5.09, 3.86, and 2.98 A

and with the ASTM card file values for olivine.

These correspond to the (020), (021), and (002)

planes, respectively, and indicate the particle

is oriented with (200) normal to the beam.

The pattern shown in plate 2a for the 0.9-M

particle in plate lc has many spots but poor

symmetry. The one d spacing that can be

measured with fair accuracy agrees reasonably

well with that for the (002) plane of olivine.

The olivine particle of plate 26 yielded no

diffraction pattern, even though it is of about

the same size as the one of plate lc that gave

the best pattern, and even though the lighter

areas around its edge indicate some transmission

of the electron beam.

Plates 2c to 3c show enstatite particles and

their diffraction patterns. Plates Id and 36

show that even a particle as large as 4 M can

give a diffraction pattern if thin edges are

present. In this case it is a ring rather than a
ELECTRON DIFFRACTION STUDIES OF VENUS FLYTRAP PARTICLES GREENMAN-GILPIN 287

spot pattern. Also the pattern is not complete,

probably because those parts of the beam

diffracted toward the central thick portion of

the particle are not transmitted. Spacings

of 2.31 and 1.64 A are obtained from the

rings.

The spot pattern of plate 3a is from the

0.4-M particle of plate 2c. The spots give d

spacings of 3.62 and 2.18 A. All four spacings

in plates 2d and 3a agree reasonably well with

those from X-ray measurements of this same

material, or with the ASTM card file values for

enstatite.

The two enstatite particles of plate 3c gave

no diffraction patterns although, like the olivine

particle of plate 26, lighter areas indicative of

electron-beam transmission are present around

the edges.

From the above observations and from observations on other olivine and enstatite

particles, it can be concluded that crystalline

silicate particles at least as large as 4 n and

ranging down to about 0.1 or 0.2 n, though

opaque to the electron beam, can yield diffraction patterns from thin, partially transparent edges. There is some limiting size, in

the neighborhood of 0.1 to 0.2 M, for which the

particle is still opaque to the electron beam but

is too small for thin edges to be present or to be

effective; such particles generally give no diffraction pattern. Particles smaller than this

limiting size are thin enough to be transparent

to the electron beam and again can give diffraction patterns. In the larger particles, in

which the diffraction is from thin edges, the

part of the beam that is diffracted into rather

than away from the particle is not transmitted,

so that incomplete or asymmetrical patterns

may result (plate 2c). Possibly some of the

unpaired spots that appeared in the heatannealing tests with the Venus Flytrap particles

may have been due to this effect. If so, perhaps a higher degree of crystallinity or a larger

percentage of particles with new crystallinity

was produced than was originally supposed.

The conditions under which diffraction patterns can be obtained are as follows. First,

the substrate must be thin. Second, observation and photographic recording must be made

rapidly before the buildup of contamination

due to electron-beam decomposition of vacuumsystem hydrocarbons. The diffraction pattern

is much more sensitive to contamination buildup

than the particle image, and in a number of

cases the former was seen to disappear while

being observed whereas the latter showed no

change. Third, a tilting stage should be used

to allow the most favorable crystallographic

orientation to be selected. Because of the very

short wavelength of the electron beam, only

crystallographic planes that are nearly parallel

to the beam can produce observable diffraction

spots. Therefore, a detectable pattern appears only in some, not all, orientations. The

particles shown in plates 26 and 3c may have

failed to yield diffraction patterns because of

unfavorable orientation within the 15° range

of the tilting stage, although it is also possible

that excessive contamination built up during

the observation before a favorable orientation

was found.

Application to Venus Flytrap studies

In applying these results to our Venus Flytrap

studies, we can easily meet the first two of the

above conditions. The substrates being flown

on the present series of Venus Flytrap flights

have been carefully prepared to be of optimum

thickness for this type of study. Also, the

problem of contamination can be solved by

suitable instrument modification, such as better

cold traps on the vacuum system of the electron

microscope, and by rapid observing and photographing of the diffraction patterns. However,

the problem involved in the third condition,

that of unfavorable orientation, may prove

troublesome. Unfavorably oriented Venus Flytrap particles, even though crystalline and

with visibly thin edges, will appear amorphous

before and after the heat-annealing tests,

assuming, of course, that the particles do not

change position during the heating runs. The

same can be said of any unfavorably oriented

particles that are radiation damaged. On

the other hand, in the absence of a severe

biasing factor, a significant proportion of the

particles can be expected to have favorable

orientation within the range of the tilting stage;

with these a pattern will be found after heating

where none was present before if annealing of

radiation damage occurs. Therefore, by examining a large number of particles, we should
288 SYMPOSIUM ON METEOR ORBITS AND DUST

be able to establish whether or not radiation

damage is characteristic of those that are extraterrestrial. Additional study is being devoted

to methods of obtaining diffraction patterns

in all cases in which the particles are crystalline.

Acknowledgment

We would like to thank Mr. Don Paul for his

valuable assistance with the electron microscopy.

References

GREENMAN, N. N.

1964. Heat annealing experiments performed

upon "Venus Flytrap" particles. Ann.

New York Acad. Sci., vol. 119, pp. 298-317.

RYAN, J. A.

1964. Corpuscular radiation produced crystalline

damage at the lunar surface. In The

Lunar Surface Layer, ed. by J. W. Salisbury

and P. E. Glaser, Academic Press, N.Y.,

pp. 265-312.

SOBERMAN, R. K.; HEMENWAY, C. L.; RYAN, T. G.J

CHREST, S. A.; FRISSORA, J.; FLLLAM, E. F.; BALSAMO, J. J.; COLE, J.; HALLQREN, D.; YEDINAK, P.;

GOODMAN, A.; and HOFF, G.

1963. Micrometeorite collection from a recoverable .-in i in I inn rocket, parta I and II. In

Proceedings of the Symposium on the

Astronomy and Physics of Meteors.

Smithsonian Contr. Astrophys., vol. 7,

pp. 89-98.
ELECTRON DIFFRACTION STUDIES OF VENUS FLYTRAP PARTICLES GREENMAN-GILPIN 289

a

PLATE 1

Venus Flytrap particle, heated to 400° C for 1 hour. Grainy material is the aluminum shadow coat that forms part of the

substrate, b, Selected area diffraction pattern of figure a. The ring pattern is due to the aluminum and is the only pattern

generally appearing in the unheated particles. The two symmetrical spots inside the innermost ring are supposedly due to

crystallinity produced by the heating. The d spacing is 3.62 A. c, Olivine particles, d, Selected area diffraction pattern of

smallest (0.5 M) particle of figure c. The diffuse rings are due to the carbon substrate. The prominent d spacings are 4.82,

3.82, and 3.07 A, corresponding to the (020), (021), and (002) planes.
290

SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 2

a, Selected area diffraction pattern of second largest particle (0.9 M) of figure \c. Most prominent d spacing is 3.12 A. b, Olivine

particle, d, Selected area diffraction pattern of figure 3c. The d spacings are 2.31 and 1.64 A. c, Enstatite particles.
ELECTRON DIFFRACTION STUDIES OF VENUS FLYTRAP PARTICLES OREENMAN-OILPIN 291

PLATE 3

a, Selected area diffraction pattern of smaller particle (0.4 y) of figure 2c. The d spacings are 3.62 and 2.18 A. b, c, Enstatite

particles.

Aerosol Samples Obtained from 9- to 12-km Altitude

C. E. MELTON »

Introduction

Aerosol samples have been obtained at monthly

intervals in the altitude range from approximately 9 to 12 km over the southern California

area. This air-borne monitoring program has

been conducted in an effort to investigate the

spatial density of the dust and determine the

particle types and size distributions as functions

of altitude and time. Particular attention has

been directed toward detecting increases in

specific types of particles that may be associated

with meteor-shower activity. Such an approach

has been undertaken in view of results obtained

by previous investigators, namely, Parkin,

Hunter, and Brownlow (1962) and Parkin and

Hunter (1962), who have noted metallic flakes,

some with amorphous attachments, in collections obtained shortly after peak meteor-shower

periods, and Crozier (1962), who has noted

possible shower-related increases in the deposition rate of black metallic spherules.

To date, aerosols from a total of 14 collection

flights have been examined visually. The experimental procedures used in the collection

program and the results and conclusions are

discussed in the following sections.

Collectors

Ram-jet-type collectors are used in the aerosol

collection program. These are identical with

those used in the Extraterrestrial Dust Project

of the Smithsonian Astrophysical Observatory,

and have been described previously (Melton,

1964). The assembled collectors, prepared

for high-altitude chamber test, and the struts

used to mount the collectors on the aircraft are

1

 Space Sciences Department, Douglas Missile and Space Systems

Division, Santa Monica, California.

shown in plate 1. The wiring is attached to the

rear of the collectors for altitude chamber test

only. In actual collection, a solenoid-activated

valve is opened, air is admitted through the

6-mm forward opening, passed into an expansion chamber, and filtered by a commercial

cellulose-type filter. When the valve is closed,

the air flow is diverted before reaching the

collection chamber.

The collectors are mounted on the nose of the

DC-8 and protrude about 25 cm from the

plane's surface so that they are well into ambient

air. Two collectors were flown on all flights:

one was used for the aerosol collections, while the

other served as a control and was not opened

during flight.

Assembly procedure

In order to minimize contamination problems,

the collectors used are cleaned and assembled

under clean-room conditions. The exposed

collection filters as well as the blank controls

are also handled under clean-room conditions.

The detailed procedure has been described previously (Melton, 1964). After exposure, the

filters are mounted as illustrated in figure 1,

and then subjected to optical examination.

Laboratory observational procedure

Filters were examined under direct lighting

with magnifications up to 500 X. Attention

was directed toward the central exposed area

of the filter, encompassing 269 mm2. Particles^ 4 n were mapped and counted. Colored

and transparent particles were mapped but

not included in the count, since work by previous investigators (Hodge, 1961; Hodge and

Wright, 1962; Fireman and Kistner, 1961)

293
294 SYMPOSIUM ON METEOR ORBITS AND DUST

FILTER PAPER

COVER GLASS

0.18 mm THICK

GLASS SPACER

0.18mm THICK

GLASS SLIDE

50 mm

FIGURE 1.—Mounting assembly for optical examination of aerosols.

has indicated that these types are probably of

terrestrial origin. Obvious collector fragments

were also excluded.

Results and discussion

The flight data and results obtained from 14

collections are summarized in table 1. The

particles counted on all filters were grouped

into two general categories, spherules and

opaque irregular types.

The total opaque particle density varied

widely and showed no dependence on altitude,

within the 9- to 12-km range. Also, no relationship could be established between particle

spatial density and geographical location, i.e.,

number density of particles collected over

inland areas varied as greatly as that observed

in collections made from 50 to 100 km off the

West Coast. Spatial densities of all opaque

particles collected with sizes> 4 n ranged from

about 20 to 200 particles/m8. These results

are typical of those obtained by other investigators (Hodge and Wright, 1962) for this

altitude range.
AEROSOL SAMPLES FROM 9- TO 12-KM ALTITUDE—MELTON

TABLE 1.—Summary of flight data and results

295

Flight

1

2*

3

4

5

6

7

8

9

10

11

12

13

14

Date

July 19, 1963

July 20, 1963

Aug. 18, 1963

Aug. 19, 1963

Sept. 17, 1963

Oct. 8, 1963

Oct. 9, 1963

Oct. 22, 1963

Feb. 8, 1964

May 12, 1964

June 19, 1964

Aug. 5, 1964

Aug. 10, 1964

Nov. 17, 1964

Altitude

(km)

12. 0-12. 2

11.9-12.2

10.7-11.3

10. 3-10. 9

10. 6-10. 9

10.9-11.7

9.4

10. 9-11.2

10.6-11.4

11.0

10. 6-12. 0

11.2-11.3

10.8-11. 1

9.9-11.0

Volume

sampled

(m»)

7. 16

9.03

30.0

6.94

22.5

22.8

11.5

17. 1

18.2

11. 1

40.2

13.2

16.0

11.3

Total

opaque

particle

density

(> 4M)

per m1

143

—

39

117

17

22

47

32

48

180

58

110

45

81

Highly

irregular

number

( > 4M)

1

0

2

2

1

0

1

1

0

1

1

2

3

1

Glassy spherule

number

Test

0

1

0

0

0

0

1

1

1

0

4

0

0

1

(> 4 M)

Control

0

0

2

1

0

0

0

0

0

1

1

0

0

0

Opaque

spherule

density

(> 4M)

per m1

6.95

3. 12

2.56

5. 76

1.33

0.88

1.75

2.34

3.88

5.45

4 4 6

3.03

1.88

2.73

•Control filter torn.

Irregular particles

Although irregular particles are expected to

predominate in the total extraterrestrial dust

influx, little conclusive work has been done

on them owing to the formidable contamination and discrimination problems involved. In

the present program an attempt has been

made to surmount these problems by looking

for time variations in the spatial density of

irregular particles correlated with meteorshower activity. It was reported in a previous

paper (Melton, 1964) that certain irregular

fluffy-type particles were detected on filters

exposed shortly after the Perseid meteor shower

(August 1963). Similar particles were collected on flights during the 1964 Perseid shower

(see table 1). However, as can be noted from

table 1, a few such particles have also been

found on several of the other flights.

A total of 16 of these highly irregular particles

has been observed; none has been evident on

the control filters. All the irregular particles

have been collected during months in which

there is considerable shower activity (see

table 1). The single flight during the showerfree period, February-April, revealed no particles of this type. While this quiet period is

long enough to ensure that even shower-related

particles with slow fall times should not be

present in any significant numbers, additional

flights will have to be performed during the

shower-free periods to provide more conclusive evidence that these irregular particles

are indeed shower-associated. Several of the

irregular particles are currently being prepared

for electron-microprobe analyses, and data

concerning the nature of these particles should

be available shortly.

Spherules

The second group of particles, the spherules,

are very conspicuous and are easily classified.

Two distinct groups of spherules have been

noted: transparent, sometimes colored, glassy

types and opaque types.

The glassy spherules are of interest because of

current theories concerning their possible origin

as material that has been ejected from the lunar

surface through meteoroid shower impacts.

The present study provides no support for this

theory, since there is no correlation of the number of glassy spherules collected with shower activity or with the relative position of the moon.

Furthermore, since many of these spherules

appeared on control filters, there is no evidence

to indicate that any spherules collected were

of extraterrestrial origin.
296 SYMPOSIUM ON METEOR ORBITS AND DUST

Among the smooth, opaque, perfect spherules, those that are black and metallic-appearing have been selected for detailed study, since

they are the types often considered by other

investigators as being meteoric in origin.

Smooth, gray spherules as well as roughappearing or slightly irregular spherules have

been rejected from the present study. Particular attention has been directed toward determining any flux increase in black spherules that

might be related to shower activity. The results for the spherule counts are given in table 1.

It can be seen that the ratio of the number of

spherules to the total particles remains approximately the same; that is, from 3 to 8 percent of

the total, with the largest percentage of spherules collected on the February 1964 flight

(during the quiet period). These data give no

indication of marked variation with shower

activity.

From the observed total number of metallic

spherules in each l-n interval, a size distribution

over the range 4 to 8 n was obtained by least

squares. The equation for the size distribution

may be given as

5.43 X104

:

 J3.63 > (1)

where w(l) is the number of spherules per micron

of diameter I (microns), corrected for a collector

efficiency of 10 percent (F. W. Wright, 1963,

private communication). The differential distribution (1) can be used to compute a cumulative flux distribution for comparison with

results from other investigations. Since equation (1) is presumably reliable only to about

10 n, the differential size distribution was extended to 50 n by a function representing an

inverse 4.6-power law, fitted to equation (1) at

1 = 10 n. The inverse 4.6-power represents a

convenient exponent for the approximate differential size distribution obtained from Crozier's

(1962) data for spherules in the size range 10 to

50 n. The contribution from spherules of

diameter >50 n was neglected. A fall velocity

based on Stokes' law has been assumed for

spherule sizes to 50 MThe results of the present study as plotted in

figure 2 are apparently in good general agreement with the other results shown. For the

most part, the differences among these results

can probably be accounted for by differences

in experimental conditions, uncertainties in the

efficiencies of collectors, and locations at which

collections were made.

The differential size distribution given by

equation (1) has been used to obtain an estimate

of the mass accretion rate by the earth, in the

size range 4 to 10 M- That is,

"5.43X10' v r

[TM yv r ,,

where v=Al2, fall velocity from Stokes' law,

V= total air volume, and - pi3 = mass of spherule

o

of diameter I. The total volume measured was

237 m3. The constant in the expression for the

fall velocity has been evaluated with i/=10~*

in/sec for a spherule of diameter 10 p. The

density p was taken as 5 g/cms.

The mass influx obtained is S.4X10* metric

tons over the surface of the earth per year in

the size range 4 to 10 n. This is compared in

table 2 with results from other investigators.

The mass influx derived above is apparently

consistent with results obtained by others in the

given size range. Extrapolation of the present

differential size distribution, given by equation

(1), beyond 10 n seems to be incorrect, as noted

previously. Such extrapolation leads to a

spherule mass influx upon the earth of approximately 4.2X106

 metric tons/year, which is much

too high when compared with observation

(Crozier, 1962; Schmidt, 1963). This result

provides additional evidence that the decrease

in the number of spherules with increasing size

is indeed much greater for spherules whose diameters exceed 10 n than for those in the interval studied here.

Summary and conclusions

Results from the 14 flights analyzed so far can

be summarized as follows: The spatial density

of all opaque particles collected (>4/i) at an

altitude of 9 to 12 km varied widely, ranging

from about 20 to 200 particles/m3. These particle spatial densities show no dependence on

altitude. Some highly irregular particles have

been found but have not as yet been definitely

related to shower activity. The results give no

evidence that extraterrestrial glassy spherules

were collected. There is no indication of an
AEROSOL SAMPLES FROM 9- TO 12-KM ALTITUDE;—MELTON 297

10

o

10

CVJ

'£tide

s par*

X

=>

—i

u.CL

E PARTI

UJ

6

4

2

io3

8

6

Z>

O

8 -

4 -

2 -

-4

10

1 L 1 1

\A

\ \

v \

Y

\

E\

\

\

\

\

1 II I

1 1 1

A-PRESENT STUDY

B-CR0ZIERU962)

C- LAEVASTU AND MELLIS (1961)

D-HODGE,WRIGHTAND

LANGWAY (Greenland) (1964)

\ E - HODGE etd. (South Pole) (1964)

vc \\ °

\ \ \ \ \ \ \ \ \ \ \ - \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ _ \ \ \ \ \V\\\

4 6 8 10 20 40 60 100

SPHERULE DIAMETER

FIGURE 2.—Cumulative flux distribution for spherules.

increase in the spatial density of metallic

spherules associated with meteor showers. The

differential size distribution for the collected

metallic spherules follows approximately an

inverse fourth-power law. This distribution

leads to values of the cumulative flux of particles and of the total earth accretion rate in the

observed size range that are consistent with

results of other investigators.

Acknowledgments

I wish to thank Drs. F. W. Wright, Smithsonian

Astrophysical Observatory, and P. W. Hodge,

University of California, Berkeley, for permitting me to use one of their collectors in this program. I am also greatly indebted to Dr. J. A.

Ryan and Mr. M. B. Baker, Douglas Missile

and Space Systems Division, Santa Monica, for

many valuable discussions and comments. The
SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 2.—Estimated annual deposit of metallic spherules over the earth

Particle size range

00

30-250

10-170

5-160

5-60 ( > 15

3-30

3-15

> 3

> 5

4-10

Source for particles

Pacific sediments

Antarctic snow

Greenland snow

Air

Air

Air

Air

Greenland ice

Air

Accretion rate

(metric tons/year)

2.4X10* to5X10»

1.2X 105 (average)

9.1X105

1.6X10" (5X104)

3X10* to3X10»

5X10»

2X10»

2X10»

8.4X10*

Reference

Pettersson and Fredriksson (1958)

Schmidt (1963)

Langway (1963)

Crazier (1962)

Fireman and Kistner (1961)

Hodge and Wildt (1958)

Wright and Hodge (1962)

Wright, Hodge, and Langway (1963)

Present study

cooperation of the Douglas Flight Test Group,

Long Beach, in the aircraft flights, and the

assistance of Mr. R. H. Edwards in the collection program are greatly appreciated.

References

CROZIEB, W. D.

1962. Five years of continuous collection of black

magnetic spherules from the atmosphere.

Journ. Geophys. Res., vol. 67, pp. 2543-

2548.

FIREMAN, E. L., and KISTNER, G. A.

1961. The nature of dust collected at high altitudes. Geochim. et Cosmochim. Acta,

vol. 24, pp. 10-22.

HODOE, P. W.

1961. Sampling dust from the stratosphere.

Smithsonian Contr. Astrophys., vol. 5,

no. 10, pp. 145-152.

HODGE, P. W., and WILDT, R.

1958. A search for airborne particles of meteoric

origin. Geochim. et Cosmochim. Acta,

vol. 14, pp. 126-133.

HODOE, P. W., and WEIGHT, F. W.

1962. The space density of atmospheric dust in the

altitude range 50,000 to 90,000 feet.

Smithsonian Contr. Astrophys., vol. 5,

no. 14, pp. 231-238.

HODGE, P. W.; WBIGHT, F. W.; and LANGWAY, C. C, Jr.

1964. Studies of particles for extraterrestrial

origin, 3: Analyses of dust particles from

polar ice deposits. Journ. Geophys.

Res., vol. 69, pp. 2919-2931.

LAEVASTU, T., and MELLIS, O.

1961. Size and mass distribution of cosmic dust.

Journ. Geophys. Res., vol. 66, pp. 2507-

2508.

LANOWAT, C. C, Jr.

1963. Sampling for extraterrestrial dust on the

Greenland ice sheet. Int'l. Assoc. Sci.

Hydrology, publ. no. 61, pp. 181-198.

MILTON, C. B.

1964. Atmospheric aerosol collections near 40,000

feet with a DC s. Ann. New York

Acad. Sci., vol. 119, pp. 116-125.

PARKIN, D. W.f and HUNTER, W.

1962. Meteorites and cosmic dust. In Advances

in Astronomy and Astrophysics, ed.

by Z. Kopal, Academic Press, New

York, pp. 105-163.

PARKIN, D. W.; HUNTER, W.; and BROWNLOW, A. E.

1962. Metallic cosmic dust with amorphous attachments. Nature, vol. 193, pp. 639-

642.

PETTERSSON, H., and FREDRIKSSON, K.

1958. Magnetic spherules in deep sea deposits.

Pacific Sci., vol. 12, pp. 71-81.

SCHMIDT, R. A.

1963. Microscopic extraterrestrial particles from

the Antarctic Peninsula Traverse. Univ.

Wisconsin Geophys. and Polar Res. Ctr.

Rep. no. 63-3.

WRIGHT, F. W., and HODGE, P. W.

1962. Space density of dust in the stratosphere.

Nature, vol. 195, p. 269.

WRIGHT, F. W.; HODGE, P. W.; and LANGWAY, C. C ,

Jr.

1963. Studies of particles for extraterrestrial

origin, 1. Chemical analyses of 118

particles. Journ. Geophys. Res., vol.

68, pp. 5575-5587.

Abstract

Aerosol samples have been obtained at monthly intervals in the altitude range from 9 to 12 km over the southern

California area. The spatial density of all opaque particles collected (> 4 M) varied widely, ranging from about 20

to 200 particles/m*, and showed no dependence on altitude. Certain highly irregular particles have been found, but

have not as yet been definitely related to meteor-shower activity. No increase in the spatial density of metallic

spherules was determined to be associated with meteor showers. The differential size distribution for the collected

metallic spherules follows approximately an inverse fourth-power law. This distribution leads to a mass influx of

8.4 X10* metric tons per year upon the earth.
AEROSOL SAMPLES FROM 9- TO 12-KM ALTITUDE—MELTON 299

PLATE 1

Aerosol collectors mounted for high-altitude chamber test.

Measured Velocities of Interplanetary Dust Particles from

OGO-1

C. S. NILSSON * and W. M. ALEXANDER

 2

An Interplanetary Dust Particle Experiment

was flown on the OGO-1 satellite launched

September 5, 1964. The primary purpose of

the experiment was to measure the speeds and

directions of arrival of dust particles within

120,000 km of the earth's surface, and thus

determine the orbits of these particles. If

sufficient orbits had been measured, the nature

of the apparent dust cloud around the earth

(Whipple, 1961) could have been determined.

Troubles were encountered with both the

spacecraft and the experiment, however, and

only three probable dust-particle impacts were

recorded. The probable orbits of these particles

are described in this paper in greater detail

than in an earlier report (Nilsson et al., 1965).

The detector array consists of four tubular

detectors aligned along the three body axes

of the spacecraft. One detector looks radially

away from earth (—Z direction), and the other

three look in a plane normal to the Z direction.

Each detector accepts particles with an apparent radiant not more than 6° removed from

the detector axis (see fig. 1). An impacting

micrometeoroid first encounters the front thin

film sensor, which comprises two thin films and

a grid. The plasma generated by the passage

of the particle through these films starts a

2 mc/sec clock, which is stopped when the

particle impacts on the rear sensor 10 cm down

the tube. Thus, the time of flight over 10

cm is measured, and the particle velocity

following the penetration of the front sensors

i Smithsonian Astrophysical Observatory, Cambridge, Mass.; formerly

at Goddard Space Flight Center, National Aeronautics and Space

Administration, Oreenbelt, Md.

1

 Temple University, Philadelphia, Pa.; formerly at Goddard Space

Flight Center, National Aeronautics and Space Administration,

Oreenbelt, Md.

ZRCONATE CRYSTAL

FIGURE 1.—The OGO-1 micrometeoroid sensor, which determines particle mass and velocity.

is determined. The deceleration suffered by a

10~10 g iron particle passing through the front

sensor at speeds around 3 km/sec has been

experimentally determined to be about 10

percent.

The rear sensor performs two main functions:

First, there is a thin film capacitor deposited on

a glass plate. This capacitor momentarily

shorts when a particle impacts and the resultant

signal stops the time-of-flight clock. Second,

a lead zirconate transducer bonded to the back

of each glass plate provides a measure of the

momentum of each impacting particle. With

the velocity known, the particle mass can be

determined. It was found from the impact of

small iron particles accelerated to 3 to 5 km/sec

that the transducer system would respond to

momenta exceeding 3X10"8 dyne-sec.

Thus, each tubular detector can provide a

measure of the velocity, direction of arrival,

and mass of an impacting dust particle.

Three particle impacts were recorded on one

tube during the first 10 days of operation.

Spacecraft trouble was such that the experiment

was turned on for only 56 hours of this time,

301
302 SYMPOSIUM ON METEOR ORBITS AND DUST

and data were recorded for only 4 of these 56

hours. It can be seen from figure 2 that a

total of 17 hours of data was received during

these 10 days, but 13 hours of this corresponded

to times during which the experiment was

turned off. We cannot tell from the data

alone whether the experiment was turned on

or not; only from the records of the power

commands transmitted to the spacecraft do we

know the periods for which power was applied

to the experiment. This fact is of importance

in our assessing the reality of the impact data,

as will be shown below. Unfortunately, the rear

sensor capacitors can suffer a permanent short

when subjected to particle impact with the

power off the experiment. There was no provision for clearing such a short on this particular

experiment, and we believe that three of the

four capacitors were dead before experiment

data were received. The experiment was again

turned off for a short period after the third

impact had been recorded, and although a

great quantity of data has been received since,

no more impacts have been noted. This

suggests that the fourth sensor was shorted by

impact when the experiment was turned off on

the 10th day after launch.

In view of the paucity of data (the impacts

total only 10 bits of information with no

redundancy), we had to look rather closely into

the statistical reality of the data, considering

both experiment noise and telemetry noise.

There is no history of the former in our experiON 56hr

DATA 17 hr

ON WITH DATA 4 hr

3HtTS

DATA

ON WITH DATA

OHrrs -

STATSTICAI. REALITY Of DATA

3 FALSE

» 2 FALSE

» I FALSE

ALL REAL

TELEMETRY NOISE

TO DAr 270

ID 10"1

1.7 10*

1.8 10"'

87 10"'

- TOTAL

PROBABILITY

1J 10*

2.9 10"'

1.1 10'

89 10"'

FIGURE 2.—Details of operation of the micrometeoroid

experiment on OGO-1. The lower table indicates the likelihood of the three impacts being false.

ence with the instrument flown. The unit is

well shielded electrically, and also a time-offlight measurement requires two independent

events to occur within a very restricted time

interval. There were no spacecraft commands

sent at the time of the three events, nor did the

neighboring telemetry words show any signs

of radio-frequency interference. We have considered the possibility of telemetry noise indicating false impacts, and treated the first

weeks of data in considerable detail. The

probabilities of events occurring by chance in

43 hours' data are given in the left-hand

column of figure 2. Thus, we can see that

there is less than 1X 10~* probability that all

three events recorded to day 270 were due to

chance telemetry noise. This strongly suggests

that at least some of the data are real, and

that the cessation of events after day 250 was

due to the failure of the last sensor. This

being the case, we can strengthen the probabilities of the events being real. The experiment

was turned on only during 4 of the 17 hours

for which we received data from launch through

day 259. All three apparent impacts were

extracted from the data without knowledge of

whether the experiment was on or off. Subsequently, we found that all three events

occurred during the 4 hours that the experiment

was turned on. This fact is not only heartening, but can be used to improve the probability

figures concerning the reality of the data.

The right-hand column includes' this information. There is only a 0.1 chance that any one

impact is false, and less than 3 X 10~3 probability

that two of the three events are false. These

figures could be further improved by our

decreasing the data interval from day 270 to

day 260, and also by our using the fact that all

three hits were recorded on the one sensor.

The details of the three impacts are shown

in table 1. The first two were recorded within

27 min of each other at altitudes in excess of

several earth radii, and the observed velocities

were in the range 30 to 50 km/sec. These

velocities preclude any possibility that the

particles were in closed orbits around the earth.

The third impact indicates a low-velocity particle that impacted at a much lower altitude and

may have had a mass an order of magnitude

greater than the masses of the first two. No
VELOCITIES OF DUST PARTICLES FROM OGO-1 NILS80N AND ALEXANDER 30 3

TABLE 1.—Impact parameters of particles observed by the cosmic-dust experiment on OGO-1

Time of impact

UT 1964

Altitude (km) Observed velocity (km/sec)

Geocentric velocity (km/sec)

Mass (g)

Hit 1

Hit 2

Hit 3

257««03h45»

257d04b12»

259<»18h35-

22, 490

28,740

2,960

40<>0<50

33<»o<4O

40<t>,<70

30<t>,<60

8<t>,<15

<7X 10-»

<ixio-»

<7X10-»

minimum values for the particle masses are

given, as in each case there was no recorded

output from the transducer, presumably because the impact momenta were below the

threshold of the experiment.

The uncertainty in the observed velocity

arises partly from the necessity to digitize the

time of flight for telemetry and partly from the

uncertainty in the actual deceleration through

the front sensor. The maximum deceleration

allowed in computing the possible geocentric

velocities was 30 percent. The attitude of the

spacecraft at the times of the three impacts was

unfortunately not known, so that the range of

geocentric velocities possible for each impact

was broadened even further to the values given

in table 1. Even with the true geocentric

velocities being subject to such wide limits and

with only the spin axis of the spacecraft known,

it has been possible to deduce something about

the probable orbits of these three particles before impact.

The probable orbital elements of each particle have been computed in the following manner. The total acceptance angle of each tubular

sensor is about 12°, so we have divided the spin

revolution into 36 intervals of 10° each and

then computed the orbit of each particle for 36

directions of arrival. In addition, we have

considered four possibilities for the time-offlight digitizing error and four values of deceleration through the front thin films. Thus,

there are 16 possibilities for the true velocity

and 36 possibilities for the direction of arrival

of the particle. This totals 576 possibilities.

By computing the orbital parameters for each

of the 576 cases and summing them, one can

obtain a probability distribution for each orbital

element. We have done this for each of the

three particles.

Consider hit 3 first. The particle could have

been in either a closed geocentric orbit or an

orbit of low eccentricity around the sun. There

is little we can learn about the geocentric orbit,

owing to the large uncertainty in the velocity

vector, so we shall consider only the heliocentric possibilities. Figure 3 shows the probability distribution for the reciprocal semimajor

axis. The orbit must have been similar in size

to that of the earth. From figure 4 we can see

that the orbital eccentricity must have been

small, probably less than 0.3. Finally, from

figure 5, we see that the inclination to the

1 1 1

1

—1

HIT 3

/ i = 1.0

i i i i

5

1.4 1 2 1.0 0. 8 0.6 0.4 0.2 0-0. 2

RECIPROCAL SEMIMAJOR AXIS. I/ a

FIGURE 3.—The probability distribution for the semimajor

axis of the orbit of particle 3.

JU

40

30

20

10

n

-

HIT 3

/A = 1.0

n

1 1

1 1 1 1 ! 1

u0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

ECCENTRICITY, e

FIGURE 4.—The probability distribution for the eccentricity

of the orbit of particle 3.
304 SYMPOSIUM ON METEOR ORBITS AND DUST

plane of the ecliptic must also have been small.

Thus, if this particle was in a heliocentric orbit

at the time of impact, the orbit must have been

direct, of small inclination and low eccentricity,

and of a size similar to that of the earth's orbit;

the particle would have stood a good chance of

being captured by the earth.

In figure 6 we see the probable geocentric

velocity of the first particle. The velocity relative to the earth could have been anywhere

from 40 to 70 km/sec, with a most probable

value around 50 km/sec. We cannot learn

much about the size of the orbit, but the eccentricity shows a meaningful distribution, as can

20 40 60 80 100 120 140 160 180

MCUNATMMM

FIGURE 5.—The probability distribution for the inclination

of the orbit of particle 3.

10 20 30 40 50 60 70

GEOCENTRIC VELOOTY.Vg [km/sec]

80

be seen in figure 7. All the cases for which the

computed eccentricity is greater than 1.4 have

been excluded from the distributions. This

value corresponds to a very markedly hyperbolic orbit around the sun, and any particle in

such an orbit would quickly leave the solar

system. Thus, we are not likely to meet many

of these particles. The particle probably had a

high eccentricity. Two histograms are shown

for different values of the effective gravitational

constant p. Radiation pressure is quite significant for particles of this size and, like

gravity, radiation pressure decreases as the

square of the distance from the sun. Thus, we

can allow for radiation pressure by reducing the

effective gravitational constant. We have used

0.75, an arbitrary value for M, to assess the

importance of this phenomenon. In this case,

it slightly increases the probability of a high

value of eccentricity.

Figure 8 shows a distribution of inclination

to the ecliptic plane for hit 1, which is quite

revealing. The orbit was possibly retrograde,

or at least of high inclination. The particle

could not have been traveling in a direct orbit

near the ecliptic plane. Da vies and Gill (1960),

Hawkins (1962), and Nilsson (1964) have

detected radio meteors in high-inclination

orbits, but generally these are orbits of low

24

20

16

12

8

4

0

HIT1

H- = 1.0

/i = 0.75

r—|—P4—J

-i J

r —

i

•

•

•

!

H

02 0.4 0.6 0.8 1.0

ECCENTRICITY, e

1.2 1.4

FIGURE 6.—The probability distribution for the geocentric

velocity of particle 1.

FIGURE 7.—The probability distributions for the eccentricity

of the orbit of particle 1. The distribution M=0.7 5 corresponds to a value of effective gravitational constant reduced by radiation pressure.
VELOCITIES OF DUST PARTICLES FROM OGO-1—NILSSON AND ALEXANDER 305

HIT 1

i—i

20

16

I 12

4

0 20 40 60 80 100 120 140 160 180

MCUNATKM.i

FICUKE 8.—The probability distributions for the inclination

of the orbit of particle 1.

eccentricity, say e<0.5. Hit 2 has similar

orbital parameters to those of hit 1, so here

we have two particles in high-inclination orbits

of high eccentricity. For masses less than

10~n g we would not expect the particles to remain in these orbits for periods much greater

than 103 or 10* years, so probably they were

of relatively recent origin, perhaps from a longperiod comet. The direction of the spin axis

of the spacecraft precludes any possibility

that the two high-speed particles came from

the moon. They must have been in heliocentric orbits.

Finally, it should be noted, without too

much emphasis, that the flux based on these

three impacts in 4 hours is in excellent agreement with the microphone data recorded by

previous near-earth satellites (Alexander et al.,

1963).

Acknowledgment

One of the authors (C. S. N.) has been supported

in this work by a NAS-NASA Research

Associateship.

References

ALEXANDER, W. M.; MCCHACKEN, C. W.; SECRETAN,

L.; and BERG, O. E.

1963. A review of direct measurements of interplanetary dust from satellites and probes.

In Space Research III, ed. by W. Priester,

North-Holland Publ. Co., Amsterdam,

pp. 891-917.

DAVIES, J. G., and GILL, J. C.

1960. Radio echo measurements of the orbits of

faint sporadic meteors. Monthly Notices

Roy. Astron. Soc, vol. 212, pp. 437-462.

HAWKINS, G. S.

1962. Radar determination of meteor orbits.

Astron Journ., vol. 67, pp. 241-244.

NILSSON, C. S.

1964. A Southern Hemisphere radio survey of

meteor streams. Australian Journ.

Phys., vol. 17, pp. 205-256.

NILSSON, C. S.; ALEXANDER, W. M.; MCCRACKEN, C.

W.; BERG, O. E.; and SECRETAN, L.

1965. Measured velocities of interplanetary dust

particles. Nature, vol. 208, pp. 673-674.

WHIPPLE, F. L.

1961. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

Measurements of Interplanetary Dust-Particle Flux from

Explorer 16 CdS and Wire Grid Dust-Particle Detectors

L. SECRETAN

 1

Introduction

Explorer 16 (plate 1) was designed essentially

to assess the micrometeoroid hazard to thin

sheet metal exposed in space. Two other

experiments were added in the form of wire

grids and a mylar-covered CdS photoconductor.

The purpose of this paper is to describe these

two experiments and to analyze the data

derived from them.

Explorer 16 was the third satellite in a series

of three Scout S55 launches. The first launch

failed, and the second partially failed without

providing data. The latter launch was aloft

long enough to show a defect in the design of

the CdS detector. This was corrected and the

detector operated normally in Explorer 16, and

will be described presently. Explorer 16 was

launched on December 16, 1962. It had a twin

telemetry system A and B. System A operated

normally until May 29, 1963, and B operated

until July 25, 1963. A report on all the experiments for the first 28 of 221 days of satellite

operation is given by Hastings (1963). The

description of the wire grid and of the CdS

experiments follows, but no attempt is made to

compare these with the other experiments

aboard the satellite.

Description of the two sensors

C DS CELLS.—The design of the Explorer 16

CdS sensors was derived from the original

design used successfully on Vanguard 3 (1959??)

(LaGow, Secretan, and Giuliani, 1958) and on

Explorer 7 (1959 il) (LaGow and Secretan,

* Goddard Space Flight Center, National Aeronautics and Space

Administration, Greenbelt, Md.

1963). Figure 1 shows a cross section of the

cell with the mylar stretched across the face of

the cell. The vent holes, shown in plate 2, are

designed to provide large air passages, but do

not permit the sunlight to reach the sensitive

cell.

The mylar film covering the cells was coated

on both sides with aluminum in order to provide

absolute opacity and to ensure that any light

input would be caused by perforation and not

by surface erosion or flaking. There is one cell

for each telemetry system A and B. The

effective area of each cell is 2X10"3 m2. The

mylar film of cell A was left completely opaque,

while the film of cell B was perforated with a

nominal 0.002-inch hole for in-flight calibration

purposes. When the satellite was in orbit, the

initial resistance of cell B dropped to a value

near 40 K ohms, which showed that the system

started operating as expected with a solar

aspect angle of 30° from the normal. During

the lifetime of the experiment, this aspect

angle was 30° or less.

COPPER WIRE GRIDS.—The wire-wound cards

are shown in figure 2, and their dimensions are

given in table 1. Hastings (1963) has described

the wire-grid experiment in detail.

307
3 0 8 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 1.—Wtre thicknesses and the areas of the wire cards 1000

100

Diameter

of wire

(inch)

0.002

0.003

(M)

50

75

Number

of

sensors

14

32

Area/

sensor

(ft»)

0.0474

0.0948

Total area

m

0.664

1.517

(m>)

6. 1X10-*

14. IX10-*

Total projected area=20.2X 10-» m*=0.2 m»

FIGURE 2.—The copper-wire card detector.

Calibration of detectors

C DS PHOTOCONDUCTORS.—About a dozen CdS

cells were tested and calibrated to find two

that had nearly the same sensitivity to light

inputs. The calibration established the change

of resistance of each cell for a given light input

through calibrated pinholes. The cells with

the most uniform light sensitivity across their

entire surfaces were selected. The calibration

curve applicable for the two cells in orbit is

shown in figure 3. The abscissa shows the

area of the pinhole in square millimeters; the

calibration pinholes used were 0.001, 0.002, and

0.004 inch (or 25, 50, 100 n) in diameter. The

ordinate shows the resistance of the cells in

K ohms. The line drawn through the mean

values, obtained when the cell was rotated for

5 min in a xenon arc beam, has been used to

evaluate the telemetered resistance data. Preliminary tests were made to establish the

correlation between the light intensity of the

xenon arc and that of the sun. The scatter in

the data for figure 3 represents the variation

in sensitivity over the complete area of the

cell established by the positioning of single

pinholes during the calibration. The cumulative characteristics of the detector were established during laboratory calibrations. Since

to

MEAN RESISTANCE (R)

MEAN DEVIATIONS

FROMR

1

0.0001

AREA OF OPENING (mm2)

I I

j 0.001 [ J0.0I 0.1

0.001 0.002 0.004

DIAMETER OF CALIBRATION PIN HOLES (inch«t)

FIGURE 3.—Calibration of Explorer 16 CdS celb.

in flight the detector measures the cumulative

area of many necessarily random perforations,

the resistance value for a large number of holes

approaches the mean value shown in figure 3.

The relationship between the perforated hole

diameter in %-mil mylar and particle size has

been established in the laboratory by Friichtenicht (1961) and independently by the

author. For iron particles, p=7.8 g/cm3, the

hole size is 1 to 1.5 times larger than the

penetrating particle.

The CdS cells were calibrated with respect

to temperature, and a linear relationship

between resistance and temperature was determined for the expected operating thermal

range.

Wire grid thermo-electric compensation

The copper-wire grids were temperature-compensated for resistance changes, which were

not to exceed 3 percent between —20° C and

60° C. Figure 4 shows the circuit of the 21

TE5 compensating thermistor and associated

wire grids. The resulting resistance curves

are shown for 0.003- and 0.002-inch wires,

compared with a curve for uncompensated wire.

Results of CdS cell and wire-grid experiments

The processed data from the two experiments

were received in the following forms: (1)
INTERPLANETARY DUST-PARTICLE FLUX FROM EXPLORER 16 DETECTORS—SECRETAN 309

450 470 490

RESISTANCE (ohm)

0.002" WIRE GRID

0.003" WIRE GRID

FIGURE 4.—Thermo-electric compensation of copper-wire

grids.

resistances of cells A and B (ohms), (2) temperature of cells A and B (°C), (3) information

indicating continuity or breakage of a wire on

one or more cards, and (4) length of interrogation, date, and station.

The resistance data were normalized to the

launch temperature of the cells (35° C) by

means of the empirical linear relationship

between temperature and resistance: Rt=R3S-\-

K(t—Tu), where #=66 0 ohms and t is the

cell temperature in °C.

The thermal relationship remained valid for

cell B until December 31, 1962. After this

date the temperature correlation changed and

it became impossible to establish a relationship

between resistance and hole size. For cell A

the case was more favorable, and the data

could he followed to February 5, 1963, when,

as a result of successive perforations, the

minimum recordable resistance was obtained.

The changes of aspect to the sun have been

considered. The geometry of the orbiting

vehicle is such that after 55 days the sensor

aspect is the same as at launch time. The

data are interpreted in terms of total cumulative

perforated areas. Intermediate changes tabulated are affected by an aspect uncertainty

factor of 2.

A simplified diagram of the compensated

CdS data is shown in figure 5. Cell A remained

dark at about 300 K ohms until 2 days after

launch. The first indication of light penetration was on December 18, 1962, when the cell

showed a decrease in resistance. The first

marked event happened on December 23, 1962.

The cell was still showing darkness in twilight

December 23, 1962, at 11:40, but showed an

0.002-inch hole during the next pass at 12:30.

Further penetration measurements of cells

20

DAYS IN ORBIT

16

DECEMBER

1962

20 3 2

JANUARY FEBRUARY

1963

FIGURE 5.—Drop of resistance of cells A and B with time in

orbit.
310

SYMPOSIUM ON METEOR ORBITS AND DUST

A and B occurred, as may be seen from tables

2 and 3.

The wire grids were monitored for the lifetime of the satellite. Two breaks occurred,

one of the 3-mil and one of the 2-mil wire.

Owing to the satellite's rotation with respect

to the sun, the resistance of the cell is lowest

when the sun's rays are normal to the mylar

film. For this reason the lowest resistance

readings have been considered exclusively as

data points in evaluating the size of the perforations. Dates of those readings and the estimated additional cumulative perforated areas

are tabulated in chronological order in tables

2 and 3. It must be emphasized that the data

TABLE 2.—Cell A data compensated to 85° C for a 65-day

period

Date

December 16

December 18

December 21

December 23

December 24

January 7

February 4

February 9

Cumulative

days

2

5

7

8

22

50

55

Hole area (mm1)

Total

area

0

0.00015

0.00024

0.0020

0.011

0.023

0.033

0.080

Additional

perforated

area

0

0.00015

0.00009

0. 00178

0.009

0.012

0.010

0.047

Total additional area=0.080

TABLE 3.—Cell B data compensated to 85° Cfora 20-day

period

Date

December 16-17

December 18

December 19

December 21

December 23

December 26

January 4

Cumulative

days

2

3

5

7

10

19

Hole area (mm*)

Total

area

0.0012

0.0016

0.0020

0.0022

0.0025

0.0065

0.0080

Additional

perforated

area

0

0.0004

0.0004

0.0002

0.0003

0.0040

0.0015

Total additional area=0.0068

in these tables do not represent discrete events,

but cumulative status readouts when the

satellite was in a suitable position both as to

orbit and aspect to the sun.

Data analysis

Tables 2 and 3 are interpreted in the following

manner: The CdS cell detectors measured the

cumulative perforated area caused by in-ftight

impacts on the mylar by dust particles. As

previously stated, the accuracy of the measurements increases with the number of perforations. Therefore, the method of analysis

applied in this paper is as follows:

1. From hypervelocity microparticle-impact

experiments performed in the laboratory, it is

found that the threshold mass of the perforating

particles is approximately 10~I0gfor the denser

and 10~* g for the less dense particles. The

diameter of the hole in mylar is 1 to 1.5 times

the diameter of the perforating particle, allowance being made for the range of specific

gravity of the impacting particles.

2. It is considered that the total perforated

area is caused by particles of masses near the

threshold limit of the detector.

3. A model for the cumulative flux distribution of dust particles in the vicinity of the

earth is assumed in order to compute an expected rate of perforation.

4. Finally, the expected cumulative area of

perforations is compared with the data.

5. Due to uncertainties in aspect and

thermal corrections, the expected accuracy

of the cumulative perforated areas is limited to

a factor of 2.

The computations were carried out for:

(1) a cumulative flux mass distribution model

log / = —17.0-1.7 log M (eq. 1 of Alexander et al., 1963); (2) three different mass

threshold sensitivities, 10"10, 10"', 10"8 g mass;

and (3) three different possible densities of

particles, px = \ g/cm8 (ice), pa=4 g/cm3 (stone),

and P3=8 g/cm3 (iron).

The expected cumulative perforated areas

as a function of time for masses 10~10, 10"*,

and 10~8 g and densites of 1, 4, and 8 g/cm3

have been computed from the above-mentioned

equation 1 (tables 4, 5, 6, and 7).

The data from cell A showed a cumulative

perforated area of 0.08 mm2 for the 55-day
INTERPLANETARY DUST-PARTICLE FLUX FROM EXPLORER 16 DETECTORS—8ECRETAN

TABLE 4.—Area of one hole in mylar

311

Diameter

of particle (M)

Diameter

of hole

(mm)

Area of

hole

(mm>)

Mass=lX10- 1 0 g

Density of particle g/cm •

p = l p = 4 p= 8

5.8 3.6 2.9

0. 0087 0. 0054 0. 0044

5.9X10-* 2.3X10-* 1.5X10-»

Mass=lX10-*g

Density of particle g/cm *

p=l p=4 P=8

12. 4 7. 9 6. 2

0. 0189 a 0119 0. 0095

2.8X10"* 1.1X10-* 7.1X10-*

Mass=lX10-»g

Density of particle g/cm1

p=l p=4 p=8

26. 9 16. 9 la 7

0. 0404 0. 0254 0. 0206

12.8X10-* 5.1X10"4 3.3X10-4

TABLE 5.—Cumulative flux: log /=-17—1.7 log M

log Af=-10

7=1X1O«=1

impacts/in* sec

logM=-9

7=1X10-"

impactfl/m1 sec

logM=-8

7=lX10-»-4

impacts/m* sec

experiment lifetime. The expected cumulative

area for 10"10 g particles, as shown in table 7,

varies from 0.055 to 0.143 mm2 as the specific

gravity is varied from 4 to 1 g/cm3. Table 7

gives similar information concerning cell B.

It is concluded from this analysis that, within

the frame of our assumptions concerning the

physical parameters of the particles and

sensor threshold sensitivity, the particles detected in this experiment were predominantly

in the mass range of 10~10 and 10~9 g for densities' between 1 and 4 g/cm3

.

Concerning the wire grids, it is shown in

Appendix A that equation (1) predicts six

impacts, while only two have been observed.

Conclusion

The data from the mylar-CdS experiment

described in this paper are interpreted as due

to perforations through an opaque cover by

microparticles in the vicinity of the earth.

If the cumulative flux expressed by Alexander et al. (1963) is used as a guideline, good

agreement is obtained for masses ranging

between 10"!0 and 10"9 g for densities of 1 to

4 g/cm3.

The wire-grid experiment confirms the above

statement for masses of the order of 10"7 g of

probably higher densities.

A discussion follows on the possibility of

erosion of the front coating of the mylar film.

Discussion of results

In the course of the discussion at this symposium on the results of the CdS experiment,

it was pointed out by Professor Whipple that

the drop of resistance of the CdS cells may

have been due to the transparency of the coating of the mylar film, or to pinholes, in case

the total front area had been eroded.

The experiments on Vanguard 3 and on

Explorer 7 have proved conclusively that the

front film did not erode comjle ely; the cells

remained "dark."

Regarding the transparency of the back

film, the following experiment has been performed with a spare film fabricated at the same

time (and by the same people) as the flight

films.

1. The front film was completely etched

away.

2. The film was placed on a CdS cell of

the same type as the flight unit.

3. A strong light spot 1 cm in diameter

was focused on the cell. A reading was obtained.

4. The same arrangement was repeated,

replacing the film with a clear pinbole 0.0025

cm in diameter. The same reading was obtained as with the 1-cm cleared-up film. The

ratio of areas was roughly 2X10*. The flux

required to erode an equivalent area would be

5 orders of magnitude greater and the particle
312 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 6.—Impacts per day

Mass (g)

lO-io

io-»

10-"

Particle influx

1X10° or 1

IX10-1-

7

ixio-»4

Sensor area

(m»)

2X10-*

2X10-*

2X10-*

Area X time (AT)

1. 73X 10» m» sec

1. 73X 10» m» sec

1. 73X 10» m» sec

Impacts per

day

1. 73X 10»

a 45

6. 91X10-*

TABLE 7.—Expected cumulative perforated areas

Particle

mass

(g)

IX10-"

ixio-»

lXlO-8

Specific

gravity

(g/cm»)

1

4

8

1

4

8

1

4

8

Expected cumulative perforated

areas (mmJ)

20 days, cell B

5.2X10-J

2.0X10"1

1.2X10"J

4.8 XIO"1

1.9X10-*

1.2X10-'

4.4X10-*

1.7 XIO"4

1.1X10-*

55 days, cell A

1.43X10"1

5.5X 10-»

3.6X10-*

1.32X 10~a

5.2X 10-»

3.4X10-*

1.21X10-3

4.8X 10-*

3.1X10-*

mass would be of the order of 10~14 g. The size

of these particles would be in the range of

1000 A. Because of radiation-pressure effects

it is improbable that these particles exist in the

vicinity of the earth.

Appendix A: Micrometeoroid impacts on wire

grids

From equation (1) below, we can compute

the number of impacts N for the wirewound sensors. First let the particle with a

diameter 60 M and a density of 1 g/cm3 be the

mass (M—-10-7 g) that would break the copper

wires used; then

Since

log / = -17.0-1.7 log M

= -5 ,

/ = 1X 10~5 impacts/m2 sec.

4T=62X10*m2sec,

N=ATI=62X 10*X 10~5

=6.2 impacts.

(1)

This value compares favorably with the

experimental results, which show two broken

wires. In considering the impacts upon the

wire-wound grids, we see that the wires will

not always be hit head on (i.e., the particles

may graze the wire or merely penetrate the

insulation surrounding each of the wires).

If the above calculation is performed for

particles with A/=10~6 g, then N=0.l impact.

Therefore, since the actual number of impacts

must be greater than those recorded (i.e., all

the micrometeoroids will not hit the wires head

on), the particles detected by the wire grids are

of the order of 10"7 g or larger.

References

ALEXANDER, W. M.; MCCRACKEN, C. W.; SECHETAN,

L.; and BERG, O. E.

1963. Review of direct measurements of interplanetary dust from satellites and probes.

In Space Research III, ed. by W. Priester,

North-Holland Publ. Co., Amsterdam,

pp. 891-917.

FRIICHTENICHT, J. F.

1961. Study of crater physics. Space Technology

Labs., Ramo Wooldridge Inc., Report

no. 3, July 18.

HASTINGS, E. C, Jr., Compiler

1963. The Explorer XVI micrometeoroid satellite: Description and preliminary results

for the period December 16, 1962,

through January 13, 1963. NASA Tech.

Memo. X-810, February.

LAGOW, H. E., and SECRETAN, L.

1963. Results of micrometeorite penetration experiment on the Explorer VII satellite

(1959 Iota). NASA Tech. Note D-1722,

April.

LAGOW, H. E.; SECRETAN, L.; and GIULIANI, J.

1958. Experiments for satellite environmental

measurements. In International Geophysical Year, vol. 6, parts 1-4, Pergamon Press, New York, pp. 319-321.
INTERPLANETARY DUST-PARTICLE FLUX FROM EXPLORER 16 DETECTORS—8ECRETAN 313

Abstract

The CdS dust-particle detectors on Explorer 16 provide a means of determining the flux of dust particles in the

vicinity of the earth by measuring the area of the perforations due to impacts of dust particles > 10~10g through a

1

4-mil aluminized mylar film.

One of the CdS detectors measured a total area of 0.08 mm* perforated by dust particles for a period of 55 days.

(The other measured an area of 0.068 mm1 in 19 days.) The perforated area is proportional to the cumulative flux

of all impacting particles > 10~10g.

The flux measured by the detectors is compared with several models provided by other satellite and various

ground-based observations. Wben the flux model derived from the direct satellite measurements is used, where

log / = —17.0—1.7 log M, it is found that approximately 10* impacts would occur. The area opened up by these

impacts is in excellent agreement with the results of the CdS detector experiment. Flux models derived from groundbased observations predict too few impacts for the mass range of particles considered here.

The wire grid experiment would detect particles of 10~7 g and larger. Two wires were broken. This is in good

agreement with the dust-particle flux model derived from direct satellite measurements.

240-022 O— 67 21
314 SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 1

Explorer 16.
INTERPLANETARY DUST-PARTICLE FLUX FROM EXPLORER 16 DETECTORS—6ECRETAN 31 5

PLATE 2

Ring showing the vent holes for the CdS cell.

Dust Dynamics in the Magnetosphere and Interplanetary

Space

 x

S. F. SINGER

 2

Introduction

Evidence regarding the size distribution and

other properties of interplanetary dust comes

from different types of observations, such as

optical observations of the zodiacal light, impacts of dust particles on satellite detectors,

and collection of dust in the ionosphere and

stratosphere.

Unfortunately, the evidence is conflicting.

The greatest amount of analysis has gone into

the interpretation of zodiacal-light data. The

earliest analyses, and those made until very

recently, have tended to favor a rather flat

distribution, J(a) da~a~2ida, with the radius a

of the order of 20 to 50 MMore recently, work by Ingham, Giese, and

Weinberg (for the review, see Weinberg, 1964)

has tended to stress another interpretation

that gives a much steeper spectrum, with an

exponent of 4 or even greater, extending to

particles of submicron size. According to R. H.

Giese (private communication, 1965), there

still exists a basic uncertainty between these

two rather different possibilities.3

i Adapted from a paper entitled "Dust and Needles In the Magnetosphere," delivered at the American Geophysical Union Annual Meeting,

Washington, D.C., April 19,1963.

1

 University of Miami, Coral Gables, Fla.

* One novel method of investigating this point has been suggested by

Bandennann and Singer (1985). It consists of measuring the neutral

hydrogen produced when the ionized solar wind recombines on the surface of interplanetary dust particles. Under certain assumptions regarding the dust-particle size distribution, sufficient neutral hydrogen is

produced to be easily detectable through the scattering of Lyman-a

photons. On the other hand, an absence of an appreciable Lyman-a

contribution coming from the plane of the ecliptic would indicate that the

number of particles present is insufficient to release hydrogen. Extreme

assumptions, both on the high and low sides, for dust-particle distributions give hydrogen release rates of 1.8xi0-:

/cm3 down to l.6xl0-»/cmJ

at 1 a.u., withaneutral hydrogen lifetime of 2.5X10«sec. Concentrations

of hydrogen can be obtained, from barely detectable to those that give

more than an optical depth.

Dynamic effects of minor forces

We will assume that particles of very small

size are present and that, therefore, the effects

of minor (nongravitational) forces cannot be

neglected. Just what constitutes a small particle depends on the particular application. In

general, since the minor force produces a perturbation on the major (gravitational) force,

the product of perturbation and time is significant. The longer the time scale over which

forces are considered to act, the larger is the

size of the particle that we find interesting to

consider; i.e., in the Poynting-Robertson effect,

we may consider particles of size 100 n or more,

while for a discussion of the effects of Lorentz

forces, the particles would be of submicron

size.

The influence of these minor forces then

leads to some very surprising effects. So

far none of these effects has been observed,

nor have they been particularly looked for.

Therefore, many of the phenomena I shall

describe must await experimental verification.

We shall see how the observations agree with

the predictions.

Since I shall discuss many new effects, it is

necessary first to deal with the minor forces

and then to list their effects.

One minor force is radiation pressure due to

the solar radiation. The larger the area-tomass ratio of the particle, the more important

radiation pressure becomes. Table 1 gives

typical values for the radiation pressure, and

compares it to the gravitational forces. It

can be seen how the importance of radiation

pressure increases as the size of the particle

decreases. For submicron particles the com317
318 8YMPO8IUM ON METEOR ORBITS AND DUST

TABLE 1.—Ratio of solar-radiation pressure to solar

gravitational force (independent of distance to sun)

Particle

radius

(M)

100

10

1

0.3

0.1

0.005

small

Iron (density 7.8)

0.002

0.02

a 25

1.0

1.8

2.0

ML 1

Particle material

Dielectric (density 3.3)

Large refractive index m

tt 0015

0.014

0. 13

0.8

1.8

1.4

small

m=1.5

0.0005

(tt 004)*

(0. 08)*

0.5

a 39

0.085

small

* Uncertain because of unknown diffraction effects in this critical site

range.

position plays an important role: metallic

particles smaller than 0.3 M are blown out of

the solar system, while nearly transparent

dielectric particles can survive down to any

size.

A second important minor force is the

Covlomb drag or electric charge drag. I have

considered its effects first on dust particles

(Singer, 1956), and, more recently, on the

West Ford needles (Singer, 1961b), which I

consider as artificial dust particles. The

Coulomb drag arises because bodies in space

acquire an electric charge due to the presence

of the plasma and of solar ultraviolet radiation. I have discussed the charging process

before and state here only that close to the

earth the charge is negative, while in interplanetary space it becomes positive. A minimum is reached somewhere between, probably

at about 1 earth radius, but the uncertainties

here are very large.

The Lorentz force has been considered

earlier (Singer, 1956), and again more recently

by Parker (1964).

I shall now review four topics in which the

effects of these minor forces enter in an important way: (1) the question of the dust shell

around the earth; (2) the possibility of a

morning-to-evening difference between incident interplanetary dust; (3) the question of

dust particles in captured orbits, trapped

in the gravitational field; and (4) the question

of the sweepout of dust from interplanetary

space.

DUST SHELL AROUND THE EARTH.—A theory

published in 1961 (Singer, 1961a) predicts

the existence of a dust shell around the earth

(fig. 1). Specifically, we should look for the

existence of a maximum in the dust-particle

flux at an altitude of about 2000 to 3000 km

above sea level.4 In other words, there should

be a decrease below this altitude. Unfortunately, the observations are difficult and are

complicated by the fact that the motion of the

100

u/v^'0.5

1.0

FIGURE 1.—The concentration (particles/cm1) and the impact

rate (impacts/cmVsec) are both shown as a function of

distance from the earth's center. The distance unit y is

inversely proportional to distance r, and is expressed in

earth radii R. Thus, y = 1.0 corresponds to the earth's

surface (or just above the atmosphere), while y= 0 corresponds to infinity. It can be seen that the theory gives

only a modest increase in concentration as one approaches

the earth, with a maximum before one reaches the earth's

atmosphere. Note that the impact rate, however, depends

on the particle-size distribution chosen and can increase

by 2 orders of magnitude or more when the geocentric

velocity is small.

4

 These results have been confirmed by work of Colombo, Lautman,

and 8hapiro (W65) and by Hale and Wright (1864), bnt not by others.
DUST DYNAMICS IN MAONETO8PHERE AND INTERPLANETARY SPACE—SINGER 319

detector itself influences the measurement.

Note particularly that while the dust flux

increases by a factor of 10* or 103 between

interplanetary space and the earth, the dust

concentration increases only by a factor of

2 to 5.

It should be noted that the main component

of interplanetary dust consists of particles that

are so large that the minor forces do not affect

the distribution around the earth, particularly

since the major contribution to the flux comes

from particles in hyperbolic orbits that simply

go past the earth or may hit the earth, but do

not remain in the earth's vicinity for a long time.

MORNING-EVENING ASYMMETRY.—The effects

of radiation pressure from the sun acting on

small dust particles in interplanetary space lead

to a very peculiar phenomenon. The particles

orbit around the sun at a smaller velocity than

that of the earth. Hence, the earth catches

up with them and overtakes them. In essence,

therefore, the earth runs into particles on the

morning side at 6 a.m. However, the proper

analysis of the problem shows that the measured

flux will be greater on the evening side and not

on the morning side. The effect is shown in

figure 2. It can be seen how the magnitude of

the effect increases as the particle size diminishes.

In fact, this method could be used to measure

the size distribution of the incoming dust

particles in a completely objective manner by

measuring the morning-to-evening asymmetry

in the flux (Singer, 1963).

There will also be a seasonal asymmetry

observed in the dust flux that should be independent of the dust particles' size. This

seasonal asymmetry is caused by the fact that

the earth has a slightly eccentric orbit, while the

orbit of dust particles in interplanetary space

should be nearly circular. It would be interesting to look for this effect. In the winter

we should have more dust particles on the

evening side, and in the summer we should

observe more dust particles on the morning side.

DUST PARTICLES IN TRAPPED ORBITS.—One of

the most intriguing questions that have been

considered for many years is whether dust particles exist around the earth in satellite orbits.

The observations of large dust-particle fluxes

10.0

5 0

2 0

10

0 5

02

01

- \/ \

V

-

-

^N^(M <

l

i | i i i < |

RAO. PRESS.

v N . SOtAR 6RAV

(K \10.0

3RNING)

I i i | i i . i

-

~t y 7 ~- -~. EARTH ORBIT

(EVENING)

\

t . . 1 ... .

10

r/RE

20 50

FIGURE 2.—The impact rate of dust particles on a stationary

impact detector as a function of distance from the earth's

center. The existence of a maximum above the earth's

surface is clearly shown. The curve marked 0 applies

to particles of large dimension unaffected by radiation

pressure. The curves marked "evening" and "morning"

correspond to the impact rates observed on the evening

and morning sides of the earth for particles having a directed

geocentric velocity (FB—FD) of 10 km/sec; this rather

extreme value corresponds to a particle of submicron size

that is sufficiently affected by radiation pressure so that

its orbital velocity FD around the sun is 19.8 km/sec;

P,=29.8 km/sec.

near the earth, seen in satellites and space

probes, have led various people to suggest that

there must be many trapped dust particles.

This is not necessarily the case. I am persuaded

that the evidence so far does not require trapped

dust particles for their explanation; the theory

explained above, namely, gravitational concentration of particles coming from infinity, is

adequate. However, there must be some particles in trapped orbits and the question is:

"How important are they?"

I have looked into this subject from time to

time for several years, but much patience is

required. It is not sufficient to inject particles

into trapped orbits. We must also make sure

that their lifetime is long. It is the product of

injection rate and lifetime that gives a large,

steady-state concentration. I have looked into

capture of small dust particles into trapped orbits through the effect of the Coulomb drag. I
320

SYMPOSIUM ON METEOR ORBITS AND DUST

find that this is possible only if the particles

are extremely small or if they have highly

unusual shapes, for example, if they are needle

shaped. A paper given in December 1960

(Singer, 1962) investigates where the particles

could spend a long time and, therefore, be

quasitrapped: at an altitude of about 4000

miles, where their potential might be a minimum. On the whole, however, this particular

investigation was not too promising.

I have now attempted another approach—to

study the injection of particles by the moon.

The mechanism has been suggested by Whipple

(1961): it consists of meteoroids hitting the

lunar surface and splashing out material. I

have tried to see how much material is splashed

out and how much of it can be trapped. I find

that in order to be trapped, the splashed-out

particles must have a velocity greater than 2.38

km/sec to escape the moon's gravitational field,

and less than 2.78 km/sec not to escape the

earth's gravitational field. The number of

particles in this narrow velocity interval is

small. In addition, most of them are again

swept up (in ~380 years), since on subsequent

orbits they will intersect with the moon (fig. 3).

A smaller number will experience enough drag

(Coulomb drag) to shrink sufficiently within

the moon's orbit so that they will miss the

moon. Naturally, only small particles can be

affected this way. Fairly rough estimates show

that the lifetime cannot exceed, in any case, 10*

years and that the equilibrium density will be

small. The uncertainties in the calculation are

such that we can exclude only the possibility of

increasing the flux by a large factor or by orders

of magnitude, but cannot exclude, say, a factor

of 2.8

DUST PARTICLES IN INTERPLANETARY SPACE.—

In interplanetary space, dust particles are

affected by a solar gravitational field, by solarradiation pressure (and the resulting PoyntingRobertson effect), and finally by the Coulomb

drag caused by the interaction between the

electrically charged particle and the inter-

• A similar problem has been considered by Colombo, Lautman, and

Shapiro (1965), but with an important difference: instead of Coulomb

drag, they consider radiation-pressure perturbations. CoincidentaUy

however, their final conclusion regarding the existence of particles in

trapped orbits is similar to ours.

-6 -5 -4 -3 -2 -1

logJQ m (g)

FIGURE 3.—Schematic diagram indicating the ejection of

particles from the lunar surface by a meteorite incident

on the lunar surface. Particle A is large and subject only

to gravitational fields. Particle B is small and assumed

to be affected by Coulomb drag. The diagram shows the

approximate lifetime of ejected particles as a function of

their mass. Particles greater than 10~* g are eventually

swept up by the moon or ejected from the earth-moon

system. Particles smaller than 10"1 g shrink in orbit and

are absorbed by the earth.

planetary plasma. The radiation pressure is

given by the following expression:

F*p=1.5X10-W(4r

The Poynting-Robertson (PR) effect produces a tangential "drag" force which causes

the particles to spiral in toward the sun. Its

magnitude is given by

_ energy/sec v

<- c c = J

= 1.5X10-8a

a

r4r

and the rate of spiraling-in is given by

\-' km

year

= /2-4X10~8\ / r \~l a-u-

\ a )\R / yea yearr

where a is the particle radius, r the distance

from the sun, R the earth-sun distance, v the

particle velocity, and c the velocity of light.
DUST DYNAMICS IN MAGNETOSPHERE AND INTERPLANETARY SPACE—SINGER 321

It is seen that it is the tangential forces that

really determine the fate of the particle, its

lifetime in the solar system.

Finally, we evaluate the (tangential) Coulomb

force Fc for a particle in a near-circular orbit

having an electric potential of 30 volts (taken

as an upper limit). We consider two extreme

cases: (1) a cold nonrotating plasma, density

n=10/cm3; (2) a plasma corotating with the

sun's angular velocity, n=10/cm8.

(1) Nonrotating plasma

i)

*. (km/year) -(¥)(•£ •

(2) Co-rotating plasma

Fc

fc (km/year)

Thus the Coulomb drag, case (1), enhances

the PR effect and causes the particle to spiral

in faster; for example, a 10-AI particle would

have a lifetime of only about 10* years.

On the contrary, a corotating interplanetary

plasma decreases the Pi? effect, at a rate that

becomes greater as the particle approaches the

sun. We can form the ratio

•fc(rot)

= 1.67X10-2(4r

PR

It becomes unity at a value r/R=0.07, well

within the orbit of Mercury.

It can be seen that the Coulomb drag introduces interesting cosmological consequences for

the interplanetary dust.

Unfortunately, no final statement can as yet

be made; e.g., the effects of the Lorentz force

are surely important; dynamic effects due to

the (moving) solar wind and moving magnetic

fields need to be considered.

It is clear, however, that the traditional view,

which considered only the Poynting-Robertson

effect, will not be adequate to deal with the

problem.

Acknowledgment

I wish to thank Mr. Lothar W. Bandermann

for his assistance in the calculations. The

work was supported under NASA Grant NGR10-007-011.

References

BANDEBMANN, L., and SINGER, S. F.

1965. Neutral hydrogen in interplanetary gas

(abstract). Trans. Amer. Geophys.

Union, vol. 46, p. 133.

COLOMBO, G.; LAUTMAN, D. A.; and SHAPIRO, I. I.

1965. Dynamics of small particles in the solar

system (abstract). Trans. Amer. Geophys. Union, vol. 46, p. 428.

HALE, D. P., and WRIGHT, J. J.

1964. Meteoric flux and density fields about an

infinitesimal attractive center generated

by a stream monoenergetic and monodirectional at infinity. Journ. Geophys.

Res., vol. 69, pp. 3709-3717.

PARKER, E. N.

1964. The perturbation of interplanetary dust

grains by the solar wind. Astrophys.

Journ., vol. 139, pp. 951-958.

SINGER, S. F.

1956. Measurements of interplanetary dust. In

Scientific Uses of Earth Satellites, ed.

by J. A. van Allen, Univ. of Michigan

Press, Ann Arbor, pp. 301-316.

1961a. Interplanetary dust near the earth.

Nature, vol. 192, pp. 321-323.

1961b. Interaction of West Ford needles with the

earth's magnetosphere and their lifetime. Nature, vol. 192, p. 1061.

1962. Distribution of dust in cislunar space. In

Lunar Explorations and Spacecraft Systems, ed. by R. Fleisig, Plenum Press,

New York.

1963. Dust and needles in the magnetosphere

(abstract). Trans. Amer. Geophys.

Union, vol. 44, p. 29.

WEINBERG, J. L.

1964. The zodiacal light at 5300A. Ann. d' Astrophys., vol. 27, pp. 718-738.

WHIPPLE, F. L.

1961. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.
322 SYMPOSIUM ON METEOR ORBITS AND DUST

Abstract

The major forces acting on dust particles near the earth or in interplanetary space are produced by gravitational

fields. For very small bodies of micron or submicron size, however, we must take into account minor forces, such as

radiation pressure, Coulomb drag, and the Lorentz force. These minor forces can produce significant effects on dust

particles near the earth, e.g., an evening-morning asymmetry in dust impacts. They also affect the distribution and

lifetime of dust in interplanetary space.
Extraterrestrial Dust Concentrations in the Upper Atmosphere

R. K. SOBERMAN *

Introduction

Particle sampling of the northern latitude

mesopause has produced new data regarding

the phenomenon of noctilucent clouds (Hemenway, Soberman, and Witt, 1964; Soberman

and Hemenway, 1965). These data have,

however, not explained the reasons for the

formation of these clouds. The present paper

presents a highly idealized mechanism that

attempts to explain the results of the sampling

experiments and other observations. Since

we will utilize the results from the "Kronog&rd

62" program, it is useful to present a brief

description of how the data were obtained.

A complete description of the experimental

apparatus is given in Soberman et al. (1964).

The particle collectors were carried by the

two-stage Nike-Cajun solid propellant rockets,

which burned out before reaching an altitude

of 15 km but continued to ascend to a peak

altitude of 110 km. The sampling began at

the altitude of 75 km and was terminated at

98 km while the vehicle was still ascending.

The collection surfaces were mounted perpendicular to the axis of the rocket (plates

1 and 2). The efficiency of the nose cone

design was greater than 95 percent for particles

with a diameter larger than 0.01 fi. Of the

four types of collection surfaces used, only

the aluminum-shadowed nitrocellulose will be

considered here. The others were intended

primarily for the study of the individual

noctilucent cloud particles. We shall be concerned here with comparative numbers of

particles. The nitrocellulose surfaces were

approximately 200 A thick and were coated

• Air Force Cambridge Research Laboratories, Bedford, Mass.; now

at General Electric Co., Valley Forge, Pa.

with a thin film of aluminum deposited by

vacuum evaporation. Extreme cleanliness precautions were observed throughout all phases

of the experiment to minimize contamination

from terrestrial particles collecting on the

surface during the preparation, handling, and

analysis procedures. A number of techniques

were used to identify such contaminant particles. These included aluminum shadowing

and the use of a portion of the collection surface

as a control by shielding this area from particles

collected during the flight. These control

techniques have been described in detail

elsewhere (Hemenway and Soberman, 1962;

Hemenway et al., 1964).

The Kronogard launch site in northern

Sweden, which was used for the K-62 experiments, was located at latitude 66° N and

longitude 19° E. Two collections were successfully recovered during the program. The

first was obtained at a time when no noctilucent

clouds were visible to a system of airborne and

ground observers distributed over several hundred kilometers about the launch area. The

last previous cloud sighting had been 13 days

earlier, and the next did not occur until 4 days

afterward. The vehicle, termed Nattpip 1,

was launched on August 7, 1962, at 0147 hours

local time (0047 UT). The second successful

collection was obtained in the presence of a

noctilucent cloud display that was seen and

photographed by the ground observer network.

The Nattpip 2 was launched on August 11,

1962, at 0240 hours local time (0140 UT).

From the limited data available, the two

flights appear to have been similar in all

respects, with the possible exception of the

coning. The Nattpip 1 remained within 6°

323
324

SYMPOSIUM ON METEOR ORBITS AND DUST

of the vertical throughout the sampling portion

of the flight, whereas the Nattpip 2 may have

had a coning angle as large as 30° or more.

The collection surfaces were examined by

electron microscopy in several laboratories in

the U.S. and Sweden. Plate 3 indicates the

type of micrographs obtained. Particle-size

distributions for the two flights are presented

in figure 1. There was some variation in these

results, as was pointed out by Hemenway

et al. (1964). To eliminate one source of the

variation, both the curves of figure 1 were obtained by one microscopist utilizing the same

model instrument. The data have been previously presented (Hemenway et al., 1964;

Soberman and Hemenway, 1965). The data of

figure 1 have been normalized for diameter

intervals of 10~2 M- The curves were fitted by

eye.

a. -.01 VI

E

u

Z LO

G

7

6

5

4

3

2

1

0

1 1 l

O

-

O NATTPIPI- K62

AUGUST 7, 1962

- A NATTPIPIE-K62

AUGUST 11,1962

1 1 1

1

\

A A

CP

O

1

\

\

o

o\

°\

\

o

1

-

-

-

\

\

\

\

O

\ —

1 "

IO"2

5 10"' 2

DIAMETER./i

Discussion

Since it was concluded from the measurements

that the noctilucent cloud particles or the

nonvolatile nuclei of the ice-coated cloud

particles were extraterrestrial in origin (Hemenway, Soberman, and Witt, 1964), then the first

obvious explanation of the clouds is simple

enhancement of the influx of meteoric dust.

Although we cannot rule out this hypothesis,

several items seem to argue against it. For

one, it might be expected that the same enhancement would be seen for all particle sizes.

This does not appear to be the case. We

might also ask why the clouds are not seen at

lower altitudes, lower latitudes, or at other

times of the year when enhanced meteoric activity exists. Further, this hypothesis offers no

explanation for the ice coatings that were

associated with some of the particles in the

cloud.

A class of hypotheses sometimes invoked to

explain the clouds is the concentration or

focusing of meteoric particles due to electromagnetic fields in space or in the upper atmosphere. The difficulty with this argument is the

small charge-to-mass ratio that such particles

could support. A reasonable estimate of the

maximum field at the surface of a particle in a

good vacuum is about 108 volts/m. If we use

this value, the maximum charge-to-mass ratio

for a spherical particle is

(1)

FIGURE 1.—Particle concentrations per unit area from the

noctilucent cloud (upper curve) and noncloud (lower curve)

samplings of 1962. These curves are normalized for particle

diameter intervals of 10~2 n.

where the particle density pp is expressed in

kg/m3 and the diameter 8 is in meters. For a

particle with a specific gravity of 3 and a

diameter of 0.04 n, the ratio is 44 coul/kg.

This is a factor of about 2X106 smaller than

the charge-to-mass ratio for a proton at rest.

As an example, it would require a field of 0.2

volt/m merely to counteract the acceleration of

the near-earth gravity field. As can be seen

from equation (1), the situation is worse for

larger diameter particles.

Another possible mechanism that could produce noctilucent clouds is a vertical wind or

updraft. The simplest form of this updraft

hypothesis is a vertical wind at the mesopause

of sufficient strength to counter the terminal
EXTRATERRESTRIAL DUST CONCENTRATIONS IN UPPER ATMOSPHERE—SOBERMAN 325

fall velocity of the particles. If we take the

noncloud results of figure 1 (the lower curve) to

be due to the "normal" meteoric influx (with

no vertical winds) and calculate the flux in the

manner of Soberman and Hemenway (1965),

we arrive at a flux of 3X10~2 cm"2 sec"1 (10"2 n)'1

for spherical particles of 0.04-M diameter and a

specific gravity of 3. For this flux to produce

the concentration of the same size particles

observed in the cloud measurement (upper

curve, fig. 1) would require an updraft with a

speed of about 5 cm/sec acting for 3X107 sec

or about 1 year. Clearly this time requirement is unrealistic.

From the foregoing, we are led to the conclusion that the particles that form noctilucent

clouds must come from below the mesopause.

That is not to say that these particles are of

terrestrial origin, but that they must be "stored"

at lower altitudes and then be lifted to the

altitude at which the clouds are observed.

To compute the conditions necessary to produce the measured concentration, we first look

at the "normal" condition again. A small

measure of confidence in assuming the 1962

noncloud sampling as a norm is gained when

we compare this measurement with a similar

measurement made in June of 1961 at White

Sands, New Mexico. These two measurements

yielded calculated particle fluxes that agreed

within a factor of 3 (Soberman and Hemenway,

1965). Thus, from the lower curve of figure 1

we compute the normal (no vertical wind) concentration of meteoric dust particles in the

upper atmosphere. This is done from the

relation

r,(8,Z)=<p(6)/V,(6,Z), (2)

where »j(5, Z) is the number of particles per

unit volume (a function of diameter and altitude), <f>(S) is the flux, and Vp(8, Z) is the terminal velocity of the particles. The values of

the lower curve in figure 1 are taken to be

equal to

N0(S)= =4>(8) F

J Z

l

dZfV,(S, Z), (3)

where Zo and Zx are the altitudes at which the

sampling was begun and terminated (i.e., 75

and 98 km, respectively). The terminal velocities were calculated from the relation (Kennard, 1938)

(4)

where m is the particle mass, g the acceleration

of gravity, c the ambient mean atmospheric

molecular speed, a the particle cross section,

pa the ambient atmospheric density, and a an

empirical constant that can be taken as

(1.4) 4x/3. We again assume spherical particles

with a specific gravity of 3 and use the tables of

the U.S. Standard Atmosphere (1962), for

atmospheric values. Curves for several particle diameters are shown in figure 2.

To determine what sort of updraft would be

necessary to lift these particles back to the

mesopause, we wrote a one-dimensional computer program that adds a vertical upward velocity to the fall velocity of the particles. The

distribution for a given diameter is originally

divided into 1-km intervals and then moved

upward. As the number of particles in a grouping moves upward, the velocity varies in

accordance with

(5)

where VU{Z) is the imposed wind velocity,

which can also be varied with altitude.

Implicit in the model is the assumption that

the atmospheric properties at each altitude are

not disturbed by the process. The program

is terminated when the particle concentration

at any altitude reaches a predetermined value,

or when the "updraft" has been operating for

a predetermined time.

UOG CONCENTRATION, cm'3 I0"2 fi'

FIGURE 2.—Normal (no vertical wind) distribution of meteoric

dust in the upper atmosphere.
326

8TMPO8IUM ON METEOR ORBITS AND DUST

Two wind models were used. The first, for

simplicity, was a constant velocity model

independent of altitude. The first step was to

apply the model to particles 0.04 p in diameter.

When the concentration in the 75- to 98-km

region reached 1.05X10* cm"2 (the value read

from the upper curve of fig. 1), the time was

read out. The same wind velocity was then

allowed to operate for that length of time on the

other particle sizes. The resultant concentrations in the 75- to 98-km range were then read

out. The results for wind speeds of 0.50 and

0.25 m/sec are shown in figure 3. The times

involved were 6.8X10* and 1.4X10* sec,

respectively (or about % and 1% days). In

figure 3 we have replotted the size distribution

of noctilucent cloud particles (upper curve,

fig. 1). To this we have added the points

obtained by simply normalizing the lower or

noncloud curve at the 0.04-M diameter point

and the computed concentrations. Notice

that the smaller wind velocity appears to give

6 -

(M

'E

x 0.5m/sec CONSTANT MODEL

• 0.25 m/sec CONSTANT MODEL

O 0.5 m/sec EXPONENTIAL MODEL

• MULTIPLE VALUES

INCLUDE ABOVE MODELS,

1.0m/sec EXPONENTIAL MODEL,

2.0m/sec EXPONENTIAL MODEL,

AND NONCLOUD NORMALIZED

icr2 2 3 icf 2 3 ic

DIAMETER, ,i

FIGURE 3.—Calculated noctilucent cloud particle concentrations. The solid curve was obtained experimentally.

the better fit for the larger diameter particles.

This wind model predicts that each size will

concentrate at the altitude where the net

velocity is zero. It is to be noted that the

two largest diameter points of the 0.25 m/sec

wind model fall below the noctilucent cloud

curve. This is because peak concentration

altitudes for these larger particles occur just

below 75 km, where the sampling began.

Winds faster than 0.50 m/sec or slower than

0.25 m/sec give poorer fits. It was not deemed

worthwhile to seek the optimum wind velocity.

C. Rooth (private communication) pointed

out that the constant-velocity model was unrealistic in that it violated the conservation of

mass for a continuous updraft. To conform to

the conservation laws and yet keep the program reasonably simple, we imposed a wind

velocity that varied inversely with the atmospheric density (i.e., p.Vm=const). The magnitude of this "exponential" updraft was

specified at the 80-km level and set equal to

zero above that height. The results for the

2.0, 1.0, and 0.5 m/sec wind models are also

shown in figure 3. We see that, to a first approximation, the higher velocity models yield the

same results as normalizing the noncloud curve.

The 0.5 m/sec model also follows these same

points with the exception of the two largest

diameters, where the wind velocity can no

longer suspend the particles in the sampling

regime. The times necessary to build these

distributions are 6.4 X 10s, 1.3X109, and 2.6 X

10* sec, or approximately 1 week, 2 weeks, and

1 month for the 2.0, 1.0, and 0.5 m/sec cases,

respectively. Faster and slower models gave

poorer fits. Again, it was not deemed worthwhile to seek the optimum velocity profile.

Conclusions

While none of the models fit the experimental

results with any great precision, it must be

remembered that they are extremely naive and

are intended only to serve as guideposts for

a more sophisticated approach. The major

uncertainties are in the available experimental

data, the use of the standard atmosphere, and

in the use of a model that holds densities and

temperatures constant while major mass motions are taking place. Nonetheless, the conclusions and predictions that result from these
EXTRATERRESTRIAL DUST CONCENTRATIONS IN UPPER ATMOSPHERE—SOBERMAN 327

simple models are of interest. It is important,

therefore, to clarify the hypothesis being put

forth. It should be clear that we do not

propose that the vertical winds or updrafts

are necessarily in operation at the place where

the noctilucent clouds are being observed.

Rather, it is far more likely that these persistent updrafts are the result of the continuous

solar heating of the ozone below the mesosphere

during the Arctic summer.

In the present models the smaller particles

come from altitudes as low as 42 km. It is

far more likely that the particles are raised

from above the 50-km temperature inversion.

This inversion would also serve as a barrier

against the mixing of extraterrestrial and

terrestrial particles. The low altitudes from

which the particles are drawn in these computations probably result from the use of

the standard-atmosphere tables. The supplemental seasonal and latitude atmospheres

(Cole and Kantor, 1963), reliable at these

altitudes only to 60°, show increased densities

(fig. 4) and an increased lapse rate (fig. 5)

during the summer months, which would

increase the altitudes above which the particles need be raised. The suggested updraft

could be part of a large-scale cellular convective

pattern, as suggested by C. Rooth (private

communication), in which the noctilucent

clouds are seen as particles in horizontal transit

following the atmospheric flow from the region

of updraft to the region of downdraft (in the

earth's shadow). In so moving, they would

cross the twilight where observation is possible.

Due to the Coriolis effect, they would be seen

moving from northeast to southwest. The ice

coatings on the particles would result from

the water vapor, raised with the particles,

which proceeds to condense on the particles

at the extremely low temperatures of the

arctic summer mesopause. For this reason,

the additional mass of the ice coatings on the

particles was not considered in the above

computations of the updraft mechanism. Since

the lifting would occur in the region of 24-hour

daylight, this would explain why the increased

concentration is not observed at lower altitudes during the course of the buildup. It

would further explain why noctilucent clouds

KM

80

70

60

50

40

30

20

10

-20

-

-

-

-

-

1

1

- \

' ,11

\

115^30°

V

i

/

I

7

// :75d

K

K

145° 60'

/ /

/

N

JULY

-

N

-

•

-

-

-

-

1

KFT

- 250

- 200

- 150

z 100

- 50

20 40 6 0 %

FIGURE 4.—Density departures from the standard atmosphere

as a function of latitude (after Cole and Kantor, 1963).

are phenomena of the summer months at

high latitudes and why the clouds are seen

at higher latitudes later in the season (Hemenway, Soberman, and Witt, 1964). The long

times required for the lower updraft velocities

would also explain why the cloud displays are

seen with greater frequency during July and

August.

One major point that the updraft mechanism

does not explain is the sporadic nature of

noctilucent cloud displays. It is believed that,

although the proposed updraft mechanism is

necessary for the occurrence of noctilucent
328 SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 5.—Temperature variation as a function of height and

latitude (after Cole and Kantor, 1963).

clouds, it is not sufficient. An enhanced influx

of meteoric material into the updraft would

explain not only why the clouds occur sporadically but also why the clouds can be seen to

appear and then disappear within a 24-hour

period, while meteoric showers are usually not

that sharply defined in time. Such a combined

mechanism would also explain why some

experienced noctilucent cloud observers will

claim (privately) that the probability of having

a display on certain dates is higher than for the

rest of the season.

In the discussion of the sampling experiments (Hemenway, Soberman, and Witt, 1964)

it was pointed out that the ratio of cloud to

noncloud particles collected is likely to be 103

or greater. The enhancement expected from

meteoric showers is probably not much more

than one order of magnitude, and the present

proposed mechanism cannot raise the concentration much over the two orders of magnitude indicated. It is therefore probable

that only the combined effects of meteoric

showers and the raising of particles from below

can produce the needed particle concentrations.

In conclusion, the present hypothesis predicts that noctilucent clouds should be observed at high southern latitudes during the

latter summer months at periods of high

meteoric activity. The direction of motion

in the Southern Hemisphere should be southeast

to northwest.

Acknowledgments

The author wishes to thank Dr. Claes Rooth

of the Woods Hole Oceanographic Institute

for a stimulating discussion during which he

made a number of helpful suggestions. Thanks

are also due to Mr. Neil Grossbard, of General

Computing Services Inc., who programmed

the problem and put it through the computer.

Mr. Grossbard's services were made available

under contract AFl9(628)5005 to the Data

Analysis Branch of the Air Force Cambridge

Research Laboratories. For their help in the

preparation of the paper, the author is indebted

to Mrs. Pauline Sullivan and Messrs. Christopher Brayton and Ralph Carnevale of the

Advanced Metals Research Corporation.

References

COLE, A. E., and KANTOR, A. J.

1963. Air Force interim supplemental atmospheres to 90 kilometers. Air Force Surveys in Geophysics, no. 153, AFCRL-63-

936.

HEMENWAY, C. L.; FTJLLAM, E. F.; SKRIVANEK, R. A.;

SOBERMAN, R. K.; and WITT, G.

1964. Electron microscope studies of noctilucent

cloud particles. Tellus, vol. 16, pp.

96-102.

HEMENWAY, C. L., and SOBERMAN, R. K.

1962. Studies of micrometeorites obtained from a

recoverable sounding rocket. Astron.

Journ., vol. 67, pp. 256-266.

HEMENWAY, C. L.; SOBERMAN, R. K.; and WITT, G.

1964. Sampling of noctilucent cloud particles.

Tellus, vol. 16, pp. 84-88.

KENNARD, E. H.

1938. Kinetic Theory of Gases. McGraw-Hill

Book Co., New York, 438 pp.

SOBERMAN, R. K.; CHREBT, S. A.; MANNING, J. J.;

REY, L.; RYAN, T. G.; SKRIVANEK, R. A.; and

WILHELM, N.

1964. Techniques for rocket sampling of noctilucent cloud particles. Tellus, vol. 16,

pp. 89-95.
EXTRATERRESTRIAL DUST CONCENTRATIONS IN UPPER ATMOSPHERE—SOBERMAN 32 9

SOBERMAN, R. K.. and HEHENWAT, C. L. U.S. STANDARD ATMOSPHERE

1965. Meteoric dust in the upper atmosphere. 1962. U.S. Standard Atmosphere 1962. Prepared

Journ. Geophys. Res., vol. 70, pp. 4943- under NASA, USAF, and USWB,

4949. Washington, D.C., 278 pp.

Abstract

A theory for the mechanism of formation of noctilucent clouds is presented. It is suggested that the clouds are

composed of extraterrestrial particulate matter, coated with ice, which is following a major mesospheric convection

motion across the arctic twilight. Computer calculations based upon the results of particulate-sampling experiments

show that mean updrafts of less than 1 m/sec could produce the particulate concentrations measured in the noctilucent clouds. It is proposed that the required persistent updraft results from the continuous solar heating of the ozone

layer during the arctic summer. This updraft serves to "reraise" particles that have settled through the mesopause.

These, combined with the enhanced influx of particles during a meteoric shower, produce a cloud of particles that

follows the convective cell across the twilight to a downdraft on the dark side of the earth. The convective motion

also serves to raise water vapor that condenses on the particles in the arctic mesopause. The theory explains a number of the peculiarities of noctilucent clouds, such as the times of appearance and the direction of motion, and yields

predictions for future experiments.

240-022 O—67 22
330 8YMPO8IUM ON METEOR ORBITS AND DUST

PLATE 1

Forward section of Nike-Cajun sampling payload with the spring-ejected outer nose tip. Sampling ports are shown open.

PLATE 2

One of the two sampling cans with cover. One can is located below each sampling port of nose cone.
EXTRATERRESTRIAL DUST CONCENTRATIONS IN UPPER ATMOSPHERE—SOBERMAN 331

A

PLATE 3

Electron micrographs from the Kronog&rd-62 sampling experiments: (a) typical field from noctilucent cloud collection, (b) typical

particle from noncloud collection, (c) typical contaminant. Scale equals 1 M-

Photographs of Particles from an Aerobee Rocket at 130- to

204-km Altitude

R. TOUSEY,1 M. J. KOOMEN,1 R. E. MCCULLOUGH,1 and R. T. SEAL

 l

Introduction

A white-light coronagraph, flown in an Aerobee150 rocket from the White Sands Missile Range

on June 28, 1963, was successful in photographing the sun's white-light corona from 3.5

to 10 solar radii (A*,), something not previously

accomplished without the aid of a total solar

eclipse. The luminance of the white-light corona was found to be approximately twice that

recorded by experiments conducted during total

eclipses (e.g., Blackwell, 1955). This doubled

luminance was interpreted as evidence for dust

within a few earth radii, which was illuminated

by full sunlight in the rocket experiment, but

was within the umbra or penumbra during an

eclipse (Koomen et al., 1964; Tousey, 1965).

A similar result has been found with the U.S.

Naval Research Laboratory (NRL) photoelectric coronagraph on the second orbiting solar

observatory (OSO-2) launched by the National

Aeronautics and Space Administration (NASA).

The coronal photographs were covered with

artifacts of various types that resulted in much

obscuration of the coronal features. Many

were tracks of small particles, slowly crossing

the field of view; some were close, and others

far from the rocket. The altitudes at which

the photographs were made ranged from 131 km

to 204 km.

The instrument was a small Lyot coronagraph, with objective lens of focal length 30 cm

and diameter 25 mm. An external occulter

prevented direct sunlight from falling on the

objective lens; sunlight diffracted from the oc1

 E. O. Hulburt Center for Space Research (sponsored jointly by the

Office of Naval Research and National Science Foundation), U.S. Naval

Research Laboratory, Washington, D.C.

culter's edge was directed away from the lens

by use of the saw-toothed occulter design of

Purcell and Koomen (1962a,b). The residual

stray-light background level was about 10 percent of the coronal luminance for quiet solar

conditions over the entire field of the instrument. The coronagraph was kept pointed at

the sun with an accuracy of better than ± 1 arcmin, but there was no control of rotation around

the solar vector. A slow rotation of the focal

plane was produced by the precession of the

rocket, its rate varying during the precession

cycle from 0 to a maximum value of « ±0.8

deg/sec. At the margin of the field, R=l0R,,

this was equivalent to about 2 arcmin in yaw

or pitch per sec.

The coronagraph proved to be an excellent

camera for photographing tiny particles in

space; however, a requirement for photographing them is that they cross the field of view

with a rather small angular velocity, that is,

that they be moving at very nearly the same

velocity as the rocket, or else be far away and

very bright. This ruled out detecting small

particles in geocentric orbits.

The reason that the coronagraph was able to

photograph small particles is that they shone

so brightly by scattered sunlight, because of the

Mie effect. From the inner to the outer edge

of the field the scattering angles ranged from 1°

to 2?5. The theory of Mie shows that the

forward-scattered intensity within this range of

angles is enhanced over the intensity at other

angles by a very large factor; for l-/i diameter

dielectric spheres of refractive index 1.33, the

factor is =103, and for 10-M spheres, =105.

333
334 SYMPOSIUM ON METEOR ORBITS AND DUST

In the 23 exposures made during flight, reproduced in plate 1, many particle trails were

photographed. Some of these were close by,

as evidenced by their unsharp, and often very

broad trails; others were far away, since their

tracks were in perfect focus.

The question is, did these objects come from

the rocket, or were they a small sample of

natural objects in space? One would suppose

at first that they must have come from the

rocket, since then they would have almost

exactly its velocity, the condition required to

photograph their trails. There is, however,

another possibility that is difficult to rule out.

Although meteorites at these altitudes would

in general be moving much too fast to be

photographed, there should be a few particles

of natural origin having velocities very close

to that of the rocket.

Particle tracks were recorded by Newkirk

and Bohlin (1965; private communication)

with their similar but larger balloon-borne

coronagraph, flown on September 10, 1960.

These particles, however, were shown to have

originated from some styrofoam insulation,

because on a flight in 1965, when this material

was not used, almost no trails were present.

Moreover, these particles must have been very

large, since the balloon reached only 30-km

altitude. Here the sky luminance is still

sufficient to produce a background that would

swamp the trails of faint particles.

Explanation of pictures

The photographs in plate 1 contain various

features that must be explained for the particle

tracks to be interpreted. The separate exposures are arranged in sequence, but each picture

is oriented with solar north at the top and east

to the left. The external occulter and the arm

supporting it cast a conspicuous shadow.

This was very diffuse, because the instrument

was focused for infinity and the occulter was

only 20 inches from the objective lens. The

occulter therefore gave rise to a strong vignetting action. This can be seen from the last

picture in plate 1, which is an exposure made

with a uniform field in the laboratory. By

chance the vignetting function and the radial

brightness function of the corona just about

neutralized each other; therefore, the background exposure, produced by the corona, was

approximately uniform in density over the

entire field. The individual exposures ranged

from 1.1 to 55.8 sec, causing their densities to

differ widely. In the reproduction they were

printed to appear as nearly alike as possible.

Of the various artifacts present, an array of

permanent bright spots is conspicuous on each

exposure. These spots were fixed in position

from exposure to exposure, and are explained

as having been caused by particles loosened

from the interior of the instrument and deposited on a lens surface during launch. There is

a bright patch at the right edge of the occulter

shadow, which gradually becomes less intense,

until it is nearly absent in the last exposure.

This was caused by a slight mispointing of the

biaxial pointing control, which allowed a little

of the light diffracted from the edge of the

occulter to reach the objective lens. Also present are faint scratches on the film, produced

during transport; these are the very sharp,

parallel straight lines that are visible in the

shortest exposures. The great lune in exposures 3 and 4 is a double exposure, caused by

failure to transport the film far enough to

separate the frames completely.

The amount of rotation caused by the rocket

precession is shown for each exposure by the

arrow at the left edge of the frame. Absence

of the arrow indicates negligible rotation.

Also shown is the mean position of the center

of the shadow of the occulter support; this

position rotates gradually in correspondence

with the precession cycle of the rocket, as do

the permanent specks on the optical surfaces.

Particle tracks

The tracks of more than 2 dozen fairly wellestablished particles are indicated in plate 1 by

the letters a to z. They vary from extremely

sharp tracks, such as x, to great blobs of light

like f produced by a particle within a foot or so

of the lens. A preliminary analysis of some of

these tracks has been attempted.

The distance of each particle was established

from the track width, with the assumption that

the particle was small enough to be considered

as a point source. The calculated relation

between track width and particle distance, confirmed by laboratory measurements, is shown in
PHOTOGRAPHS OP PARTICLES FROM AEROBEE ROCKET—TOU8EY ET AL. 335

figure 1. The optical system was quite well

corrected, and the image of a true point source

at infinity, as registered on Eastman Kodak

Spectroscopic 1-D, the emulsion employed,

measured a minimum of 0.02-mm diameter for

a low-density exposure. Because of the vignetting, out-of-focus images of points were

actually crescent-like; for close particles this

produced trails with a sharp inner edge like

the unlabeled streak in exposure 15. One

difficulty in estimating distances from trail

widths comes from the dependence of apparent

width on the difference between the density

of the trail and the density of the background,

an effect produced by the nonuniform distribution of intensity across the out-of-focus

image. Another, of course, lies in the assumption of a point source.

The angular velocity of particles crossing the

field was established directly from the exposure

time and the length of the trail, when both

ends of the trail could be located. Another

1000 qlOOO

— 100

0 1 23 4 5678 9 1 0

IMAGE DIAMETER, MM

12 13

method employed undulations in the tracks,

which were caused by hunting of the pointing

control. These are extremely prominent in

tracks x and w. Plate 2 shows a portion of

x greatly enlarged. Comparison of the undulation wavelength, exposure time, and trail

length led to the determination of the undulation frequency as 1 cps. This was approximately the hunting frequency of the pointing

control in both elevation and azimuth. The

double amplitude of trail x was 30 to 35 n, which

corresponds to a tracking jitter of ±10 arcsec; this was excellent stability for the biaxial

pointing control system, which was the first

of a new type designed and constructed by a

group at the University of Colorado under

the direction of F. Wilshusen. Still another

method of establishing the speed, when a trail

ended on one exposure and began on the next,

was from the gap produced by the film transport time, which was about 0.2 sec.

A conspicuous characteristic of each trail is

that there is very little change in density from

the beginning to the end, even though the particle was changing distance rapidly. There is

a simple explanation for this. For a given

particle, the flux per unit area on the film, and

hence the density, is given by

FIGURE 1.—Effect of point-source distance on image diameter

in photographic coronagraph NE 3.129.

where E is the illumination produced at the

objective by the particle at distance d, 6 is

the angular speed of motion of the image, and

w is the width of the trail. While E varies as

l/d3, the "inverse square law," 6 varies as

1/d, and w does likewise provided d is large

compared to the focal length of the lens.

Therefore, the track density is independent of

the distance, for a particle of a given velocity,

until the distance becomes so great that the

track width is limited by the resolution of the

film and optical system. Vignetting makes

no difference because it simply changes the

size of the out-of-focus image and consequent

track width but does not change the flux per

unit area.

All of the trails are curved to a greater or

lesser extent. In order to interpret the curve
336

SYMPOSIUM ON METEOR ORBITS AND DUST

it is necessary first to correct for rotation of the

image plane during the exposure. This has

been done in plate 3, which shows a composite

pieced together from exposures 19 to 23 and a

diagram giving corrected paths for particles

x, y, and w.

In table 1 a summary is presented of the

principal characteristics of the trails, to the

extent that the analysis has been carried out.

The velocity values refer to the component in

the plane normal to the solar vector; they are

relative to the rocket and are based on the

estimated distances and the measured angular

TABLE 1.—Preliminary analysis of particle trails; NE

8.1X9, June 28, 1963

Particle

a

b

c

d

e

f

g

h

i

j

k

k'

1

1'

1"

m

m'

n

o

o'

P

P'

q

r

s

t

u

V

w

X

y

z

1

2

3

Apparent

speed

(m/sec)

0.1

0.35

0.1

0.2

0.2

1.0

0.2

0.52

0.16

0.45

0.2

0.1

0.35

0.2

0.2

0.2

0.7

0.1

0.03

0.24

0.1

0.5

0.2

>1.55

>0.20

0.11

Distance

Initial

4

very close

16

9

4

very close

9

20

1

200

4

100

15

15

22

8

200

200

26

15

15

100

35

100

100

30

13

1

50

100

100

15

>500

>200

30

(m)

Final

20

21

50

3

9

70

70

200

5

100

15

15

22

15

200

200

26

15

22

100

55

44

44

90

21

9

50

200

100

27

>500

>200

30

velocity. The rocket velocity components were

approximately 90 m/sec north, 23 m/sec east,

and a vertical component ranging from 1.2

km/sec up at exposure 1, to 0 at peak, to 0.8

km/sec down at the end of exposure 23.

It is obvious that the relative velocities of all

the particles with respect to the rocket, ranging

as they do from 0.1 to 1.5 m/sec, are very low

compared to the actual rocket velocity, even at

peak. This appears to be prtma facie evidence

that they originate from the rocket. There is,

however, the alternative explanation that some,

at least, are particles of natural origin. That

they should all have almost exactly the same

velocity as the rocket is simply a result of the

selective action of the photographic coronagraph. For faint particles, only those that

move across the field with low angular velocity

will be able to expose a trail, especially when

the background is dense, as it is in the long

exposures. If there is a large number density

of small particles within the altitude range

covered by the rocket, there should be a few

within the velocity range that can be photographed.

This selective action applies principally to

the velocity component in the plane perpendicular to the solar vector, and is quite stringent. At peak, for example, it acts to select

particles having a north velocity component of

between 91 and 89 m/sec and a vertical velocity of 0± l m/sec. At exposure 22, the

vertical velocity must remain within 1 m/sec of

the rapidly increasing free-fall velocity, which

is near 700 m/sec, and the same north velocity

component restriction still holds. For the velocity component along the solar vector,

however, the selection effect is less stringent.

An estimate of particle size was made, based

on the assumptions that the particles are spherical, have an index of 1.33, and are nonmetallic.

This was done by means of the Mie theory, as

presented by Penndorf (1962), for X = 5000 A

and a scattering angle close to 0°. It was also

necessary to calibrate the coronagraph in order

to obtain approximate values of stellar magnitude for the various particles producing the

trails. Laboratory calibrations made with point

sources of light indicated that 3d-magnitude

stars were easily recorded in 2 sec, and 4 thmagnitude stars were photographable in 1 sec
PHOTOGRAPHS OP PARTICLES FROM AEROBEE ROCKET—TOUSEY ET AL. 337

when they did not move in the field. An unexpected check was obtained in flight from the

3d-magnitude star M Geminorum, which happened to lie 1°44' from the sun, well within the

field of view. This was present in most of the

pictures; it was a well-exposed point of diameter

0.02 mm in the 1-sec exposures, and was drawn

out into a short arc in longer exposures where

the rocket precession rotated the instrument.

Plate 4 shows two exposures where the star

trail is easily seen. The motion of the star also

confirmed the analysis of the rocket precession

as derived from the magnetometer and the

pointing control elevation angle.

The conclusion reached from the observed

trails and the Mie theory was that the particles

photographed must have been in the range

10-/1 diameter and larger. Particles smaller

than 10 M would have been too faint to photograph. Among the smallest and faintest is J,

in plate 1, at a distance of at least 200 m. Even

farther is particle 1 of plate 5, whose trail width,

0.02 mm, indicates a distance of 500 m or more.

According to the Mie theory the luminous intensity increases with the fourth power of the

diameter, approximately, for particles near

10-M diameter. This means that only a small

increase in diameter is required to account for

the brighter trails. It appears that 20 or 30 n

may be the upper diameter limit of particles

photographed. These particle sizes fall within

the dimension limits of particles collected by

Hemenway, Soberman, and collaborators, from

balloons and rockets following meteor showers.

One may question the assumptions involved in

applying the Mie theory, but because the magnitude change with size is so very rapid, the

shape and optical constants should not be of

too great importance in connection with the

luminosity of the particle.

With regard to the possibility of a natural

origin for these particles, it is useful to consider

some details of the trails. In the first place,

the particles seem to appear in puffs. Particles

are few or absent in the first 4 exposures, then

become prominent in the following exposures,

including the 9th, and are absent again in

exposures 11 and 12. Particles are again

evident in exposures 14 through 19, but have

subsided markedly in exposures 20 through 23.

Although this sort of behavior might perhaps

be expected of an outgassing rocket, it may

also be characteristic of meteor showers.

For exposures earlier than 13, all trails were

downward, indicating an ascending cloud of

particles through which the rocket was ascending at a slightly greater velocity. Before peak,

however, particles are present that were traveling upward faster than the rocket (exposures 14

to 16). From about exposure 20 on, the

particles appear to be traveling up as the rocket

falls and are a cloud not falling quite so fast as

the rocket. In the north and south direction

the particles for the most part show a small

velocity component relative to the rocket

toward the south.

At first sight these small relative velocity

effects may seem to be caused by atmospheric

drag; however, at these altitudes the mean free

path is very long. For example, at 204 km

it is 220 m, and at 130 km it is 14 m. Under

these conditions the drag should be quite small,

even for 10-/x particles. Moreover, one would

certainly expect the drag effect to be altitude

dependent, but there is no correlation between

particle velocity relative to the rocket and

altitude.

It is not at all easy to explain the behavior

of particles x, y, and w by changes of speed

produced by drag. Particle x is particularly

puzzling. Its trail can be followed in each

exposure, from 19 through 23, and is shown

as a composite in plate 3. Its path is also shown

replotted with the correction made for rotation

of the instrument during exposure. This

particle was far away, as evidenced by its

sharp trail. It entered the field on the descent

at 202 km, 2 km below peak, when the rocket

velocity downward was about 70 m/sec, and

stayed in the field for a full minute, until the

rocket reached 174 km, where its velocity was

650 m/sec. First it fell faster than the rocket,

but after 30 sec the rocket overtook it, and

30 sec later it left the field. In the north-tosouth direction it entered with almost no

relative velocity, for a time seemed to gain

on the rocket, but left the field traveling south

relative to the rocket. Critical inspection

of the sharpness of the trail suggests that it was

moving eastward faster than the rocket, since

the trail is sharpest at the end of exposure 23.
338 SYMPOSIUM ON METEOR ORBITS AND DUST

Its distance, on entrance, was 100 m, and after

30 sec was 200 m.

Particle w entered late in exposure 19, and

appears faint because of the dense background

of the 56-sec exposure. After correction it

makes an angle of 26° with the zenith. The

trail of particle y is closely parallel to that of

particle w, though it entered earlier and left

later. It is difficult to reconcile these two

trails with possible atmospheric drag effects.

If the south component of each is ascribed to

drag associated with the north rocket velocity,

90 m/sec, there would have to be a drag effect

on the vertical component as well. But the

constant character of the north component and

the increasing vertical velocity would combine

with the increasing drag at lower altitudes to

cause these two trails to be strongly curved;

since they probably are not of the same size

they would not be expected to remain parallel.

Exposure 15 of plate 1 contains the largest

collection of particles and is shown enlarged in

plate 5. The rocket was near the top of its

trajectory during this exposure and was approaching zero vertical velocity. This exposure

shows many particles with relative horizontal

motions in a direction opposite to the horizontal

travel of the rocket. However, there are

also particles with vertical motions that are

now in the same direction as the rocket motion,

that is, they are overtaking the rocket. In the

direction toward the sun, two are approaching

and others are receding. This situation cannot

be explained by drag. In particular, consider

particles 1, 2, m', and n (plate 5), with distances

>500, >200, 200, and 200 m, respectively;

no two paths are parallel, and their directions

range through more than 90°. Yet in this

exposure these four particles lie within 2? 5 of

each other. Without resorting to a collision

process of some sort, it would be impossible to

eject from the rocket four particles and have

them reach this small, distant region with

velocities so far from parallel.

Amongst the particles that were very close

to the coronagraph, there are many that show

strongly curved paths. These may be caused

by electrostatic effects. Another factor comes

from the precession of the rocket, since the

rocket nose, swinging around in a cone, would

impart nonlinear transverse velocities to the

coronagraph under certain conditions. However, strongly curved paths do not require that

these particles originate from the rocket, since

natural particles could equally well be strongly

charged and be deflected when passing close by

the rocket.

It is difficult to arrive at a really clear-cut

conclusion without making a calculation of the

number density of photographable particles,

based on known and estimated distributions at

these altitudes. The best proof that they are

natural particles is that many are far from the

rocket and their behavior is not easy to explain

on the basis of an origin from the rocket.

It is of interest that the date of the rocket

flight, June 28, 1963, lies in the month when

meteor counts are at a maximum, and is in the

period of the Corvid, 0-Taurid, and Draconid

showers, and only a few days after the Ariel id

shower. Moreover, from May through

November in the year 1963, according to

Mclntosh and Millman (1964) and Ellyett

and Keay (1964), there was an unexpected

increase in the meteor count, especially for

small particles. Perhaps meteors entering more

or less parallel to the earth's surface produce,

in the breakup process, enough fragments

moving upward and reaching the 200-km level

with relatively low velocities to account for the

photographed trails.

Acknowledgment

This work was supported in part by the

National Aeronautics and Space Administration.

References

BLACKWELL, D. E.

1955. A study of the outer corona from a

high altitude aircraft at the eclipse of

1954 June 30. I. Observational data.

Monthly Notices Roy. Astron. Soc, vol.

115, pp. 629-649.

ELLYETT, C. D., and KEAY, C. S. L.

1964. Meteors: An unexpected increase in 1963.

Science, vol. 146, p. 1458.

KOOMEN, M. J.; PURCELL, J. D.; SEAL, R, T., Jr.;

and TOUSEY, R.

1964. Solar corona photographed from a rocket

(abstract). Journ. Opt. Soc. Amer., vol.

54, p. 1409.

MCINTOSH, B. A., and MILLMAN, P. M.

1964. Radar meteor counts: Anomalous increase

during 1963. Science, vol. 146, p. 1457.
PHOTOGRAPHS OF PARTICLES FROM AEROBEE ROCKET—TOU8EY ET AL. 33 9

NEWKIRK, G., Jr., and BOHLIN, J. D. light properties. Journ. Opt. Soc.

1965. Coronascope II. Observation of the white Amer., vol. 52, pp. 596-597.

light corona from a stratospheric balloon. 1962 b A coronagraph imprOvement. Sky and

Ann. d'Astrophys., vol. 28, pp. 234-238. Telescope, vol. 24, p. 197.

PENNDORF, R. p

1962. Angular Mie scattering. Journ. Opt. Soc. TOUSEY, R.

Amer., vol. 52, pp. 402-408. 1965. Observations of the white-light corona by

PUBCELL, J. D., and KOOMEN, M. J. rocket. Ann. d'Astrophvs., vol. 28,

1962a. Coronagraph with improved scattered- pp. 600-604.

Abstract

Photographs were obtained of the solar corona from 1° to 2?5 from the sun's center, at altitudes from 131 km

to 204 km, by means of an externally occulted Lyot coronagraph flown in an Aerobee-150 rocket on June 28, 1963.

They show many trackB produced by particles, Bhining brightly by sunlight scattered forward at a small angle. Analysis of the trails indicates that the particle diameters were 10 to 30 it. Distances from the rocket ranged from 1 to

500 feet or more. The velocities relative to the rocket were 0.1 to 1.5 m/sec. This is not surprising, because particles

with greater relative velocities would not have been detected photographically. It is difficult to explain the behavior

of the distant particles on the assumption that they came from the rocket. It is proposed that some arc natural

particles, of meteoritic origin.
340 SYMPOSIUM ON METEOR ORBITS AND DUST

Photographs taken with rocket coronagraph on June 28, 1963.
PHOTOGRAPHS OF PARTICLES FROM AEROBEE ROCKET—TOUSEY ET AL. 341

—< Ji I u

°- "S
342 SYMPOSIUM ON METEOR ORBITS AND DUST

UJ

M

O UJ

2°

UJ
125.8 SEC-H

SOLAR NORTH

h-118.8 SEC

SOLAR NORTH

143.5 SEC k-139.7 SEC

FRAME # 3,7. 0 SEC, 137 KM FRAME #5,3.8 SEC, 160 KM

/j. GEMINORUM, Mag 2.86

AEROBEE NE 3.129 (CORONAGRAPH) JUNE28J963

PLATE 4

Expoiures 3 and 5, showing image of p Geminorum, mag +2.86, Aerobee NE 3.129 (coronagraph), June 28, 1963.
SOLAR NORTH

45 M

O.IO M/SEC

14 M0.3 M/SEC

OCCULTER

SUPPORT

236.5 SEC —

17 M

0.11 M/SEC

240.4 SEC

50 M/SEC AT 236.5 SEC

10 M/SEC AT 240.4 SEC

Vx= 9 0 M/SEC

30 M

0.16 M/SEC

6 0 M

0.22 M/SEC

45 M0.I7M/SEC

>500M

> 1.55 M/SEC

100 M

0.37 M/SEC

>200M

>O.I8M/SEC

>200M

>0.52 M/SEC

PLATE 5

Exposure 15, near peak of rocket trajectory, at 3.8 sec, 204.2 to 204.3 km, Aerobee NE 3.129 (coronagraph), June 28, 1963.
Vertical Distribution of Dust in the Stratosphere

J. M. ROSEN

 l and E. P. NEY l

Introduction

The estimation of meteoritic-dust influx from

particle samples collected in the atmosphere

and on the earth has been plagued by the

problem of identifying terrestrial contamination. Because of the similarity between the

meteoritic and terrestrial dust, physical and

chemical methods of distinguishing the two

components are very difficult, if not impossible

(Wright and Hodge, 1964; Merrihue, 1964).

Testing for the presence of cosmogenic nuclides

in dust samples would seem to offer a possible

solution to the problem, but the contrary

results of researchers leave this method still in

question (Merrihue, 1964; Schaeffer, Megrue,

and Thompson, 1964).

Measurements of the vertical distribution of

dust, on the other hand, can distinguish the

particle source by the spatial distribution of

particles in the atmosphere. This method

affords a relatively simple way of obtaining the

total meteoric-dust influx.

Instrumentation

A balloon-borne photoelectric particle counter

was used of the type invented by Gucker

and collaborators at Armour Research Foundation (Gucker and O'Konski, 1949). It is a

relatively simple instrument capable of counting

and sizing particles down to 0.25-M diameter.

A diagram of the instrument is shown in figures

1 and 2. It is basically a dark-field microscope

in which an individual dust particle in the

sampled air scatters light into a photomultiplier. A complete description of the instrument can be found elsewhere (Gucker and

O'Konski, 1949; Rosen, 1964).

1

 School of Physics and Astronomy, University of Minnesota, Minneapolis, Minn.

240-022 O—6T 23

PHOTOMULTIPUER

MtTAl SHIELD

FIGURE 1.—Optical system of the photoelectric counter.

I*

FIGURE 2.—Air-flow system of the photoelectric particle counter.

Results

Representative data from four balloon flights

are shown in figures 3 through 6. With the

exception of Flight 747, the data indicate that

the dust concentration above 100 mb is proportional to the pressure (that is, the dust

exhibits a constant mixing ratio). A different

graph was used to plot the data of Flight

747 so as to show clearly that it is composed of

discontinuous segments along which the mixing

ratio is constant.

Discussion

The problem of dust falling through a diffusing

atmosphere has been given rigorous mathe345
346 SYMPOSIUM ON METEOR ORBITS AND DU8T

IB 10 KX> -40 O 40

NUMBER /cm* WITH DIAMETER >06/i TEMPERATURE (*C>

FIGURE 3.—Dust concentration on ascent of Flight 667,

August 20, 1963.

NUMBER /cm5 WITH D s 0 45 and

FIGURE 4.—Dust concentration on ascent of Flight 719 and

ozone concentration on descent of Flight 720, August 18,

1964.

oo -co -4o -io o a

OUST CONCENTRATION (NUMBER/cm WITH DIAMETER S0.5 and 0.7fl TZHPERAWREK)

FIGURE 5.—Dust concentration on ascent of Flight 729,

August 28, 1964.

matical treatment by a number of authors

(Lettau, 1951; Junge, Chagnon, and Manson,

1961). The important results of such a treatment, however, can be obtained by a simple

physical argument.

- LINES OF

CONSTANT

MIXING RATO

OI234S6789I O -00 -40 -20 0

FIGURE 6.—Dust concentration on ascent of Flight 747,

April 28,1965.

The vertical distribution of dust from a constant source above a quiescent atmosphere is

governed only by the gravitational fall velocity

of the particles. Since the fall velocity in the

stratosphere is inversely proportional to the

pressure, it follows that the dust concentration

must be proportional to the pressure. Now

taking into account the motion of the atmosphere, the effect of turbulence is to mix the

atmosphere in such a way as to keep the ratio

of dust particles to air molecules a constant,

that is, to preserve the constant mixing ratio

and not destroy it.

The vertical distribution of dust from a constant source at 100 mb would be considerably

different. In this case, there is a direct competition between atmospheric turbulence trying

to establish a constant mixing ratio and the

settling of dust trying to destroy it. From

what is known about the magnitude of diffusion

in the stratosphere, the mixing ratio would

drop sharply above a 100-mb dust source

(Junge, Chagnon, and Manson, 1961).

In summary, the behavior of the mixing

ratio of dust in the stratosphere is a criterion

for the source of dust: if the mixing ratio is

constant in a given region, then the source is

above that region. If, on the other hand, the

mixing ratio drops sharply in the given region,

then the source is below that region.

Conclusions

There can be little doubt that the source of the

stratospheric dust observed on the balloon flights
VERTICAL DISTRIBUTION OF DUST IN 8TRATO8PHERB—ROSEN AND NET 347

r

HEMENWAY AND SOBERMAN (1962)

JUNGE, CHAGMON AND MONSON (I960 AUGUST 26,1958

PHOTOELECTRIC COUNTER AUGUST 20, 1963

CONSTANT MIXING

RATIO UNE

- » — - •

KT tf* Kf Kf K>' Kf

NUMBER/cm3 4 0.9-ft. DIAMETER

FICUKE 7.—A comparison of dust concentration measured

in the stratosphere with that measured at high altitude

in the Venus Flytrap experiment. The line of constant

mixing ratio connecting the high-altitude dust concentration

with the low-altitude dust concentration suggests that most

of the dust is of meteoritic origin.

was above 27 km. Flight 747 suggests why

the mixing ratio is not always constant even

though the dust may be of meteoritic origin.

If the influx over the earth's surface is not

uniform, then horizontal mixing in the stratosphere should produce layers in which the

mixing ratio would be constant; at the boundaries of these layers, however, the mixing ratio

would be discontinuous. This argument would

seem to explain the data of Flight 747.

The evidence that the stratospheric dust is

of meteoritic origin is given in figure 7. Only

the results of experiments involving the direct

sampling of dust particles in the size range

0.5 to 2 M are shown (Junge, Chagnon, and

Manson, 1961; Hemenway and Soberman,

1962). Since all the data fall nearly on the

same line of constant mixing ratio, it seems

likely that the stratospheric dust is mostly

extraterrestrial in origin.

The particle flux observed with the photoelectric particle counter is about 4X10~2

 cm"2

sec"1 for diameters between 0.5 and 2 n. This

implies a mass flux of about 4X106 meteoric

tons per year over the earth.

Acknowledgment

This research was supported under Contract

No. Nonr-710(22).

References

GUCKER, F. T, Jr., and O'KONBKI, C. T.

1949. Electronic methods of counting aerosol

particles. Chem. Rev., vol. 44, pp.

373-388.

HEMENWAY, C. L., and SOBERMAN, It. K.

1962. Studies of micrometeorites obtained from

are coverable sounding rocket. Astron.

Journ., vol. 67, pp. 256-266.

JUNOE, C. E.; CHAONON, C. W.; and MANSON, J. E.

1961. Stratospheric aerosols. Journ. Meteorol.,

vol. 18, pp. 81-108.

LETTAU, H.

1951. Diffusion in the upper atmosphere. In

Compendium of Meteorology, Amer.

Meteor. Soc., Boston, pp. 320-333.

MERRIHUE, C. M.

1964. Rare gas evidence for cosmic dust in modern Pacific red clay. Ann. New York

Acad. Sci., vol. 119, pp. 351-367.

ROSEN, J. M.

1964. The vertical distribution of dust to 30

kilometers. Journ. Geophys. Res., vol.

69, pp. 4673-4676.

SCHAEFFER, O. A.; MEGRUE, G.; and THOMPSON, S. O.

1964. Experiments to test the presence of cosmogenic nuclides in ocean sediments.

Ann. New York Acad. Sci., voL 119,

pp. 347-350.

WRIGHT, F. W., and HODGE, P. W.

1964. Compositional studies of extraterrestrial

particles. Ann. New York Acad. Sci.,

vol. 119, pp. 287-297.

Meteoric Dust in the Stratosphere Determined by Optical

Scattering Techniques

G. NEWKIRK, JR. 1

Introduction

Light-scattering measurements have long been

used to estimate the size distribution and

concentration of meteoric material in the zodiacal light. Only more recently have similar

techniques been employed to determine the

meteoric content of the atmosphere, where the

concentration of cosmic particles is magnified

many orders of magnitude over the interplanetary value. Of course, many of the meteoroids

are destroyed or modified upon entering the

atmospheric trap, and the existence of contaminating aerosols adds a new dimension to

the problem of determining the influx rate of

material. Moreover, the months or years of

residence time of meteors and meteoric debris

in the atmosphere below 100 km imply that

any such observation of influx rate represents

average conditions over a similar period.

Although the light scattered from a collection

of aerosols (meteoric as well as other particles)

contains sufficient information to fix the size

distribution and concentration of the particles,

several limitations in the technique occur. For

mathematical simplicity it is usually necessary

to assume the particles to be spherical—a condition that the work of Hemenway and Soberman (1962) has shown to be questionable for

many meteoric particles. Also the refractive

index of the particles may be only approximately known. Frequently, measures of the

angular distribution of scattered light cannot

be made over a sufficient range of angles to

allow the size distribution of the aerosol to be

1

 High Altitude Observatory. Boulder, Colo.

determined unambiguously. In the forward

scattering lobe (for scattering angles <t> less

than 20° to 30°) the gradient of scattered

intensity with increasing scattering angle becomes steeper with increasing a. Thus, smallangle scattering measures can, in principle, lead

to a good estimate of the size distribution of

particles. Radiation scattered at large angles,

however, contains no such unambiguous signature of the particle size, and the size distribution

can be fixed within only very broad limits. In

fact, only the most precise large-angle scattering measures can distinguish between a change

in the particle concentration and a change in

particle size. This latter limitation does not

apply, of course, to determinations of the

scattering from individual particles.

It must also be remembered that scattering

measurements are intrinsically effective for

only those particles whose radii are of the

order of the wavelength of the radiation.

Scattering at optical wavelengths thus allows

the size distribution of the particles to be

determined only over the range 0.1 jx<r<3 p.

One unique advantage possessed by lightscattering measurements of atmospheric aerosols is that a large sample of particles is

examined at once. For example, a photometer

looking upward from the stratosphere receives

radiation from the particles in about 107 m3

for every square degree of viewing angle.

As part of a program to investigate the

feasibility of observations of the corona out

to 5 solar radii, the High Altitude Observatory

has flown an externally occulted coronagraph

up to heights of 25 km to measure the angular

349
350 SYMPOSIUM ON METEOR ORBITS AND DUST

and wavelength distributions of the daylight

sky. The instrument and the details of the

observations and their interpretation in terms

of the scattering of sunlight by aerosols have

been described elsewhere (Newlrirk and Eddy,

1962, 1963, 1964). The basic data consisted

of sky radiances at scattering angles from 1?67

to 57?8 measured at altitudes of from 6 to

25 km at 4400 A.

An example of the variation of sky radiance

with height at one scattering angle appears

in figure 1. The observations are compared

with what would be expected if the sky radiances were measured in a pure, molecular

atmosphere with three different models of the

radiation originating from below. Both the

observations and the calculated values, taken

from Coulson, Dave, and Sekera (1960), include the effects of the variation of the solar

zenith distance during flight. Attention is

called to the sharp approach of the observed

sky radiance toward the calculated values

above an altitude of 20 km.

20

10

0 8

' 0 2

01

008

20 25 km

0-10*3

X-Q52/X

Krinov Albedo, Air Neglected lr.

-—CoulsonAlbedo.TotoiArmos he ^'So""' " A X \ "' t

—Coulson Albedo. Pressure CorrJ Sekera (l96a0) N: N B F

Observed

. e Doubtful

10 20 30 4 0 50 60 70 80

HEIGHT (THOUSANDS OF FEET)

FIGURE 1.—Photoelectric observations of the sky radiance at

a scattering angle of 10?3 at X=0.52 M- The "hook" at

82,000 feet was produced by the variation of solar zenith

distance during the floating period of 2 hours. The observations are compared with three models of the radiation

from a pure molecular sky.

Interpretation

In order to interpret observations such as

those shown in terms of the size distribution

of aerosol above the balloon at any moment,

we must solve the equation governing the

transfer of radiation through a turbid atmosphere. To this end, Sekera (1956) and Deirmendjian (1957, 1959) have demonstrated the

convenience of dividing the equation of transfer

into two simultaneous equations—one describing the intensity due to scattering by the

molecules, and the other describing the intensity due to scattering by the aerosols. The

first, governing the intensity in the pure molecular or Rayleigh atmosphere, has been solved

by Chandrasekhar (1950) and tabulated by

Coulson, Dave, and Sekera (1960). By considering that, insofar as the overall transfer

of radiation is concerned, the Mie scattering

in the upper atmosphere represents a small

perturbation on the solution of the Rayleigh

problem, we can use their tabulated solution.

Subtraction of the radiance of the pure molecular sky from that observed then yields the

residual sky, which is attributed to scattering

by the larger particles. By assuming that

the irradiation of Mie particles by the rest

of the atmosphere and by the ground is

negligible and that M^MO, we can write an

approximate equation

where

M=COS Z,

Z=zenith distance of the point in the

sky,

BMt—radiance of the sky at height h, in

the,;'01 polarization component, due

to the scattering by large particles,

2?©=mean radiance of the solar disk

observed at the height h,

«©=solid angle subtended by the sun,

h—height in the atmosphere,

i

J

(a, </>) = Mie scattering intensity function

in the j* " polarization component

for a spherical drop of size parameter a, of refractive index TO, scat

tering through an angle <£ (see van
STRATOSPHERIC METEOR DUST: OPTICAL SCATTERING TECHNIQUES—NKWKIRK 351

de Hulst (1957) for a complete

definition),

<£=scattering angle counted from the

direction of forward scattering,

a=2xr/X=size parameter of the droplet,

N(r, h) = particle concentration in a column

above height h with radii between

r and r-\-dr.

The unit of N is cm"2 per micron dr. The

usual convention is that,;=l refers to radiation

with electric vector vibrating perpendicular to

the scattering plane, while,;=2 refers to radiation with electric vector normal to this plane.

Calculation shows that the errors committed

by using the simplified equation in the stratosphere are of the order of 15 percent. Since

most of the published Mie scattering coefficients

are for m=1.33, we have made our interpretation in terms of the scattering by spherical

water drops. All particles are considered to

have their radii between the limits rx and r3.

The size distribution of the scattering aerosols

is taken to have the form

(2)

where

*=0, -SI.

Junge, Chagnon, and Manson (1961) have

found by direct sampling, and Volz (1954),

Newkirk (1956).. Deirmendjian (1957, 1959),

and Volz and Bullrich (1961) have inferred

from optical measurements that such a form

adequately describes the size distribution of

atmospheric aerosols.

Comparison between calculated and observed

angular distributions of the residual skylight

(fig. 2) sets the parameter 8 of the size distribution at 5^3.5 in the stratosphere. As

is shown in figure 3a these optical data yield

concentrations and size distributions that are

quite consistent with those obtained by direct

sampling.

By differentiation of the size distributions

with respect to height, one can determine the

variation of particle concentration with altitude

(fig. 36). Quite clearly, our observations con10

•

•0.1

•

g

0.01

i i i i 1 i 1 1 1 1

\ \

X---h> 15.2 km \ >

_ Aigebroic Average \

• •Individual Values \

X-044/ A \

•,• 10 \

i i i 11111 1

i i

V \

'"2\ r

i i

\ -

\ ;

?

^ i

4 6 8 10

<f> (Degrees)

20 4 0

FIGURE 2.—The observed angular distribution of residual sky

radiance at heights above 15.2 km (dots and dashed line) is

compared with theoretical angular distributions (solid

curves) differing only in the parameter 5. Individual values

<Ofor^=20?7 and ^=31?4 are not shown on the diagram.

The particles are assumed to be spheres of refractive index

1.33. The observations are normalized at $=2°.

firm the conclusion of Junge and his collaborators that an aerosol layer at a height of

approximately 20 km exists. The form of such

a layer suggests that the majority of particles

in it are of terrestrial origin and that the maximum is due either to the concentration of

particles by advection or by in situ formation.

Meteoric influx rates

The sharp drop of particle concentration with

height above the maximum of the aerosol layer

can be further interpreted under the assumption

that a steady state prevails and only two

mechanisms—diffusion and sedimentation—

govern the flow of particles. Junge, Chagnon,

and Manson (1961) write the vertical flux of

particles yt as

yt=—n,wl—n~D, (3)

where

n,=concentration of particles of radius r,

to,=fall speed of the particles of radius r,

n—concentration of air molecules (number per

cm3),
352

SYMPOSIUM ON METEOR ORBITS AND DUST

Undated curves refer

to September 10, I960

.•

September 10,1960

• October 3, I960

x-x -x Chagnon and Junge

(1961)

'/* -

HEIGHT (THOUSANDS of FEET)

FIGURE 3.—a, The inferred particle size distributions of aerosols in the atmosphere at the heights indicated. The upper and lower

limits of the particle concentrations determined by direct sampling also appear, b, Change of the concentration of particles of

radius r with altitude. The concentrations above 7.6-km altitude from this investigation are to be compared with the distribution obtained for r=0.15 n by direct sampling. The heavy lines at approximately 3 km show the concentrations and scale

height (H=\ km) inferred in an earlier investigation (Newkirk, 1956). Particles distributed with a constant mixing ratio

with air would display a decrease in concentration with altitude parallel to the bottom curve.
STRATOSPHERIC METEOR DUST: OPTICAL SCATTERING TECHNIQUES—NEWKIRK 353

v,=concentration of particles relative to the

concentration of air molecules,

D=diffusion parameter.

The fall speed is that given by the StokesCunningham relation (Davies, 1945), while

the diffusion parameter contains the effects of

both eddy and molecular diffusion. Within

the layers of the atmosphere of concern in our

problem, eddy diffusion is dominant (Lettau,

1951). The solution of equation (3) in an

atmosphere of scale height H yields

(4)

where the concentration is n,0 at 2=0. By

interpreting the observed drop in particle

concentration with height above the maximum

i (km)

_» 10 15

r • 0.15/A

D-IOOOO cm2/,.c

0-5000 cm'/HC

_ »n S.pt.mbt^O, jortmor,

*n October 3,1960) "" "

50 60 70 80 90

HEIGHT (1000 ft)

100 110

FIGURE 4.—The decrease of relative particle concentration

above the "source level" at 20 km as observed and as

calculated for various values of the vertical diffusion coefficient D. The calculated curves and observed concentrations are fitted to the photoelectrically measured gradients,

which are proportional to concentration, at A=20 km.

of the aerosol layer at 20 km (fig. 4) as due to

the mechanism of sedimentation-diffusion, we

can determine that the diffusion constant D

from 20 to 25 km lies in the range 2000 cm2/sec

<Z)< 10,000 cm2/sec with the best fit for

Z?«5000 cm2/sec. This value is in rough

agreement with the D~IO? estimated by

Lettau (1951) for temperate latitudes from

models of the representative zonal circulation

and the lapse rate.

The additional assumption, however, that D

is constant above 25 km allows the calculation

of the total concentration in the cm2 column

overhead of particles with radius r that have

been carried aloft by diffusion. (In fact, the

usual profile of temperature vs height above

25 km would lead to the expectation that D

should decrease slightly with height.) This

calculation yields column concentrations for

0.3 M<V< 3 n that are below those required by

the scattering observations. In other words,

the air above 25 km contains more particles

in this size range than can be explained by

diffusion from below. The origin of the excess

particles is to be found in the sedimentation

of meteoric material downward. Thus, for a

particular value of D, the observations lead

to a value of the meteoric influx y. In figure 5

appears a comparison between the meteoric

influx for 0.3 M<X 3 M derived in this manner

and as determined by various rocket and

satellite experiments. Except for Watson's

1941 (see Watson, 1956) flux estimate and that

from the "Venus Flytrap" rocket, the results

appear in good agreement.

The departure of the "Venus Flytrap" observations from the other data may be explained

by the encounter of the "Flytrap" with an

abnormally high, transient shower of meteors

or by the sampling of particles orbiting close

to the earth. If the high fluxes inferred from

the "Flytrap" actually had been precipitating

continuously into the atmosphere, the sharp

drop of particle concentration above 20 km

would not be present and the concentration of

meteoric particles at h^-20 km would exceed

the observed concentration of all particles.

The influx rates shown in figure 5 allow the

calculation of the total mass influx of meteoric

material into the earth's atmosphere. By ap-
354 SYMP08IUM ON METEOR ORBITS AND DUST

proximating the number flux of particles as

- 7 = lO"1 r"2-

6

, 0.1 MO< 3 H,

-7=2 0 r-«, 3 M <r<10M,

_ 7=r-* 8, 10 M <r<104

M ,

we determine a mass flux of 2X10"15 g cm"2

sec"1 or 103 metric tons per day or 3 X 10s metric

tons per year over the surface of the earth.

This rate of deposition is smaller than the 104

metric tons per day estimated by Dubin and

6

4

2

0

-2

-4

-6

-8

-10

-12

-14

-16

-18

-2

) l I I I

-Rocket 'Venus Flytrap"

Satellites

Visual and Radar Meteors

Zodiacal Light

FIGURE 5.—Comparison of the meteoric influx rates inferred

in this paper (labeled HAO) with the fluxes determined

from the rocket "Venus Flytrap" (Hemenway and Soberman, 1962), from satellites (Alexander et al., 1963), from

visual and radar meteors (Whipple, 1961a), from zodiacal

light (van de Hulst, 1947), and from visual meteors (Watson,

1956). The higher HAO curves refer to the results of

September 10,1960; the lower curves, to October 3,1960. For

Z)=2000 cm1 sec"1 the solid HAO curves apply, while for

D= 10,000 cm1 sec"1 the dashed curves apply. The lower

size limit of particles to remain in the solar system against

radiation pressure and the upper size limit of particles to

survive passage through the atmosphere (Whipple, 1950,

1951) are indicated.

(HAO curve)

(satellite curve)

(visual and radar meteors curve)

McCracken (1962) and others (Dubin, 1960;

LaGow and Alexander, 1960; Whipple, 1961a)

from the extrapolation of the satellite observations to the radiation pressure limit (under

the assumption that rocket and satellite sample particles are actually precipitating into the

atmosphere). We interpret our smaller daily

influx rate as evidence that above 100 km a

significant fraction of the particles in the size

range 0.3 MO< 3 M are in geocentric, quasiclosed orbits. This hypothesis is strengthened

by the agreement of our estimates with the

rate of approximately 10* metric tons per year

for meteoric dust settling through the air

or deposited on the ground (Crozier, 1960;

Laevastu and M ell is, 1961; Pettersson, 1960;

Crozier, 1961; Thiel and Schmidt, 1961;

Crozier, 1962; Wright and Hodge, 1962). An

alternate explanation is that the majority of

meteoric particles are too fragile to survive

passage through the atmosphere.

Meteoric fluxes in the atmosphere of 4X106

tons per year and 2X107 tons per year recently

estimated by Rosen (1964) and Fiocco and

Colombo (1964) require special comment.

Rosen's determination is apparently based on

the misconception that all aerosols at an

altitude of 20 km in the size range 0.5 n<r<2 p

are of meteoric origin. As is shown in the

next section, only 1 to 10 percent of the stratospheric aerosols are meteoric. The discrepancy

with the optical radar estimates may well be

resolved by the suggestion of Fiocco and Colombo that the particles at 120 km are meteoric

fragmentation products of radii r~0.1 n, which

naturally escape detection in our measurements.

Although their interpretation has been criticized

(Deinnendjian, 1965), it should be remarked

that the sedimentation of particles in the concentrations inferred for 120 km (about 10"'

cm"3) down to 20 km would not be in excess of

the Aitken nuclei counts at the lower altitude

(Junge, Chagnon, and Manson, 1961). The
STRATOSPHERIC METEOR DUST: OPTICAL SCATTERING TECHNIQUES'—NEWKIRK 355

overwhelming proportion of Aitken nuclei in the

stratosphere, however, are believed to be of

terrestrial origin.

Concentration of meteoric particles in the

stratosphere

The relative concentration of meteoric particles

in the stratosphere is of interest in the analysis

of dust-sampling studies as well as to the

meteorologist. Bowen's (1953) hypothesis that

meteoric activity influences world rainfall presupposes that either a substantial fraction of

the particles in the lower stratosphere are of

meteoric origin or that meteoric debris is outstandingly effective as a nucleating agent.

Although we do not intend to discuss the second

alternative, the fluxes inferred from our measurements show that meteoric dust represents

a small fraction of the particulate matter below

20 km (see table 1). Above 25 km meteoric

debris appears to constitute a major part of the

aerosols with radii larger than 0.3 n.

TABLE 1.—Relative concentration of meteoric debris

(ordinary numbers refer to measurements of September 10,

I960; those in parentheses, to October 3, I960)

r(n)

0. 1

0.3

0.5

1.0

2.0

nmritoric/n observed

Local concentration

A = 20km

0

0. 10

(0)

0. 12

(0.01)

0.13

(0.02)

0.13

(0.04)

A = 25km

0

0.42

0.53

0.55

0.55

"meteoric/

•Wobierred

Column

concentration

(A>25 km)

0

0.76

0.95

0.99

1.00

Temporal variations of meteoric influx

Although showers of visual and radar meteors

are frequently spectacular, temporal variations

in the meteoric content of the stratosphere and

lower atmosphere appear to have eluded consistent detection. Bigg (1956), from measurements of the twilight, and Zacharov (1952),

from determination of the transparency of the

atmosphere, claim to have identified an increase

in the dust content of the atmosphere associated

with the Perseid shower; however, the precise

twilight photometry of Volz and Goody (1962)

shows only a broad maximum of stratospheric

turbidity in the winter months. Similarly,

measurements of the radiance of the zenith sky

at 28 km from May through September 1962

(before the Bali volcanic eruption) by Newkirk

and Bohlin (unpublished) fail to show any clear

influence of the Perseid shower. Apparently,

the storage of debris for many months or years

in the atmosphere effectively smooths out the

variations of meteoric influx present at the top

of the atmosphere.

Concentration of interplanetary material

For particles that are not destroyed in their

passage through the atmosphere, the interplanetary concentration nn> is related to the

influx rate by

—y=nI Pv, (5)

where v is the geocentric speed with which

particles leave the interplanetary medium and

impinge upon the upper atmosphere. The

interplanetary concentrations obtained with

u=30 km sec"1 from the HAO data and from

the measurement of meteor impacts on rockets

and satellites are compared with the concentrations inferred from the photometry of the

zodiacal light in figure 6. A detailed critique

of the interpretation of the zodiacal light is not

necessary. Although quite some divergence

appears in the concentrations of interplanetary

particles from the various zodiacal light models,

two facts seem outstanding. First, for r>10 y.

the meteor concentrations exceed the zodiacal

light concentrations by about a factor of 10.

Second, for smaller radii our concentrations

exceed those from the zodiacal light by a factor

of about 1000. (For the extrapolated satellite

curve the excess would be still larger.) We

thus conclude that a geocentric condensation

of interplanetary dust, such as suggested by

de Jager (1955), Beard (1959), Hibbs (1961),

Singer (1961), and Whipple (1961a, 1961b),

does indeed exist. The magnitude of this condensation (approximately 103

 for the smaller

particles) is in agreement with the theoretical
356 SYMPOSIUM ON METEOR ORBITS AND DUST

FIGURE 6.—Comparison of the concentration of interplanetary

dust particles as inferred in this paper (labeled HAO) with

the concentrations determined from satellites (Alexander

et al., 1963) and visual and radar meteors (Whipple, .1961a)

as well as with the various determinations from the photometry of the zodiacal light. The fact that the zodiacal

light concentrations are approximately a factor of 1000 lower

than those determined by our analysis is taken as evidence

for a local gravitational condensation of the interplanetary

dust in the neighborhood of the earth. Note that the model

inferred by Allen (1946) refers only to the concentration

required if all the particles are of a given radius between 1

and 100 n rather than a true size distribution.

calculations. The fact that the observed geocentric condensation is much smaller for larger

particles (r>10 n) suggests that the PoyntingRobertson effect has not sufficiently reduced

the eccentricities and major axes of the orbits

of these larger meteoroids for effective capture

by the earth. The Poynting-Robertson theory

predicts that smaller particles in the solar

system will take circular orbits more rapidly

and hence will be more effectively captured by

the earth.

Acknowledgments

This discussion has been largely based upon the

joint work of John A. Eddy and myself with

support by the Office of Naval Research under

contract Nonr 393(05).

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L.; and BERQ, O. E.

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BEARD, D. B.

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BLACKWELL, I) K . and INQHAM, M. F.

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CROZIER, W. D.

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1945. Definitive equations for the fluid resistance

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pp. 259-270.
STRATOSPHERIC METEOR DUST: OPTICAL SCATTERING TECHNIQUES—NEWKIRK 357

DEIRMENDJIAN, D.

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and radiative transfer. Ann. Geophys.,

vol. 13, pp. 286-306.

1959. Theory of the solar aureole, II: Applications to atmospheric models. Ann.

Geophys., vol. 15, pp. 218-249.

1965. Note on laser detection of atmospheric

dust layers. Journ. Geophys. Res.,

vol. 70, pp. 743-745.

DE JAQER, C.

1955. The capture of zodiacal dust by the earth.

Mem. Soc. Roy. Sci. Liege, vol. 15,

pp. 174-182.

DUBIN, M.

1960. IGY micrometeorite measurements. In

Space Research, cd. by II. KallmannBijl, North-Holland Publ. Co., Amsterdam, pp. 1042-1058.

DUBIN, M., and MCCRACKEN, C. W.

1962. Measurements of distributions of interplanetary dust. Astron. Journ., vol. 67,

pp. 248-256.

ELSASSEK, H.

1954. Die raumlichc Verteilung dcr Zodiakallichtmaterie. Zeits. f. Astrophys., vol. 33,

pp. 274-285.

Fiocco, G., and COLOMBO, G.

1964. Optical radar results and meteoric fragmentation. Journ. Geophys. Res., vol. 69,

pp. 1795-1803.

GlESE , R . II.

1962. Light scattering by small particles and

models of interplanetary matter derived

from the zodiacal light. Space Sci. Rev.,

vol. L, pp. 589-611.

GIESE, R. H., and SEIDENTOPF, II.

1962. Optische Eigenschaften von Modellen der

interplanetaren Materie. Zeits. f.

Astrophys., vol. 54, pp. 200-216.

HEMENWAY, C. L., and SOBERMAN, R. K.

1962. Studies of micromcteorites obtained from n

recoverable sounding rocket. Astron.

Journ., vol. 67, pp. 256-266.

HIBBS, A. R.

1961. The distribution of micrometeorites, near

the earth. Journ. Geophys. Res., vol.

66, pp. 371-377.

JUNGE, C. E.; CHAGNON, C. W.; and MANSON, J. E.

1961. Stratospheric aerosols. Journ. Meteorol.,

vol. 18, pp. 81-108.

LAEVASTU, T., and MELLIS, O.

1961. Size and mass distribution of cosmic dust.

Journ. Gcophys. Res., vol. 66, pp.

2507-2508.

LA GOW, II. E., and ALEXANDER, W. M.

1960. Recent direct measurements of cosmic dust

in the vicinity of the earth using satellites.

In Space Research, ed. by H. KallmannBijl, North-Holland Publ. Co., Amsterdam, pp. 1033-1041.

LETTAU, H.

1951. Diffusion in the upper atmosphere. In

Compendium of Meteorology, Boston,

Amer. Meteorol. Soc, pp. 320-333.

NEWKIRK, G. A., Jr.

1956. Photometry of the solar aureole. Jourii.

Opt. Soc. Amer., vol. 46, pp. 1028-

1037.

NEWKIRK, G. A., Jr., and EODY, J. A.

1962. Daytime sky radiance from forty to eighty

thousand feet. Nature, vol. 194, pp.

638-641.

1963. Influx of meteor particles in the upper

atmosphere of the earth as determined

from stratospheric coronagraph observations. In Space Research III, ed. by

W. Priester, North-Holland Publ. Co.,

Amsterdam, pp. 143-154.

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pp. 35-60.

PETTERSSON, H.

1960. Cosmic spherules and meteoritic dust.

Sci. Amer., vol. 202, pp. 123-132.

ROSEN, J. M.

1964. The vertical distribution of dust to 30

kilometers. Journ. Geophys. Res., vol.

69, pp. 4673-4676.

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1956. Recent developments in the study of the

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in Geophysics, vol. 3, ed. by H. E.

Landsberg, Academic Press, New York,

pp. 43-104.

SINGER, S. F.

1961. Dust shell around the earth (abstract).

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2561.

THIEL, E., and SCHMIDT, R. A.

1961. Spherules from the Antarctic ice cap.

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310.

VAN DE HULST, H. C.

1947. Zodiacal light in the solar corona. Astrophys. Journ., vol. 105, pp. 471-488.

1957. Light Scattering by Small Particles. J.

Wiley and Sons, Inc., New York, 470 pp.

VOLZ, F. E.

1954. Die Optik und Meteorologic der atmospharischen Triibung. Ber. Deutsch.

Wettcrdienstes, vol. 2, no. 13, 47 pp.

VOLZ, F. E., and BULLRICH, K.

1961. Scattering function and polarization of

skylight in the ultraviolet to the near

infrared region, with haze of scattering

type 2. Journ. Meteorol., vol. 18, pp.

306-318.

VOLZ, F. E., and GOODY, R. M.

1962. The intensity of the twilight and upper

atmospheric dust. Journ. Atmos. Sci.,

vol. 19, pp. 385-406.
358 SYMPOSIUM ON METEOR ORBITS AND DUST

WATSON, F. G.

1956. Between the Planets. Rev. ed, Harvard

Univ. Press, Cambridge, Mass., 188 pp.

WHIPPLK, F. L.

1950. The Theory of micrometeorites, I: In an

isothermal atmosphere. Proc. Nat.

Acad. Sci., vol. 36, pp. 687-695.

1951. The theory of micro-meteorites, II: In

heterothermal atmospheres. Proc. Nat.

Acad. Sci., vol. 37, pp. 19-30.

1961a. The particulate contents of space. In

Medical and Biological Aspects of the

Energies of Space, ed. by P. Campbell,

Columbia Univ. Press, New York, pp.

49-70.

1961b. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

WRIGHT, F. W., and HODGE, P. W.

1962. Space density of dust in the stratosphere.

Nature, vol. 195, p. 269.

Z.VCHAROV, J.

1952. Influence des Perseides sur la transparence

atmospherique. Bull. Astron. Inst.

Czechoslovakia, vol. 3, pp. 82-85.
Dynamics of Orbiting Dust Particles'

I. I. SHAPIRO,2 D. A. LAUTMAN,3 and G. COLOMBO

 4

Abstract

We have studied the forces affecting the motion of small dust particles orbiting in interplanetary

space. Combinations that may contribute substantially to a concentration of such dust around the

earth were also analyzed. These included gravitational focusing, Jacobi capture, ejection of dust

from the moon via meteor impact, and the capture of dust into long-lifetime geocentric orbits through

the combined action of air drag and sunlight pressure. Our calculations indicate that, sensibly

defined, an increase in flux near the earth of only about a factor of 102 over the interplanetary value

is understandable. Even this relatively modest factor depends vitally on the assumption that a

substantial fraction of the dust at the boundary of the earth's sphere of influence has a speed on the

order of 1 km/sec with respect to the earth. The more reasonable choice of 3 km/sec for this speed

reduces the enhancement to a factor less than 10. This result is to be contrasted with the widely

accepted deduction, based on satellite experiments and zodiacal cloud observations, that the enhancement is about 104

. Aside from questioning the data analysis, we are unable to offer any solution to this apparent paradox.

1

 Published as The Earth's Dust Belt: Fact or Fiction? (Pts. 1-4), Journ. Geophys. Res., vol. 71, pp. M85-5741, 1966.

- Massachusetts Institute of Technology, Lincoln Labororatory, Lexington, Mass., operated with support from the U.S. Air Force.

3

 System Development Corporation, Lexington, Mass., and Smithsonian Astrophysical Observatory, Cambridge, Mass.

1

 University of Padua, Padua, Italy, and Smithsonian Astrophysical Observatory, Cambridge, Mass.

35U

Concentration of Magnetic Dust in the Stratosphere

T. GRJEBINE *

The quantity of dust in the troposphere and

stratosphere has previously been studied with

several techniques The former studies concentrated on the relationship of dust and

radioactive debris (fallout) at a time when few

observations of cosmic dust were available.

The main result of these studies (Junge,

Chagnon, and Manson, 1961; Chagnon and

Junge, 1961; Junge and Manson, 1961) has

been to show that at an altitude of 20 km there

is an increase in particles per unit volume of

air of at least 1 order of magnitude.

Hodge and Wright (1961) have also shown

that the concentration was variable. Many

samplings and studies have been made by

Friend et al. (1961), with results similar to

those previously quoted. The size range of

the particles was reported to be between 0.1

and 1, and the maximum concentration was

found at an altitude of about 20 km. The

particle concentration was estimated by counting techniques to be about 1 particle/cm3

 or

approximately 10~8 g/m3; however, the study

reported that the same amount of material

measured by chemical techniques yields a

concentration of 1.3X10"7 g/m3. It is difficult to know whether this difference of 1 order

of magnitude between the different techniques

depends on the fact that particles smaller

than 0.1 were not counted. The chemical

abundances reported indicate that calcium

was the main constituent (10~7 g/m3), followed

by phosphorus (10~8 g/m3) and iron (10~8

g/m3). In all cases, to the amount of the

chemicals detected, the amount of the other

elements should be added.

1

 Centre National de la Recherche Scientiflque, Centre des Faibles

Radioactivity, Qif-sur-Yvette (S.O.), France.

240-022 0 «7 24

Whatever the source of the dust, it is difficult

to believe that it is composed mainly of calcium.

If we consider calcium as being the most

easily detected element in a normal abundance

of elements on the earth (Mason, 1958) where

it contributes only 1.07 percent of the total

mass, then the total mass of dust should be

around 10~5 g/m3. We mention this point

because it is typical of the discrepancy that

can be introduced by comparing collections

analyzed by counting techniques and total

integrating collection techniques.

By an* optical counting technique Rosen

(1964) has studied, in situ, the quantity of

dust up to an altitude of 30 km. The amount

at the level of maximum concentration, 20 km,

is approximately 3 particles/cm3 or a mass of

about 10"5 g/m.3

We have measured three types of collections,

two made by Lambert (1963) with balloonborne collectors and one by Ch. Phillipot with

airplanes. These collections were planned for

radioactive measurements only; hence, their

use for measurements of total dust content

is subject to some uncertainty and the possibility of contamination. We have performed

blank experiments, however, and it appears that

the risk of contamination is slight, at least for

the balloon collections.

Lambert used two designs of collectors.

The first design was a two-stage turbine forcing

air through a paper filter. After measuring the

radioactivity of the sample, we calcinated

the filter and measured the magnetic attraction

of the residue on a curie magnetic torsion

balance. Therefore, we were following exactly

the procedure as with ground collections made

361
362 SYMPOSIUM ON METEOR ORBITS AND DUST

lt| m

• m •

g Alp.du.t/rT>5

FIGURE 1.—Concentration of magnetic dust in the stratosphere

versus the altitude of collection.

® collection made with surgical gauze; mean concentration/in3

 up to the maximum altitude of flight.

• collection made with balloon air-borne turbine.

• different ground collections, mean value for several

months in meteorological station; ground level on

mountain and sea level on meteorological ship.

with CRAPAL collectors previously reported

(Grjebine, 1963, 1964).

The purpose of the calcination is to reduce

the volume, but since it is not a high-temperature calcination there is not complete destruction of all the organic filter material and

therefore it is not possible to establish a direct

relationship between the force of magnetic

attraction and sample weight. To calibrate

the curie balance in terms of sample weight

per cubic meter, we used a collection made on

the top of Aiquille du Midi in the French

Alps at an altitude of 3800 m. Comparing

that sample with the Fe2O3 a phase, we found

that 1 mg Fe2O3 a=0.07 mg dust; the magnetism of the sample is therefore 20 percent

higher than the dust previously used to calibrate the CRAPAL collector network (Grjebine,

1963, 1964). If we assume that the magnetic

susceptibility of the dust collected at 20 km

is the same as the susceptibility of the Aiquille

du Midi sample, we find a dust concentration

at an altitude of 20 km of 2X10~4 g/m3. ]f

the stratospheric dust is more magnetic, there

would of course be a lower concentration in

weight.

The samplings made with the turbine collectors give, for the average values for radioactive debris, results that are very similar to

those made by other collectors up to an altitude

of 20 km. In particular, they agree quite

well with values reported by the Ash Can

project up to this altitude; however, at 30 km

altitude, Lambert's samples show about 10

times the activity of the Ash Can project

samples. The same difference of 1 order of

magnitude appears for magnetic measurements made at 20 and 30 km. It seems likely

that for altitudes greater than 20 km, Lambert's

results should be decreased by an order of

magnitude. It should also be pointed out

that for some of Lambert's filters, which are

highly magnetic, there is also a high degree of

radioactivity, possibly indicating that the

magnetic dust is a carrier for the radioactive

debris. All these measurements are plotted

against altitude in figure 1.

Only one measurement has been carried out

on a filter supplied by the United States

Atomic Energy Commission. This sample

showed such a high magnetism that the

measurement had to be made with the use of

only a small part of the filter. It is not plotted

on the curve (fig. 1) because the volume of air

filtered was not exactly known.

The second technique used by Lambert

involved an integrating collector. A surgical

gauze filter was mounted on a plastic ring and

was attached with a long string to a balloon.

As the balloon ascended and fell, the filter

swept a volume of air equal to twice its cross

section times altitude. The efficiency of this

collector for radioactive debris was about 5

percent; even with this low value a large

quantity of debris and also magnetic dust was

collected. The average value of measurements made with this technique falls between

ground-level measurements such as those made

at sea level (Fregate Meteorologique) and at

Mont Ventoux in the French Alps and the

values found at 20-km altitude from the

turbine-collecting technique.

The third series of measurements made with

aircraft-mounted filtering devices appears more

doubtful. The average value is not greatly

different from the ground-level values, but the

level of radioactivity appears to be about an
CONCENTRATION OF MAGNETIC DUST IN STRATOSPHERE—GRJEBINE 363

order of magnitude less than the concentration

measured at the same time and latitude by

other experimenters (Machta, List, and Telegadas, 1964; Lambert, 1963). Apparently the

filters did not capture all of the particles that

impacted; eddy currents generated on the

surface of the aircraft probably removed

particles as well as deposited them. An ideal

aircraft-collecting area should be from 103 to

104 times the area of the aperture admitting

the air in the collector, and this was not the

case for these collectors.

Conclusions

The values for stratospheric dust concentration

obtained by magnetic measurements are 10 to

100 times larger than values obtained by

chemical analysis methods, and a factor of 10

greater than the values from automatic optical

counting techniques (10~8 g/m3). These discrepancies are not exactly discrepancies, because

the collection method is an integrating technique that does not discriminate with respect

to particle size or shape, while other techniques

usually involve a limit on size and sometimes

on shape of the particles. Most of the limitations introduce a difference of about 1 order

of magnitude (Grjebine, 1965).

It is difficult to decide what part of the dust

collected is cosmic and what is terrestrial. It

does not seem that industrial contamination

can be an important contributor when one

considers the large total mass of dust involved.

In 1961, when the measurements were made,

there had not been any volcanic activity for

several years; hence this contribution is probably also negligible. The magnetic susceptibility of ground rock is quite low, so groundrock erosion could not introduce a great error

in the magnetic measurements. It also appears unlikely that any calibration errors have

been introduced.

If we accept a magnetic dust density at the

altitude of maximum concentration of 2X10"4

g/m3 and we estimate that the stratospheric

reservoir has a mean depth of 10 km, between

15- and 25-km altitude, and this reservoir is

uniform around the earth, we conclude that it

will contain some 109 tons of dust.

When comparing the magnetic dust measurements with the CRAPAL collector sample, we

obtain a figure of 2X109 tons/year for the total

accreted mass of dust. This means that the

stratospheric reservoir is renewed twice each

year and there is an average half-removal time

of three months. These data are certainly

compatible with the other sources of information we have concerning the removal time of

this reservoir. For large particles, the curves

published by Crozier (1962) show that peaks

of the number of particles in the 5- to 10-M

range decrease within a period of about 1 month.

For smaller particles, the removal time of

radioactive debris from the stratosphere has

been estimated at less than 2 years (Machta,

List, and Telegadas, 1964; Lambert, 1963).

Our measurements fall between these limits,

and therefore appear to be quite reasonable,

and represent mainly cosmic material.

References

CHAONON, C. W., and JUNOE, C. E.

1961. The vertical distribution of submicron

particles in the stratosphere. Journ.

Mctcorol., vol. 18, pp. 746-752.

CROIIEK, W. D.

1962. Five years of continuous collection of black,

magnetic spherules from the atmosphere.

Journ. Geophys. lies., vol. 67, pp.

2543-2548.

FRIEND, J. P.; FEELY, H. W.; KREY, P. W.; SPAR, J.;

and WALTON, A.

1961. The high altitude sampling program

(HASP). Defense Atomic Support

Agency, vol. 5, DASA 1300.

GRJEBINE, T.

1963. Accumulation dc poussieres cosmiques sur

la terrc. Compt. Rend., vol. 256, pp.

3735-3738.

1964. Study of the distribution of cosmic dust.

Ann. New York Acad. Sci., vol. 119, pp.

126-142..

1965. Les poussieres cosmiques. Sciences ct

Enseignement des Sciences, vol. 35, pp.

45-55.

HODGE, P. W., and WRIGHT, F. W.

1961. The space density of atmospheric dust in

the altitude range 50,000 to 90,000 feet,

Smithsonian Contr. Astrophys., vol. 5,

no. 14, pp. 231-238.

JUNGE, C. E.; CHAGNON, C. W.;and MANSON, J. E.

1961. Stratospheric aerosols. Journ. Metoorol.,

vol. 18, pp. 81-107.

JUNGE, C. E., sind MANSON, J. E.

1961. Stratospheric aerosol studies. Journ.

Geophys. lies., vol. 66, pp. 2163-2182.
3 6 4 SYMPOSIUM ON METEOR ORBITS AND DUST

LAMBERT, G. and Safety Laboratory), pp. 243-271,

1963. Etude du comportement des aerosols New York.

radioactifs artificiels. These a la Faculty ^ \SON B

des Sciences, Paris, Rapport CEA R. 19 5 8 p rinciple 8 o f Geochemistry. J. Wiley and

2347, U.S.A.E.C. Translation tr. 6548, ^ , Ne w Yor k 31( )

November.

MACHTA, L.; LIST, R. J.; and TKLEOADAS, K. KOSEN, J. M.

1964. Inventions of selected long lived radio-

 1964

-

 Th(>

 vertical distribution of dust to 30

isotopes produced during nuclear testing. kilometers. Journ. CJeophys. Hes., vol.

U.S.A.E.C. Report HASL 142 (Health 69, pp. 4673-4676.

Abstract

The amount of magnetic dust in the stratosphere has been investigated by means of balloon-l>orn<' gauze filter*

and filters flown in airplanes. The concentration of dust is increased at an altitude of 20 km. A transformation

of magnetic attraction into weight for a sample collected in the Alps at an altitude of 3800 m gives a concentration

of 2X 10r* g/msfor that level. This is compatible with ground measurements of fallout of magnetic dust and residence

time of dust in the stratosphere.
Role of Meteoric Dust in the Lower Ionosphere1

R. PARTHASARATHY

 2 and D. B. RAI 2

Abstract

The effect of the meteoric dust particles on

the steady-state distribution of electrons and

ions in the lower ionosphere (50 to 90 km) has

been investigated. It is shown that the effective recombination coefficient obtained is

higher than that obtained by ignoring the

presence of dust. The expression for the effective recombination coefficient thus obtained is

of the form

Dt+\DNe '

where Df, D+, and D~ are the dust-capture

coefficients for electrons, positive ions, and negative ions, respectively; rj and y are the ratios

Ef/D^ and D~/D+, and the other symbols have

the usual meanings. In the limit of zero dust

concentration this expression reduces to the

one derived by ignoring dust, i.e.,

«etf=(l+X)(a*+Xa<),

since (1J+X7) tends to (1+X), while the coefficients De, D+, and D~ each tend to zero.

The coefficients De, D*, and D~ are derived

by an extension of Natanson's theory of charg1

 Published in Radio Sci., vol. 1, pp. 1397-1408,1966.

1

 Geophysical Institute of the University of Alaska, College, Alas.

ing of aerosols by capture of ions. The height

dependence of these coefficients comes mainly

through the height distribution of the dust

particles, for which Divan's results from twilight studies are utilized. It is found that only

particles with a radius of the order of Ko M or

larger contribute significantly. The recombination coefficients for the region 50 to 90 km

have thus been computed and are in excellent

agreement with those deduced empirically by

us from the multiple-frequency (5 to 50 Mc/sec)

radiowave absorption data in the auroral zone.

The empirical method consisted of comparing

the electron-density profile derived from the

multiple-frequency radiowave absorption with

the ionization-rate profile calculated from

satellite-measured particle flux. The deduced

recombination coefficients may occasionally be

an order of magnitude larger than the coefficients obtained without taking cognizance of

the dust population.

Considering the fact that dust particles of

meteoric origin are always present in the lower

ionosphere, it appears to be reasonably confirmed that their contribution to the steadystate distribution of electrons and ions in this

region of the atmosphere is quite significant

365

Infrared Optical Characteristics of Ice Spheres

W. M. IRVINE

 l

Introduction

The scattering and absorption properties of ice

particles are important for the study of radiative

transfer in the atmospheres of the earth and,

possibly, of Venus and Mars, as well as for

studies of interplanetary and interstellar dust

particles. Published calculations of these parameters for infrared wavelengths are extremely

limited (see the review by Feigel'son, 1964); a

number of computations have been made by

Greenberg (1966), but the cross sections themselves have not been published.

The quantities that are most appropriate for

describing the scattering by ice particles will

depend on the given physical situation. In the

present paper, values of the normalized extinction cross section (efficiency factor) Qtxu the

single-scattering albedo a, and the asymmetry

factor (cos 0) are presented for spherical, homogeneous particles of radii 1.0, 4.0, 7.5, 10.0,

12.5, and 15.0 M for the wavelength interval

1M^X^150M - These quantities are of particular interest in the approximate solution

of problems of diffuse reflection and transmission by ice clouds, and in the study of the

radiative heating of an atmosphere containing

such clouds. For other studies (of the zodiacal

light, for example) the angular distribution of

scattered radiation would be a more relevant

quantity.

Before the present results can be applied to

a physical problem, it is necessary to evaluate

the effect of the simple particle model considered. The assumption of homogeneity is

1

 Harvard College Observatory and Smithsonian Astrophysical Observatory, Cambridge, Mass.; now at University of Massachusetts,

Amherst, Mass.

probably quite good for cloud crystals, but is

possibly seriously wrong for interplanetary

particles. An extension of the calculations to

radially inhomogeneous spheres would present

no computational problems, however, if a

reasonable model for the variation of refractive

index with radius were available (Levine and

Kerker, 1963; Levine and Olaofe, 1965). More

serious is the restriction to spherical shape;

however, results of Greenberg et al. (1963) for

scattering by spheroids and cylinders indicate

that the relative magnitude of integrated

quantities, such as Qtxt and a, will not be greatly

influenced by departures from sphericity (cf.

also Donn and Powell, 1963).

Method and results

We made calculations using the Mie theory in

the manner described elsewhere (Irvine, 1965).

The results are presented in figures 1 to 3.

Values of the real part n of the index of

refraction of ice were taken from Kislovskii

(1959). which seems to be the best present

compilation.

Values of the imaginary part n', which is

related to the absorption coefficient k by n' =

k\/4ir, were obtained by intercomparison of

several sources for:

1.0<X<2.65M: Reding (1951) (see also

Hornig, White, and Reding,

1958), Ockman (1958), and

Luck (1963).

2.8<X<7.5 n: Fox and Martin (1940).

7.5<X<25M : relative values from Ockman (1958), scaled to agree

with Fox and Martin (1940)

at overlap.

367
368 SYMPOSIUM ON METEOR ORBITS AND DUST

1.0

.9

.8

.7

.6

a

.5

.4

.3

.2

1 1 1 1 " 1 1 ' II I

:

;

-

-

_

-1.0

\h -—=4.0

IV

! I'

1 f\

l\

\

i \

•

1 s l l

•

; ; ^' \ 1

J \

I 1

\

\

-

-

a \i \ V ^

1 1 1 1 1 V* 1 >-- ! 1 I 1 1 1 I T

2 3 4 5 7 10 20 30 50 70 100 200 I

X

.0

9

8

.7

.6

a

.5

4

3

.2

.1

1

-

-

-

-

_

-

_

_

b

i

i

IV

i

7.5

10.0

I

| i | i l | | | i | i | i i |

-

i A

1 1 <i

i

:

 \

\ V N

v \

1111 1 i i . 11111 1

2 3 4 5 7 10 20 30 50 70 100 200

.2 - - = 12.5

*— = 15.0

I I I I I I I I I I I ! I I I I I I

2 3 4 5 7 10 x 20 30 50 70 100 200

FIGURE 1.—a, b, c: Single-scattering albedo a of spherical ice

particles as a function of wavelength X (in microns) for

particle radii r=l.O, 4.0, 7.5, 10, 12.5, 15 M.
4 0

INFRARED OPTICAL CHARACTERISTICS OF ICE SPHERES—IRVINE

| I I < I " I I I I I ' l'l |

369

1.0

—•— =40

a

4 0

1.0

I I I ' I " I I ' I " I

2 3 4

b

4.0 -

FIGURE 2.—a, b, c: Normalized extinction cross section

(efficiency factor) Qext for spherical ice particles. Wavelength X and particle radii r=1.0, 4.0, 7.5, 10, 12.5, 15 are

in microns.
370 SYMPOSIUM ON METEOR ORBITS AND DUST

I ' I'M

u

9

8

7

6

.5

4

3

2

I

0

1 11 IM"I

v'V

-

-

-

- • - 7.5

— • 10.0

-

-

L

0

1 I I I I I i.1

1 1 ' I

\

\ \

1 II I

I ' M

-

_

i 1 i .1 *•

2 3 4 5 67 10 20 30 50 70 100 200

A

s

V

. u

9

.8

.7

.6

.5

.4

.3

.2

.1

0

1

-

—

_

-

-

-

c

1

i 1 1

_ • —

—«—

i i I

1 I' M

- 1

i

12.5

15

Mill

1 1 1 ' 1 I' M

-

\ \A - \\• \ i \

\

\

\ -

\ \

\ \

i i i 1111. i

2 3 4 56 7 10 20 30 50 70 100 200

FIGURE 3.—a, b, c: Asymmetry factor (cos 8) of spherical ice

particles. Wavelength and particle radii as in figures 1

and 2.
INFRARED OPTICAL CHARACTERISTICS OF ICE SPHERES—IRVINE 371

25 < X < 50 M : relative values from Zimmerman n and Pimentel

(1962), scaled to agree with

Cartwright (1935) and with

shorter wavelength data at

overlaps.

50<A< 150 n: Cartwright (1935).

Concentrating first on the single-scattering

albedo a, we note that there are large differences

in the relative strength of absorption features

for the different particle radii (see figs, la, b, c).

This indicates the possibility of using absorption

spectra to determine approximate particle size

in reflection from ice clouds (particularly if the

clouds are thick, so that the only parameters in

the approximate radiative transfer theory are

a and (cos 6)).

Irvine and Pollack (in preparation) have

made a comparison of the absorption spectrum

(a versus X) for water and ice. Although the

curves are generally similar, the magnitudes of

absorption features may be quite different, and

the positions are shifted slightly. Such details

may provide the possibility of differentiating

between water and ice clouds in planetary

atmospheres.

The spectra of ^, x t and (cos d) are more

complicated (see figs. 2a, b, c; 3a, b, c) because

the maxima and minima due to changes in

absorption are combined with the familiar Mie

theory oscillations, which arise from interference effects (see van de Hulst (1957) for

Qnl, Irvine (1963, 1965) for (cos 8)). The

positions of the extrema are thus sensitive to

the distribution of particle sizes present in a

given physical situation.

Acknowledgments

I am grateful to Dr. J. B. Pollack for his evaluation of the references on the absorption coefficient of ice, to Dr. J. M. Greenberg for

several helpful conversations, and to Mrs.

M. Huguenin and Mrs. M. Bocchino for assisting in the computations. This work was

supported in part by NASA Grant 89-60.

References

CARTWRIGHT, C. H.

1935. Extreme infrared absorption of D}O, ice

and DjO in dioxano. Nature, vol. 136,

p. 181.

DONN, B., and POWELL, R. S.

1963. Angular scattering from irregularly shaped

particles with application to astronomy.

In ICES Electromagnetic Scattering,

ed. by M. Kerker, Macmillan Co., New

York, pp. 151-158.

FEIGEL'SON, E. M.

1964. Radiatsionnye Protessy v Sloistoobranznykh Oblakakh. lid. "Nauka,"

Moscow.

Fox, J. J., and MARTIN, A. E.

1940. Investigations of infrared spectra (2.5-

7.5 M) : Absorption of water. Proc. Roy.

Soc. London, vol. 174A, pp. 234-262.

GREENBERG, J. M.

1966. The optics of interstellar grains. In

Spectral Classification and Multicolor

Photometry, ed. by K. Lod&i, L. O.

Loden, and U. Sinnerstad, Academic

Press, New York, pp. 291-300.

GREENBERG, J. M.; LIND, A. C ; WANG, R. T.; and

LIBELO, L. F.

1963. The polarization of starlight by oriented

nonspherical particles. In ICES Electromagnetic Scattering, ed. by M.

Kerker, Macmillan Co., New York,

pp. 123-133.

HORNIG, D. F.; WHITE, H. F.; and REDING, F. P.

1958. The infrared spectra of crystalline H,O,

D,0 and HDO. Spectrochem. Acta,

vol. 12, pp. 338-349.

IRVINE, W. M.

1963. The asymmetry of the scattering diagram

of a spherical particle. Bull. Astron.

Inst. Netherlands, vol. 17, pp. 176-184.

1965. Light scattering by spherical particles:

Radiation pressure, asymmetry factor,

and extinction cross section. Journ.

Opt. Soc. Amer., vol. 55, pp. 16-21.

KISLOVSKII, L. D.

1959. Optical characteristics of water and ice in

the infrared and radiowave regions of

the spectrum. Opt. Spec., vol. 7, pp.

201-206.

LEVINE, S., and KERKER, M.

1963. Scattering of electromagnetic spheres, when

outer shell has a variable refractive index.

In ICES Electromagnetic Scattering, ed.

by M. Kerker, Macmillan Co., New

York, pp. 37-46.

LEVINE, S., and OLAOFE, G.

1967. ICES-2. Proc. 2d Interdisciplinary Conf.

on Electromagnetic Scattering, ed. by

II. S. Stein and R. L. Rowell, Gordon

and Breach, New York, in press.

LUCK, W.

1963. Beitrag zur assoziation des fliissigen

Wassers, I. Ber. Bunsenges. physik.

Chem., vol. 67, pp. 186-189.
3 7 2 SYMPOSIUM ON METEOR ORBITS AND DUST

OcKMAN, N . VAN DE HlJLST, H. C.

1958. The infra-red and Raman spectra of ice. 1957. Light Scattering by Small Particles.

Adv. Phys., vol. 7, pp. 199-220.

 J Wile

y

 an d Sons> Ne w York

-

 47° PP-

„ ZlMMERMANN, It., and PlMENTEL, G. C.

EDING, *. V. 196 2 Th o infrare d Spectrum of ice temperature

1951. The vibrational spectrum and structure of dependence of the hydrogen bond poseveral molecular crystals at low temper- tentift l function . Proc . int>i. Meeting

ature. Ph. D. Thesis, Brown Univ. Molec. Spectros., Bologna, 1959, vol. 2,

Providence, R.I. pp. 726-737.
Evidence for Extraterrestrial Particles in Polar Ice

E. L. FIREMAN

 !

The earliest method of searching for extraterrestrial particles was to examine dust collected

at remote places on the earth. Our work on

dust in polar ice is a natural extension of this

method. The high-elevation regions of the

polar ice sheets are the most remote places on

the earth where contamination by terrestrial

and industrial dust is minimal. The annual

accumulation layers in the ice sheets provide

excellent time markers for determining the

deposition rate. Sufficiently large samples of

material can be collected from the polar ice

for examination by modern isotopic methods.

These methods have been used for the past

decade in meteorite studies and have not only

revealed many facts about the history of

meteorites but have also determined whether

certain questionable objects were extraterrestrial. For example, an iron object now

called the Washington County meteorite was

examined about seven years ago by the meteorite curators at two large museums; they concluded that this object was terrestrial. A

short time later the measurement of isotopes

in this object proved that it was extraterrestrial; it was then accepted as a true meteorite.

Meteorite curators now seek isotope information before deciding on the possible extraterrestrial origin of questionable objects. Our

work modernizes both the earlier collection

methods and the earlier methods of examination.

Collection of dust

The collection and study of a large mass of

dust from the Greenland ice sheet were undertaken jointly with Mr. C. C. Langway, Jr.

1

 Smithsonian Astrophysical Observatory, Cambridge, Mass.

Several years ago we concluded that it should

be possible to collect grams of extraterrestrial

material from the polar ice sheets. To be more

specific, an accretion rate, of 500,000 tons per

year for the earth gives 1 g of extraterrestrial

material in 200,000 liters of ice at Camp

Century, Greenland. Many million liters of

ice were melted at Camp Century. This

camp, maintained by the U.S. Army Research

Support Group, is situated under the ice

77° 10' north latitude, 61°08' west longitude,

and at an elevation of approximately 2000 m.

The mean annual precipitation is 30 cm, and

the mean annual temperature is —25° C.

The air temperature rarely rises above 0° C

during the summer.

Surface snow at Camp Century is permeable;

however, at a depth of 30 m the snow is compressed into a form that is impermeable to

water. Ice melted below this depth will form

a subsurface lake or well. The volume of

water in the well is determined by the amount

of heat injected; the shape of the well is determined by the manner in which the heat is

injected into the water. Since the heat conductivity into the surrounding snow and ice is

low, a subsurface lake more than a million

liters in volume will not freeze solid for decades.

Plate 1 is a photograph of the tunnel under

the snow leading to a well where large volumes

of ice either had been or were being melted.

The floor of the tunnel is approximately 20 m

below the surface of the snow. At the top of

the well on the floor of the trench is an A frame

that supports cables to the submersible pump,

the water hose to deliver water from the bottom

of the well, and the heating unit to melt ice.

A schematic cross-sectional diagram of the

373
374 SYMPOSIUM ON METEOR ORBIT8 AND DUST

shape of the well below the tunnel is given in

figure 1. This well, which supplied the camp's

entire water consumption between 20,000 and

40,000 liters per day, was made by steam

melting a vertical shaft of 3 m in diameter to

the impermeable snow layers at a depth of 30

to 40 m (Rodriguez, 1963). The steammelting unit was held at this depth to form a

concave-bottomed subsurface lake 20 to 30 m in

diameter. The depth of the water in the lake

varies according to the rate of water withdrawn.

A submersible pump, attached to the melting

unit, pumps water to 5000-gallon aluminum

storage tanks, which are in essence settling

tanks for the particles contained in the melted

ice. Our first collections were made by cleaning the particles off the bottom of the storage

tanks. During the summer of 1963, when the

well was 85 m deep and of the configuration

shown in figure 1, we installed a filter system

at the top of this well consisting of replaceable

3-/x and 0.45-M corrugated paper cartridges

mounted in a cylindrical steel housing. Several

frame

supporting

winch and pipe

string

FIGURE 1.—Cross-sectional sketch of water well no. 3, Camp

Century, Greenland, on July 18, 1963. Taped depth to

bottom of well, 85 m.

million liters of water were filtered through

these cartridges.

A new filter system was installed at the same

site in the summer of 1964. In this system

the water passes through Millipore filter papers,

which have a very low ash content and permit

an accurate determination of the weight of the

collected material. Approximately 2.6 X10"4

g of material per liter of water was collected;

most of the material was organic. After the

organic material was removed by ashing, the

weight was 5X10"8 g/liter for the 8-M paper,

6X10"* g/liter for the 3-M paper, and 7X10"5

g/liter for the 0.45-M paper. The collected

material contained black magnetite spherules

similar to those that have been extensively

studied by C. C. Langway, Jr., P. W. Hodge,

F. W. Wright, and others. The black spherule

content of our collections comprised about

one-tenth of the total insoluble nonorganic

material. Langway (1963) has estimated an

accretion rate of a half-million tons per year

for the earth on the basis of the black spherule

content of Greenland ice. The nonorganic

material collected from the melted ice consisted

largely of magnetite, hematite, quartz, and

feldspar. The nickel content was quite low

compared to that in meteorites. A chemical

analysis gave a Ni/Fe ratio of 0.012 in a light

fraction (density less than 3.3) and 0.005 in a

heavy fraction (density greater than 3.3). The

magnesium content was also low compared to

that in stony meteorites and in most terrestrial

materials. The Mg/Fe ratio was approximately 0.016 in the heavy fraction, and 0.13

in the light fraction.

No large mass collection of the dissolved

solids was attempted. Since some extraterrestrial material is probably dissolved, we plan

to make a large collection of the soluble components and examine them for indications of

extraterrestrial origin.

Isotope analysis

Isotope analysis can prove whether there is

extraterrestrial material in the dust. The size

of the Greenland collections made possible

meaningful isotope studies. Two positive isotope indications for the presence of extraterrestrial material in the Greenland collections

were found: (1) a Co90 radioactivity, which
EXTRATERRESTRIAL PARTICLES IN POLAR ICE—FIREMAN 375

appears to be due to Fe60, and (2) an argon

anomaly identical to that found by Merrihue

(1964) in a magnetic fraction of a deep-sea

sediment. The other isotopes searched for

were Al28, He3, Ne21, and Ar39. None was

found except for a small positive He3 excess

in one sample. The presence of certain isotopes

and the lack of others can be explained either

by the dissolution of the magnesium-containing

constituents in the dust or by an unusual

chemical composition.

The bombardment of small particles in

space by cosmic rays, solar flares, and solar

wind can modify the abundance of certain

isotopes. Cosmic rays, which consist of highenergy hydrogen and helium nuclei (>1 Bev),

produce by nuclear interactions a small amount

of a large variety of isotopes that are lighter

in mass than the bombarded element. Solar

flares, which consist mainly of low-energy

hydrogen and helium nuclei « 1 Bev), produce a larger amount of the isotopes that are

approximately the same mass as the bombarded element. Most of the solar-flare particles (also solar-wind particles) are of such low

energy that they can be implanted in the dust.

The production of the radioactive isotope

Fe80 will be used as an example to illustrate

isotope production by nuclear interactions.

Helium nuclei (also tritons) interacting with

iron and protons (also helium nuclei) interacting with nickel produce Fe80

 in the following

eight ways:

Reaction

He4 + Fe»-*nFe»+2H t

H»+Fe«->FeM+H «

He4+Ni«a-»Fea04-4H «

He4+Ni«'-»Fel)°+4H + N «

He4+Ni"-» Fe" -f 2H + He4 c

H + Ni«-»Fe«°+3H i

He4+Ni"-» Fe«°+2 He4 «

H + Ni«-»FeM+H + He4 c

mb

r~50

r~200

r~10

r~10

r~30

r~30

r~100

r~100

%

0.33

0.33

26.2

1.2

3. 7

3. 7

1. 1

1. 1

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

The value for the cross section written after

each equation is an estimated maximum value,

and the percentage is the isotopic abundance

of the bombarded element. Fe80 will be produced mainly by solar flares rather than by

cosmic rays since its mass is approximately

the same as that of the bombarded elements,

iron and nickel. A solar-flare flux of 103

helium nuclei cm"2 sec"1 would produce 0.1

dpm/g of Fe80 by reaction (1). The other

reactions would more than double the production rate estimated from reaction (1) alone.

The solar-flare flux averaged over long periods

is not well known. One estimate (Wasson,

1963) gives 2000 protons cm"2 sec"1 (>5

Mev). The average helium abundance in

flares is also not well known. The abundance

of helium in flares varies; in some flares the

helium content exceeds the hydrogen content,

while in most flares the reverse is true. In

view of the evidence a solar-flare flux of 103

helium nuclei cm"2 sec"1 is not unreasonable.

Fe80 has been observed in the Odessa meteorite. It decays to the 5.2-year state of Co80

,

which emits a 1.17-Mev and a 1.33-Mev

gamma ray in coincidence. Roy and Kohman

(1957) originally estimated the half-life of

Fe80 to be 3X105 years but now (private

communication) would revise this estimate to

105 years. On the basis of studies with a copper

target, Roy and Kohman found that Fe80

decays to the 5.2-year Co80 radioactivity by

way of a 10-min isomeric state. R. McCorkell

(private communication), on the basis of similar

studies on a copper target, found a 30-min

cobalt isomer from Fe80. The decay scheme for

Fe80 based on these results is given in figure 2.

The 1.17- and 1.33-Mev coincidence gamma

rays of Co80 were found and measured in

various Greenland dust samples by the gammagamma coincidence method. The gammagamma coincidence unit used for measuring

Co60 is described by me (Fireman, 1966).

Figure 3 gives the gamma coincidence spectrum of the analyzer crystal when the trigger

crystal is set at 1.25±0.12 Mev for 25 g of

Greenland dust «14 0 mesh). In addition

to the peaks at 1.17 and 1.33 Mev due to Co80,

there is a peak at 0.58 Mev due to Tl208, probably a terrestrial contaminant. The relative

heights of the Tl208 and Co80 peaks vary in

different samples so that it should be possible

to separate the Tl208-containing minerals from

the Co60-containing minerals.

Since Co60 is a common industrial contaminant, it is necessary to show that the Co80

actually comes from the Fe80, which can be only

of extraterrestrial origin. This was done in

two different ways:

1. All the cobalt was removed from the
376

SYMPOSIUM ON METEOR ORBITS AND DUST

6 0 (lOyr)

0

Co

102 kv (30min)

86 kv

59 kv (IO.5min )

2.50 Mev

5.2 yr

Ni

.60

1.33 Mev

FIGURE 2.—Decay scheme for FeM (-^lO5 yr) activity.

10 20 30 40 80 60 70 80 Chonml

6O0 -

500

a

z

1 400

5

2 300

1 1 1

0.96 Un^I

fl1

1

1 1 1 1

1 1 1

7 1N.J

l\ ]/

\

'i i L i

i i

6-INCH CRYSTALS

COINCIDENCE WINDOW

113 to 137 Mev

SAMPLE COUNT 8359 min.

BACKGROUND " 80a0min~

• ' T •"••!"'

1 1

0 2 0.4 0.6 0 8 1.0 1.2 1.4 1.6 1.8 2.0 Mev Energy

FIGURE 3.—Gamma coincidence count for 25 g of Greenland

dust «14 0 mesh).

iron to see whether any new cobalt activity

grew in the purified iron. In this procedure

it was easier to work with the short-lived

rather than with the 5.2-year cobalt isotope,

since the short-lived isomer reaches saturation

quickly and the measurement can be repeated

many times. McCorkell removed the cobalt

from a Greenland dust sample, which contained

15 dpm of Co60, and purified the iron. He then

milked cobalt from the purified iron and

counted the cobalt in a thin window. Figure

4 gives his results for four separate extractions.

He observed an activity with a half-life between

25 and 40 min. In other words, McCorkell

found a similar cobalt activity in cobalt milked

from iron purified from Greenland dust to the

one he found in iron purified from an old

copper target. This indicates that the Co60

is due to Fefl0.

2. The Co80 activity in the Greenland

dust was measured as a function of time.

During 1 year of observation no decay was

observed. Table 1 gives the Co60 in two

samples of Greenland dust. A sample was

collected on a 3-M filter and showed no decay

in 15 months. The other sample, which was

collected from the settling tank, also showed

no decay in a year. During the course of the

year, however, some material was removed

from this sample for mass-spectrometric measurements, and the measured activity had to

be corrected accordingly. Since the 5.2-year

cobalt should have decayed by approximately

20 percent during this period, the lack of decay

is evidence for the Fe60 origin of the Co60

activity. We believe that it is important also

to measure the buildup of the 5.2-year Co90 in

the iron purified from both samples, and we are

currently proceeding along these lines. There

is approximately 0.1 dpm/g of Co60 in all our

Greenland dust samples. There is a factor of

FIGURE 4.—Short-lived activity of cobalt extracted from iron

purified from Greenland dust.
EXTRATERRESTRIAL PARTICLES IN POLAR ICE—FIREMAN 37 7

TABLE 1.—Cow activity in Greenland dust samples measured by 7^7 coincidence counting (at various times)

Sample

3-M filter-P9

3-M filtcr-P9

Settling tank

Settling tank

Settling tank

Settling tank

Settling tank

Weight (g)

—

(34)

(34)

*(31)

t(25)

t(25)

Date counted

May 1964

Aug. 1965

May 1964

Aug. 1964

Sept. 1964

May 1965

June 1965

Water volume

(liters)

185, 000

185, 000

~10«

~10«

0.91X10*

0. 73X1O«

0.73X10*

Sample

preparation

none

none

< 140 mesh

< 140 mesh

< 140 mesh

< 140 mesh

< 140 mesh

Counts/min

1.17+1.33 Mev

0.080 ±0.005

0.087 ±0.005

0.73 ±0.01

0.74 ±0.01

0.64 ±0.01

0.52 ±0.01

0.51 ±0.01

dprn/lO* liters

4.3±0.2

4.7±0. 2

~7.3

7.4

7.0

7.1

7.0

'Removed 3 K Aug. 38, 1964.

tRemoved 6 % Sept. 18, 1064.

2 higher activity in the magnetics and in the

fines than in the bulk material. The Co80

activity is in the range of activity expected

from solar-flare interactions (0.2 dpm/g). The

agreement with our calculated estimate of the

production rates would be fortuitous if a large

percentage of the Co80 in our samples were due

to industrial contaminants.

Another radioactive isotope that can be

measured by gamma-gamma counting is Al28.

The half-life and decay scheme of Al26 are well

known. Its half-life is 840,000 years, and it

decays by positron emission followed by a

1.82-Mev gamma ray. No Al28 activity was

observed in any of the collections. The Al28

results previously reported (Fireman and Langway, 1965) are summarized in table 2. In

some of the samples the Al28 activity is less than

one-tenth of the Co80 activity. Solar-flare protons interacting with magnesium in dust would

produce Al28 by the following reaction:

a~250 mb, 11%. (9)

Solar-flare protons interacting with aluminum

and silicon would also produce Al28.

These reactions should produce more Al28

than the Co80 produced by reactions (1) through

(8) unless the exposure age of the extraterrestrial particles containing Mg, Al, and Si is less

than 50,000 years, or unless these particles are

dissolved in the water. The amount of magnesium dissolved in the water was 10 times larger

than the undissolved magnesium in the dust

collection. This result leads us to believe that

Al28 \v»is not observed because most of the

extraterrestrial magnesium components were

dissolved in the water. Large mass collections

of the soluble constituents are planned for the

near future.

Argon-39, a radioactive isotope that would be

produced mainly by high-energy cosmic rays,

was not observed in the collections. The

absence of Ar39 is not surprising because it can

be lost in three ways: (1) by recoil immediately

after formation, (2) by diffusion out of the small

dust particles in space, and (3) by diffusion from

the particles while they are heated during their

passage through the atmosphere.

The stable rare-gas isotopes in dust are interesting. The He3

, Ne21, and Ar38 isotopes are

enriched if they are produced by cosmic-ray

and solar-flare interactions. He3 and Ar3* can

also be enriched by solar-flare and solar-wind

implantation; however, diffusion loss would

reduce the rare-gas content. Table 3 gives the

He3 and Ne21 contents of Greenland dust

samples. The measurement on the 0.43-g sample of magnetics was made in collaboration with

Dr. O. A. Schaeffer at Brookhaven National

Laboratory. There was a slight He3 excess of

(2.0±0.5)X10~9 cc/g. This small excess could

be implanted by one large solar flare. A similar

excess of He3 was observed by Merrihue (1964)

in the magnetics from a sample of deep-sea

sediment. No He3 excess was observed in two

other samples, 0.64 g and 0.50 g of fines from

the settling tank (Tilles, 1965).

No Ne21 excess was observed. Ne21 would be

produced only by high-energy cosmic-ray interactions and not by the other mechanisms.

Furthermore, Ne21 could recoil out of the small240-O22 O (57 25
3 7 8 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 2.—APt-potitron activity, At** activity, and Co*9 activity in tamplet of Greenland dutt

Sample

Settling tank

Settling tank

Settling tank

P, filter

P, filter

Pi filter

M, filter

M, filter

Mi filter

Type

magnetic

fine!140 mesh l

bulk

3 M (75%)

3 * (75%)

3 M (75%)

3 M (100%)

8 M (100%)

8 M (100%)

Weight

ST

34

34

330

—

—

—

3.6

7.6

6.1

Water volume

(liters)

~1,000,000

~1,000 000

~ 10,000,000

240,000

190,000

185,000

15,000

30,000

24,000

A1H positron

(10-* dmp/t)

<0.3

<1.0

<1.0

<0.4

<0.3

<3.0

<4.0

<2.0

<2.0

Ar*»

(10"« dpm/ 0

<0.01

—

—

—

—

—

—

—

COM

(10-« dmp/£)

6.9

7.4

4.5

—

—

4. 5±0.2

—

—

—

TABLE 3.—He* and Ne*1 contents of Greenland templet

Sample (wgt)

Magnetics from 130X 10«

cm1 of ice (0.43 g)

Fines «14 0 mesh) from

settling tank (0.64 g)

Fines «14 0 mesh) from

settling tank fraction

with density >3.2

(0.50 g)

Approximate

temperature

Sample vaporized

500° C

950° C

1050° C

1150° C

1250° C

500° C

800° C

1000° C

1200° C

1350° C

He* (cc 8TP/g)

(2. 0±0.5)X10-»

<5XlO-»

<6XlO-»

<8X1O-"

<3X10- u

—

<7X1O-"

<4XlO-»

<2X10-"

<3X10-"

<2XlO-»

Ne"* Ne»»/Ne»

(cc STP/g)

(3±2)X10-» 10. l±1. 0

(10.1).lr

<3XlO-» —

<io-» —

<3Xl0~»

<2XlO-»

—

<2X1O-"

<io-"t

<io-»»t

<4XlO-»

<5XlO-»t

Ne»/Ne»«*

30. 5± 1. 0

(34). „

—

'Indicates that value is for excess cosmogenfc Ne" relative to sir neon,

tlndicates total Ne" value.

sized particles and could also be lost by

diffusion.

There was, however, a definite positive indication for extraterrestrial origin in the argon

released at high temperature from a heavy fraction (density >3.2) of the Greenland dust.

Tilles (1965) found in this sample an Ar36

excess similar to that found by Merrihue (1964)

in the magnetics from a sample of deep-sea

sediment. The Ai*°/AxM ratio was 230 ± 5 in

the gas released at 1200°C after 1-hour heatings

at 500°C, 800°C, and 1000°C. The atmospheric

ratio is 295. The Ar^/Ar38 ratio was

5.1 ± 0.1, identical to this ratio in air. The AT36

excess is approximately 9X10"10 cc/g. If solar

flares have an argon-to-helium ratio of approximately 10~4

, then dust would be subjected to a

solar-flare flux of argon of approximately 0.1

cm"2 sec"1. A 10-M particle would then receive

approximately 20X10"10 cc/g during a solar

cycle. Since the solar argon is expected to be

low in AT40, the observed Ar* could be produced

by solar-flare implantation during one solar

cycle. In fact, the Ar86 excess in this respect is

similar to the He3 excess.
EXTRATERRESTRIAL PARTICLES IN POLAR ICE—FIREMAN' 379

References

FIREMAN, E. L.

1966. Neutron exposure ages of meteorites. Zeita.

f. Naturforsch, vol. 21a, pp. 1138-1146.

FIREMAN, E. L., and LANGWAY, C. C, Jr.

1965. Search for aluminum-26 in dust from the

Greenland ice sheet. Geochim. et Cosmochim. Acta, vol. 29, pp. 21-27.

LANGWAY, C. C , Jr.

1963. Sampling for extraterrestrial dust on the

Greenland ice sheet. A.I.H.S. General

Assembly, Berkeley, publ. no. 61, pp.

181-198.

MERRIHUE, C.

1964. Rare gas evidence for cosmic dust in modern

Pacific red clay. Ann. New York A cad.

Sci., vol. 119, pp. 351-367.

RODRIGUEZ, It.

1963. Development of glacier sub-surface water

supply and sewage systems. Tech. Rep.

1737-TB, USA Engineering Research

and Development Labs., Ft. Belvoir, Va.

ROY, J. C , and KOHMAN, T. P.

1957. Iron 60. Canadian Joum. Phys., vol. 35,

pp. 649-655.

TILLES, D.

1965. Anomalous argon isotope ratios in particles

from Greenland ice and Pacific Ocean

sediments. Trans. Amer. Geophys.

Union, vol. 46, p. 117.

WASSON, J. T.

1963. Radioactivity in interplanetary dust.

Icarus, vol. 2, pp. 54-87.

Abstract

Sufficiently large samples of Greenland dust were collected so that isotope analysis could be made. There were

definite positive indications of Fe*° and excess Ar** and a less definite positive indication of excess He1. The Fe** can

be explained by solar-flare interactions on iron and nickel; the Ar** and He* excesses can be explained by solar-flare

implantation. There was no positive indication of A1M, indicating that the magnesium-aluminum-silicon extraterrestrial constituents were dissolved.
380 SYMPOSIUM ON METEOR ORBITS AND DUST

PLATE 1

Photograph of tunnel leading to water well used for camp water supply.
On Chemical Compositions of Interiors of Possibly Cosmic

Particles and the Problem of Origin of Naturally Occurring

Iron-Rich Spherules

P. W. HODGE »•

 2 and F. W. WRIGHT 2

Introduction

There have been extensive attempts in recent

years to identify the dust component of the

influx of extraterrestrial material to the earth's

surface. (For bibliographic reviews see

Schmidt, 1965; Hodge, Wright, and Hoffleit,

1961.) Much of the effort has been expended

on the study of certain iron-rich smooth-surfaced spherical particles found in a wide range of

natural environments. It is not expected that

all or even a very large fraction of the extraterrestrial dust accumulated by the earth should

be in the form of such spherules. Their importance is due rather to their ease of location and

identification, to their potential usefulness in

glaciology and rock stratigraphy, and to the

current controversy on their origin.

Occurrence

Iron-rich smooth-surfaced spherules, ranging

in diameter from a few to 100 or more microns,

occur almost everywhere on the surface of the

earth. It was shown some time ago (Buddhue,

1950; Thomsen, 1953; Handy and Davidson,

1953; Hoppe and Zimmermann, 1954; Hodge

and Wildt, 1958) that the vast majority of

those found in or near centers of population

have an artificial origin. In isolated areas and

in geological strata, however, spherules are

found for which an artificial origin is extremely

unlikely. Table 1 summarizes the various

natural environments in which these spherules

occur.

1

 Regularly at University of Washington, Seattle, Wash.

2

 Smithsonian Astrophysical Observatory, Cambridge, Mass.

Distinguishing characteristics of particles of

known origin

SPHERULES FOUND AT METEORITE CRATERS.—

We have examined spherules found in the soil

at five meteorite crater locations: the Arizona

crater (particles collected by J. S. Rinehart),

the Sikhote-Alin craters (particles kindly supplied to the Smithsonian by E. L. Krinov),

the Henbury craters, the Boxhole crater, and

the Odessa craters. Surfaces of the SikhoteAlin and Henbury crater spherules were smooth

and shiny, but surfaces of those from the other

craters were rougher, due to what we interpret

as physical and chemical erosion. We have

carried out chemical analyses of both the surfaces and the interiors (on polished sections) of

spherules from the Sikhote-Alin and Arizona

craters, and are currently analyzing spherules

from the other craters. The Arizona particles,

all over 100 n in diameter, were analyzed by

standard microchemical techniques, while the

Sikhote-Alin particles were analyzed by the

microprobe of the Advanced Metals Research

Corporation, under the supervision of S. H.

Moll. Our results show so far that spherules

formed as ablation products from the molten

skins of meteorites have two distinguishing

characteristics: (1) iron-rich surfaces, often

with an oxidized crust, and (2) nickel-rich

interiors, often with a region where the nickel is

about five times more abundant than elsewhere.

ARTIFICIAL METEORITE SPHERULES.—Several

papers have described the artificial production

of meteoritic spherules (Fechtig and Utech,

381
382 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 1.—Environments in which iron-rich spherules have been found

Location

Atmosphere

1. Settling at surface at isolated

sites

2. At 10-15 km in stratosphere

3. At 25 km in stratosphere

4. Upper atmosphere above 80 km

Ocean sediments

5. Magnetic fraction

Ice deposits

6. Greenland 750-yr-old ice

7. Antarctic 55-yr-old ice?

8. South Pole 55-yr-old ice

9. Ice Island T 3, various depths

Sedimentary rocks

10. Paleozoic salts

11. Other sediments

Meteorite craters

12. Sikhote-Alin

13. Arizona (Canyon Diablo)

14. Henbury

Volcanic ash

15. Pacific Islands

16. North, Central, and South

America, and Hawaiian volcanoes

17. Various volcanic deposits

Industrial smoke

18. Fly ash

19. City air

Description

~ 3 to 100 M in size, uniform

rate of deposit over large

part of earth

Very rare, small

Rare, small

Extremely rare, small

Large spherules

Relatively common

Relatively common

Relatively common

Relatively common

Relatively common

Relatively common

Spherules in soil and on

meteorite surfaces

Rough spherules in soil

Smooth, perfect spherules in

soil

Rare, perfect spherules

Rare, perfect spherules

Rare, perfect spherules

Spherules common

Spherules common

References

Crozier, 1966; Hodge and Wildt, 1958;

and many others

Hodge, 1961; Melton (see pp. 293-299)

C. Mossop, 1963 (private communication)

Hemenway and Soberman, 1962

Pettersson, 1955; Laevastu and Mill is,

1955; and many othcra

Langway, 1962

Thiel and Schmidt, 1961

H. Bader, 1962 (private communication)

Stoiber ct al., 1956

Mutch, 1964

Lougheed, 1966

Krinov, 1960

Nininger, 1941; Rinehart, 1958; Wright

and Hodge, 1964

Hodge, 1965

Fredriksson and Martin, 1963

Hodge and Wright, 1964; Wright and

and Hodge, 1965a

Mutch, 1964

Handy and Davidson, 1953

Hodge and Wildt, 1958; Hoppe and

Zimmermann, 1954

1964; Schmidt, Keil, and Gault, 1965; Wright

and Hodge, 1965b). Generally, when an ironnickel source was used, the nickel was found

to be concentrated toward the center of the

spherule produced. We analyzed the interiors

of polished sections of seven artificial spherules,

three made from an iron meteorite and four

from a stony-iron. Table 2 summarizes our results. We found in general that nickel and

cobalt were usually more abundant in the central parts of the particle than at the surfaces,

but for three of the particles, known to be

formed from meteoritic material, nickel was

absent throughout. Particularly for the spherules from the stony-iron meteorite, if other

elements characteristic of the stony material in

the meteorite (silicon, calcium, etc.) were

present, neither nickel nor cobalt was detectable in the particle.

VOLCANIC SPHERULES.—Fredriksson and Martin (1963) examined volcanic material and
CHEMICAL COMPOSITION OF COSMIC PARTICLES HODGE AND WRIGHT 383

TABLE 2.—Compositions of surf aces and interiors of seven artificial meteoritic spherules (weight percent)

Particle

A. Made from Ct

1. Surface

Interior

2. Surface

Interior

3. Surface

Interior

Mg

myon D

—

—

—

—

—

—

Al

iablo octah

Si

'.drite

B. Made from Estherville mesosiderile

1. Surface

Interior

2. Surface

Interior

3. SurfaceInterior

4. Surface

Interior

—

—

—

—

—

—

—

—

0.5-1.0

6-8

1-2

4-6

7-8

20-22

8-10

Ca

<0.5

3-4

4-6

7-8

6-8

Ti

0. 1-0.5

<0. 5

0. 1-0.5

Cr

<0. 5

0. 1-0.5

<0. 5

0. 1-0.5

Mn

0. 1-0. 5

<0. 5

0. 1-0. 5

<0.5

0. 1-0. 5

Fc

70-75

67-72

70-75

68-73

65-70

65-70

68-73

65-70

55-60

65-70

40-45

40-45

40-45

28-33

Co

~0.2

0.5-1.0

~0.5

0.5-1.0

~0.5

0.5-1.0

Ni

0. 1-0.2

0.5-1.0

4-5

4-5

7-8

6-8

4-5

5-6

found that shiny magnetic spherules are a rare

but always-present component of volcanic

dust. We have collected and studied such

spherules, derived from nine different volcanoes

in various parts of the world (Hodge and

Wright, 1964; Wright and Hodge, 1965a),

and have confirmed Fredriksson and Martin's

conclusion that iron-rich spherules occur in

volcanic ejecta. Recently we have sectioned

and polished two of the most perfect volcanic

spherules, both from Kilauea Iki, and have

found that the composition varies from place

to place in the interiors of the particles (table

3 and plate la). However, the relative abundances of the elements do not vary greatly

from place to place in the interior, or from

interior to surface. In both cases, all elements tested were more abundant at the surface than in the interior. The most important conclusion from these investigations is

that the characteristic chemical constitution

of the volcanic spherules derived by us from

surface analyses applies to the whole particle

in a relative sense. That is, large amounts of

aluminum, silicon, calcium, and titanium relative to iron occur throughout volcanic spherules.

We are examining many more volcanic spherules

to check this conclusion further.

Identification of spherules of unknown origin

METEORITIC SPHERULES.—From investigations

described above, it should usually be possible

to distinguish spherules derived from iron

meteorites by the presence of nickel, often concentrated in an area near the center of the particle; however, it also appears possible that

some iron meteorite spherules will have lost all

nickel and will be almost pure iron oxide.

Many of the particles found in deep-sea sediments can be identified as meteoritic from the

nickel content (Fredriksson, 1956; Castaing and

Fredriksson, 1958; Fechtig and Utech, 1964;

Schmidt and Keil, 1966). Also, we have found

that both of our two tested spherules extracted

from New Mexico lake-bed sediments by Crozier have nickel in approximately the correct

proportions in their interiors, although only

one showed nickel at its surface.

It is much more difficult to identify any

meteoritic spherules that have lost all nickel.

We have found that one out of three artificially

made spherules is without nickel in its interior,

and that about half of the Sikhote-Alin spherules have no nickel in their interiors. These

particles have about 70 percent iron by weight

and virtually nothing from among the elements

heavier than magnesium, except occasionally

for 0.1 to 0.5 percent manganese. Many of the

spherules found in isolated sites and in historical

deposits also contain about 70 percent iron and

0.1 to 0.5 percent manganese and little else

detectable, and some or all of these may be

meteoritic (see pi. 16 and table 4). There

are, however, roughly 10 times as many iron-
3 8 4 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 3.—Composition of surface and interior of a Kilauea Iki spherule (see pi. la) (weight percent)

Surface

Interior 1

Interior 2

Interior 3

Interior 4

Interior 5

Al

13-15

9

6

y

5

5

Si

28-30

16

1<>

24

20

14

Ca

14-16

X

X

X

X

X

Ti

1-2

1.2

i.:s

1.6

1.2

1.2

Cr Mn

< 0. 5

0.03

0.04

0.04

0.06

0.06

Fc

14-16

7

7

7

9

8

NOTE: In the interior point analyses, probes were made for only Al, HI, Ti, Cr, Mn, Fe, and Ni.

TABLE 4.—Composition of a surface and interior of a

typical spherule from Greenland ice (sec pi. lb)

(weight percent)

Surface

Interior 1

Interior 2

Interior 3

Interior 4

Interior 5

Al

0. 1

0. 1

0. 1

0. 1

0. 1

Si

5-6

0.1

0. 1

0.2

1. 1

1. 1

Ti

< 0. 5

0.7

0.8

0. !>

1. 1

1.2

Cr

—

—

—

—

—

Mn

~(). 5

0.2

0.2

0.2

0.2

0.2

Fc

60-65

68-73

68-73

68-73

68-73

68-73

manganese particles as there are iron-nickel

particles, which argues against the possibility

that all or even the majority of the ironmanganese particles are meteoritic.

We tentatively conclude that a small fraction,

perhaps 1 to 2 percent (Hodge, Wright, and

Langway, 1964), of the iron-rich spherules

found in glacial deposits, sediments, and the

atmosphere at isolated sites is derived from

iron meteorites. Apparently a much greater

fraction of the deep-sea spherules comes from

iron meteorites.

Judging from the composition of the "stony"

meteoritic spherules that we have made artificially, some of the other naturally occurring

spherules may be derived from stony meteorites,

which are about 10 times as abundant as irons

in interplanetary space. Estimates suggest

that perhaps 10 percent of the spherules that

we have analyzed may be such ablation products from stony meteorites. Thus, perhaps

a total of 10 to 12 percent of the spherules

found in isolated sites is meteoritic.

VOLCANIC SPHERULES.—Analyses of the surfaces and interiors of known volcanic spherules

show that the relative abundances of iron,

aluminium, silicon, calcium, and titanium arc

fairly characteristic and consistent. On this

basis, we find that several of the spherules

collected from arctic and antarctic ice are

volcanic in origin. We estimate that roughly

5 percent of all Greenland ice-cap spherules

can be volcanic according to their chemical

composition, and their abundance relative to

irregular particles confirms this estimate (Hodge

and Wright, 1964).

Giovinetto and Schmidt (1965) find evidence

for a much larger fraction of volcanic spherules

at the South Pole. Their evidence, as yet

unpublished, is based on an increase in the

number of spherules found at the time of the

Krakatoa eruption. Our chemical analyses of

several South Pole spherules do not confirm

their general conclusions, and we point out

that if 5 percent of the spherules is normally

volcanic, this percentage may greatly increase

at the time of a violent volcanic eruption.

ORIGIN OF OTHER SPHERULES.—The majority

of the spherules found in isolated sites, polar-ice

deposits, and ancient sediments do not have a

composition similar to that of any spherules

of known origin. An industrial origin has been

suggested for them by Schmidt and Fredriksson

(1967), who neglect to take into account the

fact that our Greenland samples are from

750-year-old ice deposits and that there was

very little industrial activity anywhere in the

world in the 13th century.

We believe it possible that most of these

spherules of unknown origin are ablation

products from cometary meteors. No other

reasonable explanation has yet been proposed,

and Crozier (1966) has pointed out that the
CHEMICAL COMPOSITION OF CO8MIC PARTICLES—HODGE AND WRIGHT 385

rate of fall of spherules seems to be correlated

with the rate of incidence of radar meteors.

It should be stated, however, that we regard

the evidence concerning the origin of most of

the spherules as still inconclusive. There may

be some explanation that is quite different

from any so far suggested.

Acknowledgmen t

We wish to express our gratitude to C. C.

Langway, Jr., who has collaborated with us

on most of the projects discussed here, to F. L.

Whipple for his continuing interest, and to

M. F. Comerford, who took the microphotographs reproduced here.

References

Bl Ulilll K. J. I).

1050. Meteoritic dust. Univ. of New Mexico

Publ. in Meteoritics, no. 2, Univ. of Now

Mexico Press, Albuquerque, 102 pp.

CASTAING, It., ami FREDKIKSSON, K.

1958. Analyses of cosmic spherules with an Xray microanalyzer. Geochim. ct Cosmochitn. Acta, vol. 14, pp. 114-117.

CROZIER, W. D.

1966. Nine years of continuous collection of black,

magnetic spherules from the atmosphere.

Journ. Geophys. Hes., vol. 71, pp. 603-

611.

FECHTIG, H., and UTECH, K.

1964. On the presence or absence of nickel in dark

magnetic cosmic spherules and their mechanics of origin. Ann. New York Acad.

Sci., vol. 119, pp. 243-249.

FREDRIKSSON, K.

1956. Cosmic spherules in deep-sea sediments.

Nature, vol. 177, pp. 32-33.

FREDRIKSSON, K., and MARTIN, L. It.

1963. The origin of black spherules found in

Pacific islands, deep-sea sediments, and

Antarctic ice. Geochim. ct Cosmochim.

Acta., vol. 27, pp. 245-248.

GIOVINETTO, M. B., and SCHMIDT, It. A.

1965. Spherules from four centuries of snow deposits at the South Pole. Trans. Amor.

Geophys. Union, vol. 46, p. 116.

HANDY, R. L., and DAVIDSON, 1). T.

1953. On the curious resemblance between fly ash

and the meteoritic dust. Proc. Iowa

Acad. Sci., vol. 60, pp. 373-379.

HEMENWAY, C. L., and SOBERMAN, R. K.

15)62. Studies of micrometeoritos obtained from a

recoverable sounding rocket. Astron.

Journ., vol. 67, pp. 256-266.

HODUE, P. W.

1961. Sampling dust from the stratosphere.

Smithsonian Contr. Astrophys., vol. 5,

no. 10, pp. 145-152.

1965. The Henbury meteorite craters. Smith

sonian Contr. Astrophys., vol. 8, no. 8

pp. 199-213.

HODGE, P. W., and WILDT, It.

1958. A search for airborne particles of meteoritic

origin. Geochim. et Cosmochim. Acta,

vol. 14, pp. 126-133.

HODGE, P. W., and WRIGHT, F. W.

1964. Studies of particles for extraterrestrial origin, 2: A comparison of microscopic

spherules of meteoritic and volcanic origin. Journ. Geophys. Res., vol. 69, pp.

2449-2454.

HODGE, P. W.; WRIGHT, F. W.; and HOFFLEIT, D.

1961. An annotated bibliography on interplanetary dust. Smithsonian Contr. Astrophys., vol. 5, no. 8, pp. 85-111.

HODGE, P. W.; WRIGHT, F. W.; and LANGWAY, C. C, Jr.

1964. Studies of particles for extraterrestrial origin, 3: Analyses of dust particles from

polar ice deposits. Journ. Geophys.

Res., vol. 69, pp. 2919-2931.

HOPPE, J., and ZIMMERMANN, H.

1954. Separation of interplanetary from industrial

particles. Die Sterne, vol. 30, pp. 33-36.

KRINOV, E. L.

1960. Principles of Meteoritics. Trans, by I.

Yidziunas, ed. by H. Brown, Pergamon

Press, New York, 535 pp.

LAEVASTU, T., and MELLIS, O.

1955. Extraterrestrial material in deep-sea deposits. Trans. Amer. Geophys. Union,

vol. 36, pp. 385-389

LANGWAY, C. C, Jr.

1962. Some physical and chemical investigations

of a 411-meter deep Greenland ice core

and their relationship to accumulation.

Int'l. Assoc. Sci. Hydrol. Commission

of Snow and Ice, publ. 58, pp. 101-118.

LOUGHEED, M.S.

1966. A classification of extraterrestrial spherules

found in sedimentary rocks and tell.

Ohio Journ. Sci., vol. 66, pp. 274-283.

MELTON, C. E.

1967. Aerosol samples obtained from 9- to 12-km

altitude. Smithsonian Contr. Astrophys., vol. 11, pp. 293-299.

MUTCH, T. A.

1964. Volcanic ashes compared with Paleozoic

salts containing extraterrestrial spherules.

Journ. Geophys. Res., vol. 69, pp. 4735-

4740.

NlNINGER, II. H.

1941. Collecting small meteoritic particles. Pop.

Astron., vol. 49, pp. 159-162.

PETTERSSON, H.

1955. Magnetic spherules and meteors. Naturwiss., vol. 42, pp. 387-388.
386 SYMPOSIUM ON METEOR ORBITS AND DUST

RlNEHART, J. S.

1958. Distribution of meteoritic debris about the

Arizona meteorite crater. Smithsonian

Contr. A8trophys., vol. 2, no. 7, pp.

145-160.

SCHMIDT, R. A.

1962. A survey of data on microscopic extraterrestrial particles. Contributions The

Univ. of Wise. Geophys. Polar Res. Ctr.,

Madison, Wise, no. 88 (revised June

1964); NASA TN D-2719, March 1965.

SCHMIDT, R. A., and FREDRIKSSON, K.

1967. Comments. Journ. Geophys. Res. (in

press).

SCHMIDT, R. A., and KEIL, K.

1966. Electron microprobe study of spherules

from Atlantic Ocean sediments. Geochim. ct Cosmochim. Acta, vol. 30, pp.

471-478.

SCHMIDT, R. A.; KEIL, K.; and GAULT, D. E.

1965. Electron microprobe study of a crater and

cjecta produced by hypervelocity impact

against a Ni-Fe target. Proc. 7th

Hypervelocity Impact Symp., Tampa,

Fla., vol. 5, pp. 105-121.

STOIBER, R. E.; LYONS, J. B.; ELBERTY, W. T.; and

MCCREHAN, R. H.

1956. The source area and age of Ice-Island T-3.

Final report under contract AF 19(604)-

1075, Dartmouth College, Dept. of

Geology, Hanover, N. H.

THIEL, E., and SCHMIDT, R. A.

1961. Spherules from the Antarctic ice cap.

Journ. Geophys. Res., vol. 66, pp. 307-

310.

THOMSEN, W. J.

1953. The annual deposit of meteoritic dust.

Sky and Tel., vol. 12, pp. 147-148.

WRIGHT, F. W., and HODOE, P. W.

1964. Compositional studies of extraterrestrial

particles. Ann. New York Acad. Sci.,

vol. 119, pp. 287-297.

1965a. Studies of particles for extraterrestrial

origin, 4: Microscopic sphcrulco from

recent volcanic eruptions. Journ. Gcophys. Res., vol. 70, pp. 3889-3898.

1965b. Analysis of artificial meteoritic Hpherulcs.

Smithsonian Astrophyu. Obs. Spec. Rep.

No. 192, 10 pp.

Abstract

Iron-rich spherules, ranging in diameter from a few to over 100 M, have been found in nature in the following

environments: the atmosphere up to heights of at least 25 km, ocean sediments, urctic and antarctic ice deposits,

sedimentary rocks, the soil around meteorite craters, volcanic ash, and industrial smoke. Evidence based on our

investigations and those of numerous other scientists indicates that careful studies of the chemical, mineral, mul

physical properties of individual particles can lead to conclusions about their origins. Our recent investigation of

polished sections of 23 spherules points to a clear distinction between spherules from different types of sources. Some

of the naturally occurring iron-rich spherules are probably volcanic in origin and some are probably meteoritic, but

the majority are unlike spherules of known origin.
CHEMICAL COMPOSITION OF COSMIC PARTICLES HODGE AND WRIGHT 387

a

PLATE 1

Polished interior of a 30-ju spherule: a, from Kilauea Iki;

b, from Greenland ice, with sketches of points probed.

Recovery of Magnetite Spherules from Sedimentary Rocks

T. A. MUTCH

 l and J. T. PARR '

Studies of possible extraterrestrial spherules

contained in various types of sedimentary

rocks have been undertaken. The present

preparation and separation procedures result

in extraction of spherules composed primarily

of the mineral magnetite. While there are

no chemical nor mineralogical features that

point uniquely to an extraterrestrial origin,

the formation and preservation of ablation

droplets of this character are reasonable. By

contrast, the authors can think of no terrestrial

origin that adequately explains the morphology,

composition, and abundance of such spherules

in the sedimentary rocks under consideration.

These rocks include rock salt, limestone,

argillite, quartzite, and radiolarian chert. Ages

range from Precambrian to Permian.

Preparation of samples involves solution or

disaggregation of the rock. Since magnetite

is a reasonably insoluble mineral, acids as

reactive as HF can be used, providing the

reaction time and pH are closely controlled.

Magnetite spherules appear to undergo only

limited superficial etching during this treatment. Since most silicate minerals are soluble

in HF, almost any sedimentary rock can be

1

 Department of Geology, Brown University, Providence, R.I.

examined by means of this preparation procedure. Less reactive acids (HNO3, EDTA)

are sufficient for disaggregation of carbonateand sulfate-rich rocks.

Total disaggregation of a rock is a prerequisite for complete recovery of all spherules.

The separation itself is effected magnetically.

Consequently, extraterrestrial particles of low

magnetic susceptibility, if present, are not

isolated. The fact that the majority of spherules are small, less than 25 y. in diameter,

means that the trapping procedure must be

highly efficient. Problems in sample preparation or in magnetic separation may result

in deceptively low spherule counts. Finally,

before influx rates can be established, some

estimate must be made regarding the depositional rate of the total rock. In all cases

such estimates are tenuous.

Faced with these difficulties, one should be

understandably cautious in saying anything

regarding influx rates in the past as cornpared

with those of the present. Work to date on

rock salt suggests that Silurian spherule size

distributions and influx rates are similar to

present day figures. Additional data are

needed for confirmation of this suggestion.

Fusion Crust of Iron Meteorites and Mesosiderites and

Production of Cosmic Spherules

A. E L GORESY

 l and H. FECHTIG

In the last few years many authors have expressed the opinion that a great part of the

so-called cosmic spherules may have been produced by ablation of iron meteorites in the

atmosphere. This opinion could be proved for

the spherules collected during the Albatross

deep-sea expedition. These spherules, investigated by Castaing and Fredriksson (1958),

show iron-nickel-cobalt cores eccentrically located in the inside of magnetite spherules. The

nickel content of these cores is approximately

30 percent, which is appreciably higher than

the average content of nickel in iron meteorites.

In the magnetite shells no nickel, or only traces

of nickel, could be found.

Many of the cosmic spherules, however, do

not show those cores. Instead of the cores there

are holes. No nickel could be detected in

these magnetite spherules.

The geochemical characteristics of iron, nickel, and cobalt in magnetite spherules have been

discussed by many authors in recent years.

Many arguments have been offered for and

against the siderophile behavior of nickel, and

its presence or absence in magnetite spherules

is given as an indication of cosmic or terrestrial

origin, respectively. It seemed to us very important to study, both mineralogically and with

the microprobe, natural fusion crusts of some

iron meteorites and stony irons, since those

crusts have been formed in extremely short

times under oxidizing conditions favoring the

formation of magnetite and wustite from kamacite, taenite, and troilite. The fusion crusts of

the meteorites Sikhote-Alin (hexaedrite) and

• Max-Planck-Instttut fiir Keinphysik, Heidelberg, Germany.

Pinaroo (mesosiderite) will be discussed here in

detail.

It is well known that fusion crusts of iron

meteorites are in general broader than those of

stony meteorites because of the high heat conductivity of the metal phase compared with

that of the silicates (Maringer and Manning,

1960). Ramdohr (1965) made a detailed study

on this subject. In our specimens, however, the

fusion crusts are not so thick as expected (they

have a maximum thickness of 1 mm). Microscopic studies showed that they are formed of

successive and sometimes alternating layers,

and not exclusively of magnetite, as has often

been mentioned.

In the Sikhote-Alin meteorite we observed

the following layers:

1. An innermost layer close to the unaffected metal composed of recrystallized nickeliron and sometimes displaying melting textures.

This zone contains throughout few but finely

distributed magnetite patches.

2. A magnetite-rich zone with finely disseminated metal particles. The borders between the former and this zone are not sharp,

and the increase of the magnetite content from

the first to the second zone is gradual. The

outer boundaries of this layer do not follow

the outlines of the first zone, but are strongly

curved and show stalactite-like textures (pi.

la). Under high magnification one recognizes

that it is formed of alternating magnetite-rich

und metal-rich thin sheets. Magnetite is sometimes locally concentrated in big patches (pi.

la). A salient feature is the skeletal form of

the magnetite indicating rapid cooling and

:$9i
392 SYMPOSIUM ON METEOR ORBITS AND DUST

crystallization from a melt (pi. 16). In the

interstices of the magnetite skeletons there are

a large number of iron-nickel spherules of

different sizes. The big metal spherules contain fine schreibersite worms intersecting the

main iron-nickel mass (pi. 16). From plate 16

it is also evident that iron-nickel is likewise

disseminated in the magnetite as very fine

particles (1 n and smaller). The presence of

such iron-nickel particles will surely affect the

microprobe measurements and give the false

impression that nickel is present in magnetite

and not in the metal phase. Metal-free

magnetite patches are in general very rare.

This demonstrates excellently the importance

of optical studies and the efficiency of firstclass polishing. Microprobe measurements

without careful optical studies in incident light

may reveal misleading results.

3. A metal-rich zone following the complicated second zone. In texture and composition it resembles the first zone. Magnetite

shows everywhere the typical skeletal form.

4. The outermost zone containing two

layers: (a) An inner shell formed mainly of

wiistite with excellent skeletal crystals. Ironnickel spherules are distributed in this shell,

sometimes with local concentration. Wiistite

can be recognized from magnetite by its lower

reflectivity and its dark gray color. It is likewise cubic, and hence isotropic. (b) An outer

magnetite shell with typical skeletal crystals

and a large number of holes of different sizes.

Large iron-nickel spherules are sometimes

present (pi. la). Magnetite also contains here

fine iron-nickel particles. For microprobe

measurements only those parts of magnetite

must be chosen that are free of iron-nickel

particles.

The points a to h, as shown in plate la,

were analyzed for iron, nickel, and cobalt with

the microprobe. The results are given in

table 1. The most interesting results are given

by the nickel distribution. Both in the ironnickel spherule (point a) and in the point b,

the nickel content has increased up to 70

percent, which is more than a factor of 10

higher than the nickel content of the kamacite.

Usually there is only a very thin layer enriched

in nickel along the unaltered metallic phase

of the meteorite. The magnetite itself shows

TABLE 1.—Iron, nickel, and cobalt contents in the

Sikhote-Alin fusion crust (all results are corrected

for background, dead time, mass absorption, and

fluorescence excitation)

Points

a

b

c

d

e

f

g

h

Iron

31.5

26.3

89.9

92.3

53.2

87.2

66.0

88.9

Nickel

59.4

71.7

8. 1

5.2

5.5

11.4

0.02

9.0

Cobalt

2. 1

1.7

0.6

0.7

0.4

0.6

0.03

0.6

Total

93.0

99.7

98.6

98.2

59. 1

99.2

66. 1

98. 5

Remarks

+ Phosphorus

+ Oxygen

+Oxygen

a surprisingly high amount of nickel (point e:

5.5 percent) but, as shown in plate 16, very small

islands of metallic iron-nickel spherules with

high nickel content are usually present. Point

g, however, is located in a magnetite area where

no iron-nickel islands could be seen. In this

case the nickel content is 0.02 percent. The

points f and h show the composition of the

nonoxidized material in the neighborhood of

the nickel-free magnetite area. The general

result is that nickel and, to a lesser extent,

cobalt migrate toward the nonoxidized parts

of the melted material during an oxidation

process.

In the meteorite of Pinaroo the fusion crust

is mineralogically more complicated, and its

composition varies laterally because of the

presence of a large number of minerals that

behave differently when heated, e.g., olivine,

pyroxene, chromite, troilite, schreibersite, kamacite, and taenite. Olivine and pyroxene are

mainly fused to a silicate glass with a relatively

low thickness. Behind the fused thin silicate

layer inside the meteorite, the silicates are

intact and show no effects of heating. Troilite,

whose melting point is considerably lower than

that of silicates, has been molten and intruded

between the silicates and even soaked into the

fine cracks in the silicate crystals. In parts

where only troilite is present it shows a fluffy

texture. Because of the oxidizing conditions

during formation of the fusion crust, part of

the troilite has been roasted to magnetite

with abundant vesicles indicating escape of

SO2 vapor.
FUSION CRUST OF IRON METEORITES AND MESOSIDERITES—EL GORE8Y AND FECHTIG 393

Heat has a very interesting effect on chromite

in the fusion crust. In general, chromite is

known as a refractory mineral. Magnetite

separated during fusion overgrows the stable

chromite because of the resemblance of the

cell edge of both minerals. By strong and

direct fusion, chromite itself shows partial

breakdown into chromium-poor spinel and

eskolaite (CrtO3) separated as fine lamellae

parallel to (111) of chromite. The breakdown

of chromite and the eskolaite intergrowth

was observed for the first time by P. Ramdohr

(private communication, 1965) in fusion crusts

of stony meteorites and mesosiderites. In

parts where schreibersite together with taenite

was captured in the fusion crust, schreibersite

occurs as skeletal crystals in taenite with

preferred orientation indicating separation from

a metal-phosphide melt.

Where only kamacite and taenite are affected

by fusion, the textures very much resemble

those of Sikhote-Alin. In Pinaroo three layers

(pi. 2a) were observed: (1) a nickel-rich metal

layer with indication of melting following the

unaltered metal; (2) a wiistite layer with nice

skeletons and a large number of very fine metal

particles; (3) a broad magnetite zone, also

with wonderful skeletal crystals (pi. 26).

The amount of the fine iron-nickel disseminated

between the magnetite skeletons varies from

place to place. We also found here some big

iron-nickel spherules whose size permits quantitative microprobe measurements. Magnetite

is partially oxidized to hematite at the outermost

layer. The fusion crust of Pinaroo is markedly

intersected by tension cracks that are filled

with weathering products like goethite and

lepidocricite.

We carried out microprobe investigations,

similar to those of Sikhote-Alin, on the fusion

crust of the Pinaroo meteorite. The analyses

were made at the points a to i indicated in

plate 2a. Again the elements iron, nickel, and

cobalt were measured and the results are given

in table 2. Point a gives the composition of an

inner part in the unaltered meteoritic material.

Point g gives the analysis of an iron-nickel

spherule visible in the oxidation zone. The

nickel content is 62.8 percent, which is 7 times

higher than in the Kamacite phase of this

meteorite (8.4 percent). The points h and i

240-022 O—07 2«

TABLE 2.—Iron, nickel, and cobalt contents in the Pinaroo fusion crust (all results are corrected for background, dead lime, mass absorption, and fluorescence)

Points

a

b

c

d

c

f

g

h

i

Iron

86.1

25.7

42.2

52.6

Nickel

8.4

38.8

37.8

40.9

40.4

49.5

62.8

3.2

0.6

Cobalt

0.7

1.6

0.2

0.08

Total

95.2

90.1

45.6

53.3

Remarks

lOnly nickel

[was measured

J + Phosphorus

+ Oxygen

+Oxygen

are in the magnetite zone. Here the nickel

content is respectively 3.2 and 0.6 percent,

which represents very small iron-nickel islands

distributed in the oxidation zone (pi. 26).

Surprisingly, the points b, c, d, e, and f are

located in a larger area of approximately

200 MX200 M with a nickel content up to

50 percent. This zone, however, turned out

to be a very thin layer of nonoxidized ironnickel alloy. In the case of a thin layer of

iron-nickel metal, the electron beam of the

microprobe may reach the magnetite, which

is underneath the iron-nickel layer (fig. 1).

Three measurements were made with 12, 20,

and 35 kv electron energy to determine the

nickel content in this area, and the result is

given in table 3. Because the penetration

increases with increasing electron energies, the

nickel content is highest at the lowest electron

energy.

The results on the fusion crust of the Pinaroo

meteorite are the same as for the Sikhote-Alin

iron meteorite: very high nickel and relatively

high cobalt content either in the small nonoxidized iron-nickel islands or in the outermost

layer located along the unaltered metallic part

of the meteorite. *

The production of cosmic spherules by ablation necessarily occurs in the nonoxidized outermost zone preferably consisting of magnetite

with islands of nickel-enriched iron-nickel alloys.

So it might well be possible that magnetite

spherules are produced without any nickel or

with a nickel-rich metal core. This result is in

agreement with the experiments of Fechtig and
394 SYMPOSIUM ON METEOR ORBITS AND DUST

electron beam

iron-nickel zone

magnetite without nickel

FIGURE 1.—Nickel content dependence of voltage in a thin

layer.

TABLE 3.—Nickel content dependence of voltage in a

thin layer

Voltage

12

20

35

(kv) Nickel (%)

• J< V • 5

21.0

17.3

Utech (1964) carried out both on meteoritic

material and on artificial iron-nickel alloys.

The authors could artificially produce an oxidation crust that shows a small nickel-rich zone

between the oxidized material and the nonoxidized iron-nickel alloy. The results are also

in agreement with the experimental results of

Schmidt, Keil, and Gault (1965), who investigated the chemical changes caused by a highvelocity impact of a small nickel-iron projectile

into the same nickel-iron alloy as a target.

They also observed an oxidation process, and

the nickel content of the ejecta material (magnetite spherules) decreased by a factor of 10.

The results show that the lack of nickel in

the magnetite spherules is not necessarily an

indication against an extraterrestrial origin.

An important mineralogical fact should be

taken into consideration in order to differentiate

between volcanic magnetite and cosmic magnetite. It is well known that the majority of

volcanic magnetites are by no means pure

crystals but, in fact, are formed of mixed

titanomagnetites, i.e., members of the complete solid-solution series raagnetite-ulvospinel

(FetFeOrFe,TiO4) (Ramdohr, 1960). Many

volcanic magnetites belong also to the group

known as unmixed titanomagnetites, which are

magnetite grains with ilmenite lamellae parallel

to (111) of magnetite. Both mixed and unmixed titanomagnetites are present in nearly

every volcanic rock (Ramdohr, 1940). The

titanium content may reach 20 percent in those

magnetites. In questionable cases the presence

of titanium can indicate a volcanic, and exclude

a cosmic, origin.

References

CASTAINO, R., and FREDRIKSSON, K.

1958. Analyses of cosmic spherules with an x-ray

microanalyscr. Ueochim.rtCosmochim.

Acta, vol. 14, pp. 114-117.

FECHTIG, H., and UTECH, K.

1964. On the presence or absence of nickel in dark

magnetic cosmic spherules and their

mechanics of origin. Ann. New York

Acad. Sci., vol. 119, pp. 243-249.

MARINGER, 11. E., and MANNING, G. K.

1960. Aerodynamic heating of the Grant meteorite. Gcochim. et Cosmochim. Acta,

vol. 18, pp. 157-161.

RAMDOHR, P.

1940. Die Erzmineralien in gewflhnlichen magmatischen Gesteinen. Abh. Preuss. Akad

Wiss., Math. Nat. Kl. Nr. 2, pp. 3-43.

1960. Die Erzmineralien und ihre Verwachsungen. Akademie Verlag, Berlin.

1965. The opaque minerals in stony meteorites

Unpublished monograph.

SCHMIDT, R. A.; KEIL, K.; and GAULT, D. E.

1965. Electron microprobe study of a crater and

ejecta produced by hypervelocity impact

against a nickel-iron target. Proc. 7th

Hypervelocity Impact Symp., Tampa,

Fin., vol. 5, pp. 105-121.

Abstract

Detailed mineralogical and microprobe studies have been carried out on the fusion crusts of the Sikhote-Alln

and Pinaroo meteorites. The fusion crusts in the specimens studied are about 1.5 mm thick and are composed of complex

metal and iron-oxide layers. The innermost layer is relatively thin and is composed mainly of recrystallized metal.

This layer is followed by a magnetite-metal layer. Magnetite shows skeletal crystals, droplets, and stalactitic textures typical of crystals separating from a melt by fast cooling. Magnetite is partially intercalated by nickel-iron

spherules. In the outermost layer some nickel-iron spherules were observed, as well as a thin sheet of wustite (FoO).

Some of these nickel-iron spherules show eutectic intergrowth between nickel-iron and schreibersite. Other spherules

are composed mainly of nickel-iron.
FUSION CRUST OF IRON METEORITES AND MESOSIPERITES—EL OORE8Y AND FECHTIG 39 5

Microprobe measurements of the nickel-iron spherules, the magnetite zone, and the border between the magnetite

and the unaltered meteorite have been carried out for nickel, iron, and cobalt. The results show an enrichment, as

high as 60 percent, of the nickel in these spherules and in the outer part of the nonoxidized meteoritic material. The

nickel content of the magnetite in those areas in which no metallic islands can be seen is below 0.03 percent. The

cobalt distribution in these zones is similar to that of nickel, but to a lesser extent.

The results strongly support the production of the cosmic spherules by ablation as far as they consist of magnet ite.

There is, furthermore, a good agreement with similar investigations on an artificially produced oxidation crust in

iron meteorites and iron-nickel alloys as reported by Fechtig and Utech (1964).
396 SYMPOSIUM ON METEOR ORBITS AND DUST

Mounting

material

Magnetite shell

Layer 4

Wiistite shell

Layer 3

Layer 2

Layer I

Unaltered

meteorite

PLATE 1A, B

Sikhote-Alin fusion crust (magnification X 400). Skeletal crystals of magnetite (gray) with iron-nickel spherules of different

sizes. The big metal spherules contain schreibersite worms (magnification X 800).
FUSION CRUST OF IRON* METEORITES AND MESOSIDERITES—EL GORESY AND FECHTIG 39 7

Magnetite zone

Secondary iron-oxide

veins

Unaltered meteorite

a • a

b

PLATE 2A,

Pinaroo fusion crust (magnification X 180). Excellent skeletal magnetite crystals (light gray). Notice

iron-nickel particles between the magnetite skeletons (the upper right part of the photograph) (magni

the presence of fine

magnification X 800).

Some Studies of Separated Fractions of Low AccumulationRate "Dust"

D. TlLLES

Introduction

Fine-grained material, tentatively identified as

extraterrestrial in origin, has been found in

deep-sea and polar deposits and studied scientifically for 90 years (see Buddhue, 1950, for a

review of the early work and bibliography);

however, the uncertainties in mineralogical,

chemical, and morphological characteristics of

possible extraterrestrial material have greatly

hampered progress in these studies. Much

attention has been devoted to searching out

and studying "cosmic spherules"—dark magnetic iron-rich spheres, some of which have

cores of metallic nickel-iron. Because of the

extreme rarity of terrestrial native metallic

iron, the unknown terrestrial occurrence of

native metallic iron with nickel abundance

greater than 1 or 2 percent, and the obvious

plausibility of creation of such spherules by

atmospheric ablation and oxidation. of the

iron-nickel meteorites, such magnetite spherules with iron-nickel cores are perhaps the

only fine-grained material found on earth for

which a nonterrestrial origin is almost universally accepted.

As a result of the great difficulty of definitive

identification of extraterrestrial material, substantial effort has been devoted in recent years

to searching for the presence of cosmic-rayproduced radioactive or stable isotopes or

other stable isotope anomalies in samples

suspected to contain extraterrestrial dust.

Isotopes sought in sea sediments have included

Cl89 (Schaeffer, Megrue, and Thompson, 1964),

1

 Smithsonian Astrophysical Observatory and Harvard College Observatory, Cambridge, Mass.

Few (C. M. Merrihue, unpublished), AP

(Lai and Venkatavaradan, 1965), and those

of the noble gases (Schaeffer, Megrue, and

Thompson, 1964; Merrihue, 1964; R. Bieri,

private communication). Isotopes studied in

particular matter from polar ice include AP

(Fireman and Langway, 1965), Ar39, and Co90

(Fireman, DeFelice, and Langway, 1965).

Most of these searches have given negative

results. The Co80 results, while positive, require further work to distinguish terrestrial

contaminants from the daughter product of

long-lived Fe". The specific activities of AP

reported for two cores of sea sediment are

only about twice the probable errors of the

measurements.

Merrihue (1964) reported evidence of He3

and of anomalous argon isotope ratios in gas

extracted during heating of a magnetic separate

of a Pacific red clay sediment. He also found

evidence of anomalous neon isotope ratios.

Bieri (private communication) has found much

smaller argon anomalies in one Pacific sample

and none in others. Schaeffer, Megrue, and

Thompson (1964) found no evidence of cosmogenic He8

 or Ne21 in magnetic concentrates

of sea sediments from several locations.

The work reported here was begun in the

hopes of confirming the results of Merrihue

and extending these results to other geographic

locations and to other mineralogical concentrates. This is a progress report on continuing

work.

Samples

A new magnetic separation was made by

Cassidy of the same Pacific red clay previously

399
400 STMPO8IUM ON METEOR ORBITS AND DUST

studied by Merrihue. This sample, designated BBD no. 1, is from 14°05' S latitude,

155°09' W longitude, and was collected from

the top of the sediment surface at approximately 2660 fathoms. Since no efforts were

made to homogenize the dredged material,

the small samples from which the different

magnetic fractions were separated may

represent somewhat different depths below

the sediment surface.

Other measurements reported here were made

on material collected by Langway in 1962 from

a tank in the water-supply system of Camp

Century in Greenland. The camp is located

t 77°10' N, 61°08' W at an altitude of 70000

feet, and about 145 miles from Thule. The

water-supply system of Camp Century consists

of steam-melted ice from the Greenland ice

sheet. The particulate matter used for the

studies described here was a fraction of that

collected from a 20,000-liter aluminum storage

tank through which an estimated 107 liters of

melted ice had passed (Langway and Fireman,

1965). This particulate material, collected by

Langway in 1962, was accumulated before

Langway and Fireman installed the filter

systems at the ice well. A more complete

description of the Camp Century water supply

has been published by Fireman and Langway

(1965).

Experimental

Half-gram samples were wrapped in aluminum

foil and given preliminary bakeout before

commencement of runs. For the sea-sediment

measurements the bakeout lasted 4 hours at

300° C; for the Greenland samples it was continued overnight at 150° C. The gas extraction and cleanup system was similar to that

described by Merrihue (1964), with a revised

furnace design.

The mass spectrometer was a 6-inch radius

glass machine, of 60° sector, similar to those

described by Reynolds (1956) and Schaeffer

(1959). It has electron multiplier detection,

but was used with no source magnet. Mass

discrimination was small, and optimum source

settings were essentially independent of mass.

Both spectrometer and sample system were

baked out. Spectrometer sensitivity and mass

discrimination were calibrated with 1/80 cc air

samples (enriched with He3), cleaned up with

the sample system. The absolute amounts of

gas are believed reliable to better than 40

percent.

It should be noted that, except for the He3

in the calibration spikes and the samples of

rare gases extracted from the sea sediments and

Greenland samples themselves, no anomalous

nor nonair rare gases had previously been run in

either the sample system or the spectrometer.

Spectrometer memory was thus minimized, and

any remote possibility of gas exchange with

meteoritic or other anomalous rare-gas samples

in the furnace or cleanup procedures was

completely eliminated.

Complete blank runs were made at several

temperatures before commencement of an actual

sample run. Gases were analyzed in three

fractions: helium and neon with all others condensed on charcoal with liquid nitrogen; argon

released from charcoal at dry ice temperatures;

and krypton and xenon released from charcoal

at room temperatures.

Since it was already expected from Merrihue's

work that no argon anomalies could be detected

in the ratios of the total gas extracted from the

magnetic fraction of sea sediments, aH samples

were degassed with successive 1-hour heatings

at increasing temperatures, with extracted gas

at each temperature purified and examined

with a mass spectrometer. The heating was

done with a radio-frequency induction heater.

Temperatures are approximate, being determined in some cases with both a thermocouple

sunk in a hole in the furnace and an optical

pyrometer, and in others with just the pyrometer, which looked directly down into the

interior of the furnace.

Argon results

SEA SEDIMENTS.—The results on two separate

magnetic samples of red clay are given in table

1. The argon released at low temperatures had

an Ar^/Ar36 ratio greater than that in air for

both samples. The apparent amount of radiogenic argon is the same for the two samples, in

spite of the differences in low-temperature

isotopic ratios. A potassium abundance of 1.28

percent was determined by flame photometry.

If we assume that all Ar38 in the temperature

fractions with Ar^/Ar39 ratios greater than in
SEPARATED FRACTIONS OF LOW ACCUMULATION-RATE DUST—TILLES

TABLE 1.—Argon in magnetic fraction of sea sediments

401

Sample

Magnetic sea

sediment - 1

Magnetic sea

sediment - 2

Weight (g)

0.51

0.50

2nd cleanup

Approximate

temperature (°C)

500

900

1200

1450

500

950

1200

1200

1400

AT" (lO-8 cm*

STP g->)

520

70

50

110

310

60

20

30

10

Ar"/Ar»«

472 ±17

311±9

198 ± 6

290 ±30

787 ±20

358 ± 16

194 ± 10

193 ±12

239±11

Ar»«/Ar»«

4. 95 ±0.32

5. 29±0.25

5.00±0.25

5. 15±0.4

4.98±0.3

4.7 ±0.6

4.88±0.53

4.85±0. 5

5.30±0.5

air is in fact air argon, we can calculate an

apparent potassium-argon age of about 40X10*

years for these samples.

All Ai^/Ar38 ratios were consistent with air

ratios.

The 1200° C fractions of argon from both

samples had Ar^/Ar8* ratios less than 200, and

the ratio for the 1400° C fraction of one of the

samples was about 240—still well below the air

ratio of 295.

The minimum observed value of Ati0IAiM,

which was 193 ±12, is slightly higher than

the value of 172 ± 5 observed at 1400° C by

Merrihue (1964), but our samples were a quarter

the size of Merrihue's, and hence the relative

contribution of blank air argon to our measurements is probably larger. Also, the efficiency

of separation for the two independent magnetic

concentrations may be different.

As a check on the possibility that our mass

36 peak included a contribution from something

other than argon (which could cause a spuriously low Ar^/Ar8

*), the 1200° C fraction of one

of the samples was recondensed onto charcoal at

liquid nitrogen temperatures and was stored

overnight while the spectrometer was

thoroughly pumped out. It was then given a

complete second cleanup over hot titanium

foil that had been degassed again at high

temperature while being pumped on. Following this second cleanup, the sample was readmitted to the spectrometer and remeasured.

Within the limits of error no change in ratios

was observed.

Our results for these measurements are compared in figure 1 with those of Merrihue. The

agreement is considered satisfactory, particularly in view of our smaller sample size.

These results confirm the anomalously low Ar40/

AT38 previously reported by Merrihue for a

similar sample.

GREENLAND DUST.—Encouraged by the good

agreement for the argon anomalies in the sea

sediments, we next turned to Greenland dust.

We initially studied the gases released from a

bulk sample that was untreated except for being

sieved to pass a 140 mesh screen. About an

order of magnitude more argon was found in this

material than in the magnetic sea sediments,

and Ar^/Ar38 ratios of nearly 5000 were measured. The argon was enriched in radiogenic

AT40 at all temperatures of release (table 2). A

potassium determination of 0.64 percent when

combined with the argon measurements gave

an apparent potassium-argon age of about

2.7 X109 years.

Since this value (with its associated uncertainties) seemed well within the possible age

range for Canadian shield rocks, and since there

are immense exposures of these rocks that could

provide a source for windblown mineral grains,

it was decided to try to remove the potassiumbearing material with a density separation.

A sample was centrifuged in methylene iodide

of density 3.2 g/cm3. About one-fifth of the

sample sank at this density. The heavy fraction was recentrifuged and was then subjected

to the same kind of gas extraction, purification,
402 SYMPOSIUM ON METEOR ORBITS AND DUST

800

700

600

500

400

300

200

\

Ar*7ArS6IN MAGNETIC FRACTIONS

OF PACIFIC RED CLAY

5 0 0 700 900 1100 1300 1500

TEMPERATURE (°C) OF 1 - HOUR HEATING

FIGURE 1.—Ar^/Ar" ratios in gas released from magnetic

separates of Pacific red clay during successive 1-hour

heatings. The solid line and black circles are the measurements of Merrihue (1964).

TABLE 2.—Argon in unseparaied Greenland material—/

«14 0 mesh)

Approximate

temperature

(°C)

500

950

1050

1150

1250

1650

Ar"

(10-» cm*

STP g-i)

7000

5200

1400

200

40

125

Ar«/Ar»

945

3340

4700

2050

1250

400

and mass spectrometxy as were the sea-sediment

samples.

The concentrations of Ar40 before and after

the density separation are given in figure 2.

The argon isotope ratios found in the dense

fraction are given in table 3 and figure 3. The

1200° C fraction released argon with Ar^/Ar36

of 228 ±5. After a complete second cleanup

this ratio was 232 ± 5, identical to the previous

value within errors. The Ar^/Ar38 ratio of this

temperature fraction was 5.21 ±0.08.

10

5xl03h

2xlO3

i o 3-

5*10* -

1

0

_ •

-

-

-

-

- ,

0

o

AMOUNTS OF Ar40

IN GREENLAND DUST

lO^cm'sTPg'1

1 1

1

o

•

1

1 1 1

o UNSEPARATED

• DENSE FRACTION

-

o

o

-

—

* _

50 h

20

10

5 ^

500 700 900 IIOO 1300 1500 1700

TEMPERATURE (*C)0F 1-HOUR HEATING

FIGURE 2.—Amounts of Ar40 in gas released from Greenland

dust during successive 1-hour heatings (10 " cm' STP

K"1)- Open circles: unseparated. Solid points: fraction

with density greater than 3-2.

TABLE 3.—Argon in Greenland material—t (denaity>3.t)

Approximate

temperature

500

800 • •

1000

1200*

1200 b

1200 •

1350*

1700

A T "

(10"» cm*

STP g->)

1200

480

480

—

96

101

6

- 1 0

Ar«/Ar"

320 ±1 5

576 ±4 3

471 ±1 9

238 ±1 5

228± 5

232 ± 5

308 ±2 8

350 ±3 0

Ar"/Ar»«

5.1 ±0.2

4.9 ±0.6

—

4.98±0. 4

5.05 ±0.15

5. 21±0. 08

4.5 ±1.2

—

• Small aliquot (~10 percent) of gas release for ratios;

b

 Rest of gas release;

• Rerun on mass spectrometer after overnight storage and complete

additional cleanup;

• This is lower than typical blanks at these temperatures.

The same kind of anomalous Ar^/Ar36 ratio

was therefore observed for the dense Greenland

material as for the magnetic sea sediments,

and at the same temperature. Although the

ratio was not so low as observed in the magnetic

sea sediments, the apparent concentration of

excess Ar3* and Ar38 is somewhat higher.

The measured potassium abundance of this

dense fraction was 0.14 percent, giving an
SEPARATED FRACTIONS OF LOW ACCUMULATION-RATE DUST—TILLE8 403

TABLE 4.— Upper limits for H&

500 800 1100 1400

TEMPERATURE CC) Of 1-HOUR HEATING

1700

FIGURE 3.—AH'/Ar** ratios in gat released from Greenland

dust fraction with density greater than 3.2 during successive

1-hour heatings.

apparent potassium-argon age for this material

of about a billion years.

Other rare gases

No evidence of anomalous XeIW was found.

Upper limits for He3 and Ne" were also determined. The He8

 values are given in table

4. These upper limits are consistent with

those determined by Schaeffer, Megrue, and

Thompson (1964). The Ne" upper limits

found in the magnetic fraction of the sea

sediment were consistent with measured

amounts found by Merrihue at comparable

release temperatures. The He3 upper limits

are much lower than the values reported by

Merrihue for comparable temperatures of

release from the magnetic fraction of the Pacific

red clay. The reason for this disagreement

is not clear. Our upper limit is essentially

determined by HD+ from hydrogen not completely cleaned up by titanium. Our preliminary bakeout of the magnetic sea sediments lasted for 4 hours at 300° C; Merrihue's

extended over 15 hours but at only 150° C.

However, Merrihue found He3 released after

an hour at 600° C, and twice as much He8 after

an hour at 1000° C. Since an hour at 600° C

had not released most of the He3 from his

sample, it is not expected that 4 hours at 300° C

would have done so from ours. There may be

real variations of He3 abundance from sample

to sample, although no large differences in

argon anomalies were found in the same

samples.

Sample

Magnetic sea

sediment - 1

Magnetic sea

sediment - 2

Greenland - 1

Greenland - 2

(density >3.2)

Weight

(g)

0.51

0.50

0.64

0.50

Approximate temperature

(°C)

500

900

1200

1450

500

950

1200

1400

500

950

1050

1150

1250

500

800

1000

1200

1350

He» (cm*

STP g-1)

<10-10

<8X 10-»

<8X 10-»»

<io-«

<io->«

<5XlO-»

<3X lO"11

<4X10"»

<5X10""

<6X 10-»

<8X10-"

<3X10-»

—

<7X 10-»

<4X10-">

<2X 10-"

<3X10-»

<2X10-»

Measurements of He4 and Ne" in the unseparated Greenland material and the dense

Greenland fraction are given in table 5.

In the gas released at 500° C from the dense

Greenland fraction, a He4/Ne* ratio of about

420 was found. This is similar to the estimated

cosmic-abundance ratio and to the values

observed in many gas-rich or "primordial gas"

meteorites; however, the contribution to this

ratio of radiogenic helium released at this

temperature is not known.

The apparent potassium-argon age of the

dense fraction is much less than the age of the

total sample. Yet the He4 concentration at the

lowest temperatures is higher in the dense

fraction than in the total sample, and the total

He4 concentrations are similar. Either there

is much more uranium and thorium in the

dense fraction than in the total sample, or

there is nonradiogenic helium in the dense

fraction. The former is possible, since minerals such as zircon are resistive, dense, and

high in uranium and thorium concentrations;

however, no evidence of such minerals was

seen in the X-ray powder pictures. The latter
404 SYMPOSIUM ON METEOR ORBITS AND DUST

TABLE 5.—He* and Ne*° in Greenland material (em3 STP g~

l

)

Sample

Greenland - 1

Greenland - 2 (p>3.2)

Temperature

(° C)

500

950

1050

500

800

1000

1200

He*

3. 3X 10-»

2. OX 10-«

<2X10~»

5. 2X 10-»

9. 4X 10-'

7X10-"

<ixio-8

Ne»

1. 7X10-*

2X10-»

ixio-»

1. 2X 10-"

7. OX 10-«

7X10-*

5X10-"

HeVNe*>

194

100

< 2

420

13

1

<0. 2

explanation seems more probable, but can only

be verified by uranium and thorium measurements.

Similar ratios of HeVNe20 for the magnetic;

sea sediments are suspect, since an order of

magnitude more high temperature He4 was

found in the first of the two samples than in the

second. The second sample, loosely wrapped

in aluminum foil, was in a side arm of the

furnace during the gas extractions from the

first sample, and was subjected to intense

radio-frequency discharge. It is possible that

such discharge may have released gas prematurely from the second sample and allowed

it to be measured as part of the gas from the

first sample. This may also explain the observed increase in argon concentration found

for the highest release temperature of the

first magnetic sea-sediment sample measured.

Such an increase was not observed for the

second sample. The possibility of such loss

also unfortunately weakens the reliability of

the He3 measurements in the second sea-sediment sample, although it cannot have affected

the measurements in the first sample.

Merrihue found at 600° C a ratio for HeVNe20

of 470, in a magnetic fraction of sea sediment,

similar to that observed at 500° C in our dense

Greenland fraction. He also found in the gas

released at 600° C and 1000° C more of both

He4 and Ne20 in the magnetic fraction of the red

clay than in the nonmagnetic fraction.

Too few samples have as yet been studied to

provide a strong demonstration of the presence

of excess He4 and Ne20. For both the sea

sediments and Greenland samples, however,

there is an indication of the presence of higher

concentrations of He4 and Ne20 in the dense or

magnetic material, and the observed ratio of

these two isotopes in the lowest gas release

temperature is similar to the "cosmic" ratio.

Determination of potassium-argon and uranium-helium ages in high-purity mineral concentrates should help distinguish radiogenic

helium from any excess helium that may be

present.

Mineralogy of samples containing anomalous

argon

Considerable effort has been devoted to determining the mineralogical composition of the

samples in which anomalous argon isotope

ratios have been observed. Mineralogical data

may help to explain the present observations,

and are in any case essential for further, more

complete concentration of individual mineral

fractions, which are required for future mass

spectrometric investigations.

W. A. Cassidy has estimated (private communication) that the abundance of the magnetic

material that he separated with a hand magnet

from the Pacific red clay is at least 4 percent of

that sample, with some additional material still

being removed with further separations. We

have made X-ray diffraction studies of several

size fractions of material separated magnetically

from another aliquot of this same barrel dredge.

We performed the size separations by settling in

0.002 N NH40H, and the magnetic separations

by using a Frantz Ferro-filter and varying

field-strength hand magnets.

X-ray diffraction powder photographs indicate that the Ferro-filter and Cassidy's handmagnet separations give crudely similar separation efficiencies and roughly the same assemblage of minerals, which includes magnetite,
SEPARATED FRACTIONS OF LOW ACCUMULATION-RATE DUST—TTLLES 405

ilmenite, augite, phillipsite, hypersthene, and

some glassy material. There is no evidence of

any major difference in mineral abundances

between a coarse-grained magnetic fraction (5

to 60 M for magnetite density) and a very finegrained magnetic fraction (less than 1.5 n for

magnetite density).

Essentially all of the dense Greenland fraction

appears, from X-ray diffraction studies, to be

magnetite and hematite; the sample is highly

magnetic.

The one mineral apparently common to

anomalous argon-bearing samples from both

Greenland and the Pacific is magnetite. It

sooms probable that the anomalous argon must

be present in magnetite from both locations.

However, our current data do not exclude its

presence in more than one mineral, or in minerals undetectable in X-ray studies of the

present concentrates. Mass spectrometry on

much purer mineral concentrates will be required to verify these possibilities.

Furthermore, the lack of detection of anomalous argon in nonseparated bulk samples of

these materials cannot be considered as evidence

for its nonpresence in nonmagnetic fractions, for

the only nonmagnetic or bulk samples studied to

date have in all cases been assemblages of

minerals including a much larger total of radiogenic argon, which would tend to mask any of

the kind of anomalous argon isotope ratios so

far found in the magnetic or dense fractions.

Here again, more extensive mineral separations

are required.

Discussion

The only confirmed isotope anomalies in finegrained material suspected to include an extraterrestrial component are the apparent presence

of excess Ar36 and Ar38 released at high temperatures. The minimum amount of excess Ar36

can be calculated by assuming that if the Ar40/

Ar36 ratio is observed to be greater than that

in air, the argon is a mixture of contemporary

air argon and radiogenic argon from decay of

potassium, and if the Ar^/Ar36 ratio is observed

to be less than that in air, the argon is a mixture

of contemporary air argon and excess Ar38 and

Ar38, with no radiogenic Ar40. Minimum

amounts of excess Ar36, derived in this way,

are given in table 6. All observed ratios of

Ar36 to Ar38 are consistent with air ratios.

It is seen that the apparent minimum concentrations of excess Ar38

 are similar for the

magnetic fractions of the Pacific red clay and for

the dense fraction of Greenland dust. This

approximate agreement of measurements on

samples collected from two extremely different

environments and from two very distant locations on the earth's surface suggests that we

are dealing with a worldwide phenomenon.

The most obvious similarity in these separate

collections is that both come from locations of

very low total accumulation rate of dust, sediment, and debris from all terrestrial and extraterrestrial sources combined.

The accumulation rates in the red clay areas

of the South Pacific are of the order of 1 mm of

sediment per 1000 years (Sackett, 1964; Goldberg and Koide, 1962) corresponding to about

2X10"* g cm"2 yr"1, so that if the measured

magnetic fraction had an abundance of 4 percent it would have an accumulation rate of the

order of 8X10"' g cm"2 yr"1.

The Greenland tank collection corresponds

to a total accumulation of 1.5 X10"8 g cm"2 yr"1

(Langway and Fireman, 1965), although this

is a minimum value since the overall collection

efficiency is not known. The corresponding

minimum accumulation rate for the dense

Greenland fraction is 3X10"7 g cm"2 yr"1.

Both the magnetic Pacific and dense Greenland materials are, of course, mixtures of unknown proportions of terrestrial and extraterrestrial materials.

TABLE 6.—Minimum AT** excess per gram* (units: 1O~10

cm* STP g~

l

)

Sample

Sea sediments (magnetic

fraction)

Sea sediments (magnetic

fraction)

Sea sediments (magnetic

fraction)

Greenland dust (dense fraction)

Concentration

7

8

6

9

Reference

Merrihue

This work

This work

This work

•Assuming (1) all Ar" is air whenever Ar"/Ar*<air ratio; (2) no excess

A.r» whenever Ar"/Ar*>air ratio.
406 SYMPOSIUM ON METEOR ORBITS AND DUST

Since all of the identified minerals in the

anomalous samples measured are of widespread

occurrence on the earth's surface, and since the

argon isotope ratio has probably changed with

time both within the earth and in the earth's

atmosphere, the question of whether these

observed argon anomalies are terrestrial or

extraterrestrial in origin must be critically

examined. The lack of confirmation of the

presence of He 3 underlines the importance of

such an examination.

There are, in principle, four ways in which

samples of anomalous rare gas with isotope

ratios different from those of the present atmosphere might be produced or incorporated into

terrestrial rocks or minerals: (1) radioactive

decay: e.g., He* and Ar40, fission xenon; (2)

nuclear reactions: e.g., of neutrons, alpha

particles, cosmic rays; (3) trapping of a sample

of ancient atmosphere; and (4) solidification in

the presence of gases from incomplete outgassing

of the interior of the earth itself.

We will not discuss (1) and (2) further here

as they do not appear capable of accounting

for the observed anomalous argon.

If the atmospheric Ar40/ArM ratio has increased as a function of time, then a sample of

an ancient terrestrial atmosphere would have

Ar^/Ar38 lower than the contemporary value.

If sedimentary material had cemented together

in the presence of atmospheric gases sufficiently

tightly so that it did not lose its trapped-gas

content, and had then melted a t depths in the

earth a t high temperature, again in a gas-tight

environment, some minerals might have incorporated samples of the rare gases in an

ancient atmosphere; however, this model places

severe constraints on the age of the minerals in

the sediments and on their potassium content.

The minerals will contribute excess radiogenic

AT4 0, which will be mixed with the ancient

atmosphere before solidification from the melt,

thus masking any lower-than-contemporary

AT4 0 /AT3 8 ratios. It also places severe constraints

on the inherited argon from within any other

part of the gas-tight region of magma.

An alternative possibility for sampling an

ancient atmosphere may be submarine extrusive vulcanism at great depths in the oceans.

This process would solidify minerals in contact

with very high hydrostatic pressures, and the

argon dissolved in the ocean (Bieri, Koide, and

Goldberg, 1964), which would be in equilibrium

with the argon in the atmosphere, might be

forced into solidifying mineral lattices. Samples

of ancient deep-seated submarine extrusive

rocks, if obtainable, might enable us to investigate this problem. At present this explanation

seems unlikely because of the findings of the

anomalies in material from Greenland. With

the known great difficulty in finding or obtaining samples of truly ancient submarine rocks,

the surface of the ice in Greenland appears

an unlikely place to discover such samples.

There exists in principle another way of

eliminating some terrestrial origins for the

argon anomalies. Let us assume that the

ratio of Ax^/Ar38 in the atmosphere or in the

ocean is a function of time, given by the ratio

of the independent functions of time describing

Ar*°(0 and Ar 3 8 ^). Then

Ar40

(ti) Ar*«0 )

If we denote present time by tt and the time of

solidification of an old mineral by to, we have

the ratio R:

295

Ar40

Ar38 tto) A r 4 0 ],

yX

A T 3 6 ] ,

A T 3 8 ] 4.5X10 yn

If we assume that Ar40 is outgassed on the

average fairly rapidly after its formation from

K

40

, we can use the K40 decay constant as a

degassing rate as well, and have

Ar40]4 S X I Q » l _

where T is the contemporary potassium-argon

age corresponding to solidification at UThe time dependence of Ar38

 is a function of

the history of the atmosphere assumed. Two

reasonable limits may be: (I) constant from

some time early in the earth's history (Suess,

1949), and (II) increasing linearly with time

(Tilles, 1965).
SEPARATED FRACTIONS OF LOW ACCUMULATION-RATE DUST—TILLES 407

We have, then, for these two cases,

(I)

(ID

.5X10 yr»

X109yr. 4.5 X10 9

and assembling these factors we get

(I) 5 = J

r i-e-xaixioP) -|r4.5V10'-7n

" |_1_€-x(4.«xio»-r,J|_ 4.5 X109 J

Although these expressions are dependent on

the model of outgassing of Ar40 assumed, they

are not critically so for young potassium-argon

ages and can be modified to take account of

more realistic models.

If we now consider a mineral of potassiumargon age T that incorporated a sample of

terrestrial atmospheric or oceanic argon in its

structure when it crystallized, we can calculate

the value of ArA0/AiM expected for this "inherited" argon. If this ratio agrees with the

observed ratio of the anomalous component,

this type of terrestrial origin is supported.

Let us use the apparent potassium-argon age

(109 years) of the dense Greenland fraction to

demonstrate this calculation. By substituting

and solving, we have for (I), 5=1.09 and for

(II), 5=0.85. The observed value for 5 =

295/232=1.33 at 1200° C for this sample.

A more striking case is that of the magnetic

fraction of the sea sediment with a potassiumargon age of about 40 million years. In this

case, for both (I) and (II) the model value of 5

is within a percent of unity. Yet the observed

value is 5=295/195=1.51. This difference is

larger than the uncertainties in model atmospheric ratios, or potassium-argon age determinations. It also shows no correlation of

magnitude of anomaly with apparent potassiumargon age.

Several of the uncertainties that might affect

the comparison of model and observed ratios

will increase the discordancy. These include

the following: (1) any radiogenic Ar40 that is

released at the temperatures where the anomalous argon is observed (the rapidly decreasing

Ar40 concentrations as the temperature of release is raised suggest that this may well be

significant and may reduce the apparent Ar40/

AT38 anomaly from the actual); (2) any dilution

by contemporary air blanks; and (3) any inherited excess Ar40

, such as is found in beryls,

pyroxenes, etc., will also, of course, reduce the

magnitude of the apparent anomaly.

Thus, this type of analysis argues against an

inherited terrestrial origin for these anomalies.

It is possible, however, that part of the potassium in the magnetic sea sediment is in "zeroage" terrestrial minerals in the surface sediments

(phillipsite, for example) and that the real potassium-argon age of that fraction of the sample

containing the anomalous argon is older. In

such a case the usefulness of the above analysis

is reduced.

Samples of terrestrial rocks that have inherited significant amounts of their initial complement of cosmic gases are currently unknown.

Measurements of terrestrial rocks (Butler, Jeffery, and Reynolds, 1963) suggest that primordial xenon has been at least substantially

outgassed from the earth. Argon would be

expected to be more completely outgassed than

xenon.

Terrestrial natural gases are enriched in Ar40

relative to air (Zartman, Wasserburg, and

Reynolds, 1961; Wasserburg, Mazor, and Zartman, 1963; Clarke and Thode, 1964). Certain

minerals have been found to inherit excess argon

(Aldrich and Nier, 1948; Damon and Kulp,

1958; Hart and Dodd, 1962). These include

beryl, cordierite, tourmaline, and pyroxenes.

All evidence to date indicates that the inherited

argon is highly enriched in radiogenic Ar40; however, only total gas has usually been measured,

and not that released as a function of temperature.

Through investigations of argon in fluid inclusions in quartz and fluorite Rama, Hart, and

Roedder (1965) and Lippolt and Gentner (1963)

also have found gas with Ar^/Ar38 ratios greater

than in air.

Keevil, Joliffe, and Larsen (1942) and Cherdyntsev (1961) have reported evidence of inherited excess helium in some terrestrial magnetite samples. Argon has not yet been
408 SYMPOSIUM ON METEOR ORBITS AND DUST

studied in known terrestrial magnetites; we

are planning such studies.

The arguments against terrestrial origin of

the anomalies can be summarized as follows:

1. No terrestrial samples with Ar^/Ar38

ratios less than in contemporary air have ever

been observed.

2. Terrestrial samples known to be rich

in excess or inherited argon are generally also

rich in radiogenic argon, with high Ar^/Ar36

ratios.

3. Tentative comparison of potassiumargon ages of minerals containing anomalous

Ar^/Ar36 with model atmospheric ratios leads

to differences.

However, further experimental studies of

known terrestrial samples with differential gas

release as a function of temperature are desirable.

We consider next extraterrestrial mechanisms

of origin. No conclusive evidence for the presence of cosmic-ray or energetic solar-flare

particle-produced spallation isotopes in these

anomalous samples has been found to date.

The Ai^VAr38 ratio in the 1200° C dense Greenland fraction can be used to place an upper

limit on the amount of cosmogenic argon in the

sample with the highest measured amount of

anomalous gas. The limit is less than 1 percent

of the total Ar36 released at 1200° C, or less than

4 X10"" cm3 STP g-1. This is lower by a factor

of 102 to 104 than the amounts of spallation

argon found in iron meteorites, and is consistent with the lack of any positive evidence in

this work and in that of Schaeffer, Megrue, and

Thompson (1964) for the presence of spallation

He3 or Ne21.

Since much of the spallation argon in finegrained material will be produced by energetic

particles interacting with iron, its production

rate in small particles exposed to solar flares is

probably not radically different from that in

meteorites exposed to cosmic rays. We then

make three extreme assumptions:

1. There has been no loss of spallation

argon by diffusion or recoil.

2. All of the dense Greenland material is

extraterrestrial.

3. The density of the individual particles

before atmospheric entry was 8, and their composition was pure iron.

With these assumptions and our argon

measurements we can calculate an upper limit

for the exposure time of the dust and compute

an average-sized particle corresponding to a

Poynting-Robertson limited lifetime.

The calculated exposure time is 0.1 X 10s

years; for material spiraling in from 3 a.u. this

lifetime, if limited by the Poynting-Robertson

effect, corresponds to an average size of 20 ».

It is also of interest to note that this is roughly

the size below which dense grains can enter

the atmosphere without melting, and above

which they will melt and ablate. Thus, larger

grains, which would have longer lifetimes in

space and greater concentrations of spallationproduced gases, will not be expected to survive

entry intact and will probably be degassed

during atmospheric entry.

The calculation is in a sense an academic one,

since the assumptions, while as precise as any

others that might be made at this time, are

certainly unrealistic; however, it does serve to

demonstrate that the lack of cosmogenic argon

is not an extraordinary surprise, and serves

also as a useful reminder of the expected

difficulty of searching for long-lived radioactive

isotopes in the probably briefly exposed dust

grains.

Merrihue (1964) suggested the possible contributions of stopped solar-wind or solar-flare

ions to the gas content of extraterrestrial dust.

I have noted that if small particles are exposed

in space for lifetimes limited by the PoyntingRobertson effect, they will accumulate, embedded in their surfaces, an amount of solar

gas per gram that is independent of density or

of size distribution (Tilles, 1965).

For material arriving at the earth from a

distance of Ao a.u., and assumed bombarded by

a radially decreasing solar-wind flux of Wo

atoms cm"2 yr"1 at 1 a.u., this concentration

is 107 Wo In Ao atoms per gram. Estimates for

solar-wind flux, argon abundance in solar wind,

and dust-grain origin give about 5X10~3 cm3

Ar^-rAr38 per gram of extraterrestrial dust.

This concentration is 107 times that observed.

A combination of circumstances may account

for this factor:

1. We may be measuring material heavily

diluted with terrestrial contaminants.
SEPARATED FRACTIONS OF LOW ACCUMULATION-RATE DUST TILLES 409

2. Solar-wind atoms will mainly be very

shallowly embedded and may be almost entirely

lost during atmospheric-entry heating. Only

some kind of high-temperature Maxwellian

tail of the initial distribution may remain to be

released at temperatures of 1000° C or above.

3. If the present grains had any coating

of volatile or organic material while in space,

the stopped solar-wind atoms would almost

entirely be in this coating, which may be

vaporized or burned coming into the atmosphere.

4. The surfaces of grains may have been

slightly etched during storage in the ocean or

water tank prior to sample collection.

5. Gas may be lost from grain surfaces

by sputtering in space, or by diffusion either in

space or during terrestrial storage and prebake

of experiment.

6. Our derived minimum values may

significantly underestimate the excesses of Ar38

and Ar38 present.

7. The lifetimes of small particles in

space may be limited by other perturbations

than the Poynting-Robertson effect, and may

be much shorter than calculated (Shapiro,

Lautman, and Colombo, see p. 359).

8. The grain surfaces, which are expected

to be highly reduced in space by solar-wind

protons, may lose most or all of their shallowly

implanted rare gases on oxidation during

atmospheric entry or terrestrial storage.

For all of these reasons, the disagreement

between estimated source intensity and measured values cannot be used as evidence against

the existence of the solar-wind atmospheric

source, although it does suggest that the solar

wind is probably not the source of the noble gas

anomalies in dust observed to date.

It is of interest to note that with an extraterrestrial dust influx rate of 2X10~7

 g cm"2

yr"1 averaged over the earth's surface for 4.5

X109 years, solar wind embedded in small

grains appears capable of providing for one-fifth

of the present atmospheric Ar38 and Ar38 abundances (Tilles, 1965). However, this calculated figure assumes no loss in space, which is

certainly unrealistic. Sputtering alone may

result in important losses for grains of micron

size and larger, with the fraction of gas retained

inversely proportional to density and radius

of grains.

As an alternative to a solar-wind source,

stopping of solar-flare ions, as has been observed

with satellite material in the cases of He3 and H3

(Schaeffer and Zahringer, 1962; Fireman,

DeFelice, and Tilles, 1961; Tilles, DeFelice,

and Fireman, 1963), might also provide Ar38

and Ar38 excesses.

Solar-flare ions, having much higher energies

than solar-wind ions, will be stopped more

deeply and uniformly in grains in space. They

are thus more likely to be observed at high

release temperatures.

Lai and Venkatavaradan (1965) have recently

found Al28 in sea sediments. They conclude

that cosmic-ray spallation of atmospheric argon,

ablation of chondrite meteorites, and galactic

cosmic rays bombarding extraterrestrial dust

are all inadequate to account for the observed

activity of Al26. They calculate, however, that

if: (1) 10* tons/day of extraterrestrial dust falls

on earth, (2) this dust has chondrite composition, and (3) the dust particles are in space long

enough for the establishment of secular equilibrium concentrations of Al28

, then a flux of 20

solar-flare protons cm"2 sec"1 averaged over the

dust particles' orbits and having an energy >10

Mev would account for the observed Al28

activities. To the extent that the average lifetimes in space are in fact shorter, this flux is

increased.

If the ratio of argon to protons in the flare

stream is 2X10"8—an assumed cosmic abundance we have used already (Tilles, 1965)—then

the observed excess Ar36 and Ar38 in the anomalybearing samples of sea sediment and Greenland

dust can be accounted for by the stopping of

the same intensity of solar-flare ions as is

required to produce the Al28 by spallation.

We can state this same fact in another way.

The 20 flare protons cm"2 sec"1 required by Lai

and Venkatavaradan is a flux lower by 107 than

the expected solar-wind flux at 1 a.u. But our

anomalous Ar38 and Ar38 concentrations are

themselves lower by a factor 107 than that

expected from the solar-wind source.

Of course, because of terrestrial dilution, uncertainty in dust lifetimes in space, and the

possibility of gas loss, the precision of this

agreement is certainly fortuitous. Nevertheless, both the amount and observed release

temperatures of the anomalous argon, and to
410 SYMPOSIUM ON METEOR ORBITS AND DUST

a first approximation the He4 and Ne20 also,

seem in much better agreement with what is

expected for stopped solar-flare ions2 than for

stopped solar-wind ions.

Finally, it is possible that extraterrestrial

material such as cometary matter may have

incorporated rare gases into its structure during

its early history of condensation and solidification (Urey, 1952a, b).

Thus there seem to be plausible explanations

for the argon anomalies if the samples contain

extraterrestrial material. No terrestrial origins

seem probable.

The only mineral found with X-ray diffraction in both kinds of anomalous samples is

magnetite. It is of interest to suggest that

magnetite is a plausible form in which to expect

extraterrestrial iron. Magnetite is abundant

in Renazzo, a meteorite suggested by Wood

(1963) to be very primitive, and magnetite

(or trevorite) is a major constituent of Type I

carbonaceous chondrites (Mason, 1962). Magnetite spherules, believed to be extraterrestrial,

are often suggested to be the result of atmospheric ablation of meteoritic metal. It is

possible that magnetite may be the stable

chemical form of iron in a suitably fractionated

solar gas (Studier, Hayatsu, and Anders, 1965)

at low temperatures, which might be typical

of the environment from which comets formed.

In such a case magnetite ablation spherules

might be only a small fraction of the extraterrestrial magnetite arriving at the earth.

If it can be conclusively demonstrated that

the argon anomalies are not terrestrial in origin,

these anomalies then provide a delicate probe

for investigations elucidating the detailed

physical and chemical characteristics of extraterrestrial dust on earth, and perhaps

indirectly, of comets.

Summary

We have confirmed the argon anomalies reported by C. M. Merrihue for a magnetic

fraction of Pacific red clay in other samples of

this barrel dredge of sediment. We have

found similar argon anomalies in a dense sample

of participate matter from Greenland. There

is no evidence of cosmogenic He3 or Ar38 in

'This source is more fully discussed by the author in a paper in preparation. Note added in proof: This paper has since been published in

Science, vol. 153, pp. 981-864,1066.

these samples. The only mineral detected in

samples from both environments is magnetite.

Comparison of model atmospheric argon ratios

with observed anomalous ratios and potassiumargon ages argues against a terrestrial explanation for the anomalies. The presence of

extraterrestrial dust is probably the explanation

of the anomalies, and there exist several

mechanisms to account for anomalous argon in

extraterrestrial material.

Acknowledgments

I am deeply indebted to Dr. Craig M. Merrihue

for many helpful discussions and for technical

assistance. His pioneering work in this field

opened many new possibilities. His recent

death is a very great personal tragedy for those

who knew him, and a major scientific loss.

I should also like to thank Drs. W. A. Cassidy

and C. C. Langway, Jr., for providing samples,

and Dr. O. A. Schaeffer for assistance in the

construction of our mass spectrometer. Dr. G.

Arrhenius provided invaluable guidance in

mineralogy of sea sediments, and many

stimulating comments. I also thank Mrs. U. B.

Marvin, who assisted in some of the X-ray work,

and R. Werby, who did the potassium analyses.

Financial assistance was provided by the

National Science Foundation, Grant G-16067.

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4 1 2 SYMPOSIUM ON METEOR ORBITS AND DUST

Abstract

Anomalous isotope ratios have been found in argon released at 1200° C (following successive heatings at lower

temperatures) from magnetically separated fractions of a Pacific red clay sea sediment and from a density separated

(p>3.2) fraction of Greenland dust. The minimum values of Ai-^/Ar" found in the sea sediment were 198±6 and

194 ±10 and in the Greenland material 230 ±5 . Ratios of AH'/Ar18 were consistent with air ratios, with a value of

5.21 ±0.08 for the Greenland temperature fraction containing the greatest amount of anomalous argon. Amounts

of excess Ar»», relative to air, varied from 5 to 10 X 10~10 cm* STP g->. The measurements confirm Merri hue's earlier

argon results on the Pacific red clay, and extend them to material from Greenland, demonstrating that the argon

anomalies are a worldwide phenomenon. No evidence of cosmic-ray or solar-flare-produced spallation argon nor

of solar-wind or solar-flare-imbedded He1 was observed. X-ray studies indicate that the one mineral detectable

in both Pacific and Greenland anomaly-bearing samples is magnetite. Arguments against a terrestrial origin for

the argon anomalies are presented, and possible extraterrestrial mechanisms that might account for them are reviewed.

U.S. GOVERNMENT PRINTING OFFICE : 1967-O-240-022