Smithsonian

Contributions to Astrophysics

VOLUME 7

PROCEEDINGS OF THE SYMPOSIUM

ON THE

ASTRONOMY AND PHYSICS OF METEORS

Held at

SMITHSONIAN ASTROPHYSICAL OBSERVATORY

Cambridge, Massachusetts

August 28-September 1, 1961

Sponsored by

Smithsonian Astrophysical Observatory, Cambridge, Mass.

and

Geophysical Research Directorate,

Air Force Cambridge Research Laboratories,

Office of Aerospace Research, U.S. Air Force.

Coordinated by

Wentworth Institute, Boston, Mass.

SMITHSONIAN INSTITUTION

Washington, D.C.

1963
Publications of the Astrophysical Observatory

This series, Smithsonian Contributions to Astrophysics, 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 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 we have common interests.

Another series is Annals of the Astrophysical Observatory. It was started

in 1900 by the Observatory's first director, Samuel P. Langley, and has been

published about every 10 years since that date. These quarto volumes, some

of which are still available, record the history of the Observatory's researches

and activities.

Many technical papers and volumes emanating from the Astrophysical

Observatory have appeared in the Smithsonian Miscellaneous Collections

Among these are Smithsonian Physical Tables, Smithsonian Meteorological

Tables, and World Weather Records.

Additional information concerning these publications may be secured

from the Editorial and Publications Division, Smithsonian Institution,

Washington, D.C.

FBED L. WHIPPLE, Director,

Astrophysical Observatory,

Smithsonian Institution.

Cambridge, Mass.

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington 25, D.C. - Price $2.75
Contents

Session 1

Welcoming address: Col. Ernest A. Pinson, USAF 3

Limitations of radar techniques for the study of meteors: J. S.

Greenhow 5

The initial radius of ionized meteor trails: B. L. Kashcheyev and

V. N. Lebedinets 19

The initial diameter of meteor trails: G. S. Hawkins 23

The relation between visual magnitudes of meteors and the durations

of radar echoes: B. A. Lindblad 27

Radio-echo measurements of meteor mass distributions: A.A.Weiss . 41

A preliminary report on radar meteor counts: P. M. Millman and

B. A. Mclntosh 45

The Harvard radio meteor project: G. S. Hawkins 53

Meteor rates observed by radio-echo techniques during the IQY-IGC

period: B. L. Kashcheyev and K. V. Kostylyov 63

The orbits of meteor streams determined by radio-echo techniques:

B. L. Kashcheyev, V. N. Lebedinets, and M. F. Lagutin . . 67

Session 2

The distribution of small interplanetary dust particles in the vicinity

of Earth: C. W. McOacken and W. M. Alexander 71

Micrometeorite measurements from Midas II (Satellite 1960 f 1):

R. K. Soberman and L. Delia Lucca 85

Micrometeorite collection from a recoverable sounding rocket.

I: R. K. Soberman, C. L. Hemenway, T. G. Ryan, S. A.

Chrest, J. Frissora, and E. F. Fullam 89

Micrometeorite collection from a recoverable sounding rocket.

II: C. L. Hemenway, R. K. Soberman, E. F. Fullam, J. J.

Balsamo, J. Cole, D. Hallgren, P. Yedinak, A. Goodman, and

G. Hoff 93

Micrometeorite collection from a recoverable sounding rocket.

Ill: R. K. Soberman and C. L. Hemenway 99

Rocket and satellite studies of meteoric dust: T. N. Nazarova . . 105

Cosmic dust showers by direct measurements: M. Dubin, W. M.

Alexander, and O. E. Berg 109

Discussion: 115

Session 3

A general survey of meteor spectra: P. M. Millman 119

Meteor spectra with high dispersion: Zd. Ceplecha and J. Rajchl . 129

A short note o n meteor spectra wit h low dispersion: J . Rajch l .. . 15 5

Spectrographic observations of meteors in U.S.S.R. in 1967-1960:

E . N . Kramer , K . A . Liubarsky , an d V . I . Ivaniko v ... . 15 7

in
Page

Diffusion effects observed in the wake spectrum of a Geminid

meteor: I. Halliday 161

On the frequency of occurrence of the auroral green line (5577A) in

Perseid spectra: J. A. Russell 171

Session 4

Negative ion s and luminosit y i n meteor trains: T . R . Kaise r ... . 17 5

Luminosit y from large meteoric bodies: H . J. Alle n an d K . K .

Yoshikawa 181

Preliminary notes on some results of photographic multiple meteorite

fall of PHbram: Zd. Ceplecha 195

Results from an artificial iron meteoroid at 10 km/sec: R. E. McCrosky

and R. K. Soberman 199

Luminous efficiency of iron and stone asteroidal meteors: A. F. Cook,

L. G. Jacchia, and R. E. McCrosky 209

Meteor ionization and the mass of meteoroids: D. M. Lazarus and

G.S.Hawkins 221

Statistical verification of the physical theory of meteors: B. J. Levin

and S. V. Majeva 229

On the color index of meteors: J. Davis 233

Image-orthicon photographs of meteors: J. Spalding, G. Colter,

C. L. Hemenway, J. A. Cole, and J. F. Dugan 237

Meteoritic erosion in space: F. L. Whipple 239

The absence of magnetic micropulsations of meteor origin: C. Ellyett

and G. B. Gillion 249

Session 5

The density distribution of telescopic meteors around the earth's

orbit: L. Kresak and M. Kresakova 253

Atmospheric trajectories of telescopic meteors: L. Kohoutek and

J. Grygar 259

Statistics of meteor streams: R. B. Southworth and G. S. Hawkins . 261

Orbital elements of photographic meteors: P. Babadjanov 287

On the structure of the 5-Aquarid meteor stream: A. K. Terentjeva . 293

Masses of Comet Giacobini^Zinner and the Draconid meteor stream:

Y. V. Yevdokimov 297

Dynamical evolution of the Perseids and Orionids: R. B. Southworth 299

A note on the cometary nature of the Tungus meteorites: V.

Fessenkov 305

A short note on the origin and age of the Quadrantids: S. E. Hamid

and Mary N. Youssef 309

Abstracts of other papers 313

IV
PROCEEDINGS OF THE SYMPOSIUM

ON THE

ASTRONOMY AND PHYSICS OF METEORS

Welcoming Address

By Col. Ernest A. Pinson, USAF *

It is my great pleasure to extend a welcome

to this distinguished assembly on behalf of the

Geophysics Kesearch Directorate of the Air

Force Cambridge Research Laboratories. We

are pleased to be associated with the Smithsonian Astrophysical Observatory in cosponsoring

this symposium, and with the Wentworth

Institute as coordinating agency. Our longstanding interests in astrophysics are emphasized this week in this symposium and in

another international astrophysical symposium

on the Solar Corona, which we are sponsoring

at Cloudcroft, N. Mex., during this same week.

The latter is Symposium No. 16 of the International Astronomical Union.

The U.S. Air Force is interested in studies

that can be applied to the solution of specific

problems of the space environment. However,

we fully recognize that theoretical and experimental studies that appear, on the surface,

only to increase knowledge of our universe

invariably lead to useful applications and solutions of specific problems.

As most of you know, the last international

meteor physics symposium was held at Jodrell

Bank in 1954. A brief examination of the

proceedings of that symposium reveals the

tremendous growth in meteor measurement and

observation techniques that has taken place

during the past few years. This meeting is

the first opportunity for people specializing in

meteor physics to gather at an international

symposium to discuss measurements made

above the earth's atmosphere. The advent of

rocket and satellite vehicles has opened tremen1

 Vice commander, Air Force Cambridge Research Laboratories.

dous potentialities for research in this field.

A good example of new opportunities for controlled experimentation is the recent artificial

meteor experiment, which will be discussed in

detail during the meeting.

Meteor physics experiments have now become

global in nature, requiring ever greater cooperation among world scientists. It is encouraging

to note that international cooperation in this

field is flourishing; information is being exchanged on a personal basis and appears in the open

literature as soon as it has been reduced and

analyzed. Our fervent hope is that such

cooperation will continue and even increase.

In this regard, I am happy to offer the use of

any space available on our research vehicles to

worthy meteor experiments that may be

forthcoming.

The extent and degree of international

cooperation that may soon be required is

illustrated by our consideration of the possibility of using a ground-based network of

photographic and radio observations of natural

meteoric phenomena for determining highaltitude winds and densities.

Briefly, the 1954 symposium spoke in terms

of local, ground-based meteor studies, and of

international cooperation. Soon, the meteor

physicist will be unrestricted—within our

solar system—as to mode and place of observation. International cooperation is therefore

even more essential.

May I again extend the greetings of the Air

Force Cambridge Research Laboratories and

our best wishes for a fruitful and provocative

exchange in this important area of research.

3

Limitations of Radar Techniques for the

Study of Meteors

By J. S. Greenhowl

Radar techniques are widely used for the

study of the physics and astronomy of meteors,

and observations of echoes from the ionized

trails have also been used as a tool for the

study of the upper atmosphere. Various scattering theories have been developed that give

the amplitudes and durations of the radar

echoes in terms of the ionization densities in

the trails, the ambipolar diffusion coefficient,

and the parameters of the equipment.

Although it was realized that departures

from the simple theories would occur at very

high frequencies (Eshelman, 1956), it has been

assumed hitherto that there are no serious

limitations at frequencies of a few tens of

Mc/sec. In view of recent work on the initial

radii of the ionized trails (Greenhow and Hall,

1960a,b) and the loss of electrons by attachment processes (Davis, Greenhow, and Hall,

1959), it is now apparent that even at frequencies as low as 20 Mc/sec serious deviations

from theory occur. The deviations are of

sufficient magnitude to introduce very considerable uncertainties into much of the previous meteor work concerned with measurements of linear electron density and of mass

and velocity distributions, and with investigations of upper atmospheric pressure and scale

height.

The probable errors arising in each of the

above measurements made with typical radars

operating at frequencies of about 5 to 600

Mc/sec are the subject of this paper. Only

the case of backscattering will be considered.

»Dr. Greenhow died in November 1962. At the time of this

symposium he was associated with Royal Radar Establishment,

Malvcrn, England.

The scattering theories

Linear electron densities less than 1012 cm'1.—

When the linear electron density a is less than

approximately 1012 cm"1, the scattering equation derived by Lovell and Clegg (1948) is

appropriate, where the received power to at

time t=Q after the formation of the trail is

given by

W e2 V .. „. W J watts '

 (1)

where P is the peak transmitted power; 6 the

aerial gain; X the wavelength; R the range; e the

electronic charge; m the electronic mass; and

c the velocity of light.

The echo amplitude decays exponentially in

the manner

A=Ao exp (- (2)

where AQ is the initial amplitude, and D the

ambipolar diffusion coefficient (Herlofson,

1947).

Linear electron densities greater than 1013

cm~

l

.—In the case of the "over-critically dense"

trails with a>1012 cm"1, giving rise to long

duration echoes, the scattering equations given

by Greenhow (1952a) can be applied, where

\mc2)

(3)

with em the maximum received power.

The echo duration TD, determined by the

time for the effects of diffusion to reduce the

electron density n, on the axis of the trail below

the critical density ne, is

(4)

638805—63 2
6 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Departures from the scattering theories.—A

number of simplifications are made in the

derivations of equations (1) to (4), and more

rigorous solutions, taking account of polarization and plasma resonance effects, have been

given by Kaiser and Closs (1952). The modifications to the echo amplitude are only of the

order 2 for certain values of a, and as we will

be discussing departures from the simple

scattering theories that are of several orders of

magnitude, these refinements need not be

considered. These very large departures from

theory are due to the effects of finite velocity,

the initial trail radius, and the loss of electrons

by attachment.

First, it is assumed in the derivation of

equations (1) and (3) that the meteor trail

is formed instantaneously, and that the echo

is obtained from a complete Fresnel zone of

radius (.KX/2)1. A sufficient condition for

this in the case of a<1012 cm"1 is that the

meteor should reach the end of the first Fresnel

zone before the ionized column at the beginning of the trail has diffused to a radius of

X/2*-, or

^ (5)

where V is the meteor velocity.

In the case of a>1012 cm"1, the condition is

that the meteor should reach the end of the

first Fresnel zone before the electron density

on the axis of the trail at the beginning of the

zone falls below ne, or

The effects of finite meteor velocity on the

echo characteristics have been computed by a

number of workers (Eshelman, 1956; Loewenthal, 1956; Hawkins, 1956). As the appropriate values for V and D for a given meteor are

usually known approximately, the magnitude

of the effect can be determined. Although the

reduction in echo amplitude or duration may

be large, there is no particular wavelength or

height at which these reductions become

catastrophic.

The second important assumption made in

the derivation of the scattering equations is

that the initial trail radius r, is small compared

with X/2TT. When a<1013 cm"1, this condition implies that all the electrons in any cross

section of the trail scatter in phase. When

rt is finite, the echo intensity given by equation

(1) is reduced by a factor

7,=exp [2(27rr</X)2]. (7)

When r<=X/2ir, the reduction in intensity is

only 9 db and the corresponding reduction in

echo amplitude is a factor of 2.7, giving rise

to a similar error in the determination of a.

This is equivalent to approximately one stellar

magnitude in the corresponding visual scale,

and can be regarded as the maximum acceptable uncertainty in a. An increase in r, or a

decrease in X by a factor of only 3, however,

increases the attenuation to almost 80 db,

introducing an error of 10* in a. Thus, once

the initial trail radius reaches the order of

X/2ir, this effect quickly assumes overwhelming

importance, and the echoes from such trails

become virtually undetectable.

In the case of an "overdense" trail, equation

(3) can be applied if the initial trail radius is

sufficiently small so that the electron density

is greater than ne on the axis of the trail at

zero time, or

(8)

The effect of increasing rt above this value will

ultimately cause the echo to appear as if it

were from an underdense trail, with a much

reduced amplitude and value of a.

Third, while the echo decay times from underdense trails given by equation (2) are less than

about 1 second for most practical values of X

and D, equation (4) readily permits echo

durations of several hundred seconds for bright

meteors. With times greater than a few

seconds, the loss of electrons by attachment

to neutral oxygen molecules is found to be

more important than the effects of diffusion

(Davis, Greenhow, and Hall, 1959), and it has

been shown that the echo duration given by

equation (4) may be in error by several orders

of magnitude. Thus values of a determined

from the echo duration will be liable to these

large errors. The choice of suitable radar

parameters for observing these bright meteors

will be considered in this paper.
METEOR SYMPOSIUM—GEEENHOW

The height variation of trail radius, attachment function, and meteor velocity

Previously the tacit assumption had been

made that most meteors ionize in a fairly

narrow band of heights centered about 95 km,

an assumption apparently supported by the

radio observations. However, it was overlooked that this concentration in heights may

be due primarily to the failure of radars to

detect the ionized trails at heights much above

100 km. Recent work (Greenhow and Hall,

1960b) has now shown that even with equipment of moderate sensitivity, the majority of

echoes above 100 km should be observable if

the effect of initial trail radius is negligible.

However, echoes above 100 km are not detected

in large numbers because of the effects of the

large trail radii.

As radar observations are widely used for

studies of the astronomy and physics of meteors, it is of considerable interest to investigate

the effects of the finite initial radius on the

observations. In order to carry out this investigation, we must construct models for the

variation of the height of maximum ionization

with meteor velocity and linear electron density, and for the variation of trail radius and

attachment time constant with height. This

construction involves a considerable degree of

extrapolation from the limited experimental

evidence available, but the extrapolations must

be carried out before the results of previous

experiments can be assessed, and further experiments planned.

The model jor the variation of meteor heights

with Vand amax.—Measurements of the variation

of height of occurrence with meteor velocity

and the maximum linear electron density amax

have been reviewed by Greenhow and Hall

(1960a). Between values of amax from about

10" to 1018 cm"1, and velocities of 15 to 70

km/sec, the height variation of the point of

maximum ionization agrees approximately with

that derived from the theoretical relation

(9)

where pm*, is the atmospheric density at the

point of ernnx.

The curve for a^^lO1* cm"1 in figure 1

has been determined from a balance between

1.3 1.4 1.5 1.6

LOG V (km/MC)

FIGURE 1.—The model adopted for the variation of the mean

height of maximum ionization for meteors of various am»»

and F.

the Super-Schmidt camera observations of

faint visual meteors with amM^lO1* cm"1

(Hawkins and Southworth, 1958), and some

low frequency radar observations of meteors

with amax~5X10u cm"1 (Greenhow and Hall,

1960b). This curve has been taken as a standard, and curves for other values of a,n«x have

been obtained by extrapolation from equation

(9). The curves in figure 1 give only the mean

height of amax for a given velocity, and in any

velocity group there is a spread of observed

heights about this mean value of about ±.H,

where H is the atmospheric scale height.

Rocket Panel (1952) density gradients have

been used in the extrapolations.

The height variation oj r<.—The only available

measurements of the initial trail radius for

meteors with am»x

<O0lt

 cm"1, with which we
8 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

are primarily concerned, are due to Greenhow

and Hall (1960b). These measurements were

made on meteor trails with values of amax between 10" and 1012

 cm"1 at heights between

90 and 115 km; it has therefore been necessary

to extrapolate to greater heights over a further

25 km in order to include all values of V and

«m»x given in figure 1. The extrapolation has

been carried out with a reference value of

T{= 140 cm at a height of 98 km, adopting the

experimentally determined relationship

r,ocp~ (10)

This value of r< at a height of 98 km is several

times greater than Manning's (1958) theoretical

estimate of 14 ionic mean free paths, although

it agrees approximately with Opik's (1955)

value. Both theories, however, predict a more

rapid height variation of the form r>

1ocp~1

.

A variation of this type would have an even

more catastrophic effect on the radar observations of meteors than that discussed in the

following paragraphs.

The attachment time constant.—The parameter

of importance for the effects of attachment is

the attachment time constant 7^=l//3ri0, where

j8 is the two-body attachment coefficient, and

n0 the density of particles capable of forming

negative ions. There is a possibility that threebody attachment is the relevant mechanism at

meteor heights (Greenhow and Hall, 1961) when

Ty=l/ynona; y is the three-body attachment

coefficient; and na is the density of particles

effective in the collision processes.

Values of To or TV=50 sec at a height of

95 km, based on the measurements of Davis

et al. (1959) have been assumed, again using

Rocket Panel density variations to extrapolate

to other heights.

The effects of finite trail radius upon the

radar observations of faint meteors

The measurement of linear electron density.—

Equation (1) is generally used to determine the

linear electron densities in meteor trails from

a measurement of the echo amplitude and from

a knowledge of the equipment parameters.

However, any observations carried out in the

region where r,>X/2x are of doubtful value, as

errors of several orders of magnitude in a may

readily be introduced. Curves of the attenuation in the theoretical echo due to finite r{

, for

meteors of velocity 15, 30, and 60 km/sec occurring at their most probable heights are therefore given in figure 2. The curves are drawn

for reductions in intensity up to 80 db, for a

selection of frequencies greater than 5 Mc/sec.

That such high attenuations may occur we can

deduce from some very high frequency observations (see p. 12); beyond this point we would

expect that departures from an assumed radial

gaussian distribution of electron density would

eventually become significant in determinations

of echo intensity.

The horizontal broken lines in figure 2 show

where r1=X/2?r, and the selection of a suitable

operating point should be restricted to the region above this line. For a velocity of 60

km/sec, it can be seen that 20 Mc/sec is the

highest frequency that can reasonably be used

to observe meteors with amax down to 1012 cm"1.

At 40 Mc/sec the echo amplitudes for trails with

this value of amax are already 100 times below

the predicted values. The position becomes

much worse for very faint meteors with amax in

the region from 108 to 1010 cm"1, where even

at 20 Mc/sec the echo amplitude is 1000 times

below the expected value. In order to observe

these meteors, we would need to use a frequency

between 5 and 10 Mc/sec.

Decay-type echoes due to fast meteors with

linear electron densities apparently of the order

of 1011 to 1012 cm"1 are observed at frequencies

at least as high as 70 Mc/sec. However, these

echoes are very probably due to overdense trails

with a of the order 1013 cm"1, but with such

large initial radii that the electron density on

the axis of the trail is already below the critical

density (Greenhow and Hall, 1960b, para. 5b).

The situation improves for meteors of smaller

velocity that ionize lower in the atmosphere;

for V=15 km/sec, a frequency of 50 Mc/sec

would be suitable for observing meteors with

«m»x~1012 cm"1, and 20 Mc/sec for trails with

<w~10 8 cm"1 (fig. 2a).

Measurement of velocity distributions: the fraction of meteors observed.—The effects of finite

trail radius on echo amplitude will have a

marked influence upon the observed distributions of meteor velocities, which will differ considerably from the true curves. It is difficult
METEOR SYMPOSIUM—GREENHOW 9

to predict the exact way in which the velocity

distributions will be modified, as this will depend upon the shape of the height distributions

that are centered about the mean heights given

in figure 1, and also upon the mass distributions.

The following attempt has therefore been made

to deduce the fraction of meteors in each velocity group that will be observed, for two limiting

equipment sensitivities.

The number distribution of meteor trails as

a function of a is generally assumed to be of

the form

N(a)daoca-'da. (11)

Although the value of s for faint meteors is

not known accurately (p. 11), it is likely to

be of the order 2, and in this case equations

80

(11) and (1) predict that the number of echoes

of given amplitude observed with any equipment is inversely proportional to the amplitude. Accepting this proportionality, and assuming no spread in heights for meteors in a

given velocity group, we find that the fraction

of the true numbers of meteors in each velocity

group that are actually observed will be of

the order ij*.

The variation of this fraction, expressed as

a percentage of the true numbers, is given in

figure 3 for various frequencies and values of

amin- (amin is the minimum value of a that

can be detected with a given equipment,

assuming equation (1) to be valid.) It can be

seen that when amin~10u cm"1, about 85

percent of the slowest meteors are seen at

5Mc/sec

10 Mc/sec

db

20

40

60

80

\

\80 Mc/sec

\

\40 Mc/sec

\

b \

10" IOI10°

10" 10 IOe

(a)

FIGURE 2.—The reduction in echo intensity over that predicted for an infinitely narrow meteor trail, due to the

effects of the finite initial trail radius, a, F=\5 km/sec;

h, T=30 km/sec; c, F=60 km/sec. Ordinates: 10 log10ij

(db). Abscissae: linear electron density On.^cm"1).

20

6 0

80

___--_^r__35 Mc/sec

10 Mc/sec

10" 10"
10

5 Mc/sec

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

i.o

5 Mc/sec

FIGURE 3.—The fraction of the true number of meteor trails with a^>amia which give detectable echoes, as a function of meteor

velocity and frequency, a, For a theoretical limiting sensitivity of ami,,"" 10" cm"1. Experimental points: x,36 Mc/sec; o,17

Mc/sec. b, For a theoretical limiting sensitivity oi amiui*»\0P cm"1.

/=20 Mc/sec, but only 15 percent of those

with velocities of 70 fan/sec. These percentages improve at lower frequencies, but decrease

tof1

amm {ELECTRONS/em)

FIGURE 4.—Curves giving the maximum usable frequency /

for the reliable observation of meteors of velocities IS, 30,

and 60 km/sec, as a function of ammx.

very rapidly as the frequency increases. Thus

at 80 Mc/sec the echo rate for velocities of

15 km/sec would be 10 percent of the true

rate, falling effectively to zero « 1 percent)

for velocities greater than 30 km/sec.

The form of these curves has been verified

at frequencies of 17 and 36 Mc/sec (Greenhow

and Hall, 1960b); the experimental points are

shown in figure 3a. There is reasonable agreement with the theoretical curves. Figure 36

is an extrapolation to a lower limiting linear

electron density of approximately 108 cm"1,

when it can be seen that a frequency of only

5 Mc/sec would be required to give a reasonably

accurate velocity distribution.

These results are summarized in figure 4,

where the maximum usable frequency is

shown as a function of a and V. The criterion

ri<X2r has been taken as the limiting condition under which acceptable observations can

be made.

Measurement of velocity distributions: The

effect of finite meteor velocity.—An effect not

previously taken into account in deriving the

echo attenuation curves is that of finite meteor

velocity, since this factor, although it may be
METEOR SYMPOSIUM—GBEENHOW 11

large, will generally be negligible in comparison

with the effects of trail radius. However,

finite velocity limitations will mean that even

if large reductions in echo amplitude due to

the finite initial radii could be tolerated, the

echoes might not show the diffraction effects

that enable us to determine meteor velocities.

Curves given by Loewenthal (1956) show

that the zone formation is effectively smoothed

out when the expression c, given by

(12)

is less than about 0.5, at which point the reduction in echo amplitude is about 2.7 greater

than that given by equation (1). With this

criterion, the areas under the broken curves

in figure 2 define the regions in which meteor

velocities would become indeterminate. This

condition is also indicated by the broken lines

in figure 4.

Meteor mass distributions.—Determinations

of the s in equation (11) have been made by

measuring the distribution of meteor echo

amplitudes, on the assumption that the scattering equation (1) is valid. This exponent is of

considerable interest as it can be related to the

meteor mass and magnitude distributions; it

would appear that sensitive radars could be

used to extend the measurements of the mass

distribution from the faintest photographic

meteors (about + 3 absolute magnitude,

aw~6X10 i a cm"1) to about +15 magnitude

(amax~108 cm"1). This method has been used

by a number of workers, and values of s lying

within the range s—2±0.2 are usually found,

irrespective of radar wavelength or equipment

sensitivity. In view of the effects of finite

initial trail radius, we must therefore consider

the significance of these measurements.

As an example of the results obtained if this

method is used, the differential numberamplitude distributions for two entirely different radars working at the very low frequency

of 32 Mc/sec (Greenhow and Watkins, unpublished) and the very high frequency of

500 Mc/sec (Barber, Sutcliffe, and Watkins,

1962) are illustrated in figure 5. The limiting

sensitivities of the two equipments, obtained

by substituting the equipment parameters in

equation 1, were amta~2X1010 and 108 cm"1

respectively. The slopes of the best straight

lines in figures 5a and 5b correspond to values

of «=1.85 at 32 Mc/sec, and s=2.0 at 500

200 100 90

NUMBCR OF ECHOES

20 »

NUMBER OF ECHOES

FIGURE 5.—Number/amplitude distributions for echoes observed at frequencies of 32 Mc/sec and 500 Mc/sec Ordinates: Echo

amplitude A (arbitrary units~receiver noise). Abscissae: Number of echoes with amplitudes >A. a, f— 32 Mc/sec; limiting

theoretical sensitivity a m | n ~ 2X 1010 cm"1, b,/=500 Mc/sec; limiting theoretical sensitivity omM««'10l cm"1.
12 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

,oV

ECHO RATE (No/IO

FIGURE 6.—Number/apparent linear electron density distributions. Ordinates: Apparent linear electron density.

Abscissae: Echo rate from trails with apparent linear

electron densities ><*. An approximate absolute scale is

given, where "No" is the number of echoes observed per

10* km * in the plane 100 km above the earth per hour.

Mc/sec in reasonable agreement with previous

measurements for sporadic meteors.

However, when the absolute echo rates on the

two equipments are compared, an anomalous

situation arises. A value s==2 implies that if

similar areas of sky are illuminated by the aerial

beams, then the echo rate with an equipment of

amta^lO8 cm"1 should be 200 times the rate

when ami,, is only 2X1010 cm"1. In fact, when

corrections are made for the different polar

diagrams, the observed echo rate on the 500

Mc/sec equipment is found to be only about

0.2 times the 32 Mc/sec rate (fig. 6), a deviation

by a factor 103 from the expected rate at the

apparent value of s. Thus it is clear that the

curve AB in figure 6 cannot represent the true

distribution of values of a in the region

108<a<109 as the lines AB and CD should be

colinear. This is not surprising in view of the

expected effects of trail radius. Similarly,

the 32 Mc/sec curve CD will not represent the

true distribution, as the majority of meteor

trails in the appropriate electron density range

are not detected. The measured values of «,

using radars at frequencies greater than 5 to

20 Mc/sec, cannot therefore be interpreted as

giving a measurement of the meteor mass or

electron density distributions. Instead, equation (11) with s~2 must be regarded only as an

empirical relationship that shows that for a

given radar, more small echoes will be detected

than large ones.

Echo rate as a function of wavelength.—For

equipments with the same theoretical limiting

sensitivity, the echo rate will decrease rapidly

because of the differential effects of a finite

trail radius. The observed echo rate for meteor

trails with a apparently greater than 10"

cm"1, where a is determined from the echo

amplitude and equation (1), is shown as a

function of radio frequency in figure 7. The

points for 17, 36, and 69 Mc/sec are from

Greenhow and Hall (1960b), while the points

for 300 and 500 Mc/sec are derived from the

observations of Barber, Sutcliffe, and Watkins

(1962). It can be seen that the observed echo

rate falls from 0.4 of the true rate of f=17

Mc/sec, to only 0.01 at 100 Mc/sec, and to

0.00001, at/=500 Mc/sec. This is an extremely

rapid variation, giving an approximate f~z

dependence of echo rate between frequencies of

30 and 500 Mc/sec.

At frequencies significantly greater than

100 Mc/sec, it is unlikely that the echoes

detected are from underdense meteor trails

with a<1012 cm"1. The few echoes that are

observed are more likely to be due to overdense trails whose amplitudes have been drastically reduced. In the case of the 500 Mc/sec

observations with amin~108 cm"1, for example,

the echo rate is only about 10~8 of the true value.

Thus it is probable that the echoes actually

FREQUENCY (Me/Me)

FIGURE 7.—Observed echo rate as a function of frequency, for

equipments that have the same theoretical sensitivity based

on equation (1). The observed rate for «>10 n cm"1 is

shown as a fraction of the estimated true rate.
METEOR SYMPOSIUM—GREENHOW 13

II 10 9

c (ELECTRONS em'1

)

FIGURE 8.—The predicted mean heights (AB) and R.M.S.

height spreads (CD, EF) for meteors with F=4 0 km/sec as a

function of linear electron density. Experimental points:

O, 36 Mc/sec; x, 69 Mc/sec; • , 17 Mc/sec (Greenhow and

Hall, 1960b, and unpublished observations); D, 300 Me/see;

• , 500 Mc/sec (Barber, Sutcliffe, and Watkins, 1962.

recorded are from trails with a^lO13 cm"1,

which are about 105 times less numerous than

those with a~108 cm"1, and whose intensities have been reduced by about 80 db below

the predicted values. Further evidence for

this supposition is given by the echo heights,

discussed in the following section.

The height distributions of echoes.—In addition to affecting the number counts and velocity

distributions, the trail radius effects will cause

the observed height distributions to differ

markedly from the true curves for meteors of

given V and amax. As an example, the expected variations of mean height and R.M.S.

height spread, for meteors of velocity 40

km/sec, are given in figure 8. Some measured

values of the mean heights for various apparent

values of a, and at a number of widely spaced

frequencies are also shown. Thus at 36

Mc/sec a decrease in a from 1013 to 10" cm"1

produces little change in the mean height of

the echoes, although it should have increased

by about 12 km. On the other hand, an

increase in mean height for a given apparent

value of a is observed as the frequency decreases. Thus the mean height of the observed

echoes is seen to rise from 95 to 103 km as the

frequency decreases from 69 to 17 Mc/sec.

This result supports the view that faint radio

meteors ionize at the predicted heights, but

that at high frequencies the radar echoes are

not detected because of the departures from

the simple scattering theory.

The 300 and 500 Mc/sec observations of

Barber, Sutcliffe, and Watkins (1962) are

extreme examples of the suppression of echoes

from faint meteors at their most probable

heights of occurrence. The observed mean

heights are 89 at 300 Mc/sec and 90 km at

500 Mc/sec, 35 km below the expected heights

for meteors with a~10s cm"1. It is therefore

apparent that the echoes that do occur at these

frequencies must be from trails with a^,1013

cm"1, which ionize near an altitude of 90 km.

This would also be consistent with the low echo

rates that are observed.

The radar observations of bright meteors

(«m-»>1012 cm"1)

Effect of attachment.—Three important errors

arise in the use of equations (3) and (4) for

the study of meteor trails of high linear electron

densities: (i) the loss of electrons by attachment processes becomes important, so that

diffusion is not the major factor in determining

echo duration; (ii) the large initial trail radii

may cause the initial volume electron densities

to be less than the critical value; and (iii)

distortion of an initially linear trail by irregular

winds may cause multiple reflections from

widely spaced centers. The effects of winds

on the trails have been studied in detail elsewhere (for example, Greenhow, 1952 a,b;

Greenhow and Neufeld, 1959; Manning, 1959)

and will not be considered further in the present

paper.

From the method discussed by Davis,

Greenhow, and Hall (1959) to allow for the

effects of attachment, the echo duration from

the point of maximum ionization is shown as a

function of frequency and amax, for several

meteor velocities, in figure 9. Figures 9a-c
14

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

10" to-

, (ELECTRONS cm"1)

FIGURE 9.—Echo durations from the

points of maximum ionization as a

function of frequency and amBX allowing

for the effects of attachment, a—c are

for a two-body attachment process

with F=15, 30, and 60 km/sec respectively; d is for a three-body attachment

process with F«=30 km/sec. AB, CD,

EF, GH, JK show where the echo

durations are reduced to er

l

, 10"1,10~*,

10"3, and 10~4 of the values expected

considering diffusion alone; xy shows

where the effects of the finite initial

trail radius become important.

(ELECTRONS cm'1)
METEOR SYMPOSIUM—GREENHOW 15

(ELECTRONS em"1)
16 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

are for a two-body attachment process, and

figure 9d is for a three-body reaction.

Let us consider figure 9c for V=30 km/sec

as typical of meteors of average velocity.

The series of lines A3 B3, C3 D3, etc., shows

the points where attachment reduces the echo

duration to e~

l

, 0.1, 0.01, etc., of the value

expected considering the effects of diffusion

alone. Below A3 B3, equation (4) can therefore

be regarded as applicable for all points along a

given trail when echo duration is proportional

to aX2D~x. Above A3 B3, the echo duration

increases very slowly with increasing a, and

indeed in some cases the echo duration for

a very bright meteor can be less than that

from a fainter trail ionizing at a greater height.

Thus at a frequency of 20 Mc/sec, for example,

a trail with a^i^lO1 4 cm"1 gives an echo duration of about 25 seconds from the point of

maximum ionization. Increasing amax to 1016

cm"1 increases the echo duration to only 30

seconds, instead of to the 3X10* seconds expected

from diffusion theory. For such trails, of course,

the longest enduring echoes would normally be

obtained from some height above the region of

maximum ionization, and curves showing the

magnitude of this effect have been given by

Davis et al. (1959).

For comparison, the effects of a three-body

attachment process for a meteor velocity of

30 km/sec are shown in figure 9d. The echo

durations are still further reduced, causing the

line A4 B4 to move to lower values of duration

for a given amM.

It is clear that the influence of attachment on

echo duration can be so large as to render the

duration of little value for the determination

of a. In order to measure the electron densities in the trails of bright meteors, we would

need to observe in the region below lines such

as A B, where the normal diffusion equation

can be applied. Thus no single wavelength

can be used to observe the full range of possible

values of a. Precise measurements of height

might be of assistance, but even so the correction factors can be so large, and the precise

nature of the attachment effects so uncertain,

that it is doubtful if any significant improvement would be gained.

Effect of finite initial trail radius.—The value

of linear electron density at which the initial

trail radius is such as to cause the initial axial

electron density to be less than the critical

value for trails with amax>1012 cm"1 are shown

by the curves X! yi, x2 y2, etc., in figure 9.

Thus, for V=30 km/sec it can be seen that at

frequencies above 40 Mc/sec the echoes from

overcritically dense trails will begin to assume

the characteristics of decay-type echoes. However, as the initial radii of the ionized columns

will necessarily be >X/2?r, the echo intensities

will be very much reduced. At frequencies of

300 to 600 Mc/sec for example, trails with

linear electron densities as high as 10" cm"1

may be undercritically dense initially. As the

trail radii are of the order of 1 meter (~10X/2ir),

the reduction in echo intensity given by equation (7) is enormous (~800 db). In this case,

it is probable that the echo intensity will be

determined by some second-order reflection

mechanism, such as partial reflection from the

sharp boundary in ionization near the meteor

itself. Such echoes would have the same

general amplitude-time characteristics as those

from low electron density trails under conditions

of extremely rapid diffusion (Eshelman, 1956).

The two classes of echoes will therefore become

indistinguishable.

Thus, in order to make satisfactory observations of overcritically dense meteor trails, we

would need to select an observing frequency

such that the operating point lies within the

region defined by areas similar to ABxy in

figure 9. Simultaneous measurements of two

wavelengths would also be of great value in

determining whether factors other than diffussion were affecting the observations.

References

BARBER, D.; SUTCLIFFE, H. K.; AND WATKINS, CD.

1962. Some observations of meteors and aurorae

at 300 and 500 Mc/s using a large radio

telescope. Journ. Atmosph. Terr. Phys.,

vol. 24, pp. 585-597.

DAVIS, J.; GHBENHOW, J. S.; AND HALL, J. E.

1959. The effect of attachment on radio echo

observations of meteors. Proc. Roy.

Soc. London, ser. A, vol. 253, pp. 130-139

ESHELMAN, V. R.

1956. Short wave length radio reflections from

meteoric ionization. I. Theory for low

density trails. Stanford Univ. Contract

AF 19(604)-1031, Rep. No. 5.
METEOR SYMPOSIUM—GREENHOW 17

GREENHOW, J. S.

1952a. Characteristics of radio echoes from meteor

trails. III. The behaviour of the electron trails after formation. Proc. Phys.

Soc. London, vol. 65B, pp. 169-181.

1952b. A radio echo method for the investigation of

atmospheric winds at altitudes of 80 to

100 km. Journ. Atmosph. Terr. Phys.,

vol. 2, pp. 282-291.

GBEBNHOW, J. S., AND HALL, J. E.

1960a. The variation of meteor heights with

velocity and magnitude. Monthly Notices Roy. Astron. Soc, vol. 121, pp.

174-182.

1960b. 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.

1961. Attachment processes in meteor trails.

Journ. Atmosph. Terr. Phys., vol. 21,

pp. 261-271.

GREENHOW, J. S., AND NEUFELD, E. L.

1959. Turbulence at altitudes of 80-100 km and

its effects on long-duration meteor echoes.

Journ. Atmosph. Terr. Phys., vol. 16,

pp.384-392.

HAWKINS, G. S.

1956. Radar echoes from meteor trails under

conditions of severe diffusion. Proc.

Inst. Radio Eng., vol. 44, p. 1192.

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.

HERLOFSON, N.

1948. The theory of meteor ionization. Phys.

Soc, Rep. Progr. Phys., vol. 11, pp.

444-454.

KAISER, T. R., AND CLOSS, R. L.

1952. Theory of radio reflections from meteor

trails. I. Phil. Mag., ser. 7, vol. 43,

pp. 1-32.

LOEWENTHAL, M.

1956. Meteor echoes from underdense trails at

very high frequencies. TR Technical

Report 132, Lincoln Laboratory, Massachusetts Inst. Techn.

LOVELL, A. C. B., AND CLEGG, J. A.

1948. Characteristics of radio echoes from meteor

trails. I. The intensity of the radio

reflections and electron density in the

trails. Proc. Phys. Soc London, vol.

60, pp. 491-498.

MANNING, L. A.

1958. The initial radius of meteoric ionization

trails. Journ. Geophys. Res., vol. 63,

pp.181-196.

1959. Air motions and the fading, diversity, and

aspect sensitivity of meteoric echoes.

Journ. Geophys. Res., vol. 64, pp.

1415-1425.

OPIK, E. J.

1955. Meteors and the upper atmosphere. Irish

Astron. Journ., vol. 3, pp. 165-181.

ROCKET PANEL

1952. Pressures, densities, and temperatures in

the upper atmosphere. Phys. Rev., vol.

88, pp. 1027-1032.

Abstract

A brief review of the basic theories concerning the scattering of radio waves from the ionized trails produced

by meteors is given. Some of the fundamental assumptions used in the derivation of the various scattering equations

are discussed, and are shown to be incorrect.

Although it has been realized that the simple picture of an initially narrow trail would break down at very high

frequencies, it is now apparent that the initial radius can be an appreciable fraction of a wavelength even at frequencies as low as 20 Mc/sec. This effect has a profound influence on the observation of meteors fainter than about

+ 4 absolute visual magnitude.

The second major cause of the breakdown of the scattering theories is the loss of electrons by attachment processes, in addition to ambipolar diffusion. This effect can be serious in the case of long duration echoes, associated

with meteors brighter than about +2 magnitude, and the predicted echo durations may be reduced by several orders

of magnitude.

It is shown that much of the previous work on the determination of linear electron densities in meteor trails,

and the measurements of meteor mass distributions, velocity distributions, and upper atmospheric pressures and

scale heights, is in error. The interpretation of future radar observations of meteors must be treated with considerable caution.

The Initial Radius of Ionized Meteor Trails

By B. L. Kashcheyev * and V. N. Lebedinets *

Atoms evaporating from the surface of a

meteoroid possess energies as high as hundreds

of electron-volts. The resulting meteor trail

rapidly diffuses outward until the atoms lose

their cosmic energy. From the diffusion equation, the trail radius r for a time t after the

meteor has traversed a given point is:

1/2

where D is the coefficient of diffusion, N is

number of collisions, and X is the mean free

path. As X depends upon the velocity of the

N

meteor, in the above formula 23 M should be

*-o

substituted for iVX2, where X* is the mean free

path after the kth. collision. Then

l/2

(1)

From their quantum-mechanical computations, Massey and Sida (1955) found four values

for the cross section of diffusion Qd for collisions of atoms of Ca and Ne possessing various

values of energy E. They proposed an approximation of Qd{E), which is, however, too

complex for mathematical computations. A

better form of approximation is:

(2)

which does not differ greatly from that proposed by Massey and Sida for high values of

energies, and gives the right value of Qd under

normal temperatures.

Experimental evidence (Massey and Burhop,

1952) indicates that for collisions between

ions and atoms of neon and argon, respectively, in the range of meteoric velocities the

following relationship holds true:

<&«4.5&. (3)

According to Loeb (1934), for normal temperatures the relationship is about the same.

Hence in Qd(E) diffusion cross section depends

upon the value of energy in about the same

manner as it does in the case of neutral particles.

From equation (2) the mean free path of

ions can be expressed in the form:

where Xo is the mean free path of atmospheric

molecules, and V is the velocity of the particles

colliding. For the case when the masses of

ions and of atmospheric molecules are equal,

F=1.4X10~6 sec/cm, and <7=1.8X10s cm/sec.

Under the above condition, after one collision

an ion retains on the average two-thirds of

its initial velocity. The velocity of an ion

after N collisions is given by the formula

Vff=Voe-«»> (5)

where a=0.4.

From equations (1), (4), and (5), we obtain

"Kharkov Polytechnics! Institute, U.S.S.R.

(6)

The number of collisions before a thermal

equilibrium is reached is

where Va is the mean velocity of atmospheric

molecules.

19
20 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

The initial radius of a meteoric ionized

trail is

Values of r0/Xo for meteors of various velocities

are given in table 1. On the average, the

initial radius is found to be about 1.5 times

greater than the first mean free path of the

ions.

The time elapsed between two successive

N and N-\-1 collisions is given by the expression:

The time taken for N collisions is

(8)

The time of initial expansion is given by the

equation:

to=t(NQ)=F(- In &+-K^) X.«3.

(9)

where Xa is in centimeters and t0 is in seconds.

The initial radius is practically reached after

fewer than No collisions and <o~5XlO~6Xa.

The initial radius of an ionized meteoric

trail can be determined by simultaneous

radio-echo observations at two different wavelengths. As shown by Dudnik, Kashcheyev,

and Lebedinets (1961), the ratio of the maximum amplitudes of echoes reflected from an

under-dense meteor trail at wavelengths \i and

X2 is:

(10)

TABLE 1.—Values of ro/X» for meteors of various

velocities

Velocity Vo

(km/sec)

r A

10

2.4

20

4.2

30

6.0

40

7.8

50

9.7

60

11.5

70

13.3

A=

FX3/2

All other notations are conventional.

From equation (10) we obtain the equation:

In Ax—In 1,

 P<2 1 G

h

G

'\ 3 , Xi_, p(AQ

Ot2GT2 2 m X 2

 m p(A,)

During the measurements made at the

wharkov Polytechnical Institute in 1960, the

Kavelengths used were Xi=8 meters and X2=4

meters. Identical 5-element director antennas

were employed. In order to equalize the

effective sensitivities of the equipments, the

output power of the transmitter at X2=4 meters

was twice as great as its counterpart at Xj=8

meters, and the sensitivity of the receiver was

also somewhat higher. During the observations the powers and the frequencies of the

respective transmitters were continually recorded. Calibration markers enabled the amplitudes to be expressed in terms of microvolts.

The identity of the patterns of the two antenna

systems was checked experimentally.

Analysis of the errors made in measuring

the various quantities in equation (10) showed

that the relative errors in the determination of

r0 are as follows:

3ro= * - when r o< 0.6 m>

o=~~£- when r0>0.6 m,

(ID

where r0 is in meters.

The errors of measurement increase with

greater values of r0, since amplitudes of echoes

at X2=4 meters are in such cases lower. From

equations (11) it should be plain that for the

case considered, measurements could be made

only where O.5m<ro<lm. The errors for

the two extreme values of r0 are 24 and 11

percent. Hence, when two wavelengths are
METEOR SYMPOSIUM—KASHCHEYEV AND LEBEDINETS 21

used for measurements, only a narrow range

of values of r0 can be measured, and a quantitative relationship between r0 and heights

cannot be obtained.

The most complex consideration in measurements of this type is the determination and

selection of meteor trails to which equation (10)

is applicable. For over-dense trails equation

(10) must give ro=O. For intermediate-density

trails equation (10) gives values of r0 that are

less than real if ro^>^->^-; or greater than real if

ro<i~-y^- The appearance of the amplitudelo/Xj

time curves could not provide a means for determining whether a trail is under-dense or has

an intermediate density. A new criterion has

been introduced by Dudnik et al. (1961) to determine whether or not equation (10) is applicable in a certain case. The quantity A was

determined for Xi=8 meters in two ways, first,

from the ratio of the amplitudes of echoes at

the moments of the first and the second maxima, and second, by measuring V, R, and D.

These two values of A must be equal only for

those cases where the following requirements

are fully met: (a) linear electron density does

not vary considerably within several principal

Fresnel zones, and (b) electron density in the

trail is so low that only first-order scattering

on every electron may be taken into account.

As it is on these considerations that equation

(10) is based, we can deduce that the agreement of the two values of A indicates the

applicability of equation (10).

The application of this criterion sharply decreased the scatter of values of r0 with respect

to D and V, and also narrowed the range of

the values of D and V where the measurements

of r0 are possible. The values of r0 were measured for 39 trails. The average values are:

ro=8O cm, Z>=6.4 m2/sec, and F=32 km/sec.

From equation (7), with V=32 km/sec, we

obtain

ro=Xa.6.4«29X1.

From the above theory, for ro=8O cm and

22=6.4 m2/sec, we have

X,=2.75 cm.

20

20 30 40 50

V{ Km/sec)

FIGURE 1.—The ratio of the initial radius of a meteoric

ionized trail to the mean free path of the ions plotted

against the velocity of the colliding particles.

The value of X, can be found from the value

of the coefficient of ambipolar diffusion D:

Assuming that M=2 9 and T=220° , we find that

Xt=2.4 cm.

Thus, theoretical and measured values are in

good agreement.

Figure 1 shows a plot of ro/X< against velocity deduced from the above theory. For simplicity of comparison with the theory, it is

assumed that, with Z?=6.4 ma/sec, X4=2.75 cm.

Although the scatter of the points of figure 1

is considerable, the measurements show a high

degree of dependence of r0 upon meteor velocity. A graphic confirmation of the fact that

V greatly influences r0 is that at Xa=4 meters

no meteors were observed whose velocity would

be V^>50 km/sec, and whose trail would be

under-dense for Xx=8 meters.

Similar measurements of r0 at X!=17 meters

and X2=8 meters were made by Greenhow and

Hall (1960). As seen from above, their data

are most reliable for the cases when ro~1.5

meters. They found that, when D=13 m2/sec,

ro=1.55 meters. This value is in good agreement with our data and the theory proposed

in this paper. Greenhow and Hall found that

r0 depends only slightly upon D and does not

depend at all upon V. In view of the above
22 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

discussion, this may be explained by the fact

that their data should be subjected to a stricter

analysis. Most of the meteor trails involved

in their measurements seem to belong to the

intermediate-density type to which equation

(10) is not applicable.

References

DTJDNIK, B. S.; KASHOHBTEV, B. L.; AND LEBEDINETS,

V. N.

1961. Errors in radio-echo measurements of

meteor velocities resulting from diffusion.

Dokl. Acad. Sci. Ukraine, U.S.S.R.,

vol. 11, no. 3, pp. 229-302.

GBBENHOW, 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.

LOEB, L. B.

1934. Kinetic theory of gases. Ed. 2. McGrawHill Book Co., New York.

MASSET, H. S. W., AND BTJRHOP, E. H. S.

1952. Electronic and ionic impact phenomena.

Clarendon Press, Oxford.

MASSET, H. S. W., AND SIDA, D. W.

1955. Collision process in meteor trails. Phil.

Mag., ser. 7, vol. 46, pp. 190-198.
The Initial Diameter of Meteor Trails

By Gerald S. Hawkins *

The initial diameter of the column of ionization produced by a meteor is of great importance, since a small increase in its size produces

a large increase in the attenuation of a radio

echo. Using equation (8-25) of McKinley

(1961), we may write the decibel power loss in

the echo due to the initial diameter d as

/d\z

loss=85(-j decibels, (1)

where X is the wavelength of the radar. At a

wavelength of 8 meters an initial diameter of

4.0 meters produces an attenuation of 21.25

db, whereas the attenuation is only 5.3 db if

the diameter is 2.0 meters. Greenhow and

Hall (1960), and Greenhow (see this symposium, p. 5) measured the amplitude of echoes

at two wavelengths and deduced an average

diameter of 4.0 meters for the column at a

height of 105 km. It is important to establish whether this value is correct, for if it is,

the attenuation at normal radar wavelengths

is so severe as to make worthwhile observations

virtually impossible.

Opik (1958) and Manning (1958) have considered theoretically the initial conditions at

the meteoroid. Atoms and ions evaporate from

the heated surface of the meteoroid and are

injected into the atmosphere at the velocity

of the meteor. After approximately 14 collisions with air particles, each meteor atom or

ion is reduced to thermal velocities, and thereafter normal diffusion takes place. The mean

free path of an atom at these velocities is approximately five times greater than that of an

ion. Thus two concentric columns will be produced: a narrow column of ionized particles

surrounded by a wider shell of neutral atoms.

From the known density of the atmosphere,

< Harvard College Observatory, Cambridge, Mass., and Boston

University, Boston, Mass.

the initial diameter is given by McKinley's

(1961) equation (8-18):

loglod=0.075H— 7.6 (meters), (2)

where H is the height of the meteor column in

kilometers. At a height of 105 km the expected

diameter of the ion column is 1.9 meters, which

is considerably smaller than the value found by

Greenhow and Hall (1960). For comparison I

have plotted in figure 1 the values of Greenhow

and Hall and the values predicted by theory.

The experimental values are considerably

greater than the theoretical predictions for

heights below 105 km. Greenhow and Hall

attribute this fact to fragmentation of the

meteoroid and attach significance to the

discrepancy. On the other hand, their measurements may overestimate the diameter of the

column because of an inbalance in the two

wavelength channels, a disparity in the antenna

patterns, or other causes.

We can obtain an independent estimate of

the initial diameter by direct photography.

Our understanding of the meteor process is not

sufficient at the moment to distinguish clearly

between the column of ionization and the coma

that is emitting light. We would not, however,

expect the region of optical excitation to be any

smaller in extent than the region of ionization.

In a discussion of meteor spectra, Cook (1955)

summarizes the levels of optical excitation that

have so far been observed. Meteoric radiation

is a mixture of light from both ionized and

neutral atoms. We would expect that as a

minimum the light would be confined to the

ionized column, where excitation and recombination are taking place. At the maximum extent

the light could be generated from the core out

to the fringes of the neutral atomic column.

Although on one occasion Cook and Millman

(1955) observed radiation from the heated

23
24 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

IU -

9 -

• -

7 -

—

5

 6 "

E

I -

3 -

2 -

1 -

Leg

- x—

1

1

end:

X GREENHOW - HALL

— — — THEORY MANNING

Photographic:

O HAWKINS-WHIPPLE

• COOK- STIENON- HAWKINS

-**"""" T S*

/

I

1

I

1 X

/ ^ '

/ y

X ^

/

_

-

-

1 1 1 1

Height , Km

FIGURE 1.—Diameter meteor column as function of height.

surface of the meteoroid, this source of radiation

may be neglected for meteors that are fainter

than magnitude —5.

a

IB METEORS

MAG 0

JKHIPR.E- HAWKINS

33 METEORS

MAG * 3

9 GEMIMDS

MAS * 6

COOK-STItNON-HM

FIGURE 2.—Photographic measures of meteor trail widths.

The photographic data were obtained during

two series of observations. The first set of

measurements (Hawkins and Whipple, 1958)

was taken from the Palomar Sky Atlas, for

which meteors had been photographed with the

48-inch Schmidt telescope during the sky survey

by the Mount Wilson and Palomar Observatories and the National Geographic Society.

Photographic plates were exposed in red and

blue light; the average magnitude of the meteors

was 0 for red and +3 for blue. The results are

summarized in figure 2a,b. The mean width of

the 18 meteors photographed on the red plates

was 1.32 meters; and of the 33 meteors on the

blue plates, 1.25 meters. Although these

measurements suggest that the brighter meteors

produce wider trails, the result is not conclusive

since the estimated error of a single measurement was ±0.5 meters. We may safely conclude, however, that the width of the optical

coma for meteors with magnitude between 0

and +3 is less than the initial diameter found

by Greenhow and Hall.

The second set of measurements was obtained

by Cook, Stienon, and Hawkins (1960) during

the Geminid meteor shower of December 1957.

The 48-inch Palomar Schmidt was directed

towards the Geminid radiant so that the meteor

trails were considerably foreshortened. In this
METEOR SYMPOSIUM—HAWKINS 25

manner the limiting visual magnitude was extended to +9 , and the average magnitude of

meteors measured in this program was +6 . In

their original measurements, Hawkins and

Whipple (1958) focused the camera at infinity

to record the stellar images, and employed a

sidereal drive. These factors introduced some

uncertainty in the work since a correction had to

be applied to allow for the fact that the meteors,

not being at infinity, were slightly out of focus.

Also, the width of the meteor trails had to be

compared with the diameter of the circular star

images. In the measurements of 1957 several

photographs were obtained with the plate displaced 50 microns from the focal plane so that

the meteor trails were correctly "in focus" and

the star images were "out of focus." Since the

sidereal drive was not employed, we were able

to compare meteor trails directly with star

trails. The widths of the nine Geminids that

were measured are given in figure 2c. Seven

have widths that are distributed symmetrically

around a mean value of 0.97 meters. The other

two meteors were considerably wider, with

values of 5.8 and 5.1 meters. The estimated

error for the Geminid meteors was ±0.4 meters,

slightly less than the value obtained by Hawkins

and Whipple (1958).

If we define the 58 meteors in the quasisymmetrical distributions to be "average

meteors," then the width of the optical coma

for an average meteor is about 1.2 meters for

magnitudes between 0 and +6 . If the ionized

column is comparable in size to the optical

coma, then the attenuation for an 8-meter radar

signal for these "average meteors" is less than

2 db. On the other hand, the two Geminids of

excessive width would produce an attenuation

of more than 40 db, and would be virtually

TABLE 1.—Photographic width as a function of height

Mean width Mean height

(meters) (kilometers)

(Hawkins, Whipple)

Perseids, Orionids

(Hawkins, Whipple)

8 Aquarids, Taurids, 1

Quadrantids, Lyrids, [

Geminids J

(Cook, Stienon, Hawkins)

Mean value, Geminids

First half

Second half

0.79

1.20

0.97

1.53

0.44

104

94

100

102

98

unobservable by the radio-echo technique. We

must regard such meteors as "abnormal."

Their excessive width is probably due to explosive fragmentation.

To explore further the disagreement between

the radar measurements of Greenhow and Hall

(1960) and the optical data, we can consider

the dependence of trail width on height. In

table 1, I have used the published optical data

to group the meteors according to velocity.

The mean height of these meteors can be taken

from previous photographic data (Hawkins and

Southworth, 1958). The Geminid data of

Cook, Stienon, and Hawkins (1960) are given,

where the mean value for the height of a

Geminid of magnitude + 6 was taken to be 100

km. The two meteors of excessive width were

excluded from this sample. In addition, the

trails were reanalyzed to obtain values for the

mean diameter of the first hah* of the trail, and

that of the second half of the trail. From table

1 we obtained the five values of diameter that

are shown in figure 1. The optical coma corresponds in size to the initial diameter of the

ionization column as predicted by Manning

(1958). It is difficult to see how the initial

ionization column can be any larger in diameter

than the measured optical values, i.e., of the

order of 1.0 meter over the normal range of

meteor heights from 90 to 105 km. Above a

height of 110 km, the trails may indeed be

extremely wide, but photographic meteors

seldom appear in this region of the atmosphere.

The majority of meteors with visual magnitudes between 0 and + 6 are narrow enough to

avoid the extreme attenuation effects suggested

by Greenhow and Hall (1960). There is no

optical evidence to support the idea that faint

meteors produce an optical coma that is wider

than the coma of the brighter photographic

meteors.

References

COOK, A. F.

1955. The nature of meteoric radiation. In

Meteors, ed. T. R. Kaiser, Spec. Suppl.

Journ. Atmosph. Terr. Physics, vol. 2,

pp. 8-15. Pergamon Press, New York.

COOK, A. F.; STIENON, F. M.; AND HAWKINS, G. S.

1960. Meteor trail widths. Interim Report 47,

Harvard Radio Meteor Project, Harvard

College Observatory, Contract AF 19

(122)-458, Subcontract no. 57.
26 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

COOK, A. F.f AND MILLMAN, P. M.

1955. Photometric analysis of a spectrogram of a

Perseid meteor. Astrophys. Journ., vol.

121, pp. 250-270.

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., AND SOTJTHWOBTH, R. S.

1958. The statistics of meteors in the earth's

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

HAWKINS, G. S., AND WHIPPLB, F. L.

1958. The width of meteor trails. Astron.

Journ., vol. 63, pp. 283-291.

MANNING, L. A.

1958. The initial radius of meteoric ionization

trails. Journ. Geophys. Res., vol. 63,

pp. 181-196.

MCKINLET, D. W. R.

1961. Meteor science and engineering. McGrawHill, New York.

OPIK, E. J.

1958. Physics of meteor flight in the atmosphere.

Interscience, New York.
The Relation Between Visual Magnitudes of Meteors

and the Durations of Radar Echoes

By B. A. Lindblad1

Observations of the luminous and ionized

trails of meteors have shown that meteors in

the visual brightness range give rise to radar

echoes with durations ranging from a fraction

of a second to several minutes. Observational

evidence for a relation between the apparent

luminosity of a meteor and the duration of the

associated radar echo was presented by Millman

(1950). This relation has been discussed by

various authors (Greenhow and Hawkins, 1952;

Kaiser, 1953).

The most extensive observations relating the

magnitudes of visual meteors to the lifetimes of

the corresponding radar echoes have been made

by Millman and McKinley (1956). From a

total of 1,405 coincidences obtained during

observations of the Perseid shower, these

workers found a linear relationship between

the logarithm of the echo duration and the

absolute magnitude of the meteor. A similar

investigation by Lindblad (1956) was based on

a rather small sample. The purpose of the

present communication is to repeat and extend

the previous work, using the larger amount of

data which is now available.

The observational data have been collected

in the course of Perseid observations carried out

at the Onsala Wave Propagation Observatory

 2

in Sweden between 1953 and 1960. The experimental technique, which has been described in

more detail elsewhere (Lindblad, 1956, 1961),

is summarized below.

Observational techniques

The radar and visual observations of the proi Lund Observatory, Sweden.

* A division of the Research Laboratory of Electronics of the Chalmers

Technical University, Gothenburg.

gram are designed to cover as completely as

possible a limited area of the sky. The radio

investigations are conducted with a beamed

radar equipment, and the field of the visual

observers is restricted to the beamed sky area.

During the observations the beam is directed

to a point in the sky whose elevation and

azimuth differ by 90° and 180°, respectively,

from those of the shower radiant.

Visual recording is made by a group of three

or four trained meteor observers. The

observers estimate meteor magnitude and train

duration, 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.

Radar observations are made with a pulsed

equipment. The transmitter generates 20-50

kw peak power with a pulse width of 20 n sec

at a wavelength of 9.2 meters. Repetition

frequency is 50 c/s. The receiver has an

overall bandwidth of 75 kc/s. The equipment

used was essentially the same during the entire

program, but the recording technique has been

improved from time to time in order to increase

the detectability of faint meteors. The present

arrangement uses two separate displays, one

intensity-modulated range-time display, and

one amplitude-time display. Both displays are

simultaneously photographed at high film speed

(25-50 cm/min). The arrangement permits

the individual echo pulses to be recognized and

gives good discrimination against the noise

background. The shortest echo duration which

can be resolved is between 0.04 and 0.02

second. Some typical registration results are

shown in plate 1.

27
28 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS Total +3.5 to+3.9 +3.0to+3.4 +2.5

to

+2.9

+2.0

to

+2.4

+1.5

to

+1.9

+1.0

to

+1.4

+0.5

to

+0.9

to ^ -1.0

to

-0.6

-1.5

to

-1.1

-2.0

to

-1.6

1*1 -3.0

to

-2.6

-3.5

to

-3.1

-4.0

to

-3.6

IN OO

~*

CO

i-H (N

35 35

(N 35

CM <—I

o o

o o o t-

(N i-i

CO

CO

IN

CO

I—1

IN

35

CO

f—I

o

©

1—1

CO

oo

oo

35

CO

T-l

3

O

i—(

oo

CO

CO

O

CO

35

CO

CO

35

O

.-i

o

io

m

35

CO

<N

IN

IN

•e

o

IN

CO

35

O

3

o

o

-

IN

co

CO

o

(N

35

O

O

io

35

CO

o

CO

oo

IN

35

i—i 6T0 - i3

o

o

1

35

oc

(N

35

(N

o

o

1

o

o

o

1

•N

lO

(N

35

CO

o

1

5

o

1

- -

IN i-l i-H

m

* <N

co

N O M

O 1-H ^

1 1 I

o o o

•*-> +J - u o o o

O1- C 1 1-Ot T- CDH

1 1 1

688

r--.

CO

OJ113 104

co

oo

<N

35

CO

co

IN

35

co

IN

.—1Dtal

H
LINDBLAD PLATE 1

Registrations obtained with fast amplitude-time and range-time radar displays. Time difference between consecutive pulses 0.02

second. Lower display, amplitude-time (~0-10jiF); upper display, range-time with superimposed amplitude-time (•-'0--100

(iF). Top photos: Short duration echoes with no associated visual meteor. Bottom photo: Long duration echo produced by

apparent magnitude 2"P0 Perseid at 22h3Sm18» M.E.T. on August 12, 1959 (Meteor No. 59-279). Range 180 km. A marker

between 40-70 km indicated simultaneous visual recording.

METEOR SYMPOSIUM—LINDBLAD 29

Reduction of data

The criterion for accepting an association between a visual meteor and a radar echo is

mainly one of time coincidence. As a rule,

no echo is accepted as a coincidence if the time

difference between the signal of the visual

observer and the echo is more than 0.5 second.

During the period of maximum Perseid activity,

the echo rate on the present equipment rarely

exceeds 120 echoes per hour. The number of

spurious associations in our data is thus less

than 2 percent. The possibility of a spurious

association is further reduced by stipulating

that the accepted radar range should produce a

reasonable mean height for the luminous trail

of the meteor.

For accepted coincidences the observed

meteor magnitudes are corrected to a zenithal

or absolute value by adding a correction

Am=10—5. log R, where R is the radio range

in kilometers of the associated echo. No correction for absorption was included, since the

comparison method of magnitude estimates

was used.

The recorded echo lifetimes are durations

above a fixed threshold level. Duration is

nominally measured to within 0.1 second, with

stricter tolerances for echoes lasting less than

0.4 second. Logarithms of echo lifetimes were

computed to within 0.01. No corrections were

applied to the echo durations.

The magnitude-duration data for each accepted association were collected on a punched

card together with other relevant information

about the meteor. The data were then grouped

in various ways and correlations between

magnitude, echo duration, and height were

investigated.

Experimental results I

Observational data.—A total of 808 meteors with

associated radar echoes was available for analysis. Of these, 688 belonged to the Perseid

shower and 120 were either members of various

other showers or sporadic objects. Since the

Perseid sample was the largest and most homogeneous group, only that group will be discussed.

The first investigation was concerned with

the scatter diagram of log echo duration versus

zenithal magnitude. This diagram for 688

Perseid meteors is shown in figure 1. The data

of this sample, arbitrarily grouped in intervals

of 0.3 in log echo duration and 0TM5 in zenithal

magnitude, are collected in table 1. Inspection

of the table shows that in any one array there

is a considerable scatter about the mean.

Since only a moderate correlation exists between

the variates, statistical methods must be used

in the presentation and discussion of the data.

Means of rows and columns for the data of

table 1 are plotted in figure 2. Inspection of the

diagram shows that the points approximate well

to two straight lines, although for very bright

meteors the means log r are somewhat low

Within the limited magnitude range covered by

this investigation, one may, however, assume

that the regression is linear.

Regression lines, computed according to

standard procedure, are included in figure 2.

The correlation coefficient for the magnitudeduration data is —0.725, and the slopes,

bx and bv, of the regression lines are —0.44

and —0.83, respectively. These results are

based on computations from ungrouped data.

Error analysis.—For a comparison with

physical theory it is desirable to express the

relation between the variates as a single

straight-line relation. The problem is best

treated by error analysis. An unknown structural relation is postulated and it is assumed

that the scatter about this relation is caused by

errors of various kinds. The structural relation is then found if we correct one (or both)

of the observed regression lines for the effect

of these errors.

Estimates of meteor magnitudes are available from visual observations only, and the

observational error in these estimates is not

negligible. There is, however, fairly general

agreement that the probable error of a magnitude estimate for a trained group of meteor

observers is not more than 0^3 or 0^4. In the

present investigation special attention was

given to correct magnitude estimates, and all

observers had previous experience of astronomical observations. It therefore appears

reasonable to adopt as the probable error in

our investigation for the combined observa638806—63 3
+3.00

ZENITHA L MAGNITUD E

FIGURE 1.—Scatter diagram of log echo duration in seconds versus zenithal magnitude of meteor.
METEOR SYMPOSIUM—LINDBLAD 31

ZENITHAL MAGNITUDE

FIGURE 2.—Array means and regression lines for table 1.

tional and reductional error a value of 0^35

(standard deviation +0^50). On the basis of

this assumption it is possible to correct the

log r-line for error in the meteor magnitudes.

Measurements of echo durations are made

directly from the radar film. With the display

used in our work, sizable errors in these measurements occur only for a few exceptionally

long persistent echoes. The duration scatter

which is present in meteor data is instead

related to the atmospheric and geometrical

conditions at the echoing point. It thus

appears difficult at this stage to give a numerical

estimate of the "errors" in the echo durations,

and even more difficult to attempt to correct

the M*-line for these errors.

In view of the above considerations the

structural relation behind the experimental

data of table 1 is sought by correcting the

log T-line for magnitude error. The correction

procedure adopted is summarized in the next

section.

Correction for error.—Two different correction

procedures were investigated. A numerical

method for correcting an observed frequency

curve, which is described by Eddington (1913),

was considered to be the best method. An

alternative method given by Seares (1944) was

used as a check on the computations.

Eddington's method was applied to the

data in the following way: Each separate

horizontal array in table 1 was corrected for

error dispersion in the magnitudes. A magnitude-error curve based on a slow increase in

the magnitude error with meteor brightness

was assumed. Eddington's second-order differences were computed from smoothed error

curves, deduced from 3-array running means

in log T. Corrected values of the correlation

coefficient and the gradient bx were then computed. The results of these computations for

two models, denoted A and B, are given in

table 2. (Both these models were based on a

mean probable error of 0^35 and differed only

in the method of applying the second-order

corrections.) In the computations A and B,

Sheppard's corrections for grouping have been

included.

The correcting of a bivariate distribution by

the numerical method and the computing of

the corrected regression lines is a rather tedious

procedure. The necessity to include corrections for grouping introduces a slight uncertainty in the final result. The error-correction

formula given by Seares was therefore also

employed. In this method one directly computes the corrected gradient. However, it is

necessary to make the assumption that the

TABLE 2.—Correlation data: bx, magnitude-duration gradient; x, mean zenithal magnitude; y, mean log echo duration

p, correlation coefficient

Observed values

Corrected values:

A

B

C

Mean of A and B

b,

- 0 . 435

- 0 . 519

- 0 . 480

- 0 . 521

—0.500

X

1*00

1.14

1.05

1.00

1>P10

V

0.52

0.52

0.54

0.52

0.53

P

- 0 . 725

- 0 . 761

- 0 . 754
32 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

magnitude error is independent of magnitude.

A constant mean probable error in the magnitudes of 0^35 was therefore assumed. The

corrected gradient bx is listed in table 2 (Model

C).

-to

-0.5

nn

1 1—

* „

100

1

150

r

200

by

°

bx

-

250

RANG E

-to

-05

cxo

80

*

o 70°

•

N

60° 50° 40°

T

o

30° 20°

i

by

10°

ELEVATIO N

1.0

05

00

-

10* *

• I

4M «

>• 30* 40'

by

0

b,

SO*

-

-

60*

ANGULAR DISTANCE FROM BEAM AXIS

FIGURE 3.—Variations of correlation quantities with range,

elevation, and elongation from beam. Symbols:p= correlation coefficient; bz

 and &,= gradients of regression lines

log T and A/,, respectively.

Inspection of table 2 shows that the results

of the different methods are in surprisingly

good agreement, all indicating similar mass

centers and a magnitude-duration gradient

after error correction of very nearly —0.50.

The correction for magnitude error has thus

only slightly increased the correlation and the

slope. It follows that most of the scatter in

the diagram of figure 1 must be related to

some other factor than magnitude error.

Observational selection.—In a following investigation the influence on the computed gradients

of different observational selections was studied.

A priori, one might expect that meteors

observed at large distances and low elevations

would exhibit peculiar effects and that they

might show unduly large scatter when plotted

in a magnitude-duration diagram. The Perseid data were therefore grouped according to

elevation and range. Correlation coefficients

and gradients were then computed for each of

these groups. The results of these computations are shown in figure 3. The dependence

of the correlation quantities on angular distance

from beam is also shown. In view of the

paucity of the data, no attempt was made to

correct the results of figure 3 for magnitude

error.

Although minor irregularities exist, the general trend of the curves of figure 3 is clearly

very similar. The trend is such that the

correlation coefficient approaches values between —0.8 and —0.9 as the variates approach

90 km, 90°, and 0°, respectively. However,

this increase in correlation is associated with

a marked decrease in the gradient bv, while the

gradient bx is not affected to the same extent.

If Gaussian error functions are assumed, it can

be shown that the observed lower value of

by indicates a reduced scatter in the echo

durations. It thus appears that part of the

scatter in the diagram of figure 1 is related to

various factors, which influence the recorded

echo durations of distant or low-elevation

meteors.

Some investigations were made in which

other groupings of the meteor data were

attempted. One point of interest revealed by

these investigations was that the derived
METEOR SYMPOSIUM—LINDBLAD 33

ZENITHAL MAGNITUDE

FIGURE 4.—Adopted linear relationship between zenithal

magnitude and log echo duration (Perseid meteors).

magnitude-duration relation is independent of

trail orientation; i.e., independent of whether

the meteors are recorded in a specular reflecting

condition or not.

Adopted magnitude-duration relation.—The

mean elevation of the recorded meteors in our

investigation is 40°. If meteors below 40°

were rejected, it follows from figure 3 that a

slight improvement in the correlation would

result. A somewhat higher gradient bx would

also result. However, the correction for magnitude error is very difficult to apply to a small

sample. The overall accuracy of the corrected

linear relation between log echo duration and

magnitude would therefore not be improved

by the rejection procedure.

In view of these considerations, the finally

adopted magnitude-duration relation was computed from the total Perseid sample. A mean

was taken of the two computations A and B.

The resulting coefficients are included in table 2.

The adopted linear relationship between magnitude and log echo duration for a radio wavelength of 9 meters is thus

log T=—0.50M.+1.08.

The adopted line is plotted in figure 4. From

the diagram it is seen that a Perseid meteor of

zenithal magnitude 0^0 produces an echo of

duration very nearly 10 seconds and a 4^0

meteor an echo of duration 0.1 second. The

relation of these experimental results to the

theory of meteor echo durations will be discussed in a following section.

Experimental results II

Echo duration and meteor height.—According

to the diffusion theory of meteor echoes, the

duration T of a persistent meteor echo is

proportional to the electron line density a and

inversely proportional to the diffusion coefficient D. For an isothermal atmosphere, D is

inversely proportional to density and pressure,

and both log D and log T will vary linearly with

height for a group of meteors with similar

electron line densities.

It thus appears of interest to investigate the

relation between log T and height in a sample

of meteors with similar visual magnitudes.

In the present investigation approximate meteor

heights were obtained from the radar range

measurement and from the plot of the trail by

the visual observer. Since these latter observations are subject to large errors, the individual

height determinations are uncertain, and only

mean heights will be used. The magnitudeduration data were arbitrarily grouped in

intervals of 0.3 in log echo duration and l'Hi in

zenithal magnitude. The mean height computed for each of these cells is listed in table 3.

Means computed from less than five observations are given in parentheses.

Inspection of the vertical arrays of table 3

shows that there is a statistical relation between the mean height and the logarithm of

the echo duration. It is seen that meteors that

lie high in the magnitude-duration diagram are

observed at mean heights below 100 km;

meteors that lie low in the diagram, are observed

at mean heights above 100 km. Inspection of

the marginal array indicates, as one would

expect, that the relation between mean height

and log echo duration is less pronounced when

an average is taken over all magnitudes.

Meteor height versus magnitude.—Meteor

theory predicts that the heights of meteors

should decrease with increasing meteor brightness. An experimental verification is provided

by the marginal means of table 3. The

variation of mean height with magnitude is

shown in figure 5 (broken line).

In a subsequent investigation those meteors

were selected which showed small scatter about
34 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABUB 3.—Mean height of Perseid meteor trails as a function of log echo duration and visual magnitude. Meteor heights

in kilometers

log*

2.00 to 2.29

1.70 to 1.99

1.40 to 1.69

1.10 to 1.39

0.80 to 1.09

0.50 to 0.79

0.20 to 0.49

-0.10 to +0.19

-0.40 to -0.11

-0.70 to -0.41

-1.00 to -0.71

-1.30 to —1.01

-1.60 to -1.31

Mean height

-10to -3.0to

-3.1 -2.1

(102)

(117)

(91)

101.7

-2.0 to

-1.1

(99)

96

97

93

(102)

96.5

-1.0 to

-0.1

99

97

97

100

99

109

(93)

(94)

98.6

Mt

-0.0 to

+0.9

95

102

96

101

104

97

104

108

(55)

100.4

+1.0 to

+1.0

(98)

(99)

98

100

101

100

101

105

105

(107)

101.4

+2.0 to

+2.9

96

91

98

98

100

100

102

(91)

98.8

+3.0 to

+3.9

(107)

(105)

99

103

(96)

(100)

101.2

Mean height

100.5

98.5

98.4

96.7

99.8

101.1

99.6

101.0

102.6

101.0

101.4

the magnitude-duration relation. A maximum

variation in log echo duration of ± 0.20 from the

adopted straight-line relation in figure 4 was

allowed. This group, consisting of 199 objects,

showed a somewhat more pronounced variation

of the mean height with magnitude (fig. 5,

solid line).

Individual meteors exhibit large scatter about

the mean height-magnitude relation of figure 5.

It is not possible to explain this scatter as the

result of observational errors alone. The

question arises whether the height scatter for

given visual magnitude is the result of a random

breakup of the meteor or if some additional

variate is involved (such as the angle of inciZENITHAL MAGNITUDE

FIGURE 5.—Mean height of Perseid meteor trails as a function

of visual magnitude.

dence of the meteor). This point requires

further study.

Duration of persistent visual train.—Meteors

are often accompanied by a persistent train,

having a visually observed duration of the order

of a second or less. In the present radar-visual

program, regular observations of these trains

were made, and time durations were estimated

by the observers.

The mean train duration in seconds, computed for each of the cells of table 3, is shown

in table 4. A meteor with no recorded visual

train has been given zero duration in the

averaging. Inspection of the marginal mean

durations of the table reveals a dependence on

visual magnitude and on echo duration. Inspection of the vertical arrays of the table indicates

a correlation with echo duration, which is

independent of visual magnitude.

From table 4 it may be concluded that

meteors that lie high in the magnitude-duration

diagram exhibit visual trains of unusual persistence. The durations of meteor trains and

meteor ionization are thus intimately connected.

The data of table 4 are published to illustrate

qualitatively a general relation. They are representative of observations made at sea level.

The measured duration of a persistent train

depends critically on the atmospheric transparency—and thus on both locality and meteor
METEOR SYMPOSIUM—LTNTDBLAD 35

TABLE 4.—Mean duration of persistent train as a function of log echo duration and visual magnitude. Train durations

in seconds

logr

2.00 to 2.29

1.70 to 1.99

1.40 to 1.69

1.10 to 1.39

0.80 to 1.09

0.50 to 0.79

0.20 to 0.49

—0.10 to +0.19

-0.40 to -0.11

-0.70 to -0.41

-1.00 to -0.71

-1.30 to —1.01

-1.60 to -1.31

Mean duration

-4.0 to -3.0 to

-3.1 -2.1

3.5

3.3

1.5

2.42

-2.0 to

-1.1

7.0

3.6

1.0

0.6

0.3

1.50

-1.0 to

-0.1

2.3

1.5

0.4

0.6

0.4

0.6

3.5

0.98

Mz

-0.0 to

+0.9

1.2

0.4

0.4

0.3

0.4

0.4

0.3

0.2

0.2

0.37

+1.0 to

+1.9

1.3

0.2

0.4

0.14

0.30

0.03

0.04

0.08

0. 16

+2.0 to

+2.9

0.02

0. 17

0.20

0.04

0.02

0.02

0.05

+3.0 to Mean duration

+3.9

5.3

2.4

1.04

0.38

0.32

0.26

0.32

0.12

0.04

0.09

0.02

elevation angle. Because of the lack of precision of the experimental data, and since the

number of trains available for analysis is rather

small, no attempt is made in this paper to treat

the train data quantitatively.

Comparison with other investigations

From radar-visual data obtained on a wavelength of 9.2 meters by Millman and McKinley

(1956), linear relations between visual magnitude and log echo duration were reduced for

several meteor showers. For Perseid meteors,

which represent the largest group, these workers

found a magnitude-duration relation (after

correction for error) of logr=—0.406 M.+0.87.

The gradient value —0.406 is considerably

lower than that found in the present investigation. The reason for this discrepancy is not

clear at present, but one factor which may

be of importance in this connection will be

mentioned.

On the basis of the diffusion theory of meteor

echoes, one expects a linear relation between log

echo duration and visual magnitude. However,

Davis, Greenhow, and Hall (1959) have shown

that the echo durations of very bright meteors

are far less than those to be expected on simple

diffusion theory. This has been explained by

the removal of electrons from the ionization

trail by attachment to neutral oxygen molecules'

to form negative ions. Although this reduction

in duration is not of great importance for fast

Perseid meteors, which ionize at a mean height

of 100 km, a slight indication of some such ceiling effect is evident in the diagrams of figures 1

and 2, where the recorded echo durations for

magnitudes — lm and —2m are slightly less than

predicted from diffusion theory.

A comparison of Millman and McKinley's

(1956) table III with our table 1 shows that

bright meteors are more common in the Canadian observations than in our survey. The discrepancy in magnitude-duration gradient between the two investigations could thus possibly

be explained as due to the attachment process,

which would systematically lower the durations

of the bright meteors in the Canadian investigation and thus also cause a lowering of the

computed slope.

A detailed comparison of the two investigations is complicated by the fact that various

elevation-dependent corrections are introduced

in the reduction of the Ottawa data. It is not

known to what extent these corrections influence their observed gradient.

Since a selection according to either elevation

or beam elongation is mainly one of distance,

the results of figure 3 lend some support to a

suggestion of McKinley (1953) that corrections
36 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

for attenuation should be applied to echo

durations. However, an attempt to apply

this type of correction to our data was not very

successful, the net result being that the

magnitude-duration scatter diagram was shifted

upwards, with no pronounced change in the

correlation quantities.

Theoretical relations between magnitude,

duration, and height

The ionized trails of meteors can be divided

into two main groups, generally referred to as

underdense and as overdense trails, in which

the linear electron density a is less or greater

than 2X1012 electrons/cm.

For low density trails with a<2X1012

electrons/cm, Herlofson (1948) has shown that

the radar echo duration to 1/e of the initial

amplitude is independent of a, and is given by

(1)

where D is the diffusion coefficient and X is the

wavelength. The echo duration is thus independent of a, being determined by the wavelength and the diffusion coefficient.

When a]>2X1012 electrons/cm, the volume

electron density in a trail exceeds the critical

density Ne. Under these conditions the duration of a meteor echo is proportional to a, and

with the assumption that the ionization is dissipated mainly by diffusion, Greenhow (1952)

and Kaiser and Closs (1952) have shown that

the echo duration is given by

4irDNe

(2)

Magnitude-duration relation.—Meteors in the

magnitude range — 2^0 to +4^0 will mainly

produce overdense ionization trails, and we

will assume that equation (2) applies to the

majority of the meteors in our survey. We

will further assume that the diffusion coefficient

is inversely proportional to the atmospheric

density p. The radar duration of visual

meteors is then given by the relation

log T=log a+log p-f const. (3)

Meteor theory predicts that the electron line

density at the point of maximum rate of evaporation of the meteor is related to the atmospheric density at the same point by the relation

Pmax OC a 1/3

mal . (4)

Meteor magnitudes are defined by the relation

log a= const—0.4 Mz. (5)

Let TmAX be the predicted echo duration at the

point of maximum evaporation. Combining

equations (3), (4), and (5) gives

log Tmax=const—0.533 Mz (6)

for the predicted variation of echo duration

with magnitude. It is thus assumed that the

final echo signal is returned from a segment of

trail near the point of maximum ionization.

Height-magnitude relation.—A relation between meteor height and visual magnitude is

derived as follows. An isothermal atmosphere

is assumed with atmospheric density p given

by

log p= const — ^ log e, (7)

where H and $? are height and scale height,

respectively. Introducing Hmwx, the predicted

height at maximum evaporation and substituting equations (5) and (7) in equation (4),

we find that

H 04

—^r log e=-^r-Mz, (8)

or

^-x=0.306M,+const, (9)

for the relation between meteor height and

zenithal magnitude.

Echo duration versus meteor heights.—It is of

interest to deduce the predicted variation of

echo duration with meteor height for a constant magnitude group. Substituting equations (5) and (7) in equation (3), we find that

log T=const-0.4 Mz——^ log e, (10)

where T, Mz, and H are echo duration, meteor

luminosity, and meteor height at the echoing

point.
METEOR SYMPOSIUM—LINDBLAD 37

Discussion of results

Comparison oj experimental and predicted gradients.—The theoretical relationships derived

in the preceding section will now be compared

with the available experimental observations.

Physical interest is focused mainly on the

gradients in the magnitude-duration and heightmagnitude relationships.

Comparison of the predicted and observed

slopes of the magnitude-duration relation shows

that the experimental data (table 2) are in very

good agreement with the predicted relation (6).

The experimental height-magnitude relationship for Perseid meteors is given in figure 5,

which shows that bright meteors penetrate

lower into the atmosphere than do faint

meteors, as predicted by theory. The observed

value of the slope is, however, not consistent

with the value inferred from equation (9). For

a scale height of 6.5 km the theoretical relation

(9) predicts a slope of approximately 1.9 km/

magnitude. From the experimental curve (B)

a gradient of about 1.2 km/magnitude is

deduced. However, taking means of the meteor

heights artificially lowers the experimental

gradient somewhat, owing to the large scatter

which is present in the data. An approximate

correction for magnitude error raises the

experimental slope to about 1.4 km/magnitude.

It should be observed that the experimental

heights refer to the midpoint of the visual track,

while the height in equation (9) is the predicted

height at maximum light. A correction to the

observed heights may be derived from photographic meteor data (Millman, 1958). This

correction, which is —0.5 km for a 3*5 Perseid

and —4.0 km for a —2*5 Perseid, is sufficient

to remove the remaining discrepancy between

the experimental and predicted slopes.

For the variation of log echo duration with

height in a constant magnitude group, the

previous theory predicts a slope of approximately —0.07 log r/km. An experimental

verification of this prediction is, however, not

possible since the scatter diagram of log r

against H indicates very large scatter in the

data even when a narrow magnitude interval

is considered.

Transitional duration and line density.—In

the present investigation it is assumed that

equation (2) is valid for all visual meteors.

The validity of this assumption will now be

discussed. For this purpose it is necessary to

estimate the approximate echo duration and

visual magnitude at which the transition from

underdense to overdense ionization trails occurs.

For an underdense trail, the echo duration

to 1/e of the initial amplitude may be computed

from equation (1), provided the diffusion

coefficient is known. For conversion of this

duration to threshold duration, an empirical

graph of signal-to-noise ratio against zenithal

magnitude was constructed and used together

with the magnitude-duration relation (fig. 4).

Assuming an exponential decay of echo amplitude, appropriate values of threshold duration,

relative duration, and visual magnitude may

be computed for a number of different values

of the diffusion coefficient.

With Z>=4.0 m2/sec we find from equation

(1) a relative duration of 0.14 second. This

duration corresponds to a meteor of approximate magnitude 3*5, a mean signal-to-noise

ratio of 4, and a threshold duration of 0.201

second. The transition between underdense

and overdense trails thus occurs near zenithal

magnitude 3*5.

For the faint visual meteors in the transition

region it may, however, be more appropriate

to use a higher value of the diffusion coefficient, since these meteors may be assumed to

ionize rather high in the atmosphere. If

Z?=13m2/sec, as determined by Greenhow and

Neufeld (1955) for a mean height of 100 km,

the computations give relative and threshold

durations of 0.04 and 0.05 second, respectively,

and a visual magnitude between 4*5 and S"H).

In this case, all meteors in a radar-visual

survey are of the long persistent type. It

thus appears correct to apply equation (2) to

all meteors in the present investigation.

The electron-line density in the trail may be

computed from the magnitude-duration relation

and equation (2), provided the visual magnitude

exceeds the transitional value. For Z>=13m2/

sec and iVe=1.33Xl07, the relation between

echo duration and line density is given by

T=4.5X1O"" a,

©38805—63 4
38 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

where a is the line density per centimeter path.

For a fourth-magnitude meteor with an echo

duration of 0.1 second, the corresponding

density is about 2.2 XlO12 electrons per centimeter. The main uncertainty in these computations rests on the assumed value of the

diffusion coefficient.

Limiting meteor magnitude.—An experimental

curve of the signal-to-noise ratio against

meteor magnitude indicated a slow decrease

with magnitude. Extrapolation of this curve

to faint meteors of zenithal magnitude 6^0

indicated that these meteors should still be

detectable. A mean signal-to-noise ratio of

two was assumed as the detection limit.

However, the shortest duration which is

recorded cannot be appreciably less than the

time interval between two consecutive transmitter pulses. For a pulse repetition frequency

of 50 c/s, this limiting echo duration is 0.02

second. The corresponding visual magnitude,

deduced from figure 4, is very nearly 5^5. It

thus appears that the limiting meteor magnitude

of the present equipment is determined by the

pulse repetition frequency and that fifth-magnitude meteors represent the limit of detectability.

Summary of results.—An analysis has been

given of the magnitudes, echo durations, and

heights of Perseid meteors. A relation between

visual magnitude and log echo duration has

been deduced, and some observational factors

influencing the determination of this relation

have been discussed. The experimental relation is found to be linear over the range of

zenithal visual magnitudes from —2ip0 to +4^0.

The observed slope is very nearly —0.50, in

agreement with theoretical predictions based

on equation (6). A variation of meteor height

with magnitude has been found in accordance

with equation (9). Meteors that brighten up,

at heights above the mean height predicted

from their magnitude, have shorter echo durations than those given by the magnitudeduration relation; meteors which penetrate

lower into the atmosphere have echoes of unusual duration. These meteors also exhibit

persistent visual trains. The experimental results as to echo durations are in general accord

with the results one might expect on the basis

of diffusion theory.

Acknowledgments

This investigation was carried out at the Onsala

Wave Propagation Observatory and at the Lund

Observatory. The author is indebted to the

directors of these stations, Professors O. Rydbeck and C. Schalln, respectively, for their

constant interest in the work. The investigation has been financially supported by the

Swedish Natural Science Research Council.

References

DAVIS, J.; GBEENHOW, J. S.; AND HALL. J. E.

1959. The effect of attachment on radio echo

observations of meteors. Proc. Roy.

Soc. London, ser. A, vol. 253, pp. 130-139.

EDDINGTON, A. S.

1913. On a formula for correcting statistics for the

effects of a known probable error of

observation. Monthly Notices Roy.

Astron. Soc, vol. 73, pp. 359-360.

GBEENHOW, J. S.

1952. Characteristics of radio echoes from meteor

trails: III. The behaviour of the electron trails after formation. Proc. Phys.

Soc. London, vol. 65B, pp. 169-181.

GBBBNHOW, J. S., AND HAWKINS, G. S.

1952. Ionizing and luminous efficiencies of meteors. Nature, vol. 170, pp. 355-357.

GBEBNHOW, J. S., AND NBUFBLD, E. L.

1955. The diffusion of ionized meteor trails in the

upper atmosphere. Journ. Atmosph.

Terr. Phys., vol. 6, pp. 133-140.

HBBLOFSON, N.

1948. The theory of meteor ionization. Phys.

Soc, Rep. Progr. Phys., vol. 11, pp.

444-454.

KAISEB, T. R.

1953. Radio echo studies of meteor ionization.

Advances in Physics (Phil. Mag.

SuppL), vol. 2, pp. 495-544.

KAISER, T. R., AND CLOSS, R. L.

1952. Theory of radio reflections from meteor

trails: I. Phil. Mag., ser. 7, vol. 43,

pp. 1-32.

LlNDBLAD, B. A.

1956. Combined visual and radar observations of

Perseid meteors. I. Observations in

1953. Medd. Lund Astron. Obs., ser. 1,

no. 189.

1961. Combined visual and radar observations of

Perseid meteors. II. Observations in

1955. Medd. Lund Astron. Obs., ser. 1,

no. 198.

MCKINLBT, D. W. R.

1953. Effect of radar sensitivity on meteor echo

durations. Canadian Journ. Phye., vol.

31, pp. 758-767.
METEOR SYMPOSIUM—LINDBLAD 3 9

MILLMAN, P. M. tudes. Canadian Journ. Phys., vol. 34,

1950. Meteoric ionization. Journ. Roy. Astron. pp. 50-61.

Soc. Canada, vol. 44, pp. 209-220.

1958. The heights of meteors. Journ. Roy. SEABBB, V. H.

Astron. Soc. Canada, vol. 52, pp. 230-232.

 1944

- Regression lines and the functional relaMILLMAN, P. M., AND MCKINLBY, D. W. R. tion. Astrophys. Journ., vol. 100, pp.

1956. Meteor echo durations and visual magni- 255-263

Abstract

This investigation is concerned with the statistical relation between visual magnitudes of meteors and radar

echo durations. For 688 Perseid meteors observed at a radio wavelength of 9.2 meters, a linear relation is deduced

between the logarithm of the duration of the echo and the absolute magnitude of the meteor. The adopted magnitudeduration relation indicates that a Perseid meteor of zenithal magnitude 0*0 produces an echo duration of 10 sees,

and a meteor of zenithal magnitude +4>PO a duration of 0.1 sec. The scatter of points in the magnitude-duration

diagram is discussed. It is shown that this scatter, for constant visual magnitude, is related to the mean atmospheric

height of the meteor. It is further shown that meteors which lie high in the magnitude-duration diagram are associated with persistent visual trains.

Radio-Echo Measurements of Meteor

Mass Distributions

By A. A. Weiss *

Method of measurement

Mass distributions have been determined for

sporadic meteors and for meteors belonging to

the major showers visible in the southern hemisphere, over the years 1957 to 1960. Measurements made with a narrow beam 67 Mc/sec

radar equipment were used.

A differential mass distribution of the form

vmccm~* dm has been assumed. Electron line

densities a have been converted to radio magnitudes Mn with the relation Mr=35—2.5 logi0a.

The value of s has been determined in the

range 6.0<Mr<7.5 from the dependence of

total echo counts on equipment sensitivity, and

in the range 0<Mr<2.5 from the distributions

of echo durations. In the former case (total

echo counts) allowance has been made for the

aerial polar diagram; and fragmentation of the

meteoroid, if present, introduces negligible

error into the value of s. In determining the

value of s for the brighter meteors, it has been

supposed that the decay of the echo is due to a

progressive reduction of the free electron density

within the trail by ambipolar diffusion and the

attachment of electrons to neutral molecules.

It has not been possible to correct for the

influence of irregular atmospheric motions on

the echo durations, but in view of the small

aerial beamwidth and high operating frequency

this effect is not expected to be serious.

A full account of the experimental method

will be found in Weiss (1961a).

Sporadic meteors

Uncertainties in the aerial polar diagram and

in the threshold sensitivity of the equipment

limit the precision with which the value of s

• Commonwealth Scientific and Industrial Research Organization,

Radlophysics Laboratory, Sydney, Australia.

appropriate to the fainter group of sporadic

meteors can be determined. Our observations

show, however, that for 6.0<C.MT<^7.5 the value

of s is close to the s=2.0 found repeatedly from

telescopic observations.

From the echo durations, «=2.5 for

—3<Mr<2.5. This may be compared with

the careful photographic determination by

Hawkins and Upton (1958) of s=2.34 for

— l<Mr<4.5 .

Even if the absolute accuracy of the present

radio determinations is open to some doubt,

these methods can still be used to obtain useful

comparisons of the mass distributions for shower

and sporadic meteors. Such comparisons are

valid because (a) the variation of the total

echo rate with equipment parameters is insensitive to the degree of fragmentation, and (b) the

incidence of trail distortion is identical for all

the major showers and for sporadics, at least

in the southern hemisphere (Weiss 1961b).

There do not seem to be any northern hemisphere observations of the incidence of trail

distortion which are directly comparable with

those of the southern hemisphere mentioned

here, but there is no reason to expect a different

result in the northern hemisphere.

Shower meteors

Geminids.—Values of s for the time of maximum

activity of this shower are given in table 1,

and are compared with northern hemisphere

measurements (Browne, Bullough, Evans, and

Kaiser, 1956) in figure 1. The echo amplitude

and durations methods used in the Jodrell

Bank measurements can be regarded as absolute; the height distribution measurement was

obtained by comparison with an assumed value

s=2.0 for sporadics.

41
42 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Values of mass distribution exponents s

Shower

7.5>Mr>6.0 2.5>itfr>1.0 1.0>Mr>0

Geminids

5 Aquarids

n Aquarids

Sporadics

1.5

1.5

1. 6

2.0

1.7

1.9

1.4

2.5

2.7

2.7

2.0

2.5

Two values of s are given for the present durations measurements, since it was found that

even after allowance for attachment the results

could not be fitted by a single value of s over

the whole range of echo durations. Kashcheyev

and Lebedinets (1959) have also observed an

abrupt increase in the value of s at about the

second radio magnitude, which is most pronounced over the time of maximum activity

of the shower and is then too large to be attributed solely to the effects of attachment, which

they neglected. A similar trend is also apparent

in the Jodrell Bank results, but only the weighted mean for the whole shower has been given

in the diagram. The new results suggest that,

at least near the time of maximum activity,

the maximum concentration of mass per unit

magnitude range occurs around Mr= + 1,

which is rather brighter than suggested by the

Jodrell Bank authors.

The 8 Aquarids.—The mass distribution

appears to be identical with that for the Geminids (see table 1). Like the Geminids

(Browne et al., 1956), the 5 Aquarids exhibit

tt MrlkvtU

FIGURE 1.—Comparison of mass distribution exponents s for

the Geminid stream, measured at Jodrell Bank and at

Adelaide.

(o) Di«trlbut!on of acho durations

• 1 July 28-31

Echo duration T (Me )

(b) Proportion of

with Mr < 2 5

( persistent KhOM)

6 Aquoridi

FIGURE 2.—Increases in the proportion of bright and very

bright meteors near the time of maximum activity of the

5-Aquarid shower, indicating a central condensation of

massive meteors within the stream.

a strong concentration of bright meteors to

the center of the stream. The evidence for

such a central condensation is presented in

figure 2. The proportion of persistent echoes

increases, and the value of s for the brightest

meteors decreases, for the 4 or 5 days centered

on the time of peak activity. At the same

time, there is no change in the value of * for

meteors fainter than 5th magnitude.

The i} Aquarids.—This shower, which is

prominent visually, gives a comparatively low

echo rate on the radar when the limiting magnitude is reduced to MT=7.5. In fact, during

the 1957 apparition, some 30 percent of all

echoes detected had MT<2.5. These results

alone suggest that s<2.0, and this is confirmed by the more accurate determinations

given in table 1. With these values of s, the

predicted proportion of persistent echoes (Mr

<2.5) to all echoes is about 10 percent. This

is only a third of the observed number; the

discrepancy is almost wholly due to prolongation of echo durations by atmospheric motions.
METEOR SYMPOSIUM—WEISS 43

Discussion

These southern hemisphere results confirm the

general picture which had emerged from the

northern hemisphere radio measurements, that

for the major showers the value of s increases

from about 1.5 for meteors of 7th magnitude

to values >2.0 for meteors of zero magnitude,

and that the mass per unit magnitude range

reaches a maximum well above the visual

threshold. The more detailed analysis of the

durations of persistent echoes has shown that

in some cases, notably the Geminids and 8

Aquarids, there is a very steep rise in the value

of s for Mr<C.-\-l, so steep that it amounts

effectively to a cut-off in meteors above the

critical mass. Sporadic meteors, by way of

contrast, do not share this cut-off, and the

value of s remains substantially constant to

the upper limit of the cometary meteoroid mass

scale. This characteristic of constant s amongst

the brightest meteors is also shared by some

showers (for example, Perseids, i] Aquarids).

In conjunction with the Jodrell Bank results,

the present observations have shown that the

Geminids and the S Aquarids, which have

similar mass distributions and in particular

share the characteristic of a steep rise in the

value of s for Afr< + 1, both exhibit a strong

concentration of bright meteors to the center of

the stream. It is interesting to speculate

whether these two features of the mass distribution are associated, since in at least one other

case (Perseids) a constant value of s amongst

the brightest meteors is coupled with an increase

in the relative number of faint meteors at the

time of maximum shower activity (Browne et

al., 1956).

In conclusion, it is well to emphasize that, so

long as the evaporation theory is used to

interpret radio-echo data, any appreciable

fragmentation, especially amongst the fainter

meteors, will result in inconsistencies in the mass

distributions derived by different methods (for

example, from relative echo rates and from the

widths of measured height distributions). This

provides us with a means for comparing the

physical structure of meteoroids belonging to

different streams.

References

BROWNE, I. C; BULLOUGH, K.; EVANS. S.; AND KAISER,

T. R.

1956. Characteristics of radio echoes from meteor

trails. II. The distribution of meteor

magnitudes and masses. Proc. Phys.

Soc. London, vol. 69B, pp. 83-97.

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.

KASHCHETEV, B. L., AND LEBEDINETS, V. N.

1959. On the structure of the Geminid meteor

stream. Astron. Journ. U.S.S.R., vol.

36, pp. 629-640.

WEISS, A. A.

1961a. The durations of persistent meteor echoes

and the derivation of meteor mass distributions. Commonwealth Scientific

and Industrial Research Organization

Australian Div. Radiophys. Rep.

RPR 139.

1961b. The distribution of meteor masses for

sporadic meteors and three showers.

Australian Journ. Phys., vol. 14, pp.

102-119.

Abstract

Mass distributions for sporadic and shower meteors are derived from radio-echo observations at 67 Mc/sec. The

data used are total echo rates for the brightness range 6.0<Afr<7.5, and durations of persistent echoes for Afr<2.5.

The mass distributions cannot be represented by simple inverse power laws with constant exponents «. For sporadic

meteors, s increases from ^2.0 for the faint meteor group to 2.5 for the brighter meteors. For the lj-Aquarid, SAquarid, and Geminid showers, a also increases as the brightness increases. In common with the major northern

hemisphere showers, the mass per unit magnitude range for these showers reaches a maximum well above the visual

threshold.

The 5 Aquarids are shown to exhibit a concentration of massive meteors towards the center of the stream.

A Preliminary Report on Radar Meteor Counts

By Peter M. Millman

 1 and Bruce A. Mclntosh*

As part of the Canadian program of the International Geophysical Year, a meteor patrol

radar was designed and constructed for use at

the Springhill Meteor Observatory a few miles

south of Ottawa, latitude 45°ll/.8 N, longitude

75°28'.3 W, elevation 310 feet above sea level.

This radar operates at a frequency of 32.7 me/

sec with a peak power approximately 20 kw,

pulse recurrence frequency 117 cps, and a pulse

length 12 n sec. Independent transmitting and

receiving aerials consist of crossed horizontal

dipoles, fed 90° out of phase and mounted 0.4 X

above a wire mesh 105 feet in diameter and some

3 to 4 feet above ground level. The antenna

pattern given by this system is essentially uniform at all altitudes and azimuths down to an

elevation of 20°. Neale gives a more complete

description of this meteor radar system.2

An air view of the Springhill Meteor Observatory appears in plate 1.

Continuous recording of meteor echoes, using

a range-time presentation, is made on 35-mm

film. A sample record is reproduced in plate 2.

Range markers appear as horizontal lines at

20-km intervals, the 100-km range markers

being bright, the others dark. Individual

seconds-markers appear at top and bottom of

the record, with a more prominent marker every

tenth second. The serial day number, 713, and

the hour and minute of Universal Time, 06.18-

06.19, are placed on the film above the trace

each minute, while various calibration dials to

check the performance of the equipment are

photographed at the bottom of the trace every

hour. The small triangular markers just below

minimum range indicate the times when the

1

 National Research Council, Ottawa, Ontario, Canada.

1

 M. J. Neale, "Radar Equipment for Continuous Meteor Observations," In press.

visual observers recorded visible meteors. On

certain specified nights a team of eight observers

manned the visual station and recorded all

meteors seen, for correlation with the radar

records.

Both the radio circuitry and the photographic

recording unit of this equipment were designed

to give maximum reliability of performance and

uniform operating characteristics over long

periods of time. The radar has been in operation on a 24-hour-per-day schedule since the

beginning of October 1957, and the total time

lost due to breakdowns of all kinds has been less

than 3 percent.

The radar film is read by means of a specially

designed viewer coupled with a standard IBM024 alphabetic key punch. The complete unit

is illustrated in plate 1. The projection of the

film moves horizontally across the viewing

screen past a transparent strip which carries

the alphabetic range coding. The operator can

vary the speed of motion with a knee pedal.

The range of each meteor echo is recorded to

the nearest 10 km from 70 km to 370 km. The

durations of all echoes are also recorded on a

5-step scale—<1 sec, 1 to 2 sec, 2 to 4 sec,

4 to 8 sec, and >8 sec. This information is

punched on primary data cards, which are then

processed in the IBM-650 computer and give a

set of 10-minute summary cards, on each of

which the totals are recorded for a 10-minute

interval. These cards then are put through the

IBM-402 accounting machine, which gives a set

of cards with hourly totals and a printed record

similar to the one shown in plate 2.

A single sheet of this record tabulates the

data for one-quarter of a day. Both individual

10-minute totals and hourly totals are repro45
46

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

duced, the column headings being self-explanatory in most cases. The numbers and letters at

the top of the range column correspond to the

punching code used. The "CLASS LONGS"

columns record the numbers of echoes in various

duration classes. The nature of the interference

evident on the film is coded in the next-tolast column. Since the sample reproduced here

is from a period near the peak of the Geminid

shower, both the echo rates and the proportion

of long-duration echoes are considerably higher

than average.

The data for the period from October 1957

through December 1960 have now been processed as described above, and approximately

4,400,000 meteor echoes were recorded during

these 39 months. We have begun a detailed

statistical study of this material and give here

only a brief outline of some of the preliminary

results.

The tabulated rates should be corrected for:

(a) The personal equation of the film readers;

(b) variation in the performance characteristics

of the radar equipment; and (c) interference in

the radar reception.

Information for finding correction (a) has

been collected, but the correction itself has not

yet been determined. In any case it will have

little effect on the type of results reported here.

The whole instrumental system was designed

to keep correction (6) as small as possible, and

we believe that, in general, this aim was

achieved. The major exception is that, for

some reason not entirely explained, the meteor

radar seems to have operated somewhat more

efficiently during the 1959-60 period than in

1957-58. No attempt has yet been made to

allow for this.

A preliminary determination of correction

(c) has been made by studying discontinuities

in the mean diurnal rate curves, the variation

in rates for specific local times in the day, and

the variation in the ratios of long duration to

total echoes. These data were correlated with

the index figures for interference as estimated

by the film readers, and a mean correction factor

was found. It varies from 1.0 for no interference to 2.5 for maximum interference. In

plotting diurnal rate curves the observed rates

have been corrected by multiplying by this

o

300

PER

if)

L JJ

X 200

LJJ :TEO

R

-E IOO

1 ' 1 r-

- . v . . •• •• •••"

1957 |

1 ' : ' —

• •.« . • •. " • .

1958

—1 '—

[

—1 1 i 1 1 1 1 1

; . '

••"••.' . •

' • • '

 - % • • ..".*••- '

••!•' . < .

'•' ^ • ""

1959 |

i 1 1 1 1 1 1

-

•• • - ' : '• . ' ':.' • • •

.;.'•- V'.•»'";;". "

 :--.vVr

- " -

;.-

I960 1

300 400 500 600 700 800 900 1000 1100 1200 1300 I40O

I.G.Y. DAY

FIGURE 1.—The mean hourly echo rate for each day. The IGY serial day is numbered from 1 on January 1,1957,
METEOR SYMPOSIUM—MILLMAN AND McINTOSH 47

300

JAN I FEB MAR APR MAY JUN JUL I AUG I SEP I OCT NOV I DEC I

FIGURE 2.—The annual variation of mean hourly echo rate for each day: upper curve, all echoes;

middle curve, echoes with durations 1 second or greater; lower curve, echoes with duration 8 seconds

or greater.

factor. Periods where the correction factor

was 2.0 or more have been omitted from the

plotted results. If we consider only the cases

where the rates were altered by more than 10

percent, for the first 18 months a correction

was made in the case of 40 percent of the observed rates, while for the last 21 months,

which were further removed from the sunspot

maximum, a correction was made for less than 7

percent of the observed rates.

Uncorrected mean hourly rates of meteor

echoes for each day are plotted in figure 1.

The IGY serial day number is based on the

system used at all the Canadian meteor and

auroral stations where January 1, 1957, is

taken as Day No. 1 and the days are counted

serially from then on. Note that the mean

hourly rates for a day vary from a minimum

near 50 during the first few months of each

year to peak rates between 250 and 300 in

June and December.

To give a general picture of the average

variation in meteor rates throughout the year,

the values from figure 1 were averaged for each

calendar day and are plotted as the upper curve

in figure 2. Below this are plotted the mean

hourly rates for each day for all echoes with

durations of 1 second or greater, and all echoes

with durations 8 seconds or greater. Most of

the minor fluctuations in these curves are probably accidental and should not be considered as

particularly significant. Some of the major
48

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1958 1959 I960

en

Q

LU

200

100

300

200

100

400

300

200

!00

f-1-

2

 1 rJAN

FEB

MAR

APR

MAY

JUN

19 I- 7 13 19 I 7 13 19 I 7 13

EASTERN STANDARD TIME

FIGURE 3.—The monthly mean diurnal echo rate curves for January to June: solid

line, all echoes; dots, echoes with durations 1 second or greater.

showers, however, stand out clearly, particularly

for the lower curves of the long-duration echoes.

Good quantitative values for the percentage of

meteors in each of these showers must await a

much more detailed study of the tabulated

records, but qualitative values can be found

from figure 2, and are listed in table 1. Eleven

well-marked shower peaks were chosen, including the strong daylight shower complex in June,

and, in addition, two other peaks near September 8 and September 30. An attempt was made

to estimate the background rate, excluding

these major showers, and the values read are

given in the first half of the table. The second

half of the table shows the peak rates that correspond to the shower meteors only.

It is necessary to remember here that all

these rates are based on averages for a complete

day. In cases where a shower radiant is below

the horizon or at low elevation for part of the

day, the peak strength of the shower will appear

smaller in the table than it actually is.
MILLMAN AND MclNTOSH PLATE 1

Springhill Meteor Observatory near Ottawa, Ontario. The meteor radar antennas appear in foreground and left background. The visual observing station is at upper right.

Meteor radar film reader coupled with IBM-024 alphabetic key punch.
MILLMAN AND MclNTOSH PLATE 2

Typical meteor radar range-time record. Over 30 meteor echoes and 2 visual marker appear on this

portion of the film.

a

a

8

8

a

UNI

DAT

1 2

1 2

It?

VEIS

I Tl

1 4

1 4

1 4 .

1 4

Al

«

0 6

0 7

O 9

1 O

1 1

I

0

3

4

5

1

3

4

O

L

3

4

5

0

1

p

3

4

5

U

1

2

3

4

NUMMH

OF

METE CMS

77

87

74

81

66

66

4 5 1

72

71

69

73

65

84

4 3 4

76

86

101

97

81

5 1 8

83

72

90

85

80

81

4 9 1

83

57

78

fl7

68

82

4 5 5

70

72

73

61

54

77

4 O 7

LONG

Out

47

52

54

47

38

32

2 7 O

36

32

25

22

25

33

1 7 3

36

37

33

36

26

2 1 O

26

25

25

27

22

22

1 4 7

2 4

1 4

1 1

1 3

1 6

1 3

9 1

1 7

1 2

1 1

i 7

6

12

6 5

350 bi

3 6

4

6 9

1 4

4

1 4

5 8

12

1 1

1 2

1

B t

1

12

1 1

5 3

1

3 1

1

2 1

•

32 4

13 4

1 1

35

1 1

4 1 O

3

3 1

1 1

3

3 1 3

8212

1

31

3 1

3 6 5

1

12

1

34 3

1

1

2 1

1

2

30

4

2

1

1

1O

|

2

9

-

I 6

I

0

5

2

1

1

1 0

1

1

4

1 3

1

1

8

4

:

l

6

1. 0. T.

N l

1

2

2

1 0

1

4

1

7

1

1 7

1

1

1 2

1

1

t

1

1

1 1

M

1

1

1

5

3

1

6

2

1 6

1

8

1

1

]

1

6

E«

3

2

5

4

2O

1

3

2

1 1

5

ZO

1

6

I S

3

1 7

]

MITIOI

25

3

2

2

1 4

1

1

2

1 5

6

1 5

3

1 1

1

1

1 4

1

1

1

5

0

4

4

1

5

2 4

2

2

4

1 6

6

5

2B

5

5

2 4

1

I S

1 7

IN

3

4

1

3

1 3

3

1

2

1O

3

3

1 9

1

6

6

1 9

6

i

2 2

8

6

5

4

2 7

4

6

5

2 2

5

1 6

1

4

L3

1 6

1 7

1 ADI O

1

3

4

1 6

8

6

2 3

6

4

2 3

a

i

1 2

1 4

Ah

*

4

2 2

;

1 9

1

I S

6

3

2 9

3 0

2 3

IG

0

1

7

3

5

2 7

7

2

6

2 6

8

4 3inmmr 5

3 0

1 0

3O

2 1

CANADA

2

3

3

1

2 2

6

2

2

2 4

1

1 8

4

i

2 3

6

3 3

1

]

1 2

1

4

3

4

2 1

3

4

3

2 2

6

2 2

1

5

3O

6

2 5

3 0

C

4

9

4

6

2 9

5

2

4

3 3

8

4

3 7

4

4

7

3 3

7

2 8

6

6

3 5

A!

15

2

6

1

1 6

1

3

3

1 7

5

6

3 6

7

6

3 9

e

E

6

4 3

8

9

1

6

3 3

SE

0

2

3

4

2 4

4

6

6

3 3

12

5

3 3

5

8

3O

5

6

6

3

7

3 1

6

6

2 4

S

7

5

8

"5

2 7

3

7

6

3 2

14

5

4 1

6

8

4 6

3

8

10

7

lO

4 7

a

4

lO

4

4

6

3 6

3

2

2

1 8

7

3

4

3 0

5

2

2

1 8

•3

6

3 1

7

6

6

2 9

f

2 7

4

1

a

1 5

3

2

3

2 0

1

•5

2 3

5

5

3 5

6

i

2 3

c

6

1 1

3 6

10

1

•?5

1 9

3

4

3

1 7

9

1

7

1

1 1

1

1 1

0

2

1

2

6

1

1

1

4

2

2

1

3

1

1

1

CL/

6

10

10

10

6 6

11

6

9

7

6

10

4 9

19

16

11

8

9 2

11

10

9

1 0

5 9

1U

6

6

3 9

i

2 1

3

15

17

1O

5

7 2

1 3

9

7

1 4

7

5 9

4

2

H

*

3 7

5

1

2 2

1

1 3

i

1 1

ONO

3

1

9 4

•3

1 4

•S

!"»

4 4

3

6 9

7

1 1

4 9

y

4

4

4

2 7

•>

i

I

3

4

3

6

2 8

4

3

3

3

5

3

2 1

1

3

3

2

1 2

3

3

i

1 7

3

1

4

1

3

1 2

1

2

4

1

1

2

1 1

T

lO.r

OAT

7 1 3

7 1 3

7 1 3

7 1 3

7 1 3

7 1 3

Typical sheet of data from the meteor radar, covering the period 6-12 hours U.T., December 14, 1958
METEOR SYMPOSIUM—MTTiLMAN AND McINTOSH

1958 1959

49

I960

JUL

NOV

DEC

EASTERN STANDARD TIME

FIGURE 4.—The monthly mean diurnal echo rate curves for July to December: solid

line, all echoes; dots, echoes with durations 1 second or greater.

On the basis of the absolute numbers of all

echoes, the Geminid shower is by far the

strongest, followed by the Quadrantid shower,

the June showers, and the peak at September

30. But if we look at the long-duration echoes

only, we see that Perseids and Geminids are

about equal in strength, while the Quadrantids

and June showers are only half as strong, and

the rest of the showers much weaker still.

638805—63 5

When we study the differences between the

meteors of the major showers and those of the

general background, the percentage of longduration echoes is of particular interest.

These have been listed in parentheses in table 1.

For the background, roughly 10 percent of all

echoes have durations 1 second or greater, and

2 percent have durations 8 seconds or greater.

We see immediately that most of the showers
50 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Mean hourly echo rate for 1 day

Date

Jan. 3

Jan. 20

Feb. 20

Mar. 20

Apr. 22

May 5

Jun. 11

Jul. 29

Aug. 12

Sep. 8

Sep. 30

Oct. 22

Nov. 20

Dec. 13

Dec. 22

Shower

Quadrantid

Lyrid

V Aquarid

Daytime

S Aquarid

Perseid

Orionid

Geminid

Ursid

Mean

all

135

110

90

105

146

160

169

170

169

165

161

156

150

142

137

145

Background echoes

>lsec

14

11

10

11

16

17

17

17

17

17

16

16

16

15

14

14(10)

>8sec

2

1.5

1

1

2

2.5

3.5

3.5

3.5

3.5

3

3

3

2.5

2

2. 5(2)

all

79

—

—

—

17

53

81

40

31

50

79

49

—

128

13

Shower echoes

>lsec

29(37)*

—

—

—

6(35)

15(28)

35(43)

11(28)

29(94)

2 (4)

3 (4)

6(12)

—

52(41)

5(38)

>8sec

9 (11)

—

—

—

3. 5(20)

2.5 (5)

9.5(12)

2.5 (6)

19. 5(63)

0.5 (1)

0.5 (1)

3 (6)

18.5(14)

4 (31)

'Figures in parentheses are long-duration echo percentages in each category.

have a very much higher percentage of longduration echoes. The Perseid shower is quite

unique in this respect, with over 90 percent of

its members having echoes of duration 1 second

or greater, and over 60 percent, 8 seconds or

greater. Most of the rest of the showers have

from 30 to 40 percent of echoes with durations

of 1 second or greater, and 10 to 20 percent, 8

seconds or greater. The Orionids and the two

September peaks seem to have about the same

percentage of long-duration echoes as the

background.

A mean diurnal hourly rate curve was now

drawn for each month, and corrected for

interference using the correction factor described earlier in this paper. These curves, for

the entire 39 months, are reproduced in figures

3 and 4. The solid lines represent values for

all echoes, and the dots represent echoes with

durations of 1 second or longer. Where heavy

interference prevented the use of data for more

than half the days in a month, the solid line is

replaced by a broken line. Examination of the

diurnal curve for December 1957 makes it

quite obvious that the mean interference

correction factor used was not adequate to

correct for the actual interference experienced

on this occasion. The problem of correcting

for interference became much less acute in 1959

and 1960.

We do not here propose to discuss the

monthly diurnal rate curves in detail. Despite

various fluctuations from year to year, it is

clear that the diurnal curve for any given

month shows certain general characteristics

throughout. This is true both for all echoes

recorded and for the much smaller quantity of

data represented by the long-duration echoes.

The two diurnal maxima which appear near

the equinoxes are particularly prominent in

March. The first of these maxima, in the

early morning hours, tends to be more prominent before March; the second, during the

daylight hours, becomes stronger after March

and has a high absolute value as the complex

of summer daylight showers becomes evident.

The diurnal peak for the long-duration echoes

does not always coincide with that for all echoes.

This is particularly true in the last quarter of

the year, and is no doubt due in part at least

to the effect of showers. The general shape of

the curves for all echoes reproduced in figures

3 and 4 bears a remarkable similarity to the
METEOR SYMPOSIUM—MILLMAN AND McINTOSH 51

FIGURE 5.—Monthly mean rates for all echoes: top curve,

diurnal peak rate; middle curve, overall average rate; lower

curve, diurnal minimum rate.

FIGURE 6.—Monthly mean rates for all echoes taken at 4

specific hours of E.S.T.

predicted diurnal curves computed by Hawkins,8

although the latter were plotted for assumed

observational conditions somewhat different

from those of the Canadian program reported

here.

The mean hourly rates for each month, together with the peak rates and minimum rates

taken from the curves of figures 3 and 4, are

* O.S. Hawkins, "A Radio Echo Survey of Sporadic Meteor Radiants." Monthly Notices Roy. Astron. Soc, vol. 116, pp. 92-104,1960.

plotted in figure 5. Here the high peak rates

in June are a prominent feature, together with

the December peaks and less regular ones in

September and October. In the minimum rates

the low values during February and March

stand out.

To illustrate the changes that occur throughout the year in meteor activity for various

hours in the day, the monthly mean rates for

four specific hours of E.S.T. are plotted in

figure 6. The highest rates definitely tend to

occur near 7 hours and the lowest near 19 hours.

Here again the high rates for the daylight hours

in June are outstanding. The mean rate for

1 hour is definitely higher for the last half of

the year, but does not show as much variation

as might have been expected.

We have begun a much more detailed study

of all these observational data. In particular,

the analysis of the range distribution will make

it possible to estimate with much greater

accuracy both the contributions and the individual characteristics of the various showers.

Correlation with the visual observations will

aid in calibrating the radar records in relation

to the visual data.

Acknowledgments

Many individuals have contributed to the

success of this Canadian IGY-IGC program.

M. J. Neale was chiefly responsible for the

design of the meteor radar equipment, and

members of the staff of the Upper Atmosphere

Research Section at NRC constructed and

maintained it. Those assisting with the film

reading and the IBM processing include Miss

A. M. Baker, Mrs. S. Baron, Mrs. H. Bone,

Mrs. E. Bradley, Miss J. Fagen, Miss D.

Gibson, Mrs. H. MacLean, Mrs. M. McCall,

Mrs. D. M. McKiernan, Miss M. Panet, Miss

J. Proudman, and Miss M. Watson.

Abstract

A meteor patrof radar equipment was put in operation at Springhill Meteor Observatory near Ottawa at the

beginning of October 1957, and a continuous recording of meteor echoes has been carried out since this date. The

antennas are omnidirectional, with operating frequency 32.7 mc/sec and peak power 20 kw. Echoes are recorded on

35-mm film in the form of a range-time record. Echo counts for each 10-minute interval, echo ranges and durations,

and the intensity of background noise are punched manually on IBM cards from the film record.

All film has been read for the 39 months of operation from October 1, 1957, to December 31, 1960, and over

4,400,000 meteor echoes have been recorded. Mean hourly echo rates range from a diurnal minimum of less than

100 to a diurnal maximum which in June at 8h local time may be over 400. The maxima of the major meteor showers

show up more distinctly in the rates for the long-duration echoes. There is a tendency for the shape of the monthly

mean diurnal rate curve to repeat itself in the same months for successive years.

The Harvard Radio Meteor Project*

By Gerald S.Hawkins2

The Radio Meteor Project has been described

by Whipple and Hawkins (1956). It is a

multistation radar system in which a pulse

train is reflected from the ion column of a

meteor. The strength of the echo varies with

time and the pulses form a Fresnel pattern as

described by Davies and Ellyett (1949). The

velocity of the meteor can be found from the

period of amplitude variations and the measured

range, while the angle of approach of the meteor

is given by the time delay between the stations.

Thus the velocity, radiant, and orbit of individual meteors can be found. Gill and Davies

(1956) developed a 3-station system for measuring orbits at Jodrell Bank Experimental Station

in England. The Harvard system has been

designed to give the same data as the Jodrell

Bank equipment and in addition to provide a

measurement of height, deceleration, and distribution of ionization along the trail. A high

sensitivity was chosen to make possible the

detection of meteors at magnitudes -j-12, some

three magnitudes fainter than the limit of Gill

and Davies.

Construction of the system

The work carried out during the construction

period has been described (Whipple and Hawkins, 1960). The completed system is shown

in figure 1. The various components of the

system are described below.

Antenna.—A double trough antenna was used

at the main site. Two 13-element Yagis were

used at the remote sites. Figure 2 shows a

sketch of the double trough, and a photograph

of this antenna is shown in plate 1.

> This research was supported by Lincoln Laboratory, MIT,

AFl9(122)-468/57; National Bureau of Standards, CST-7282, CST-7067;

and National Science Foundation Grant Q-14699. It was published In

detail as Harvard Radio Meteor Project Final Beport of CST-7282;

Dec. 13, 1957, to June 30,1901.

'Harvard College Observatory, Cambridge, Mass., and Boston

University, Boston, Mass.

The antenna pattern for the single trough is

shown in figures 3 and 4: the measurements

were obtained from a scale model. The main

beam, directed at azimuth 113° E of N, has

an elevation of 43°, and the side lobes are more

than 20 db below the gain of the beam center.

The antenna pattern of the double trough in

the vertical plane is also represented by figure 3,

while the horizontal pattern is shown in figure 5.

These patterns were obtained from measurements on the model antenna. The beam width

between half-power points is ± 14° for the

double trough, and ± 25° for a single trough.

The double trough antenna is used both for

transmission and reception and a TR/ATR

switch is used to effect the changeover.

Receivers and radio links.—Superheterodyne

receivers with an intermediate frequency of 3

me were used. Each receiver was fed from a

voltage stabilizer.

The microwave units were standard Raytheon

links (MCR-1000) with a transmitter power of

1 watt. The pulses were carried on the links

at IF frequency of 3 me to the Long Branch

field site of the Bureau of Standards at Havana,

111.

Frequency controls, gate circuits, and display

units.—The master oscillator unit, containing

the time base generator, the 150 kc oscillator,

and the associated divider units are all housed

in the console, shown in plate 1. Plate 2 contains a close-up view of the coaxial lines feeding the double trough antenna, and also a view

of the gating, triggering, and bright-up equipment. The Fresnel and range pulses were displayed on single-beam, three-inch tubes.

Computing program

A detailed computational program had been

prepared for the IBM-704 computing machine

(Whipple and Hawkins, 1956). The reduction

68
54

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

HARVARD RADIO METEOR PROJECT STATION , BLOCK DIAGRAM

MASTER

P.R.F.

GENERATOR

N.B.S.

CONSOLE

MASTER

OSCILLATOR

40.92 Me

MONITORING

EQUIPMENT

TRANSMITTER

MEGA-WATT

TRANSMITTER

STANDBY

30 Kw

TRANSMITTER

Trough-Guide

Antenna

40.92 Me

Trough -Guide

Antenna

40.92 Me

RECEIVER

VIDEO

GATE

AND

TRIGGER

UNITS

No.3 BASE

STATION

VIDEO

VIDEO

13- Element

Yag'i Antenna

13- Element

Yagi Antenna

No. 4 REMOTE

STATION

1 r--

40.92 Me

RECEIVER

6 Kmc

MICROWAVE

LINK

No. 5 REMOTE

STATION

40.92 Me

RECEIVER

I L I I

Link Antenna

6 tone

MICROWAVE

LINK

J_ I

Lpnk Antenna

6 Kmc

MICROWAVE

LINK

6 Kmc

MICROWAVE

LINK

RECORDING CONSOLE

(Na4) (NO5) 6ange)

(SCOPE INDICATORS)

FILM

RECORDING

UNIT

RECEIVERS

FIGURE 1.—Diagram of Harvard radio meteor project system.
METEOR SYMPOSIUM—HAWKINS 55

FIGURE 2.—Artist's sketch of double trough antenna.

of the Fresnel patterns is based upon a comparison of the measured pattern with the set

of theoretical Fresnel patterns derived by

Loewenthal (1956). By comparing the observations with the theoretical pattern, the 90

percent confidence limits are computed for each

Fresnel pattern. In this way we can determine

whether or not significant deceleration has

taken place.

The program was converted from IBM-704

to IBM-7090. A Benson-Lehner film viewer

complete with digitizer was used and this was

coupled to an IBM card punch.

The majority of the records were obtained

with the National Bureau of Standards Collins

transmitter with a power output of 25 kilowatts. A small amount of filming was carried

out at a power level of 1 megawatt. We estimate the limiting visual magnitude was +6 for

the low-power transmitter and +9 for the highpower transmitter.

Results

A total of 407 meteors has been completely

reduced to give radiants, velocities, and orbital

parameters, and the results were published in
56

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

HALF-POWER POINTS

0° 20° 40° 60° 80° 100° 120° H0° 160°

ELEVATION ANGLE (degrees)

FIGURE 3.—Single trough antenna gain pattern (voltage),

vertical plane.

HALF- POWER

POINTS

-80° -60° -40° -20° 0° 20° 40° 60° 80°

AZIMUTH ANGLE (d«er««»)

FIGURE 4.—Single trough antenna gain pattern (voltage),

azimuthal plane.

1/ to-

/

/ 20-

1 \

f \

I \

s

- HALF- POWtn POINTS

\

\

FIGURE 5.—Double trough antenna gain pattern (voltage),

azimuthal plane. (Pattern measured from model by

Radiation Engineering Laboratory.)

condensed form (tables 1 and 2, Whipple and

Hawkins, 1961). Before proceeding with the

discussion of the results we give a histogram of

observing hours in figure 6, since our observing

2 4 6 8 10 12 14 16

Hours central standard time

FIGURE 6.—Histogram of hours of observation.

periods will introduce a statistical bias unless

we operate on a continuous 24-hour schedule.

Not all of the films have been analyzed and the

histogram therefore covers only those films

selected for analysis. Our observations were

made most frequently between 4.00 and 11.00

hours Central Standard Time. This nonuniform coverage was due to many factors,

mainly electrical interference. Our observers

found that interference was more intense during

the daylight hours from 11.00 to midnight, and

we therefore chose to operate during the early

morning hours when our yield of echoes was

higher. We decided that this coverage was

satisfactory for preliminary work since we were

observing both the antisolar radiants and the

apex area of the sky.

The distribution of velocity is given in figure

7. The most frequently observed velocity was

between 30 and 35 km/sec, which coincides with

the peak found by other radio investigators.

The histogram from the Harvard Radio Meteor

Project differs markedly from other radio data

at the high-velocity end. The Harvard data

contain few meteors with velocities greater than

50 km/sec, whereas other observers have found

a subsidiary peak between 50 and 70 km/sec.

We attribute this difference to a statistical bias

in the Harvard data due to the fact that our

observations were made during the months of

December, January, February, March, and

April. At this time of the year the apex of the

earth's path is in a low declination region of the
HAWKINS PLATE 1

a, Console housing the master oscillator unit, b, Double trough antenna.
HAWKINS PLATE 2

a, Close-up view of the coaxial lines feeding the double trough antenna, b, View of

the gating, triggering, and bright-up equipment.
METEOR SYMPOSIUM—HAWKINS

VELOCITY DISTRIBUTION

57

90

80

70

>,r of meteors

o o

JO

J40

30

20

10

n

1 1 1 1 1

—

-

-

-

—

—

1 —

-

-

-

-

In"

1

1 1 1 1 1

20 30 40 50 60 70

Velocity, km/sec

FIGURE 7.—The distribution of velocity.

ecliptic. Our sensitivity decreases as the

radiant altitude decreases, and thus our observations of the apex will not be representative

until the latter part of the year. The poor

observability of low altitude radiants is shown

clearly in figure 8, which gives the distribution

of observed declinations. At the latitude of the

Long Branch Site a radiant with a declination

of —50° never rises above the horizon. A

radiant with 0° declination has a maximum

altitude of 50°, and one with +30° declination

is in the zenith. Photographic and visual

-30 -20 -10 0 10 20 30 40 50° 6

FIGURE 8.—Distribution of observed declinations.

observations have shown that the radiants are

fairly uniformly scattered over the sky and that

there is a broad concentration of radiants

between declinations —30° and +30°. We

presume that the discrimination of our system

against low altitude radiants has caused this

asymmetry in the distribution of declination.

During the period of observation covered in

this report the apex was between declination

0° and —23°, and the number of meteors

observed from this region of the sky was therefore considerably reduced.

Figure 9 shows the distribution of the semimajor axes of the orbits. We have chosen I/a

as our parameter rather than a since the observational errors in I/a are almost constant.

The most frequent value of a is 1.0 in our data,

whereas the corresponding value obtained at

Jodrell Bank was 3.0. In the Harvard data

40

35

30

« 25

o

I 20

o

l .5

z

10

5

0

- JODRELL (2400)

HARVARD (406 meteors) n

L

-u~U

-1.0 -.5 0 .5 1.0 1.5

FIGURE 9.—Distribution of the semimajor axes.

2.0 '/a

638805—63 6
58 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

30

27

24

1 2 .

D

•

o

XI

I 12

9

6

3

0

Q

(407) RADIO

(360) PHOTOGRAPHIC

til.

Geminld.

m m r~-i

Toroidal

group

m

8 10 12 14 16 25

Number of meteors in each stream

27 36

FIGURE 10.—Meteor groups separated by small differences in their orbital

elements.

no correction has as yet been made for the

deceleration of the meteor in the atmosphere.

This deceleration is thought to be insufficient to

account for the difference in the two distributions. A small fraction (3 percent) of the orbits in the Harvard survey was hyperbolic.

We do not consider this percentage significant;

it is the value to be expected from the error

in velocity determination.

South worth (Hawkins and Southworth, 1960)

has applied a criterion for identifying minor

streams amongst the orbits in this survey.

The orbital data were put on punched cards

and sorted so as to find meteor groups which

were separated by small differences in their

orbital elements. The results are shown in

figure 10. From the 407 orbits tested, 53

groupings were found This compares with a

total of 35 groups found from a similar search

of 360 Super-Schmidt orbits. The percentage

of streams in the two sets of data is comparable

because allowance must be made for the larger

number of radio orbits and the fact that these

orbits were concentrated in a 4-month period

of the year.

One of the streams found by this automatic

selection was, of course, the Geminids of December. This well-known major stream of

the nighttime sky serves as a useful check on the

radio system. The mean radiant and velocity

for twelve Geminids is given in table 1. For

comparison we include the mean value of the

Geminids obtained from the Super-Schmidt

camera data (Hawkins and Southworth, 1958).

The agreement in the radiant distribution is

satisfactory, though the difference in declination is a little larger than we would expect.

The difference in velocity shows the effects of

deceleration; the photographic data have been

corrected for deceleration whereas the radio

data have not been corrected. Thus we may

assume that the average deceleration of the

radio meteors in this sample of Geminids is

2.3 km/sec.

TABLE 1.—Geminid data

Radio

Photo

Radiant Position

R.A.

110?9

111?4

Dec.

+ 35?0

+ 32?5

Velocity

km/sec

33.7

36.0

The stream with the largest membership (36

meteors) represents a very complex system of

orbits of high inclination and small eccentricity.

These orbits were similar to those found by

Davies (1957) in the survey conducted at

Jodrell Bank. This grouping of meteors is

shown more clearly in figure 11, where we have

plotted the distribution in inclination for three

values of e. As the eccentricity of the orbit is
METEOR SYMPOSIUM—HAWKINS 59

30

20 -

1 • •

-

TOROIDAL

GROUP

-

r —

i

i

I

I—1_

r1

—-I

J ' —

1

1 • • 1

HARVARD

-—JODRELL

e<0.3

67 METEORS

i—i —

i—i i i

I —• 60 120 180°

20 -

1 • i 1 1

TOROIDAL

GROUP 1 '—

-

i •

r*"»

i

1 H~^ ,

0.3<»<0.7

178 METEORS

10 - -

60 120 180*

0 £ • 60 120 180*

FIGURE 11.—Inclination distribution of meteors.

decreased, there is a tendency for the meteors

to occur with inclinations of approximately

60° to the plane of the ecliptic. For comparison

we show the Jodrell Bank results, and the

agreement is good, though the Harvard data

contain a higher percentage of the circular, inclined orbits in the intermediate values of

eccentricity. These orbits are difficult to account for in terms of our present ideas of

interplanetary material. Previously the photographic observations had shown a marked

concentration of meteor orbits in the plane of

the ecliptic, and the high inclination orbits

were not detected in any great numbers. For

convenience we call this set of orbits the

"toroidal group" because the orbits form a

cylindrical toroid in space.

The time of appearance of the toroidal group

is concentrated at 9.00 hours Central Standard

Time, as can be seen from figure 6. Thus the

radiant points of this group are approximately

at the same longitude as the apex of the earth's

path, since the apex passes through the sensitive

sector between 9.00 hours and 10.00 hours

Central Standard Time.

As far as we can tell there is no reason why

the photographic survey should not have

located this type of orbit. The radiant occurs

at the same longitude as the apex, some 30°

north and south of the ecliptic. Figure 12

shows the distribution of radiant points obtained in the photographic survey (Hawkins

and South worth, 1958) plotted in ecliptic coordinates with the sun chosen as a fixed zero point.

The photographic data contain a concentration

of radiants north of the apex, but the orbits of

these meteors were not circular in nature as the

ones found by the radio survey.

We do not think that the high inclination

orbits found by the radio survey are a result

of selection effects due to the orientation of the

antenna. To investigate this possibility we

have plotted in figure 13 the position of radiants

on an altitude-azimuth diagram together with

the position of the sensitive sector of the

antenna. From the diagram we see that the

radiants of meteors are uniformly scattered

along the sector (the lack of meteors in the

northern half of the sector is caused by our

early-model triggering system which could only

record meteors coming from the southern

quarter of the sky). The radiant points of the

high inclination near-circular orbits are scattered fairly uniformly around the sector in a

manner similar to that of the other types of

orbits. Thus we cannot attribute this grouping

of orbits to a side lobe or to an area of high

sensitivity in our antenna sector.
• 

° 

o 

FIGURE 12.—Distribution of radiants of major streams, minor streams, and sporadic streams.
N "IO ! .EVA

bJ

90°

80°

70°

60°

50°

40°

30°

I0

8

0'

• Normal Radiants

0

 Toroidal Radiants

NORTH

0

 < . ~ / C_eJ_e^tial Equator

NORTHWEST

o .

Antenna Sector

I

WEST SOUTHWEST

FIGURE 13.—Position of radiants.

SOUTH 
62 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

References

DAVIES, J. G.

1957. Radio observations of meteors. In Advances in Electronics and Electron

Physics, vol. 9, pp. 95-128. Academic

Press, New York.

DAVIES, J. G., AND ELLYETT, C. D .

1949. The diffraction of radio waves from meteor

trails and the measurement of meteor

velocities. Phil. Mag., ser. 7, vol. 40,

pp. 614-626.

GILL, J. C, AND DAVIES, J. G.

1956. A radio echo method of meteor orbit determination. Monthly Notices Roy.

Astron. Soc, vol. 116, pp. 105-113.

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.

1960. Statistics of meteor streams. Interim Report No. 44, Harvard Radio Meteor

Project, Harvard College Observatory,

Contract AF 19(122)-458, Subcontract

no. 57.

LOEWENTHAL, M.

1956. Meteor echoes from underdense trails at

very high frequencies. Technical Report

no. 132, Massachusetts Institute of

Technology, Lincoln Laboratory.

WHIPPLE, F. L., AND HAWKINS, G. S.

1956. The Harvard radio meteor program. Final

Summary Report, Harvard Radio Meteor Project, Harvard College Observatory, Contract AF 19(122)-458, Subcontract no. 57.

1960. Radio meteor project. Final report, Harvard Radio Meteor Project, Harvard

College Observatory, Contract CST7067.

1961. Harvard radio meteor project. Final Report, Harvard Radio Meteor Project,

Harvard College Observatory. Contract

CST-7282.
Meteor Rates Observed by Radio-Echo Techniques

During the IGY-IGC Period

By B. L. Kashcheyev1 and K. V. Kostylyov2

Meteor rates were measured at the Kharkov

Polytechnical Institute according to the IGYIGC program. The measurements were started

in December 1957. The wavelength used was

8 meters. Twice since the beginning of the

measurements new types of antenna systems

have been introduced, and the sensitivity of the

receiving equipment has also been increased.

During the first period, from December 1957

to August 1958, a 5-element director antenna and

a half-wave dipole were employed; in the

second period, from September 1958 to March

1960, an 8-element director antenna and a

half-wave dipole were employed for transmission and reception, respectively. During

the third period, since April 1960, 5-element

director antennas have been used for both

transmission and reception. During the observation period the antenna systems were

usually oriented eastward.

The sensitivity of the equipment and the

analysis of the records show that during the

first period mentioned the overwhelming majority of echoes recorded had an absolute visual

magnitude brighter than +6*5. For the

second period this critical value lay between

+7*5 and +8*0, while for the third period it

was +9m. The successive improvements in

the equipment resulted in an increase in the

diurnal rates of meteors recorded, which were

about 1,800, 4,000, and 8,400 for the three

periods, respectively.

From December 1957 to December 1960

observations were made during 330 24-hour

periods and about 1,300,000 echoes were recorded, some 85,000 of which had a duration of

more than 1 second. About 10 to 15 percent of

i Kharkov Polytechnical Institute, U.S.S.R.

> Kazan State University, U.S.S.R.

the echoes can be attributed to major meteor

streams—primarily the Arietids, Geminids,

8 Aquarids, rj Aquarids, Perseids, Lyrids, and

others. The rest can be attributed to sporadic

meteors and the numerous minor meteor

streams that cannot be distinguished from the

sporadic background unless highly directive antennas are used for the meteor-rate measurements.

It is worth noting that the Perseid stream,

although one of the most active for photographic and visual observations, produces a

scarcely noticeable increase in the general number of radio echoes. On the other hand, the

Perseid stream is clearly discernible because

the radio echoes produced by Perseid meteors

have a duration of more than 1 second. This

can be explained by the fact that high-velocity

meteors with a brightness less than + 5 magnitude produce weak radio echoes, and that there

are few faint meteors in the Perseid stream

(Kresakova, 1958). Radio-echo techniques

lead to discoveries of new meteor streams that

cannot be observed by optical methods. The

highest meteor rates are produced by the

Arietid stream. Next highest are those of the

Geminid, Quadrantid, and other streams that

are well known from optical observations.

At the Engelhardt Astronomical Observatory

in Kazan, systematic radio-echo measurements

of meteor rates were made with fixed and

rotating antennas (Kostylyov, 1958). The fixed

antenna was directed to the west and the wavelength was 4.2 meters. With the rotating

antennas two wavelengths were used: Xi=4.2

meters and X2=8.7 meters. The antenna system was rotated in steps of 30°, and stayed in

each position for 5 minutes. Thus during 1

hour the antenna system turned 360° in a

63
64 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

o

h

400

200

n

-

/

1

3

h

i

6

h

9

h

i

I2h

i

.5h

v

I8h 2.h

24h

—

- 200

I2rI5h I8h 2lh

 24h

FIGURE 1.—Yearly means of diurnal variations of meteor

rates as measured in Kharkov in 1959 (X=8 meters); ordinate, hourly rates; abscissa, hours local time.

10

10

0

10

0

10

0

10

0

10

10

0

10

0

10

JAN

MAY

JUN

JUL

AUG

DEC

16 18 20 22 0 2 4 6 8 10 12 14

FIGURE 2.—Diurnal variations of meteor rates as measured

in Kazan in 1959 (X=4 meters); ordinate, hourly rates;

abscissa, hours U.T.

horizontal plane. With X!=4.2 meters, both

the transmitting and the receiving antennas

were 7-element directors, raised to the height of

2XX above the ground. With X2=8.7 meters,

the antennas were 5-element directors with

horizontal jibs, and the height above the ground

was X2/2.

For the 17 months of observation in the period

1958 to 1960, the equipment with fixed antenna

and Xi=4.2 meters was employed during 205

24-hour periods; 35,000 echoes were recorded

and the mean daily rate was 160. The equipment with the rotating antenna system (Xi=4.2

meters) was employed during 229 24-hour

periods in 1958 to 1960; about 30,000 echoes

were recorded and the mean daily rate was 130.

The equipment with rotating antenna system

and X2=8.7 meters was employed during 290

24-hour periods in the period 1958 to 1960;

about 369,000 echoes were recorded and the

mean daily rate was 1,270.

Figures 1 and 2 show the mean diurnal

variations of meteor rates, and figures 3 and 4

show the seasonal variations. The diurnal and

seasonal rates as obtained in Kazan and in

IO00 - - 1000

I 31 SI EC 3E 21 KI n. x 31 HE

FIGURE 3.—Monthly variations of meteor rates as measured

in Kharkov in 1959 (X=8 meters); ordinate, monthly means

of daily meteor rates; abscissa, numbers of the months.

600

400

200

FIGURE 4.—Monthly variations of meteor rates as measured

in Kazan in 1959 (X=4 meters); ordinate, monthly means

of daily meteor rates; abscissa, numbers of the months.
METEOR SYMPOSIUM—KASHCHEYEV AND KOSTYLTOV 65

Kharkov are in good agreement, so that the

data can be discussed together. The discussion here, however, will be based mostly upon

the data obtained in Kharkov, since most of

the echoes were recorded there. The survey

of seasonal variations is based upon the measurements made in Kharkov in 1959 because the

sensitivity of the equipment was kept constant

throughout that year.

The minimum monthly means of diurnal

meteor rates in 1959 occurred in February and

March and were 2,834 and 2,695, respectively,

while the maximum monthly mean, 7,832,

occurred in June. Thus there was a threefold

change of monthly means within a year. The

difference between certain daily rates is still

greater: 2,000 echoes for some dates in March

and 10,000 echoes in June during the Arietid

shower. In December 1959, during the Geminid shower, daily rates reached 8,500.

Hourly meteor rates vary widely from 30

echoes for the period 17h00m to 19h00m in January

through March, and up to 1,000 for the Arietid,

Geminid, and Quadrantid showers. In broad

outline, meteor rates show the same daily

variations from year to year. During the

year, meteor rates reach their maximum in

the neighborhood of the moment of the culmination of the apex (6h

 local time). Two more

maxima can be observed in the periods about

10h to 11* and lh to 2h. Hawkins (1956) has

shown that these maxima are explained by the

fact that most meteoroids producing meteors

brighter than +6m move directly in orbits

whose inclination to the ecliptic is small.

In May and June, the former of the two

maxima predominates (10b to ll h), while in

August and September, the latter (lh to 2h).

As has been shown by Kashcheyev, Lebedinets,

and Suvorov (1960), twice within the year (in

May-June and August-October) the earth

crosses in opposite directions a wide belt of

meteor orbits which adds to the usual background of sporadic meteors observed in December through April.

References

HAWKINS, G. S.

1956. A radio echo survey of sporadic meteor

radiants. Monthly Notices Roy. Astron.

Soc, vol. 116, pp. 92-104.

KASUCHETEV, B. L.; LEBEDINETS, V. N.; AND SUVOROV,

Y. I.

1960. Meteor rates from observations in Kharkov

during 1957-1960. In Meteors, collection of papers, V. V. Tolstov, ed., vol. 1,

pp. 11-20. Publ. House of Kharkov

Univ., Kharkov.

KOSTTLTOV, K. V.

1958. The equipment of the Engelhardt Astronomical Observatory for radio-echo

meteor measurements with automatic

recording. Astron. Journ. U.S.S.R., vol.

35, pp. 643-651.

KBESAKOVX, M.

1958. On the presence of faint meteors within

the Perseid stream. Bull. Astron. Inst.

Czechoslovakia, vol. 9, pp. 82-88.

638805—63

The Orbits of Meteor Streams Determined by

Radio-Echo Techniques

By B. L. Kashcheyev,1 V. N. Lebedinets,1 and M. F. Lagutin1

During the IGY-IGC period, special equipment was developed at the Kharkov Polytechnical Institute for radio-echo determination

of orbits of individual meteors.

The observation technique (Kashcheyev,

Lebedinets, and Lagutin, 1960) was similar to

that used at Jodrell Bank by Gill and Davies

(1956). The equipment consisted of a pulse

transmitter (X=8 meters) and three receivers.

One of the receivers was situated at the transmitter site; the other two receivers were at

distances of 4.5 and 7.1 km, and the directions

to them from the central station made an

approximately right angle. The signals as

received by the two receivers were retransmitted to the central station. Three amplitude-time patterns were recorded for every

meteor. From these patterns, meteor velocity

and time shifts between the corresponding

maxima and minima of the diffraction patterns

were determined. The orbits were computed

according to the scheme proposed by Kleiber

(1891).

The electronic computer "Ural" was used for

this purpose and it took about 5 minutes to

compute each orbit. Meteors brighter than

about +8 magnitude were recorded.

Systematic measurements were started in

November 1959. In this paper the data given

and discussed are those obtained for meteors

of the Geminid, Arietid, and S-Aquarid showers

as well as for 360 sporadic meteors recorded in

November and December 1959.

When observations of the Geminid shower

of 1959 were planned, their principal purpose

was considered to be the checking of the accuracy obtainable during observations. Dur-

> Kharkov Polytechnical Institute, TJ.8.S.R.

ing the 5 nights of the period from December

9 to December 14, 298 Geminid meteors were

recorded. Table 1 shows coordinates of the

radiants and orbital elements given as mean

values for each night.

The root-mean-square error of velocity measurements for one meteor is ±1.8 km/sec.

From an analysis it is seen that the following

factors contribute to the errors in velocity

measurements:

1. Errors made in the evaluation of the

atmospheric deceleration involved

(± 0.6 km/sec).

2. Metering errors (±0.75 km/sec).

3. Errors due to turbulent winds in the

atmosphere (±0.5 km/sec).

4. Errors due to diffusion expansion of a

meteor trail during the period when

principal Fresnel zones are being

formed.

The root-mean-square error in the determination of the coordinates of meteor radiants

is ±2°5. There are two error terms, the first

being due to errors in determination of velocity

and the second being due to errors in measurements of time delays. The latter, in their

turn, are due to turbulent winds in the atmosphere. On the average, the two errors terms

are equal.

Throughout the Geminid shower, systematic

variations of the elements of the orbit occur

as follows:

a=110°36'+52'

g=+32°18'—14'

Fa, =36.15+0.30

a=1.320+0.036

e=0.892+0.0045

(Xo-2600)

(Xo-260°)

(Xo-260°)

(Xo-260°)

(Xo-260°)

67
6 8 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Radiants, orbital elements, and meteor rates for Geminid shower, December 9-14, 1959

Dates

No.

meteors

Orbital

elements

a

S

a

vm

e

q

i

a

Dec. 9-10

31

108T90

+32!57

35.48

1.26

0.881

0.138

22 °A

257?2

326 °.O

±0?44

±0?41

±0.43

±0.04

±0. 005

±0.004

±1?1

±l?0

Dec. 10-11

40

110T28

+33?30

35.50

1.26

0.881

0. 143

24!2

258? 1

325?7

±0?52

±0?45

±0.31

±0.36

±0.005

±0.005

±0!9

±0?8

Dec. 11-12

90

lll?05

+32T43

35.83

1.29

0.889

0. 137

23 ?3

259 ?2

326 !8

±0?28

±0?23

±0. 19

±0.02

±0.003

±0.003

±0!5

±0!4

Dec. 12-13

74

111?59

+ 32 TOO

36.06

1.34

0.891

0. 139

22 ?3

260?2

325T6

±0?33

±0?27

±0.21

±0.03

±0. 003

±0. 003

±0?6

±0?5

Dec

112?50

+32?07

36.66

1.41

0.898

0. 136

23!5

261 ?2

325 "A

13-14

62

±0!3

±0?31

±0.20

±0.04

±0.003

±0.003

±0?7

±0?5

These variations agree with similar data

on 15 orbits determined by Whipple (1954)

from photographic observations of Geminid

meteors:

cr=lll°35'+46' (Xo—260°)

8=+32°35'-9' (Xo-260°)

F.=35.95+0.27 (Xo-260°)

0=1.301+0.050 (Xo-260°)

e=0.892+0.0033 (XQ—260°)

As was shown by Kashcheyev and Lebedinets

(1959), towards the end of the Geminid shower

the proportion of large particles increases.

An increase in a and e as well as a simultaneous

increase in the proportion of large particles

towards the outer periphery of the stream seems

to be due to the evolution of the meteor stream

resulting from the Poynting-Robertson effect

or from the effect of deceleration by interplanetary matter.

In the period from June 6 to June 18, 1960,

347 meteors of the Arietid stream were recorded.

Table 2 shows coordinates of the radiants and

orbital elements given as mean values for the

period of observations, and compared by

statistical methods with those obtained at

Jodrell Bank from radio-echo observations in

the period 1950 to 1952 (Lovell, 1954). The

daily motion of the radiant is Aa=+48'4;

A3= + ll!l. The data obtained from the two

stations show good agreement.

From July 14 to August 14, 1960, orbits ot

153 meteors of the 5-Aquarid stream were

determined. Table 3 shows coordinates of

the radiants and orbital elements, given as

mean values for the 153 meteors, and compared

with those obtained from five photographic

meteors (Wright, Jacchia, and Whipple, 1954).

The daily motion of the radiant is Aa= + 51'0;

A5=+22'5. The coordinates of the radiant

are given with respect to the longitude of the

sun, XO=126?9. A satisfactory agreement

of the data obtained by the two methods is

seen, but the scatter of the individual data in

both cases is rather high.

In November and December 1959 measurements were made to obtain orbits of 360 sporadic meteors; of these, 19 orbits were found to

be hyperbolic, but this may have been due to

measurement errors.

Comparison of our data with those for

photographic meteors (Whipple, 1954) shows

a rather good agreement in the distribution

of orbits according to their eccentricities.

For most of the orbits 0.7<«<1.0. For 25

percent of the orbits «<0.7; with photographic

meteors the percentage is lower, namely 10

percent. The difference is greater when the

distribution of the orbits according: to their

inclinations is analyzed; that is, there is a large

group of orbits where 40 °<i<150°. Figure 1
METEOR SYMPOSIUM—KASHCHEYEV, LEBEDINETS, AND LAGTJ1TN 6 9

TABLE 2.—Radiants and orbital elements of Arietid meteors observed from two stations

Station

Kharkov

Jodrell Bank

a

44

44

?2

S

23

22

?3

?7

38.9

38.3

a

1.

1.

Orbital elements

98

57

e

0.941

0.943

Q

0.098

0.093

i

18

17

!5

?3

n

77

77?5

u

to to

CO COO 00

Source

Kharkov

Wright, et. al.

(1954)

TABLE 3.—Orbital data

a

341

339

"A

?2

8

-16?4

-16?7

of 5-Aquarid meteors, July 14-August

Orbital elements

vm

41. 1

43.0

a

2.22

2.60

e

0.96

0.976

q

0.08

0.061

14, I960

i

28?2

29 ?3

n

306

302

!9

°.9

151

154

?3

".7

shows the distribution of the meteor orbits

according to their inclination and eccentricity.

e

i.o

0.5

o.o 50 100 150

FIGURE 1.—Distribution of meteor orbits according to their

inclinations to the plane of the ecliptic and to their

eccentricities.

A particular group of orbits (about 13 percent

of the total) appears that are not found from

photographic observations. These orbits are

characterized both by 40° <t < 150° and by

e<0.7. Orbits of that type were first obtained

from radio-echo observations at Jodrell Bank.

The importance of orbits of this type for

cosmogony is discussed by Davies and Gill

(1960).

References

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.

GILL, J. C, AND DAVIES, J. G.

1956. A radio echo method of meteor orbit

determination. Monthly Notices Roy.

Astron. Soc, vol. 116, pp. 105-113.

KASHCHETEV, B. L., AND LEBEDINETS, V. N.

1959. On the structure of the Geminid meteor

stream. Astron. Journ., U.S.S.R., vol.

36, pp. 629-640.

KASHCHETEV, B. L.; LEBEDINETS, V. N.; AND LAGUTIN,

M. F.

1960. The orbit of the Geminids of 1959. In

V. V Tolstov, ed., Meteors, Collection of

papers, vol. 1, pp. 25-37. Publ. House

of Kharkov Univ., Kharkov.

KLEIBEH, I. A.

1891. Determination of orbits of meteor streams.

St. Petersburg.

LOVELL, A. C. B.

1954. Meteor astronomy. Clarendon Press, Oxford.

WHIPPLE, F. L.

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

59, pp. 201-217.

WRIGHT, F. W.; JACCHIA, L. G.; AND WHIPPLE, F. L.

1954. Photographic 5-Aquarid meteors. Astron.

Journ., vol. 59, pp. 400-406.

The Distribution of Small Interplanetary Dust Particles

in the Vicinity of Earth

By C. W. McCracken1 and W. M. Alexander1

One of the components of the solar system is

a cloud of dust particles surrounding the sun.

The importance of the cloud arises not only from

cosmogonal aspects such as the sources and

composition of the dust particles, but also from

cosmological aspects such as the rapidity with

which changes occur in their dynamical characteristics. Properties of the dust particles and

the general shape and extent of the dust cloud

have been inferred from observations of meteors and from photometric studies of the zodiacal

light and the solar corona. Uncertainties in

conclusions reached on the basis of such inferences arise because of the differences that possibly exist between the classes of dust particles

responsible for the two vastly different phenomena. New and independent methods of

determining selected parameters of the dust

particles are needed in order to remove the

uncertainties that presently exist in the knowledge of their physical characteristics and

distributions.

A new technique that holds great promise for

supplying some of the most-needed parameters

has been developing very rapidly during the

past few years. This technique is that of

measuring (in space) various parameters of

statistical samples of dust particles. The

direct measurements that are presently available have been obtained as dust particles

impacted onto special sensors mounted on

rockets, earth satellites, and other spacecraft.

The sensors that have been flown have

necessarily been of very simple design and have

provided only limited information about the

dust particles. The experiments have been

designed primarily to give preliminary infor1

 Ooddard Space Flight Center, National Aeronautics and Space

Administration, Oreenbelt, Md.

mation about the influx rate or spatial density

of dust particles over a limited but astronomically important range of particle mass. More

sophisticated experiments capable of defining

selected parameters of individual dust particles

are possible and technically feasible in the very

near future.

Radar, visual, and photographic techniques

are used in observing meteoric phenomena

produced by meteoroidal dust particles. The

dust particles studied by direct measurement

techniques are too small to produce meteoric

phenomena and cannot be observed by the

ground-based techniques common to studies of

meteors. The magnetic spherules found in

deep-sea deposits and in high-altitude collections of atmospheric aerosols may include

extraterrestrial material, but positive identification of this component is extremely difficult.

Volatile cometary debris does not appear in

either of the collections, and there has been

little or no success in the identification of

siliceous particles as being of extraterrestrial

origin.

One is left with the conclusion that there are

basically two effective techniques of experimentally acquiring reliable information about

the distributions and physical characteristics of

small interplanetary dust particles. The first

technique is photometry of the zodiacal light

and the solar corona (from outside the atmosphere of Earth as well as from the surface of

Earth). The second technique is that of making

statistical samples within the dust cloud by the

direct-measurements technique. The directmeasurements technique can include the returning to Earth of collections of dust particles

from outside the atmosphere of Earth as well as

the direct measurements of selected parameters

71
72 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

of dust particles in space. The two techniques

must remain complementary. Each should

supply information unique to the method as

well as provide information to be used in advancing the other technique.

Spacecraft carrying instruments for obtaining

direct measurements can be used for probing

comets and meteor streams simultaneously with

studies of the dust cloud. Probes sent through

comets and meteor streams would provide

valuable information about the physical conditions and processes within such collections

of dust particles. The direct-measurements

technique represents an interesting, useful, and

almost unique means of studying small particulate aggregates of matter in selected regions

of the solar system as well as in the vicinity of

Earth.

Interpretations of direct measurements

The available direct measurements must be

periodically reviewed in order to determine how

consistently they fit into one or another pattern

that has physical meaning. The direct measurements have, until just recently, been of such a

nature that they could be given either of two

interpretations. The choice of interpretation

depended critically upon the assumptions that

one was willing to accept during an analysis of

the data.

The two interpretations of direct measurements that could be given prior to obtaining the

new direct measurements from Explorer VIII

(Satellite 1960 Xi) were: (1) The mass distribution and spatial density of small interplanetary

dust particles indicated by the direct measurements differ significantly from those predicted on

the basis of linear extrapolations (over about

six orders of magnitude) of results from observations of meteors; or (2) the direct measurements indicate the existence of an appreciable

geocentric concentration of interplanetary dust

particles. The conjectural geocentric concentration mentioned here is of the type proposed

by Beard (1959), and should not be confused

with concentrations arising from the temporary

suspension of dust particles above the temperature inversion layers in the atmosphere of

Earth.

The direct measurements obtained with

Explorer VIII strongly indicate that the first

of the two interpretations of the presently

available direct measurements is the correct

one. The second interpretation is not compatible with an analysis in which the direct

measurements from Explorer VIII are used as a

basis for analyzing other direct measurements.

The first interpretation should, therefore, be

regarded as correct until direct measurements

of the vectorial velocities of impacting dust

particles have been obtained. The direct

measurements from Explorer VIII serve as the

first firm basis for analyzing existing direct

measurements of interplanetary dust particles.

A review of the available direct measurements

(including those from Explorer VIII) obtained

with microphone systems is sufficient to

demonstrate the validity of the foregoing statements about the interpretation of the direct

measurements.

Direct measurements from Explorer VIII

A definitive set of direct measurements recently

was obtained with the satellite Explorer VIII.

Two independent systems for studying interplanetary dust particles were mounted on the

satellite. The systems provided data from

launch on 3 November 1960 until the power

supplies were exhausted on 13 December 1960.

One of the systems included a photomultiplier

tube as the sensor for measuring the luminous

energy generated in hypervelocity impacts of

dust particles. A microphone was used as the

sensor in the other system for the purposes of

counting impacts and determining the magnitudes of the impulses delivered by impacting

dust particles.

Two sounding boards of the microphone

system were mounted on the lower cone of the

spin-stabilized satellite. The spin vector of the

satellite lay within approximately 40° of the

apex of Earth's motion during the active lifetime of the satellite. The "sounding boards"

were arranged to detect dust particles for which

the radiants generally lay on the hemisphere

centered on the antapex of Earth's motion. An

average particle velocity of 25 km/sec has been

assigned for Explorer VIII until the velocity

distribution of interplanetary dust particles

can be determined.

The best calibrations that are at present

possible for the microphone system show that it
METEOR SYMPOSIUM—McCRACKEN AND ALEXANDER 73

is sensitive to a quantity which is closely related

to the momentum of an impacting dust particle.

Calibrations have been accomplished with lowvelocity particles impacting elastically onto

sounding boards to which the microphones

were attached. Hypervelocity particle accelerators are now being used in order to obtain

more realistic calibrations. The mass sensitivity of a microphone system can be computed

from the momentum sensitivity if an average

particle velocity is assumed.

The microphone system of Explorer VIII

was designed to count impacting dust particles,

and to determine in which of three ranges the

momentum of each particle lay. A preliminary

readout of the data has established approximately the number of dust particles encountered

for each of the three ranges of sensitivity. In

addition to determining the average influx rate

within each range, the data have defined the

shape of a section of an average mass-distribution curve. This section extends over a limited

but significant range of particle mass, and

provides a basis for analyzing all the other

available direct measurements of interplanetary

dust particles.

A tabulation of the preliminary data from

Explorer VIII has not been included in this

PARTICLE MASS IN GRAMS

FIGURE 1.—The average distribution curve established by

preliminary results from Explorer VIII.

paper, to avoid the unnecessary propagation of

preliminary numerical results that may change

slightly. The three datum points obtained

with the microphone system on Explorer VIII

are corrected for the effect of shielding by Earth,

and are plotted as a cumulative mass-distribution

curve in figure 1. The three datum points

represent the impacts of more than 3,100 dust

particles registered during an interval of 40

days. The large number of impacts provides

statistical weight for the datum points from the

two ranges of highest sensitivity. The spacing

of the threshold sensitivities allows one to

establish definitively the shape of a segment of

an average distribution curve that extends

over approximately three orders of magnitude

in particle mass.

Direct measurements from other satellites

and spacecraft

Direct measurements have been obtained with

rockets, earth satellites, and space probes flown

by both the United States and the Soviet Union.

Dust-particle sensors carried by these payloads

have included microphones, photomultiplier

tubes, thin films, erosion grids, wire grids, and

pressurized chambers. The microphone system

is probably the best calibrated of all the sensors,

and certainly has been flown more times and

on more payloads than any other sensor.

It is sufficient, for the analysis summarized in

this paper, to consider only those direct measurements obtained with microphone systems.

The data obtained with microphone systems are

entirely adequate to establish an average distribution curve for interplanetary dust particles

in the vicinity of Earth. It may be qualitatively stated that the direct measurements obtained with other systems do not indicate that a

distribution curve different from the one established by the direct measurements obtained

with microphone systems should be considered.

The U.S. satellites and spacecraft for which

direct measurements with microphone systems

have been obtained are listed, together with the

relevant data, in table 1. The data for Explorer I (Satellite 1958 Alpha) and Pioneer I

are those given by Dubin (1960). The total

number of impacts (145) for Explorer I was used

in computing an average influx rate even though

approximately one-half the impacts probably
74 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

represented a "shower" component (Dubin,

1961). The high influx rate during the ' 'shower"

is approximately counteracted by an interval

with a low influx rate. An influx rate computed

from the total number of impacts serves very

well as the average influx rate from Explorer I

to be used in establishing an average distribution curve. A factor of 2 was used in correcting

the influx rate from Explorer I for the shielding

effect of Earth.

The microphone system on Pioneer I registered 25 impacts, of which 17 probably represented dust particles. The average influx rate

was computed on the basis of 17 impacts. No

correction was made for the shielding effect of

Earth because Pioneer I spent most of its time

at large geocentric distances (2 to 19 Earth's

radii).

Preliminary results for the microphone system on Vanguard III (Satellite 1959 Eta) were

reported by LaGow and Alexander (1960).

Reading of the telemetered data is still in progress, so the preliminary results shown in table 1

may change slightly. Approximately 6,000

impacts were recorded during 80 days of

operation. Approximately 2,800 of the impacts

occurred during a 70-hour interval on 16-18

November (Alexander, McCracken, and LaGow, 1961). An average influx rate was computed for Vanguard III on the basis of ~ 3,500

impacts. This number allows for the sporadic

background during the 70-hour interval. A

factor of 1.5 was used to correct for the shielding

effect of Earth. An average particle velocity of

30 km/sec was used in computing the threshold

mass sensitivities for the microphone systems

on all the spacecraft listed in table 1.

Direct measurements reported by Nazarova

(1960) from the microphone systems mounted

on Soviet satellites and spacecraft are included

in table 2. Portions of the information shown

have been computed from information given by

Nazarova in order that data from United States

and Soviet spacecraft may be included in the

same analysis.

The sensitivities for the microphone systems

on the Soviet spacecraft were expressed by

Nazarova in terms of particle mass. Nazarova

computed the mass sensitivities by assuming

that the microphone systems were energysensitive and that the average particle velocity

was 40 km/sec. McCracken (1959) used 40

km/sec in an early analysis of direct measurements, but this value is almost certainly too

high.

Whipple (1957) assigned different values of

average velocity to different sizes of dust

particles. The velocities varied from 28 km/sec

for meteoroids to 15 km/sec for small dust

particles of the direct-measurements range of

particle size. In order to avoid prematurely

constraining the model distribution of interplanetary dust particles, we have assigned a

value of 30 km/sec as the average particle

velocity when the spacecraft is not oriented

or when the dust particle sensors are open to

an omnidirectional flux. Average particle velocities for oriented sensors are chosen according to the orientation of the solid viewing

angle of the sensor.

The mass sensitivities for the systems on the

Soviet spacecraft are reduced by the square

of the ratio of 40 to 30 in order to compensate

for the difference in the assigned average

particle velocities. The spacecraft—Lunik I

(Mechta, 2 January 1959), Lunik II (Lunar

Probe, 12 September 1959), and Lunik III

(Satellite 1959 Theta)—operated at large geocentric distances, so corrections for the shielding

effect of Earth are not necessary.

The influx rates measured by Sputnik III

(Satellite 1958 52) underwent tremendous

changes during the first 3 days of operation

of the equipment. The influx rates, as reported by Nazarova (1960), were 4 to 11 particles m~2

 sec"1 on 15 May (launch day), 5X10"4

particles m~2 sec"1 on 16-17 May, and less

than 10~4 particles m~2 sec"1 during the interval 18-26 May. Nazarova attributes the

high influx rates during the first few days to a

meteor shower, but the manner in which the

influx rate changed could also be suggestive

of payload interference. Only the influx rate

for the last 9 days of operation of Sputnik III

is of any value in establishing an average distribution curve. It is not clear whether

Nazarova corrected the influx rate from Sputnik III for the shielding effect of Earth, so the

influx rate is left as it was given.

The method of encoding information into

the telemetered signal for Lunik I was such

that only very crude upper limits for the
TABLE 1.—Direct measurements obtained with microphone systems on the U.S. satellites and space probes

Spacecraft

Explorer I

Pioneer I

Vanguard III

Momentum

sensitivity

(dyne seconds)

> 2. 5X10-8

> 1 . 5X10-*

>i. oxio-»

Mass sensitivity

(grams)

8. 3X10-"

5. OX 10-'

1

3.3X10-'

Effective area

(meter')

2.3X10-»

3. 9X10-*

4. OX 10-'

Exposure time

(seconds)

7.9X10*

1. 1X10

5

6. 9X10«

Erposuro

(m> sec)

1. 8X10

4

4.2X10*

2.8X10"

Number of

particles

145

25 (17)

~3500

Cumulat

(partic

Observed

8.4X10-*

4.0X10-8

1.3X10-8

TABLE

Spacecraft

Sputnik III

Lunik I

Lunik II

Lunik III

2.—Direct measurements obtained with microphone systems on the Soviet satellites and space probes

Mass sensitivity (grams)

ro-40 km/sec

8. 0X10-'—2. 7X10-8

2.7X10-8—1.5X10-7

1. 5X10-

7— 5.6 X10~«

>5. 6X10-«

2. 5X10-'—1.5X10-

8

1.5X10-8—2.0X10-7

>2. 0X10-7

2. 0X10-'—6. 0X10-'

6. 0X10-'—1.5X10-8

> 1.5X10-8

1.0X10-'—3. 0X10-'

3. 0X10-»—8. 0X10-'

> 8. 0X10-'

0O-3O km/sec

1.4X10-8—4.8X10-8

4.8X10-8—2.7X10-7

2.7X10-7—1. OX 10-"

>i. oxio-»

4.4X10-'—2. 7X10-8

2.7X10-8—3.6X10-7

>3. 6X10-7

3. 6X10-»—1. 1X10-8

1. 1X10-8—2.7X10-8

>2. 7X10-8

1. 8X10-'—5.3 X10-'

5. 3 X10-«—1.4X10-8

> 1.4X10-8

Effective

area

(meter')

0.34

0.2

0.2

0. 1

Exposure

time

(seconds)

~8X10»

3.6X10*

1. 1X1O«

2.3X10*

Exposure

(m> sec)

~3X10

8

7.2X10*

2.2X10*

2.3X10*

Number of

particles

?

< 1 6

< 4

< 1

0

0

2

1

5

1

Influx rate 

(Nazarova)

(see text)

<2X10-*

<5X10-*

<ixio-*

<5X10~

5

<5X10-»

9X10"»

4X10-*

2X10-8

4X10-*
76 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 3.—List of rockets with microphone-type dust-particle sensors

Rocket

V-2 Blossom IV-D

V-2 Blossom IV-G

Aerobee No. 58

Aerobee No. 77

Aerobee No. 80

Aerobee No. 81

Aerobee No. 87

Aerobee No. 88

Nike-Cajun AF-1

Nike-Cajun AF-2

Nike-Cajun AA6.203

Nike-Cajun AA6.204

Nike-Cajun AA6.205

Nike-Cajun AA6.206

Spaerobee 10.01

Spaerobee 10.02

Launch time and date

0819 MST

0630 MST

0730 MST

0808 MST

2212 MST

0944 MST

0533 MST

2200 CST

0600 CST

2125 CST

2145 CST

1047 CST

1327 CST

8 Dec.

31 Aug.

14 Sept.

9 Apr.

16 July

18 July

14 Oct.

16 Oct.

24 Apr.

1 May

15 Oct.

14 Oct.

17 Oct.

21 Oct.

22 Oct.

25 Oct.

1949

1950

1955

1957

1957

1957

1957

1957

1958

1958

1958

1958

1958

1958

1958

1958

Zenith

altitude

(kilometers)

~135

~135

100

27

122

146

114

167

137

151

137

143

157

177

420

Type of data

First direct measurement

Qualitatively fair data

Qualitatively fair data

No data, vehicle failure

Quantitatively good data

No data, vehicle failure

No data, telemetry difficulty

Quantitatively good data

No data, thermal interference

Quantitatively fair data

Quantitatively good data

Quantitatively good data

No data, mechanical failure

Quantitatively fair data

Quantitatively fair data

No data, telemetry failure

influx rates could be set. Only that influx rate

measured by the scale of highest sensitivity is

of any value in the present analysis.

Direct measurements from rockets

Signals that could be ascribed to no other

source than the impacts of dust particles onto

the skins of rockets were first found on the

telemetry records for two V-2 rockets. The

rockets were V-2 Blossom IV-D flown on 8

December 1949, and V-2 Blossom IV-G flown

on 31 August 1950. Microphones and the associated electronics had been designed and installed by personnel of Temple University under

the direction of Prof. J. L. Bohn. The equipment was flown for the purpose of measuring

acoustical intensities in the warheads and on the

skins of the rockets. Descriptions of the

instrumentation and the data have been given

in detail by Bohn and Nadig (1950).

Bohn and Nadig tentatively suggested that

the unexplained pulses observed on the telemetry records were caused by the impacts of

meteoric particles on the skins of the rockets.

This explanation may now be regarded as the

correct one. The data from these flights were

the first direct measurements of interplanetary

dust particles ever obtained. Both sets of data

should be regarded as being qualitatively fair

but of no use in quantitative discussions of

interplanetary dust particles.

The spare equipment from the V-2 flights

was mounted on Aerobee No. 58 and flown on

14 September 1955, as has been reported by

Dubin (1956). The rocket did not reach a

sufficiently high altitude for observation of dust

particles that had not been appreciably decelerated by atmospheric drag forces. Signals that

probably were caused by the impacts of dust

particles were recorded, but the data must be

classified as qualitatively fair.

Bohn and Nadig (1950) also proposed that

rockets carrying special acoustical systems for

counting the impacts of dust particles be flown.

Preferably, the rockets were to have nose tips

that could be ejected in order to expose a

circular diaphragm. Shielding the diaphragm

during the passage of the rocket through the

lower atmosphere served to eliminate the

possibility that spurious counts were being

introduced by the aerodynamic heating of the

sensor. The type of rocket program that was

suggested was earned further under the direction of Mr. M. Dubin, then of the Air Force

Cambridge Research Center.

A list of the rockets that have carried microphone systems is given in table 3. Aerobee

No. 77 was the fourth rocket to carry a micro-
METEOR SYMPOSIUM—McCRACKEN AND ALEXANDER

TABLE 4.—Basic corrected data for the successful OSU rockets

77

Rocket

Aero bee No. 80

Aerobee No. 88

Nike-Cajun AF-2

Nike-Cajun AA6.203

Nike-Cajun AA6.204

Nike-Cajun AA6.206

Spaerobee 10.01

Range of momentum sensitivity

(dyne seconds)

6.0X10-«-3.0X10~8

3.0X10-»-8.0X10-»

1.0X10-»-3.0X10-»

3.0X10-*-1.8Xi0-J

1.3X10-*-2.0X10"»

2.0X10-*-2.6X10-*

4.7X10-*-1.0X10"»

1.0X10-»-2.8X10-»

6.0X10-*-1.2X10-'

I.2X10-*-4.0X10-3

4.0X10-»-3.0X10-»

s.oxio-^-s.oxio-8

3.0X10-»-1.8X10-a

7.0X10-*-3.0X10-»

3.oxio-«-3.oxio-»

1.5X10"*-1.0X10-»

1.0X10-»-6.0X10-»

7.0X10-*-5.0X10"»

5.0X10-*-7.5X10-»

Effective area

(meter»)

0.05

0.05

0.5

0.5

0.05

0.05

0.5

0.5

0.2

0.2

0.2

0.2

0.04

Time

A>110km.

(seconds)

100

60

154

186

167

118

202

Exposure

A > 110 km.

(m« sec)

5.0

5.0

50

50

3.0

3.0

30

30

31

37

33

24

8. 1

Number of

impacts

39

10

2

1

5

1

10

7

30

12

3

52

3

31

1

11

1

6

20

phone system and was the first of a series of 13

rockets instrumented with microphone systems

and flown by Oklahoma State University under

contract with the Air Force. The series of

rockets was flown especially for the purpose of

directly measuring influx rates and momenta of

interplanetary dust particles. Aerobee No. 77,

like the other Aerobees in the series, had two

crystal microphones mounted on the skin of the

instrument compartment, and two microphones

mounted on a circular diaphragm that could be

exposed by ejecting the nose tip of the rocket at

an altitude of about 60 km. The diaphragm

had been highly polished by Bohn in the hope

of observing hypervelocity craters on the

recovered diaphragm. The rocket reached

zenith at an altitude of 27 km, which was too

low for proper operation of the microphone

system. The recovered diaphragm was examined photochemically by Yagoda (Dubin,

1957), who found several tiny craters resembling

those formed by hypervelocity impacts of

small dust particles.

Seven of the thirteen rockets provided data

that are of use in quantitative discussions of

interplanetary dust particles. A preliminary

readout of the data from six of these rockets

was included in an early analysis of direct

measurements by McCracken (1959). A final

readout of the unconnected data from the seven

rockets was made available as a final report on

the contract, being dated 14 April 1960 (Buck,

1960).

The data for the seven rockets are given

in table 4. Corrections have been applied for

the counts that possibly could have causes

other than the impacts of dust particles. The

data from Nike-Cajun AF-2 are slightly

rearranged in order to compensate for a change

in sensitivity that occurred as a result of a

low battery potential during the flight. A

corrected tabulation of the data from the OSU

rockets has not previously been made available

in the open literature because of the series of

corrections that were in progress and have

only recently been completed.

Only those impacts that occurred when the

rockets were at altitudes greater than 110 km

are counted. The deceleration of dust particles

by atmospheric-drag forces becomes quite

appreciable at altitudes below approximately

100 km. The velocities of the dust particles

become functions of altitude and zenith angle,

making the determination of the velocities of

the particles relative to a rocket an almost

impossible task. Setting the lower limit on
78 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 5.—Direct measurements obtained with the OSU rockets

Rocket

Aerobee No. 80

Aerobee No. 88

Nike-Cajun AF-2

Nike-Cajun AA6.203

Nike-Cajun AA6.204

Nike-Cajun AA6.206

Spaerobee 10.01

Momentum

sensitivity

(dyne seconds)

6. 0X10-*

3. 0X10-*

1. 0X10-*

3. 0X10-*

1. 3X10-4

2.0X10-5

4.7X10-4

1. OXIO"3

6. 0X10-*

1.2X10-'

4. 0X10-*

3. 0X10-*

3. OX10-*

7. OX 10-*

3. 0X10-»

1. 5X10"4

1. 0X10-"

7. OX 10-*

5. OX 10-*

Particle

velocity

(km/sec)

70

70

40

40

20

20

35

35

40

35

40

35

60

Mass

sensitivity

(grams)

8. 6X10-"

4. 3X10-10

2. 5X10-10

7. 5X10-10

6. 5X10-"

1. 0X10"»

1. 3X10-10

2. 9X10-10

1. 5X10-10

3. 0X10-10

1. 0X10-9

8. 6X10-"

8. 6X10-10

1. 8X10-10

7. 5X10-10

4 3X10-"

2.9X10-1°

2. 0X10-10

8. 3X10"11

Number

of Impacts

49

10

3

1

6

1

17

7

45

15

3

55

3

32

1

12

1

6

20

Exposure

A>110km.

(m> sec)

5.0

5.0

50

50

3.0

3.0

30

30

31

37

33

24

8. 1

Cumulative

Influx rate

(partlcles/mtysec)

9.8

2.0

6.0X10-2

2. OXlO-i

2.0

3. 3X10"1

5.7X10-1

2. 3X10"1

1.5

4.8X10-'

9. 7X10~»

1.5

8. lXlO-2

9.7X10-»

3.0X10-2

5. 0X10-1

4.2X10-2

2. 5X10"1

2.5

altitude at 110 km allows one to assume that

the majority of the dust particles impacting

onto the sensors had not been appreciably

decelerated by atmospheric-drag forces. Geocentric velocities of dust particles above the

atmosphere of Earth lie between 11 and 72

km/sec, so velocities of the dust particles

(relative to the rocket) lie approximately

between the same limits.

It seems reasonable to assign average particle

velocities for each sensor of each rocket until

the velocity distribution becomes known. The

average particle velocities have been assigned

on the basis of the region on the celestial

sphere (relative to the apex of Earth's motion)

to which each sensor was exposed. The limiting mass sensitivity of each sensor is computed

from the momentum sensitivity and the

assigned average particle velocity. Table 5

contains the limiting momentum sensitivities,

the assigned average particle velocities, the

limiting mass sensitivities, and the numbers of

impacts from which datum points for a cumulative mass distribution curve were computed.

The direct measurements made with the

rockets served as an early and preliminary

determination of the influx rate and mass

distribution of small interplanetary dust particles. The data were of considerable importance in the design of the dust-particle

experiments for the early satellites and space

probes. The degree of importance may be

partially illustrated by the fact that the rocket

data showed influx rates higher by a factor of

104 than was expected on the basis of an

extrapolation of the tabulation by Watson

(1941) of the results from observations of

meteors, and higher by a factor of 102 than was

expected on the basis of a similar extrapolation

by Whipple (1957). The weight and power

allotments on the early satellites did not permit

one to build in enough dynamic range to allow

for such uncertainties in the influx rate. It

is interesting and perhaps of moderate quantitative value if the rocket data agree with and

support the more definitive direct measurements now available from satellites. The

rocket data probably should not, however, be

used as the decisive element in a critical test

of the validity of a particular model of the

distribution of dust particles in the vicinity

of Earth.

Analysis of the direct measurements

The available direct measurements that have

been obtained with microphone systems on
METEOR SYMPOSIUM—McCRACKEN AND ALEXANDER 79

I V

1

o

0

M -1

]>*

K METI CLES/

z ATI

at -4

x'°

3

Z

Itf*

irf*

• •

V

\ •

m•

*

-

-

-

1

V

Nk

w

1

®

<•>

•

•

0

EXPLORE* S m (PRELIMINARY)

VANOUJAROID

EXPLORE* I

OSU ROCKETS

SPUTNIK m

SPACE ROCKET I

SPACE ROCKET I t

INTERPLANETARY STATION

PIONEER I

\

\

PARTICLE MASS IN GRAMS

FIGURE 2.—The average distribution curve established by

direct measurements from microphone systems for interplanetary dust particles in the vicinity of Earth. (Space

Rocket I, Space Rocket II, and Interplanetary Station are

referred to in the text as Luniks I, II, and III, respectively.)

the OSU rockets, U.S. spacecraft, and Soviet

spacecraft are shown plotted as a cumulative

mass-distribution curve in figure 2. The various direct measurements, with the exception of

the one from Pioneer I, fit remarkably well

onto the distribution curve, regardless of the

geocentric distance or sensitivity at which the

measurement was made. The departure of

the direct measurement for Pioneer I from the

average distribution curve can easily be explained on the basis of the actual fluctuations

in the influx rates measured with Explorer I,

Vanguard III, and Explorer VIII. Pioneer I

was active for about \% days and easily could

have flown during an interval of low dustparticle activity.

The direct measurements Us ted in tables 1,

2, and 5 encompass a variety of altitudes,

sensitivities, lengths of sampling interval, and

times of the year. The fact that all except

the direct measurement from Pioneer I fit the

distribution curve established by Explorer VIII

lends substantial support to the validity of the

curve shown in figure 2 as an average distribution curve that can be used until more sophisticated experiments have established the curve

over a considerably larger range of particle

mass.

It is quite advantageous to the present

analysis to point out the uncertainties that

are encountered in displaying the direct measurements as a mass distribution. Qualitative

discussions of the uncertainties are followed by

attempts to assign them numerical values.

The values of average particle velocity

assigned in converting from momentum sensitivity to mass sensitivity for the systems may

be slightly too high. The correct values

depend on the velocity distribution that exists

for dust particles in the direct-measurements

range of particle size. Lower average velocities would apply if most of the dust particles

were in geocentric orbits or direct circular

heliocentric orbits. The use of lower particle

velocities would tend to shift the direct measurements toward slightly higher values of

particle mass without markedly changing the

shape of the distribution curve. Even a

radical reduction from about 30 km/sec to the

value 15 km/sec used by Whipple would lower

the threshold mass sensitivities by only a

factor of 2.

The impulse delivered to a sensor as a dust

particle impacts at hypervelocity is almost

certainly greater than the impact-momentum

of the dust particle, but the value remains

unknown. A value greater than unity (which

is used in tables 1, 2, 4, and 5) for the ratio

of the impulse to the impact-momentum increases the momemtum sensitivities for microphone systems. The proper correction factors

probably lie between 2 and 3, and are now

being established by hypervelocity accelerators.

Allowing for the impacts of dust particles

at angles of incidence appreciably different

from 0° effectively decreases the momentum

sensitivity, but the decrease is probably less

than a factor of 2. This uncertainty can be

largely removed through the use of more

directional sensors.

The magnitude of the correction for the

shielding effect of Earth depends on the velocity

distribution of the dust particles. The corrections that have been applied involve the

assumption that the dust particles are pre-
80 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

dominantly in heliocentric orbits and are not

necessarily confined to direct circular orbits.

If this assumption is not valid, then slightly

smaller corrections would be applied. The

factors applied to correct for Earth's shielding

of the spacecraft were all less than or equal to 2.

Smaller correction factors would shift the direct

measurements toward slightly lower values of

influx rate without changing the shape of the

distribution curve.

Knowing which of the minor corrections to

apply requires a better knowledge than exists

at present of the mass distribution, velocity

distribution, and spatial density of the interplanetary dust particles. All of the direct

measurements have been handled in as consistent a manner as possible, so that introducing

minor corrections will change only the position

of the direct measurements on a plot of mass

distribution without changing the shape of the

distribution curve. It seems reasonable to

assume that likely combinations of the minor

uncertainties will leave the distribution curve

as it is shown in figure 2. Direct measurements

obtained at large distances from Earth and/or

a determination of the velocity distribution

are needed before much further progress can

be made in defining a model distribution of the

interplanetary dust particles.

The distribution curve shown in figure 2 can

be approximated reasonably well by a straightline segment. The equation of the straight

line is

log / = —17.0 —1.70 log m,

where / is the influx rate in particles m~2 sec"1,

and m is the particle mass in grams (McCracken, Alexander, and Dubin, 1961). The

equation should not be used outside the range

10"10 gm<m<10"6 gm, and applies for an

average particle velocity of 30 km/sec.

The distribution curve shown in figure 2 is

intended to be an average for dust particles

in the vicinity of Earth. Whether the distribution is the same in interplanetary space is a

question that cannot yet be answered. If an

appreciable concentration exists near Earth,

then the influx rates measured at comparable

sensitivities but at different geocentric distances

should be functions of the geocentric distance.

The influx rates measured at large geocentric

distances (Lunik II, 3.6X10* km; Lunik III,

4.7 X105 km) should fall appreciably below those

from the earth satellite Explorer VIII. The

low altitude (~150 km) rockets should have

shown influx rates considerably higher than

those obtained with Explorer VIII. With the

exception of the direct measurement from

Pioneer I, the departures of direct measurements from the distribution curve established

by Explorer VIII are negligible.

The distribution curve of figure 2 is shown,

together with the model distributions of

meteors from Watson (1941) and Whipple

(1957, 1960), in figure 3. None of the linear

extrapolations of the results from observations

of meteors fits the direct measurements. The

curves labeled "Watson (1941)" and "Whipple

(1957)" approximately represent limits for the

uncertainty encountered in placing average

influx rates for meteors on a mass-distribution

curve. The uncertainty of approximately 200

arises because the mass-to-magnitude relationships are not well known for meteors, and

exceeds by one to two orders of magnitude the

uncertainties that exist for the direct measurements. The curve labeled "Whipple (I960)"

represents a revision |by Whipple of the curve

LOG PARTICLE MASS IN GRAMS

FIGURE 3.—Comparison of model distribution curves obtained

from extrapolations of results from observations of

meteors.
METEOR SYMPOSIUM—McCRACKEN AND ALEXANDER 81

labeled "Whipple (1957)" made in an attempt

to remove the discrepancy between the linearly

extrapolated meteor curves and the direct

measurements.

Whipple (1960, 1961a, 1961b) performed an

analysis of the direct measurements and concluded that "Acoustical impacts of meteoritic

dust on counting devices that are carried by

satellites and space probes show clearly that a

high concentration of interplanetary dust occurs

near the earth" (Whipple, 1961b, p. 21). In his

analysis, Whipple used the departures of direct

measurements from the curve that is labeled

"Whipple (I960)" in figure 3 in order to show

that the geocentric concentration varied inversely as the 1.4 power of distance from the

surface of Earth. Such an interpretation

represents the second of the two interpretations

that were possible before the direct measurements were obtained with Explorer VIII.

Whipple's approach is incompatible with the

new direct measurements from Explorer VIII

and is not particularly supported by any of the

other available direct measurements.

The following paragraphs present arguments

against statements that the direct measurements confirm the existence of a geocentric

concentration of dust particles.

The datum points representing the largest

numbers of impacts (Explorer VIII, Vanguard

III, Explorer I, OSU rockets) fit the same

straight-line segment (see fig. 2), regardless of

the altitude at which a particular direct measurement was obtained.

One must allow for the differences in sensitivity of the various microphone systems before

comparing the influx rates to see if an altitude

dependence exists. This requires normalizing

all the direct measurements to a given value of

particle mass. The distribution curve used as

the normalization standard is extremely critical

to the interpretation of the direct measurements. Using the conjectural curve labeled

"Whipple (I960)" as the normalization standard leads one to the conclusion that the direct

measurements indicate a geocentric concentration. Using the empirical distribution curve

established by Explorer VIII leaves one with

no discernible evidence from the direct measurements that a geocentric concentration of dust

particles exists.

The slopes of straight-line segments of the

distribution curve shown in figure 2, separately

indicated by each of the three groups of direct

measurements (U.S. spacecraft, Soviet spacecraft, OSU rockets), are between —1.5 and

—2.0. These values differ significantly from

the value of approximately —1.2 that was used

by Whipple (1960) in order to normalize the

direct measurements in such a manner that a

geocentric concentration would be evident.

The most critical datum points in Whipple's

analysis were the direct measurements from

the OSU rockets and those from Explorer VI.

It should be pointed out that in adjusting the

sensitivities of the systems on the rockets,

Whipple has introduced an error of about 15

in the influx rate. The data from Explorer

VI have not been placed in the open literature

by the experimenters, so it should not be used

as a critical point.

Conclusions

Several interesting conclusions can be reached on

the basis of the new distribution curve that has

been established by the direct measurements of

interplanetary dust particles. Some of the more

important are discussed in the following paragraphs.

The average distribution curve established

by the direct measurements can be approximately represented over the range of mass

10~10 gm<m<10" 6 gm, by a straight-line

segment. The equation of the line segment is

log / = —17.0—1.70 log m,

where / is the omnidirectional influx rate in

particles m~2 sec"1.

Particulate aggregates of matter accreted

by Earth consist primarily of dust particles

smaller than the faintest radar meteors, with

an accretion rate of approximately 10* tons

per day on Earth. This rate is in good agreement with the earlier estimate (Dubin, 1959)

based on the direct measurement from Explorer I.

The convenient constant-mass-per-magnitude

relationship, common to discussions of results

from observations of meteors, does not hold

for dust particles in the direct measurements

range of particle mass. The distribution curve
82 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

established by the direct measurements departs

markedly from the distribution curves obtained

by extrapolating linearly the results from observations of meteors.

The available direct measurements extend

almost into the range of particle mass where

radiation-pressure control becomes important.

A rather marked change in the shape of the

distribution curve should occur as a result of

radiation pressure at values of particle mass

slightly lower than those presently covered by

the direct measurements.

The distribution curve established by the

direct measurements can be joined to a model

constant-mass-per-magnitude curve for meteors

within the range of particle size typical of the

faint radar meteors. Such a junction probably

has little physical meaning until the mass-tomagnitude relationship can be established for

meteors, or until statistically significant direct

measurements can be obtained in the range of

particle mass 10~7 gm<m< 10~5 gm.

The direct measurements now available show

(within themselves) no discernible evidence for

the existence of an appreciable geocentric concentration of interplanetary dust particles. If

a geocentric concentration does exist, then its

existence can be reliably inferred from the type

of direct measurements that is presently

available only if future direct measurements

obtained at large geocentric distances deviate

appreciably from the average distribution

curve shown in figure 2.

This curve can be used only to describe

average conditions. It is already known from

the direct measurements that fluctuations in

the influx rate of at least ±10 occur within

intervals of a few hours for particles with

masses of approximately 10"10 gm (Dubin,

Alexander, and Berg, in this symposium, p. 109).

The magnitude of the fluctuations presumably

becomes quite large for particles near the radiation pressure limit on particle size. The distribution curve is slightly biased toward the autumn

of the year because of the distribution in time of

year of the direct measurements. If the annual

variation in influx rate of dust particles resembles that of meteors, then the curve shown in

figure 2 represents influx rates that are slightly

higher than the true average values.

Large inconsistencies have been attributed

to the direct measurements several times in

the literature (Whipple, 1959; Kaiser, 1961).

The various direct measurements seem to be

remarkably self-consistent when analyzed on

the basis of the new measurements from Explorer VIII, in which the authors place much

confidence.

Discussion

Unidentified speaker.—I wonder about the

assumption of the average velocity of 25 to 40

km/sec for micrometeorites. It appears that

the average velocity of meteorites is below 20

km/sec, and I would expect these particles to

be in even more circular orbits and therefore

at even lower velocities.

C. W. McCracken.—I assumed a value of 30

km/sec. That, at most, introduces an uncertainty of a factor of 2 in the placement of the

curve on the mass distribution plot.

References

ALEXANDER, W. M.; MCCRACKEN, C. W.; AND LAGOW,

H.E.

1961. Interplanetary dust particles of micron-size

probably associated with the Leonid

meteor stream. Journ. Geophys. Res.,

vol. 66, pp. 3970-3973.

BEARD, D. B.

1959. Interplanetary dust distribution. Astrophys. Journ., vol. 129, pp. 496-506.

BOHN, J. L., AND NADIG, F. H.

1950. Researches in the physical properties of the

upper atmosphere with special emphasis

on acoustical studies with V-2 rockets.

Research Institute of Temple University,

Report No. 8, pp. 1-26.

BUCK, R. F.

1960. Acoustic detection of meteoric particles.

Research Foundation, Oklahoma State

Univ., Final Report, Contract No.

AF 19(604)-1908.

DUBIN, M.

1956. Meteoric bombardment. In Scientific uses

of earth satellites, J. A. Van Allen, ed.,

pp. 292-300. University of Michigan

Press, Ann Arbor.

1957. Discussion following paper by Thomas C.

Poulter. In Proceedings of the Second

Hypervelocity and Impact Effects Symposium, May 22-24, Washington, D.C.,

pp. 11-12.
METEOR SYMPOSIUM—McCRACKEN AND ALEXANDER 83

DUBIN—Continued

1959. Cosmic debris of interplanetary space. In

Vistas in astronautics, M. Alperin and

H. F. Gregory, eds., vol. 2, pp. 39-45.

Pergamon Press, New York.

1960. IGY micrometeorite measurements. In

Space research, H. K. Bijl, ed., pp.

1042-1058. North-Holland Publishing

Co., Amsterdam.

1961. Remarks on the article by A. R. Hibbs,

"The distribution of micro meteorites

near the earth," Journ. Geophys. Res.,

vol. 66, pp. 2592-2594.

KAISER, T. R.

1961. The incidence of interplanetary dust. Ann.

G6ophys., vol. 17, pp. 50-59.

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, H. K. Bijl, ed., pp.

1033-1041. North-Holland Publishing

Co., Amsterdam.

MCCRACKEN, C. W.

1959. An analysis of rocket and Earth satellite

measurements of micrometeoric influx.

Thesis, Oklahoma State University.

(See also Appendix B, Oklahoma State

Univ., Final Report, Contract No.

AF 19(604)-1908.)

MCCRACKEN, C. W.; ALEXANDER, W. M.; AND

DUBIN, M.

1961. Direct measurement of interplanetary dust

particles in the vicinity of Earth.

Nature, vol. 192, pp. 441-442.

NAZAROVA, T. N.

1960. The results of studies of meteoric dust by

means of Sputnik III and space rockets.

In Space research, H. K. Bijl, ed., pp.

1059-1062. North-Holland Publishing

Co., Amsterdam.

The Blakiston Co.,

WATSON, F. G.

1941. Between the planets.

Philadelphia.

WHIPPLE, F. L.

1957. The meteoritic risk to space vehicles.

Presented at VHIth Int. Astronautical

Congress, Barcelona, 1957. Published

in Proceedings, pp. 418-428; SpringerVerlag, Vienna, 1958.

1959. Solid particles in the solar system. Journ.

Geophys. Res., vol. 64, pp. 1653-1664.

1960. The particulate contents of space. Presented at Third Symposium on the

Medical and Biological Aspects of the

Energies of Space, Texas, 1960. Published in Medical and biological aspects

of the energies of space, P. Campbell, ed.,

pp. 49-70. Columbia University Press,

New York, 1961.

1961a. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

1961b. Dust halo. Space World, vol. 1, No. 8,

p. 20 ff.

Abstract

Existing direct measurements of small interplanetary dust particles in the vicinity of Earth are analyzed on the

basis of a new set of data obtained with the satellite Explorer VIII. All but one of the direct measurements made

with microphone systems fit remarkably well onto the distribution curve derived from the Explorer VIII data.

This good fit allows one to establish an average distribution curve for small interplanetary dust particles in the

vicinity of Earth.

The equation of a straight-line segment that approximately fits the new distribution curve for particle masses

in the range lO"10 gm<m <10-« gm is

log / = -17.0-1.70 log m,

where I is the influx rate in particles m~2 sec"1. One of the more important consequences of the new distribution

curve is the fact that the particulate matter accreted by Earth is dominated by particles with characteristic dimensions

of a few microns.

Micrometeorite Measurements from Midas II

(Satellite 1960 r 1)

By R. K. Soberman * and L. Delia Lucca

 2

To detect micrometeorites in the vicinity

of the earth, instruments similar to those used

on earlier satellites (Cohen, 1960) were carried

on the Midas II (1960 fl) earth satellite.

Midas II was launched, on May 24, 1960, into

an approximately 500-kilometer circular orbit

which was inclined 33° with respect to the

equatorial plane of the earth.

Five detectors were mounted on the vehicle

as shown in figure 1. Three of the detectors

were acoustic or microphone type and two were

wire-grid type. The dotted lines in the sketch

indicate a detector facing outward on the other

side of the vehicle.

The vehicle was designed to maintain a stabilized attitude, with the end shown on the right

in figure 1 pointing radially outward from the

earth. Attitude stabilization was not achieved.

Data obtained from other experiments on the

vehicle indicate that it was tumbling, but the

data are inadequate to determine the attitude

history of the vehicle.

Data from the acoustic detectors were acquired only for impacts that occurred while the

vehicle was being interrogated by a receiving

station. Provision had been made to acquire

data over other portions of the orbit, but the

vehicle recorders did not operate. The wire

grids are inherently data-storage devices.

Breaks in the wires that occur during any part

of the orbit can be detected by periodically

monitoring the continuity of the wires, and the

number of breaks is accumulated.

Data (from stations located in Hawaii,

California, and Florida) were obtained from

parts of four orbits before the telemetry system

> Geophysics Research Directorate, Air Force Cambridge Research

Laboratories, Bedford, Mass., and Northeastern University, Boston,

Mass.

* Geophysics Research Directorate, Air Force Cambridge Research

Laboratories, Bedford, Mass.

failed. Approximately 4,000 seconds of data

were acquired from the acoustic detectors,

while the grids provided data for 25,000 seconds

of exposure.

Although the amount of data is small compared to that accumulated from other satellite

vehicles, these are the first reported measurements at this altitude. In the light of recent

hypotheses (Whipple, 1961; Hibbs, 1961) regarding the altitude variation of micrometeorite

flux, it is felt that these results, although scanty,

are worth mentioning.

Sixty-seven impacts were recorded on the

three acoustic units, and were distributed over

the four partial orbits for which data were

acquired, as shown in figure 2. The solid lines

indicate the portions of the flight path where a

"clean" or noise-free signal was received. Since

the total exposed area of the three acoustic

plates was 686 square centimeters, the data

represent a mean flux of 0.25 particles per

square meter per second. The mean momentum

sensitivity of the three acoustic unite as determined by dropping spherical glass beads on

the plates was 3±lXlO~* gm cm/sec. No

shielding corrections have been applied. On

the assumption of a mean velocity of 15 km/sec,

the sensitivity represents a flux measurement of particles of mass greater than 2 X 10~10

gm. Further, if spherical particles of mean

density 3 gm/cms are assumed, the impacting

particles would be larger than 5 microns in

diameter.

No wire grids were broken. An area of 790

square centimeters of grids was exposed. The

wire diameter was approximately 20 microns.

Previous work (Cohen, Corman, and Dubin,

1959) has indicated that hypervelocity particles

10 microns in diameter or larger should break

85
86 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

MICROMETEORITE

DETECTOR

ACOU STI C

MICROMETEORITE

OE TECTOR - GRID

FIGURE 1.—Earth Satellite 1960 f 1

this size wire. Therefore, the flux of particles

larger than 10 microns in diameter is less than

5XlO~4 particles per square meter per second.

If one assumes the type of distribution function that is commonly arrived at from various

data considerations such as Whipple's meteoric

risk curve (Whipple, 1958), then the data from

the two types of detectors appear to be inconsistent. That is, the ratio of fluxes from the

two types of measurements is greater than 500

where the particle sizes differ by a factor of

2 or so, depending upon the assumptions made

regarding velocity and density.

One might thus disregard the acoustic

measurements with the assumption that the

units were not working properly, or that either

vehicle noise was being introduced or thermal

noise was occurring within the units themselves.

This is the usual manner of accounting for high

flux rates observed from the first day's data of

practically all satellite vehicles.

For several reasons it is felt that the acoustic

data should not be discarded. First, the microphones and plates were acoustically isolated

from the vehicle. There was only one instance

where all three acoustic units were triggered

during the one-second interval between readouts. This triple coincidence, shown in figure

2, was not included in the total count or in the

flux calculations. Second, although the microphone and grid measurements appear to be

inconsistent with each other, more recent information is now available that shows that the

values obtained are reproducible. A preliminary reduction of the data from the Satellite

1961 al has been completed. These results

are not yet in final form and may vary slightly.

They are presented here for comparison purposes only. Satellite 1961 al was in a circular

polar orbit at approximately the same altitude

(about 500 kilometers) as Satellite 1960 fl.

Similar experiments of approximately the same

sensitivities were carried out. Data were

obtained from parts of 23 orbits, again only

over readout stations. The data from the

acoustic units yield a mean influx of 0.34 particles per square meter per second. It should

also be pointed out that while the measured

acoustic flux shows statistical variations over

the 23 orbits, it does not appear to decrease

with time. Also on Satellite 1961 al eight

breaks occurred in the wire grids. These all

occurred after the first interrogation somewhat

as follows: No break during the first orbit;

three breaks in the next 7 orbits; 1 break in the

second 7 orbits; and finally 4 breaks in the last

8 orbits This leads to a flux of particles

detectable by the wire grids (i.e., larger than

10 microns in size) of 8X10~* m~2sec~l. The

ratio for the Satellite 1961 al acoustic-grid

measurements is about 400 as compared with

greater than 500 for Midas II. A complete

report on the Satellite 1961 al measurements

will be published shortly.

It is felt that the similarity of the measurements from Satellites 1960 fl and 1961 al

cannot be ignored. Despite the apparent inconsistency the values appear to be reliable.

Varying the assumed values for velocity and

density within reasonable limits does not change

the particle diameters appreciably since the

cube root of these values is involved in the

calculation. It may be necessary to reexamine the calibration of these devices by

means of hypervelocity techniques now available to resolve the apparent discrepancy. The

possibility of a large variation in the distribution function can be eliminated. The acoustic

units on board Satellite 1961 al had two

momentum sensitivities. The lower sensitivity

range (with the previously assumed values for

velocity and density) should have a threshold

of 10 microns. The recorded fluxes are not

consistent with the wire-grid data.

The remaining possibility that can be suggested is that fluffy particles of very low density,

that might not be able to break the wire grids,

are the major constituent of the acoustic flux.
METEOR SYMPOSIUM—SOBERMAN AND DELLA LUCCA 87

35

2O'N

I O M

ORBITS FOR

SATELLITE I960

Jo'e 'so* TTC** iW no5

iTo1* MTOTW iW w * /©5*w

LONGITUD E

FIGURE 2.—Occurrence of micrometeorite impacts.

This possibility does not agree with empirical

formulas of hypervelocity penetration, but

cannot be entirely discounted. It is not

presently possible to check this hypothesis in

the laboratory since techniques for accelerating

fluffy particles do not yet exist.

Finally, the relationship between the acoustic

data reported here and the altitude variation of

micrometeorite flux should be pointed out.

Figure 3 shows a curve similar to that given by

Whipple (1961). The acoustic flux as measured

from Satellite 1960 fl (corrected to a value of

10~9 gm by assuming a mass distribution function which is proportional to m~L2

 and a velocity

of 15 km/sec) has been added. The corrections

are the same as those applied to the other

satellite points in Whipple's paper. The early

acoustic rocket data, about which there is some

dispute, have been deleted and a new curve

with a slope of —1.1 has been fitted to the

o.o

To - 1.0

— - 2.0

- 3.0

- 4.0

-5.0

I960

ZOD

CLD

2.0 Z.0 4.0

LOG ALTITUDE (km)

5.0

FIGURE 3.—Meteoritic impact (mass = 10~* gm) versus altitude from the earth. (Revised from Whipple, 1961.)
88 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

points. It should be pointed out that with the

exception of the zodiacal cloud, all the points

were obtained with satellite acoustic detectors.

In conclusion, the data reported here establish that a discrepancy exists between the acoustic and the wire-grid measurements which must

be resolved before the dust content of the

interplanetary medium is understood. However, if one considers the acoustic measurements

in a purely relative manner, it appears that

there is a geocentric variation in the micrometeorite flux.

Acknowledgment

The authors are indebted to Dr. L. Bohn of

Temple University for his cooperation and

assistance in the preparation of this experiment,

and to Mr. H. A. Cohen, who began this experiment.

References

COHEN, H. A.

1960. Measurements of flux of small extraterrestrial particles. Geophys. Res. Dir.,

Research Notes, no. 28.

COHEN, H. A.; CORMAN, A.; AND DTJBIN, M.

1959. Calibration of micrometeoritic detectors

used in satellites and rockets. In

Proceedings 3d Symposium on Hypervelocity Impact, vol. 1, pp. 405-421.

Armour Research Foundation, Chicago.

HIBBS, A. R.

1961. The distribution of micro meteorites near

the earth. Journ. Geophys. Res., vol.

66, pp. 371-377.

WHIPPLB, F. L.

1958. The meteoritic risk to space vehicles. In

Proceedings 8th International Astronautical Congress, Barcelona, 1957, pp. 418-

428. Springer-Verlag, Vienna.

1961. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

Abstract

Five micrometeorite sensing devices were carried on board the Midas II (Satellite 1960 f 1) which was launched

into an approximately 500-kilometer circular equatorial orbit on May 24, 1960. The five devices consisted of three

acoustic detectors and two wire-grid detectors. Data were obtained for four partial orbits. These data were recorded

in real time. There were no breaks in the wire grids which could record impacts of particles larger than 10 microns.

Sixty-seven impacts were recorded on the acoustic detectors which had a momentum threshold of 3 X 10~4 gm cm/sec

and a total area of 0.0686 m3. These results indicate a flux of 0.25 m~2 sec"1 of particles 5 microns in diameter or

larger if one assumes a mean velocity of 15 km/sec and a density of 3 gm/cmJ for the particles. The discrepancy

between acoustic and wire-grid data will be discussed. These results will be compared with those obtained from

other satellite measurements.
SOBERMAN, HEMENWAY, et al. PLATE 1

Venus Flytrap nose cone. Left to right: fully closed, fully open, and partly open.
SOBERMAN, HEMENWAY, et al.

Typical micrometeorite collecting box.
Micrometeorite Collection from a Recoverable

Sounding Rocket. I

By R. K. Soberman,1 C. L. Hemenway,2 T. G. Ryan,3 S. A. Chrest,4 J. Frissora,4

and E. F. Fullam6

On June 6, 1961, at 5:31 a.m., M.S.T., an

Aerobee 150 rocket, descriptively named the

"Venus Flytrap," was successfully fired from

the White Sands Proving Ground in New

Mexico. Photographs of the nose cone or

"payload" section of that rocket are shown

in plate 1. The photograph at the left

shows the nose cone in the fully closed position

in which it was fired and traveled up through

the lower atmosphere. An electric motor then

raised the outer skin or ogive assembly (photograph at right), and finally another motor, aided

by the spin of two revolutions per second,

which was applied to the rocket, extended the

eight "leaves" outward to complete the opening

cycle (middle photograph). The nose cone

was designed to fly in this last position through

the upper atmosphere, exposing collectors

mounted on the tops of the leaves and on the

internal structure. Prior to reentry the rocket

was "de-spun," thus allowing the nose cone to

be resealed, and the booster section was severed

explosively from the payload. At an altitude

of 6 kilometers a parachute was deployed and

the nose cone descended to the ground where

recovery was effected.

Four of the leaves carried a penetration

experiment (sketched in fig. 1) which covered

a total area of 0.24 square meter. The first

1

 Geophysics Research Directorate, Air Force Cambridge Research

Laboratories, Bedford, Mass., and Northeastern University, Boston,

Mass.

1

 Dudley Observatory, Albany, N.Y., and Union College, Schenectady, N.Y.

* Geophysics Research Directorate, Air Force Cambridge Research

Laboratories, Bedford, Mass.

* Northeastern University, Boston, Mass.

* Ernest F. Fullam, Inc., Schenectady, N.Y., and Dudley Observatory, Albany, N.Y.

two layers were Mylar films 6 microns thick.

These films were examined prior to the flight

by means of a helium leak detector to insure

that there were no holes. In addition to flux,

penetration, and cratering data, it was hoped

that this experiment might yield some zenith

angle information if more than one layer were

penetrated by the impinging particles.

A second type of experiment carried on the

vehicle were surfaces which were intended to

trap particles of lesser momentum (that is,

submicron particles if such existed, or somewhat larger particles which had been sufficiently slowed down in the atmosphere).

These surfaces were mounted in aluminum

boxes for cleanliness. Eight such boxes, each

having an open area of 160 square centimeters,

were mounted on four of the leaves of the nose

cone. The lids of the boxes, on which more

collection surfaces were mounted, were fastened

to the internal structure of the nose cone.

The boxes and their covers were prepared with

high-purity materials for this experiment. All

boxes were treated and loaded in an identical

fashion and were completely interchangeable.

Since the fabrication left the inside of the

boxes extremely rough, it was found to be

impractical to try to clean the internal surfaces.

In order to prevent the collection surfaces

from being contaminated with debris from the

box, the debris was sealed to the surface with

a plastic coating, a high-purity nitrocellulose.

All the covers, clamps, screws, and washers

were cleaned in benzene to remove grease and

other contaminants. The open area inside the

gasket on the cover was coated with a nitro88

638805—63 8
90 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

60.0 will i m I • rt

2 .4 • ! Hint

I .3 Mi Mi x

3 mi Ili mat ir

pltiigl att

FIGURE 1.—Penetration experiment.

cellulose film 0.003 inch thick. This film was

held in place with 10-mesh stainless-steel

screening.

Eight different surfaces were loaded in the

boxes. There were seven lucite slides, each

% by 2 by #6 inch, covered with various substrates. The eighth surface was a large piece

of bare lucite, 1% by 5 by KB inch. A schematic

drawing of the positioning for the various

substrates used is shown in figure 2.

All the thin films, each approximately 200

A thick, were supported with 200-mesh copper

screening. The coated screening and the selfsupporting thick nitrocellulose films (0.003

inch thick) were glued to the lucite slides which

were held in place by clamps. Since there was

no past experience to go by, a number of substrate materials and handling techniques were

tried in an attempt to find the most effective and

unambiguous collection system. A photograph

of a typical box and cover is shown in plate 2.

As can be seen in this photograph, the boxes and

their lids were protected by sealed plastic covers.

Extreme care was necessary in handling these

boxes to insure that contamination would be

kept to a minimum. Therefore the nose cone

was thoroughly cleaned prior to the installation

of all the experiments. After installation of the

experiments, the nose-cone operation was

checked by cycling it twice in a precleaned

room. During these operations the protective

covers were still on the boxes and lids. Finally,

a large sealed plastic tent was erected over the

nose cone. The air in the tent was allowed to

stagnate for some 2 hours, the nose cone was

cycled for the final ground test, and during this

test the protective covers were removed from

the boxes and lids. The boxes and lids were

exposed for less than 30 seconds in the tent

before being sealed in the nose cone. An identical box was exposed in the handling room to

serve as controls for contamination. In addition, as can be seen from figure 2 and plate 2,

there were controls mounted in each box.

These controls consisted of an area approximately one-fourth of the surface area which was

protected by an aluminum shield placed a half

millimeter above the surface so that air could

flow freely under the shield. These shielded

surfaces were exposed in the same environments

and subjected to the same handling procedures,

but could not be impinged upon from above.

FIGURE 2.—Location of substrates for collection experiment:

(A) lucite slide shadow-cast with aluminum, (B) silicon

monoxide on thin formvar, (C) thick nitrocellulose film,

(D) thin formvar, (E) thick nitrocellulose coated with

carbon, (F) thin formvar shadow-cast with aluminum, (G)

thin nitrocellulose shadow-cast with aluminum, (H) bare

lucite.

The boxes were opened and closed during the

flight by the action of the leaves. Upon descent

of the nose cone the boxes were sealed by atmospheric pressure. Filtered ports at the base

of the nose cone allowed pressure equalization

inside the skin of the nose cone. The boxes however, were designed to maintain a vacuum inside.

These extreme precautions were not taken

with the penetration experiments, but care was

exercised that the film surfaces were protected

from any direct contact.

The "Venus Flytrap" system performed as

planned. The telemetry record which was

used only to monitor the rocket functions indicated that everything operated perfectly and

at approximately the preset times. From this

telemetry record the angles at which the leaves

were exposed were determined. The four

leaves containing the penetration experiments
METEOR SYMPOSIUM—SOBERMAN AND HEMENWAY 91

2 0 0

15 0

100

5 0

VENU S FLYTRA P

JUN E 6 , I 9 6 I

50 100 150 200 250 300 350 400 450

TIM E (ttcoods )

FIGURE 3.—Vehicle altitude plotted against time.

5 0 0

were exposed at an angle of 73.5° with respect

to the vertical axis of the rocket. The four

leaves on which the boxes were mounted were

exposed at an angle of 66.5° with respect to this

same axis.

An aspect camera was installed to record the

attitude of the rocket. These data have not

yet been fully reduced. However, it appears

that the rocket axis precessed from about 10°

on one side of the vertical to about 45° on the

other side of the vertical during the portion

of the flight where the nose cone was open.

The spin of the rocket was reduced from 2

r.p.s. to 1.4 r.p.s. by the opening of the leaves.

A device known as a "yo-yo" threw off two

weights and reduced the spin to essentially

zero just before the nose cone was closed.

This was necessary, since the motor did not

have sufficient power to close the leaves while

the rocket was spinning.

In figure 3 the altitude of the rocket is plotted

against time, and the curve shows that rocket

burnout occurred at an altitude of 35 kilometers.

It should be pointed out that at burnout the

fuel and oxidizer tanks were valved shut in

accordance with standard rocket procedure.

The opening of the nose cone was accomplished

in about 1 second at an altitude of 88 kilometers. The rocket then ascended for 131

seconds to an apogee of 168 kilometers, and

then descended for 105 seconds to an altitude

of 116 kilometers where closing was accomplished again in about 1 second. During this

entire exposure time the rocket remained in a

near vertical attitude (i.e., it precessed, but did

not turn over).

In figure 4 the velocity of the rocket is

plotted against time and the curve shows that

the rocket approximated a free-fall trajectory

during the time that the nose cone was open.

The nose cone was found sealed and intact.

It lay in the desert for about 1 hour after landing

before being placed in a protective plastic bag.

Samples of the desert sand were taken for control purposes. On return to the handling room

the outer skin was washed down with acetone

and the nose cone was wrapped in a clean plastic

bag for shipment. One week later in a "dust
92 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

2 .0

I .5

1.0

.5

VENU S FLYTRA P

JUN E 6, 196 I

5 0 100 150 200 25 0 300

Tl ME (seconds)

FIGURE 4.—Vehicle velocity plotted against time.

350 400 450 500

free" environment the nose cone was opened

for examination. Five of the eight boxes were

found to be still under sufficient vacuum to

require opening by injection of clean air with

a hypodermic syringe.

This experiment has been described in great

detail because we believe that these details have

an important bearing upon the validity of the

results which are presented in the next paper.

Acknowledgments

We acknowledge the debt that this project

owes to Mr. H. A. Cohen, who originally began

the program. Further, we acknowledge the

assistance of Messrs. R. Skrivanek and P.

Gustofson of the Geophysics Research Directorate at the Air Force Cambridge Research

Laboratories. We also express our thanks to

the staff at Aerojet-General Corp., particularly

to Messrs. N. Migdal, J. Smith, and J. McCabe

who fabricated the nose cone and assisted in

the preparations for the experiment. Finally

we thank Capt. T. Smith (USAF), Lt. J.

Turpel (USN), and the officers and men of the

U.S. Navy Missile Testing Center at White

Sands, N. Mex., for their wonderful cooperation

and assistance. But for the help of these and

many other support groups, the experiment

described above would still be "on the drawing

boards."

Abstract

The "Venus Flytrap" micrometeorite collector rocket was fired from White Sands, N. Mex., on June 6,1961, at 05:31

a.m., local time. Specially prepared particle impactors were exposed between the altitudes of 88 and 168 kilometers

and successfully recovered. The rocket design and performance are discussed. The experimental surfaces consisted

of 0.24 square meter of 6-micron-thick Mylar foil for impact and cratering studies, and 0.13 square meter of sealed

boxes which were loaded with high-purity materials and surfaces suitable for electron microscopy. In all, eight

different materials were used to permit an evaluation of the effectiveness of different materials and techniques for the

collection and study of micrometeoritic particles. Some of these materials were shadowed with aluminum before and

after the flight to aid in the discrimination of micrometeorite particles from contaminants.
Micrometeorite Collection from a Recoverable

Sounding Rocket. II

By C. L. Hemenway,1 R. K. Soberman,2 E. F. Fullam,3 J. J. Balsamo,4 J. Cole,1

D. Hallgren,5 P. Yedinak,6 A. Goodman,6 and G. Hoff1

As described in the preceding paper, two

types of experiments were carried out on the

"Venus Flytrap" rocket (i.e., the penetration

and the trapping experiments). In this paper

the results obtained to date from these experiments are presented.

The mylar films from the penetration experiment were tested by a helium leak detector

after return to the laboratory. Three holes,

shown in plate 1, were found in top-layer films.

There was no evidence of damage on the secondlayer films beneath these holes. The holes

shown in plate la,b were found on the same

mylar film. The first hole (pi. la) measures

90 microns across the short axis and 330

microns across the long axis. The second hole

(pi. 16) measures 450 microns across the short

axis and 1160 microns across the long axis.

The third hole (pi. lc) found on another film

which was mounted on the same leaf measures

330 microns across the short axis and 550

microns across the long axis. Note the flap

structure and curling of the mylar in all three

photographs. This flap structure and curling

are believed to be indicative of low-velocity

impact. From the appearance of the holes

it is inferred that they were caused by particles

comparable in dimension to the hole size

which impacted at relative velocities of less

than about 2 kilometers/second. Laboratory

* Dudley Observatory, Albany, N.Y., and Union College, Schenectady, N.Y.

1

 Geophysics Kesearch Directorate, Air Force Cambridge Research

Laboratories, Bedford, Mass., and Northeastern University, Boston,

Mass.

»Ernest F. Fullam, Inc, Schenectady, N.Y, and Dudley Observatory,

Albany, N.Y.

* Control Equipment Corp., Needham, Mass.

' Ernest F. Fullam, Inc, Schenectady, N.Y.

* Dudley Observatory, Albany, N.Y.

studies are presently being carried out to verify

these inferences and to determine the strength

of these films under low-velocity impact

conditions. Two holes found in an equal

number of control films appear to have been

caused by handling, and careful examination

shows no similarity with the holes that were

found on the flight samples.

A careful microscopic examination of the

top-layer mylar films was made in the hope of

finding imbedded particles or craters. It was

immediately noticed that the upper layer of

films had more particles on them than the

second layer or the controls. But as was

mentioned in the preceding paper, extreme

cleanliness had not been maintained with these

films and therefore this information could not

be used. This scanning did not result in any

further unambiguous information, since the

experiment was designed to look for punctures

and no records were kept of film defects.

There have been many attempts in the past

to collect micrometeorite particles at ground

level, on mountain tops, by balloons, and by

high-altitude aircraft. However, all these techniques have been open to criticism because of

contamination by terrestrial particles. Since

this is a very serious problem, we next discuss

the various safeguards which were built into

the "Venus Flytrap" experiment to ensure reliable identification of micrometeorites. There

were five controls for this portion of the experiment. Some have been described in the preceding paper. All five controls are listed

below with brief comments:

1. Laboratory exposures.—These were spare

boxes prepared at the same time and in the

93
94 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

same way as the flight boxes. One of these

spares was exposed in the laboratory for an

extended period to study contamination particles from the laboratory. Micrometeorite particles as described below were not found in the

laboratory controls.

2. Rocket preparation exposure.—A spare box

was exposed at White Sands during final

rocket testing. As described in the preceding

paper, it was necessary to remove the mylar

covers from the boxes at the time the nose cone

was sealed. The boxes had to be fabricated

in such a way that the nose cone could be

opened and closed and yet not contaminate the

samples while the final checkouts were being

made on the nose cone. In the room where the

nose cone was being cycled for the final time,

a spare box was opened for the full time during

which the mylar covers were off prior to the

final sealing. This operation was carried out

in a plastic tent as described in the preceding

paper.

3. Desert dust examination.—A sample of

desert dust was examined to see what kind of

particles could be expected from the air at

White Sands. To minimize desert dust contamination, the outside of the nose cone was

thoroughly cleaned in the laboratory and kept

in a plastic bag until one hour before flight and

removed only when the rocket was pressurized.

No evidence of desert dust contamination was

detected.

4. Rocket particle examination.—In a clean

environment wipings were made of the inside

of the nose cone and were mounted on electronmicroscope screens for examination. Some

metal chips and some oil were found. None of

the types of particles considered to be micrometeorites were found in these wipings.

5. Shielded flight samples.—The best controls

were the shielded areas inside each box. Approximately one quarter of the area of each box

was blocked off in such a way that air flow was

allowed beneath the shield, by separating the

shield approximately a half millimeter from the

control surfaces. Thus, if small particles were

drifting around in the air they could wander

beneath the shield, yet any particles that would

hit at high altitude would be prevented from

bitting these control surfaces. Plate 2 of the

preceding paper shows the metal shield in the

middle of an open box.

This study utilized three independent teams

of electron microscopists using three electron

microscopes. It may be relevant here to point

out some of the characteristics of electron

microscopes. The magnification of an electron

microscope is generally very high in comparison

with optical techniques and one can scan only a

few square millimeters per day. With an electron microscope, the limit of resolution is of the

order of 10 to 200 A, which is a factor of 100 or

more better than the resolution possible with

optical-microscope techniques. With an electron microscope, one can distinguish surface

details and textures of particles, can measure

particle sizes accurately, and can see how transparent the particles are to electrons. Finally,

while optical microscopes can scan large areas,

it is generally extremely difficult to distinguish

one small particle from another. When studying micrometeorites one is always working with

a "noise" or "background" level, and contaminant particles will always be present. It

will be shown that if the textures of the particle

surfaces, the shapes and sizes of the particles,

and so on, can be studied, contaminants can be

recognized and readily ruled out of consideration.

Perhaps the most effective technique utilized

in this experiment for micrometeorite identification is the shadowing technique wherein, just

before the boxes were loaded, certain of the

slides had a coating of aluminum evaporated on

the collection surface at an angle of approximately 80° from the normal to the surface.

Thus any particles that were on the collection

surface before the boxes were loaded would cast

a shadow in the direction in which the aluminum

was deposited. After the flight, another shadowing at 75° was put on at roughly right

angles to the previous shadowing. If a particle

was deposited between the two shadowings it

should have only the second shadow, and if it

was deposited during the scanning process it

should have no shadows. Contaminant particles within the films will also be shadowless.

This shadowing or flagging technique is a useful

way of reducing the ever present contamination

level. The flagging techniques had disadvantages. For example, if one attempts electrondiffraction analyses then one may be bothered
METEOR SYMPOSIUM—HEMENWAY, SOBERMAN, AND OTHERS 95

by the presence of the aluminum, although it

may be convenient for some purposes to have

a calibration standard on the same sample.

After a preliminary examination of the

various collecting surfaces it was decided, for

the initial study of the particles, to concentrate

on the surfaces on which the flagging technique

was employed. The observer scans first with

a magnification of the order of 2000 to 5000

times. He looks for single-flagged particles.

However, a single flag is considered to be a

necessary but not a sufficient requirement,

since it was possible for contaminant particles

to be deposited between the two flaggings.

The single-flagged particle is examined to determine whether it can be recognized as a contaminant at low magnification. If not, then

the magnification is increased to between 15

and 20 thousand times, and the particle

examined very carefully. In order to be counted as a micrometeorite the particle has to be

of a type not found on any of the controls.

There are three types of particles that did

not appear on the controls. These were dense

spheres with sharp edges ranging in size down

to a few tenths of a micron or even less, irregular submicron particles, and extremely irregular particles which were termed "fluffy." In

addition, some smashed fluffy particles were

found. Also a number of holes were found in

some of the thin collecting surfaces. The results described here were obtained with surfaces

of nitrocellulose and formvar (approximately

200 A thick).

Plate Id shows an optical micrograph of a

portion of a 200-mesh per inch copper screen

which has an open area roughly 100 microns

along an edge. Plates 2-6 are electron micrographs of a small portion of these open areas

in the mesh screen.

Plate 2a shows the flagging technique described above. The particle on the left has

two shadows and is therefore clearly a contaminant; the particle on the right has one shadow

and was identified as an irregular type submicron micrometeorite.

Plate 26 shows mica-like contaminants. This

type is found on all electron microscope slide

materials and apparently is in the air we

breathe. There have been no successful techniques to eliminate this type of contaminant

from electron microscope specimens. These

particles can be readily identified; they are

flat, of low density, and have sharp edges.

Plate 3a shows a rounded, medium-density,

submicron particle of the type initially difficult to identify as a contaminant. Notice the

fuzzy edge of this particle. These types of

submicron particles were found on both the

controls and the flight samples. One reason

for using high magnification to aid in the identification of micrometeorites was to discover

whether such particles had sharp or fuzzy edges.

Plate 36 shows a small spherical micrometeorite with a sharp edge and high density.

Notice that it can be readily distinguished from

the fuzzy-edged spherical particle in plate 4a.

Plate 4a shows a large irregular type of particle which looks almost like a museum meteorite. Notice that the surface is characterized

by rounded irregularities and is partially transparent to electrons (medium density). This

particle was counted as a large irregular micrometeorite; in fact, it is one of the largest

single-flagged particles found to date.

Plate 46 shows an extremely irregular particle which is termed a "fluffy" particle. All

particles not having a compact structure were

labelled "fluffy." Like the others obtained in

the Venus Flytrap experiment, this type of

particle is found in U-2 aircraft collections.

Plate 4c shows a fluffy particle obtained from

a U-2 collection.

Plate 5a shows a "sphere" with a hole. Notice that the "sphere" is not quite spherical.

It is approximately 2.25 microns in diameter

and is the largest of the spheres found thus

far. The hole is about 2.4 microns in diameter and apparently the sphere bumped into

this 200 A-thick nitrocellulose film, did not

get through, and made a flapped hole about

the same size and shape as its own body. A

number of flapped holes of this type have

been found.

Plate 56 shows a flapped hole where a smaller

spherical particle broke through the thin nitrocellulose completely. Apparently the flappedhole phenomenon appears over a wide range

of dimensions when one deals with low-velocity

collisions.
96 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

0 .25 .5 75

DIAMETER (MICRONS)

FIGURE 1.—Size distribution of irregular micrometeorites,

0.1 to 1 micron.

dN

d8

.25 .5 .75

DIAMETER (MICRONS)

1.0

FIGURE 2.—Size distribution of "fluffy" micrometeorites, 0.1

to 1 micron.

Plate 5c shows an elliptical hole where

the particle apparently penetrated the thin

film at an angle to the surface. Notice the

flaps as well as the cracks radiating from the

ends of the hole.

Plate 6a shows a portion of a smashed particle, probably a fluffy type. The debris

extended over a length of more then 100

microns. Several of these smashed particles

have been observed. Such particles are also

found in impact-type collections made with

U-2 aircraft. An attempt will be made to

measure the breaking strength of fluffy particles

to determine whether the values obtained

correspond to those required to crumble

cometary meteoroids.

Plate 66 shows a group of particles. Since

it was uncertain whether such particle groups

represented debris from the breakup of a

larger particle, this type of particle group

was not considered in the determination of

size distributions.

Figure 1 shows a distribution function for

the irregular type of particles. In the figure

only particles in the region of 0.1 to 1 micron

have been plotted. A few larger and smaller

individual particles were found.

Figure 2 shows a distribution of the "diameters" of the fluffy-type particles. It is

rather difficult to determine mean diameters.

For this determination the diameters in two

perpendicular directions were measured and

the particle was assumed to be ellipsoidal.

In figure 3 the size distribution of the

spherical-type particles has been plotted.

Notice that the size extends down to one-tenth

of a micron and apparently the number-persize range is still increasing at that point.

There are also some larger spherical particles

which are not shown on this distribution.

Figure 4 shows the distribution of spherical

holes. Notice that there appears to be a

cutoff at about 0.3 micron. The fact that the

distribution extends down to sizes as small

as this, and that spherical particles much

larger than the minimum size hole are observed,

indicates that there must have been a diversity

in the velocities of particles hitting the surfaces.

To date, 133 particles which are believed

to be of extraterrestrial origin have been found

in the range of 0.1 to 1 micron in diameter.

They were found in a total area of 17.84

square millimeters. Eleven particles larger

than 1 micron have been found in an area

of 18.52 square millimeters. This latter area

is a little larger because the less serious laboratory contamination problem associated with

larger particles permitted faster scanning.

The total number of particles larger than

0.1 micron per unit area was 7.3 per square

millimeter. If we separate these particles

according to type, 72 percent are irregular

with sharp edges and rounded texture, 16

percent are high-density spheres, and 12

percent are of the fluffy type. Of the singleflagged particles examined, two out of every

three were judged to be micrometeorites,

although this number varied somewhat from

sample to sample. In a few cases there was

some difficulty in deciding whether or not

a particle was a micrometeorite. Each operator was asked how frequently he experienced

this difficulty, and the largest number of

doubtful cases was found to be 10 percent.
HEMENWAY, SOBERMAN, et al. PLATE 1

a-c, Mylar films showing holes caused by meteorites, d,

200-mesh-per-inch copper screen used to support collecting

surfaces.

VAV
HEMENWAY, SOBERMAN, et al. PLATE 2

a, Illustration of flagging technique used to identify micrometeorites. b, Mica-like

contaminant particles. Scales, 1 micron.
SOBERMAN, HEMENWAY, etal . PLATE 3

a

•.- . • » -

.».'• -,• •

a, Submicron contaminant particle, b, Submicron spherical micrometeorite.

Scales, 1 micron.
HEMENWAY, SOBERMAN. et al. PLATE 4

<3, Irregular micrometeorite. b, "Fluffy" micrometeorite. Scales of a and b, 1 micron. c,"Fluffy"

particle obtained from U-2 collection.
HEMENWAY, SOBERMAN, et al. PLATE 5

a, Spherical micrometeorite and hole, b, Circular

hole created in 200 A-thick film by micrometeorite, c, Elliptical hole created in 200

A-thick film by micrometeorite. Scales, 1

micron.

\
HEMENWAY, SOBERMAN, et al. PLATE 6

V .

a

» V

a, Remnants of a smashed micrometeorite. b, Cluster of irregular micrometeorites.

Scales, 1 micron.
METEOR SYMPOSIUM—HEMENWAY, SOBERMAN, AND OTHERS 97

O .25 .50 .75

DIAMETER (MICRONS)

FIGURE 3.—Size distribution of spherical micrometeorites,

0.1 to 1 micron.

All doubtful cases were automatically discarded.

Actually, a few particles which really came

from beyond the earth's atmosphere were

probably discarded because of this conservative policy.

The analysis of these particles has now

begun. There are three techniques which offer

hope for determining the composition of these

particles: electron diffraction, neutron activation, and electron-beam probe techniques.

Thus far no positive results have been

obtained with electron diffraction. We are

beginning to suspect that micrometeorite

particles do not have a crystal structure and

that any original crystal structure has been

scrambled by cosmic-ray bombardment. We

may find that the lack of crystal structure is an

appropriate criterion for distinguishing micrometeorites. More work is needed to establish this point.

A second type of analysis involves neutron

activation. Gamma-ray spectra studies of activated samples are now in progress. The

third technique which will be employed is the

electron-beam probe wherein the particles are

used as X-ray targets. The wavelengths of

the characteristic X-radiation are used to

identify the composition of the particle.

In summary, we believe that extraterrestrial

particles have been collected. This belief is

based on several facts. First, the experiment

had a number of controls which were carefully

638805—63 9

dN

d8

.5 1.0

DIAMETER (MICRONS)

15 2 0

FIGURE 4.—Spherical hole size distribution from 200 A-thick

films.

chosen and lend confidence to the results.

Second, the particles were collected at altitudes

where terrestrial particles are very unlikely to

reside for any length of time. The third fact

is the distribution of holes found. By dropping

particles through a vacuum tube 2 meters long,

it was determined that particles of the order of

7 to 10 microns diameter will just break through

200 A-thick nitrocellulose collection film with

a velocity of 6 meters/second.

Figure 4 shows holes 0.3 micron in diameter

in the flight-collection films. If the strength of

the films is energy sensitive, this would suggest

relative velocities of the order of 1 or 2 kilometers/second for a particle comparable in size

to the smallest hole found. Finally, it should

be pointed out that the observers have had a

considerable amount of experience looking at

the high-altitude particles and at the contaminants which appear in electron microscopy. In

fact, four of the observers among them have

had a total of 40 years of experience in electron

microscopy. This experience increases our

confidence that the particles described and

pictured in this paper are indeed nonterrestrial

in origin.

Although there is much more to be done,

particularly on particle analysis, and these

results are only preliminary, we feel that further

study is not likely to change the present numerical results significantly.

Acknowledgments

The authors thank Miss L. Delia Lucca,

Mr. P. Manning, and Mr. R. Oppenheim for

their assistance and cooperation in obtaining

some of the results described in this paper.
98 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Discussion

E. L. Fireman.—Are these particles different

from the ones you reported as giving electron

diffraction patterns for nickel and nickel oxide?

C. L. Hemenway.—Yes. In that paper, we

were reporting on extremely small particles

found in large profusion on a U-2 flight on

November 15, 1960. There was a sufficient

concentration of these particles in a cluster to

give identifying diffraction patterns. I am

now saying that in this experiment and also in

the other U-2 flights we have been unable to

obtain a diffraction pattern from any of the

larger individual particles of suspected extraterrestrial origin. With terrestrial contaminant particles, on the other hand, we have always

been able to see some diffraction pattern.

A. F. Cook.—The low velocities with which

you feel most of the particles impacted could

be comparable to the rocket velocity at the

altitudes where the collector opened.

R. K. Soberman.—That would be the right

order of magnitude.

Unidentified speaker.—The large sphere

which you found would have had to strike the

film with a very low velocity.

C L. Hemenway.—That would have to be

the case. There were a number of similar

events.

Abstract

Three independent electron microscopes and observer teams have been used to evaluate, count, electron micrograph, and measure the micrometeorite particles. Typical particles and size distributions are shown. Particles

have been found in structure and sizes similar to those obtained at lower altitudes with U-2 aircraft and balloon

collection techniques. Approximately seven particles per square millimeter were collected during the flight. Most

of the particles were submicron in size. The micrometeorite particles collected generally fell into three types: highdensity spheres; medium-density irregular particles; and extremely irregular medium-density particles (fluffy particles). Some of the larger particles had sufficient momentum to rupture exposed films. Laboratory and nose-cone

control surfaces were carefully studied to permit identification of micrometeorite particles.
Micrometeorite Collection from a Recoverable

Sounding Rocket. Ill

By R. K. Soberman,1 and C. L. Hemenway

 2

The preceding papers have presented experimental details and preliminary results of

the "Venus Flytrap" experiment, and the

reasons for confidence in these results. The

present paper introduces interpretations, tentative conclusions, and speculations.

The results indicate first, the apparent

existence of submicron particles in the extraterrestrial flux. To account for this, one must

suppose a breakup mechanism for larger particles or speculate on the apparent inefficiency

of radiation pressure in removing submicron

particles from the solar system.

A second surprising result is the low velocity

with which the particles impinged on the collectors. Table 1 lists the terminal velocities

of particles of various diameters over the

altitude range covered by the Venus Flytrap

rocket. If one argues that the particles should

be arriving at the earth with large radial

velocities, then the velocities presented in

table 1 (particularly for the larger diameter

particles) are much lower than those that

TABLE 1.—Particle terminal velocities (km/sec)

Altitude

(km)

168

148

128

108

88

Diameter (microns)

0.1

1.5

1.0

0.52

0. 15

0.021

1.0

4.7

3.2

1.6

0.47

0.066

10.0

5.2

1.5

0.21

100

4.7

0.66

* Geophysics Research Directorate, Air Force Cambridge Research

laboratories, Bedford, Mass., and Northeastern University, Boston

Mass.

* Dudley Observatory, Albany, N. Y., and Union College, Schenectady, N.Y.

would be observed at the corresponding altitudes. However, if one assumes that the

particles had been in orbit about the earth,

then tangential deceleration at altitudes of the

order of 500 km or less would result in radial

velocities equal to, or even less than, the terminal velocities at the altitudes shown. From

the lack of high-velocity impacts observed in

the experiment, one must accept some form

of orbital trapping, or seek a mechanism of

radial deceleration or "slow down" which is

more effective than atmospheric drag for

micrometeoritic particles. Electrostatic deceleration by the ionosphere could conceivably

be such a mechanism and should be investigated. Whatever the mechanism, it will be

assumed for the present analysis that the

particles observed were moving downward

with approximately terminal velocities.

The third result is the size distribution and

numbers of particles collected per unit area.

Figure 1 shows the preliminary results from

the collectors which were mounted in the boxes.

The number of particles found (larger than a

given diameter) are plotted against the diameter. The points were normalized to a total

area of 1 square meter, and a line with slope

of —1.3 was drawn through these points. It

can be seen from the ordinate values that the

assumption of low velocities is practically

a necessity if these results are to be understood in the light of other meteoric and micrometeoric work.

With certain assumptions, a value for the

extraterrestrial flux can be calculated. If a

collector is moving through a column of unit

area in which particles are falling (fig. 2),

then the number of particles of given size

collected can be written as:

09
100

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

(1)

where <f>e is the flux on the collector, and vt

is the velocity of the collector. Equation (1)

can also be expressed as

(2)

where v9 is the velocity of the particles, and

na is the ambient particle density. The minus

sign is used when the collector is moving

downward. If one assumes a constant ambient

flux <f>a, then one obtains:

10'

The first integral is the exposure time of the

collector. The second term can be evaluated

if one assumes that vP is the terminal velocity

of the particles. That is

(4)

where pa is the ambient air density, and <r is

the cross-sectional area of the particles. Assuming spherical particles, one can write:

(5)

where 5 and pv are the diameter and the density

of the particles. For an exponential atmosphere

this equation, on integration, yields:

(6)

where H is the scale height, and the subscripts

t and / refer to initial and final values. The

quantity in the square brackets (the effective

exposure time T of the collectors) is plotted in

figure 3.

A mean particle density of 3 gm/cm3 has

been assumed. The calculation was performed

by summing equation (6) over regions where

the scale height remained reasonably constant.

Densities, scale heights, and gravitational accelerations were obtained from the standard

atmosphere tables (Minzner, Champion, and

Pond, 1959). The summation was cut off

10'

N

4

10

3-1.3

.2 2 .5 I 2 3

DIAMETER (MICRONS)

10

FIGURE 1.—Size distribution of all particles found to date

from Venus Flytrap experiment.

where vP=ve when the collector was moving

downward. Implicit in these calculations was

the assumption of 100 percent collection

efficiency. Theoretically this should be true for

particles larger than 0.01 micron at the altitudes

of interest here. The number of particles of

each size collected per square meter divided

by the effective collection time for that size

is then the flux at all altitudes. The results

are plotted in figure 4. The ordinate is the

integrated flux (i.e., the flux of particles larger

than a given diameter is plotted as a function

of the diameter). The correction factors for

the exposure angle and any shielding effect of

the ogive assembly have been neglected. In

the lower right-hand corner of figure 4 the

three points from the mylar films (i.e., the

particle sizes assumed to have caused the holes)

were plotted. These points were normalized

in the same manner as the others. Notice

that the upper slope has changed to —1.2. For

particle diameters larger than 2 or 3 microns
METEOR SYMPOSIUM—SOBERMAN, HEMENWAY, AND OTHERS 101

1

»

1

1

ft

1

1

•

1

1

»

FIGURE 2.—Moving collector in unit area column.

(the solar radiation cutoflF) a shaded area with

slope —3.6—which is the best estimate from

satellite data for these sizes (Whipple, 1961b)—

was somewhat arbitrarily drawn. Thus from

the foregoing a flux estimate of approximately

300 particles per square meter per second larger

than 3 microns in diameter is obtained. This

estimate is based, of course, on preliminary

data and may change slightly. It must be

remembered, however, that the calculation is

based on the assumption of particles moving

at terminal velocity. Were the velocities substantially higher, the flux estimate would be

raised by the ratio of the assumed effective

exposure time to the actual open time of the

collector, i.e., the flux estimate for particles 3

microns and larger would be multiplied by a

factor of approximately 4/3. On the other

hand, if it were shown that the actual particle

velocities were lower than terminal velocities

in this altitude range, then the estimated flux

would be too high. It should also be noted

that the present flux estimate does not include

the particles which penetrated the 200 A films

and were not recovered. If these particles

TRUE OPEN TIVE

10 10 30 .90 1.0 CO JO 5.0 20 30 SO BO

FIGURE 3.—Effective collection time for Venus Flytrap

experiment.

LOG

.-1.2

- 3 6

-2

0 I 2

LOG DIAMETER (MICRONS)

FIGURE 4.—Mircometeorite flux as calculated from Venus

Flytrap results.

were included, the flux would increase by

approximately 20 percent.

At this point the present estimated fluxes

can be compared with measurements made

from satellites. At first glance the derived flux

value appears to be orders of magnitude higher

than any recent measurements or extrapolations. One might, however, compare the

present values with a curve for a geocentric

distribution of particles. Such a curve is

shown in figure 5. This curve, presented by

Sobennan and Delia Lucca (see this symposium, p. 87), is similar to that given by

Whipple (1961a). For an assumed spherical

particle with uniform density of 3 gm/cm3,

this curve represents particles 9 microns in
102 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

0 .0

To - 1.0

- 2.0

- 3.0

-4.0

-5.0

I960

ZOD

CLD

2.0 3.0 4.0 5.0

LOG ALTITUDE (km)

FIGURE 5.—Meteoritic impact plotted against altitude.

diameter and larger. The curve in figure 5

would predict a flux of such particles of 0.25

m~2 sec"1 at 100 km. From figure 4, the present

estimate would be about 6 particles per square

meter per second. If one assumes, however,

that the particles measured from satellites were

low-density loose agglomerates, and if one uses

a density of 0.1 gm/cm3, then a particle with

a mass of 10~9 gm would have a diameter of

27 microns. The present estimate (from fig. 4)

of this particle size would be 0.1 m~2 sec"1,

which is in much better agreement with the

satellite observations.

To speculate briefly on the source of these

particles, it is felt that terrestrial origin can

be ruled out. A cataclysmic event immediately prior to the firing would be required to

raise particles of this size to a 90-km altitude.

No such event was observed or reported. A

possibility which cannot be ruled out at the

moment is that of a sharp increase in flux

during the time of the experiment. On June

6th, two daylight radio-meteor showers were in

progress, the Arietids which peak on June 8

and the f Perseids which peak on June 9. No

unusually high activity has been reported for

this period. If the present experiment was

performed during a period of relatively normal

activity (future experiments of the same type

will decide this question), then one is forced to

look for either a radial "slow-down" or an

orbital trapping mechanism. Whatever the

choice, one appears to be led to the conclusion

that a dust layer (either moving orbitally or

settling slowly) exists about the earth. This

conclusion follows from the number of particles

observed and the low relative velocities. The

possible origin or origins of such a dust layer

have been discussed by Whipple (1961a) and

will not be treated here.

In summary, the three results of this experiment are: (1) A preponderance of submicron

particles was observed; (2) the particles were

apparently falling at low velocity; and (3) an

unexpectedly large number of particles were

collected. These results are consistent with

one or both of the following assumptions: (1)

The breakup of larger low-density "fluffy"

particles; and (2) the existence of a dust layer

or a geocentric distribution of micrometeoritic

particles about the earth.

Acknowledgments

The authors thank Miss P. Bumham and

Mr. R. Sarkesian for then* assistance with the

computations.

References

MINZNER, R. A.; CHAMPION, K. S. W.;and POND, H. L.

1959. The ARDC model atmosphere. AF Surveys in Geophysics No. 115, Geophys.

Res. Dir., Air Force Cambridge Res. Lab.

WHIPPLE, F. L.

1961a. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

1961b. The particulate contents of space. In P.

Campbell, ed., Medical and biological

aspects of the energies of space, pp.

49-70. Columbia University Press,

New York.

Discussion

C. W. McOracken.—If we can believe the microphone measurements that you made on the

Midas II, any of these results you have submitted give added support to the early rocketprobe data.

R. K. Soberman.—We have little, if any, confidence in those early rocket results. Although

it might appear, at first glance, that our present

measurements lend support, one must recall

that we had, in this experiment, 0.25 square

meter of puncture area exposed over a trajec-
METEOR SYMPOSIUM—SOBERMAN, HEMENWAY, AND OTHERS 103

tory similar to that of the early acoustic rockets.

We do not see the large number of high velocity

punctures, which one would expect from the

interpretation of the acoustic-probe data.

C. W. McCracken.—Do you have any hypervelocity measurements showing that particles

moving with 6 to 8 km/sec velocities do not form

holes with flaps of the type you see in this

experiment?

R. K. Soberman.—We do not have such measurements, but Richards and Gehring at the

Ballistic Research Laboratory measured holes

made in mylar by particles down to 5 microns

travelling at 12 km/sec and have shown that at

this velocity one obtains typical hypervelocity

punctures, that is, small circular holes with no

flap structure.

C. W. McCracken.—We have recent data

from tests performed at the Space Technology

Laboratories with 1 to 3 micron particles impacting 0.25-mil mylar at 6 to 8 km/sec velocities. It was a shock to us to find small

cylindrical cavities instead of the more spherical

craters one might expect. The mylar was aluminum coated and we found small petals of this

aluminum around the hole. Therefore, I would

question the statement that flapped holes indicate low-velocity impact.

Unidentified speaker.—What was the relation between hole size and particle size in those

Space Technology Lab tests?

C. W. McCracken.—The holes were not more

than a factor of two larger than the particles.

This was another surprise in that we had

expected them to be larger.

M. Dubin.—You suggested that many of the

particles you observed might have been the

result of an earlier breakup. Where might

this have occurred and how?

R. K. Soberman.—This could have occurred

at altitudes below 300 km, where particles undergo deceleration of 1 g and more due to

atmospheric drag. Loosely agglomerated particles could break up under such forces. Such a

mechanism would explain why solar light pressure does not remove the submicron particles.

Abstract

The interpretation is given of the preliminary results obtained from the "Venus Flytrap" rocket. These results

are compared with those from satellite observations. The possible existence of a dust layer is discussed.

Rocket and Satellite Studies of Meteoric Dust

By T. N. Nazarova1

During the last 3 years, investigators in

both the Soviet Union and the United States

have studied meteoric dust by means of

instrumentation carried aloft by rockets and

artificial earth satellites. Despite the limited

amount of experimental data obtained, and

the considerable difficulties associated with

both the experiments and the interpretation of

the data, the results are of interest to science

as a whole and in their application to some

engineering problems.

We shall discuss the results of direct investigations of meteoric dust carried out by means

of Soviet geophysical rockets, artificial earth

satellites (Nazarova, 1961a), and space probes

(Nazarova, 1961b). Data provided by nonSoviet publications are also taken into account.

In the U.S.S.R., measurements were made

by means of ballistic piezoelectric detectors

which measure the pulse caused by ejection of

detector material when a meteoric particle

explodes on the surface of the detector (Isakovich and Roi, 1960; Komissarov et al, 1960).

From the number of such pulses, the particle

impact rate is determined.

In analyzing the experimental results we use

the theoretical relationship, derived by Stanyukovich (1961), that the pulse recorded by the

dectector is a function of the particle energy and

can be expressed as I—AE. This relation

(IccE) is not generally accepted. Lavrentyev

(1961) believes the relation should be Iccmv16,

while American investigators usually assume it

to be Iccmv.

The estimate of the masses of recorded

meteoric particles naturally depends on the

velocity assumed. We regard Whipple's (1961a)

estimate for the impact velocity of meteoric

particles with a satellite as reasonable. ThereThe U.S.S.R. Academy of Sciences, Moscow, U.S.S.R.

638805—63 10

fore, although earlier publications used the value

of 40 km/sec for the particle impact velocity,

in this paper we recalculated the recorded

masses using a particle impact velocity of 15

km/sec. In some cases, a satellite encounter

with meteor streams is possible; actual velocities

can then differ considerably from the assumed

velocity.

The observational results are listed in table

1. In the experiments which utilized geophysical rockets, the calibration of the instrumentation was redetermined. For these experiments

there is an uncertainty of half of an order of

magnitude in the recorded meteoric particle

impact rate, since the detectors reacted to

impacts not only against the operating surface

but also against the rocket body. In experiments on Sputnik III and Space Probe I

(Lunik I), results were carefully corrected for

this effect. The detectors used on Space

Probes II and III (Luniks II and III) reacted

only to impacts against the operating surface.

Table 1 lists, for all experiments, the operating

surface area S (for the geophysical rockets the

effective area is given), the time t of the instrument operation, the impact rate, and the

altitude range over which the measurements

were made.

To compare data obtained from different

experiments, it is necessary to equate them to

the same sensitivity. It is known that the

integral mass distribution of meteoric particles

has the form N(m)=km~0, where N(m) is the

number of particles with masses greater than m.

Observations of F-corona, gegenschein, and

meteors have yielded for /? the values 0.5, 0.6,

and 1.3, respectively. Comparison of direct

measurements from Explorer VI, Vanguard III,

and Explorer I has led to the value 0^1

(Moroz, 1962).

105
1U6

Vehicle

1. Geophysical

rocket

2. Geophysical

rocket

3. Geophysical

rocket

4. Sputnik III

5. First Cosmic

rocket

6. Second Cosmic

rocket

7. Third Cosmic

rocket

May

Aug.

Feb.

May

May

May

Jan.

Sept.

Oct.

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Rocket and satellite meteoric dust data

Dates

24, 1957

8, 1957

22, 1958

15, 1958

16, 17, 1958

18-25, 1958

2, 1959

12, 1959

4-18, 1959

Area S

(mi)

4

4

4

0. 34

0.2

0. 2

0. 1

Time

t (sec)

134

148

85

1.8X10*

3. 6X104

1. 1X 10s

2.3X10*

s.t.

(m« sec)

536

592

340

6. 0X103

7. 2X10*

2. 2X10*

2. 3X104

Alt. range

(km)

100-200

100-210

126-297

400-1, 880

400-700

400-700

2, 000-360, 000

2, 000-360, 000

102, 000-470, 000

Mass of recorded

particle (with »=•

15 km/sec) (gm)

io-'

10-*

10-'

6X10-*—2X10~7

2X10-8-10-'

10-7_l0-«

10-8-4X10"8

4X10-8-4X10-7

>10~7

7X10-»-2X10-8

2X10-8-6X10-8

>6X10-8

Impact rate

(m-» sec-')

0.06

0.05

0.75

4-11

5X10-*

<10~4

<2X10"»

<5X10"<

<5X10-»

<5X10-»

9X10-*

4X10-4

2X10"»

4X10-*

Figure 1 presents Soviet and American experimental data (LaGow and Alexander, 1960;

Dubin, 1960; Whipple, 1961a) equated to the

same sensitivity (tnmia=10~i gm) through the

relation Nitr^ccm'1.

The recorded impact rate is referred to the

mean height for each experiment, a procedure

which in the case of space probes may lead to

additional errors. (The graph was plotted on a

logarithmic scale, hence the points are not

centered between the altitude limits.) As is

evident from figure 1, the observations made by

means of geophysical rockets definitely reveal a

zone of increased density of dust particles near

the earth at an altitude of 100 to 300 km. The

existence of this increased concentration is independently confirmed by observations of the

twilight sky (Moroz, 1962). At altitudes between 400 and 2,000 km the impact rate is

approximately 10~3m~2sec~1. Measurements

made at greater distances from the earth are

characterized by a large dispersion in the numerical data obtained. Explorer VI and

Pioneer I yielded impact rates of 5X10"8 and

4 X10"8 m~2 sec"1, while the values for Luniks II

and III were 9X10"4 and 1X 10"3 m"2 sec"1 (all

values are corrected to mmln=10~8 gm).

It should be noted that estimates of the

density of matter in the zodiacal cloud, obtained from photoelectric measurements, range

between p=3 X 10"23 and 3 X lO^gm/cm8. From

these values the computed impact rates are 10

 5

and 10~* m"2 sec"1, respectively (Moroz, 1962).

Despite the nonhomogeneity of the experimental data (due in large part to differences in

experimental technique, instrument calibration,

and assumptions regarding the mass-velocity

dependence of the detectors) and the limited

amount of such data available, consideration of

all the available data allows the supposition

that a region of increased concentration of

meteoric dust exists at a height of 100 to 300 km

above the earth's surface. As already noted, at

altitudes between 400 and 2,000 km the impact

rate is of the order of 10~3 m~2 sec"1 (i.e., approximately one order of magnitude larger than

the density of the zodiacal cloud would indicate). Because of the great dispersion of points

at distances of the order of 10* to 105 km from

the earth (fig. 1), it is difficult to say at present

whether the decreased concentration of meteoric

matter (compared with the lower altitudes) is

real or whether the dispersion in the experimental data is indicative of fluctuations in the

spatial density.

On the basis of direct experiments it may be

concluded that the density of meteoric matter

in the vicinity of the earth is not constant. At

altitudes of 100 to 300 km, variations in the

impact rate N are not greater than one order of

magnitude. At the same time, at altitudes of

400 to 2,000 km, sporadic increases in N are

observed.
METEOR SYMPOSIUM—NAZAROVA 107

o

o

i

or

UJ

LJJ

10 -

10"'

_3

10 1

I<T4H

io-5-

10

_6

-• io

12

13

• 14

15

16

, 7

10' 10 10 10 10'

h (KILOMETERS)

FIGURE 1.—Integral impact rate of meteoric dust N as a function of altitude h for masses greater than

10~8 gm. Key: 1, 2, 3, Soviet geophysical rockets; 4-9, U.S. Air Force rockets; 10, Sputnik III,

May 15, 19S8; 11, Sputnik III, May 16, 17, 1958; 12, Explorer I; 13, Vanguard III; 14, Soviet

cosmic rocket II; 15, Soviet cosmic rocket III; 16, Pioneer I; 17, Explorer VI.

On May 15, 1958, instruments carried by

Sputnik III recorded 4 to 11 impacts per

square meter per second.2 On May 16-17, the

impact rate decreased to 5X10"4m"2 sec"1

(wm m=6X 10~8 gm according to present velocity

assumptions), which is apparently normal for

these altitudes. Since the impact rate changed

with a period equal to the precessional rate of

the satellite, instrumental origin for this effect

1

 It is likely that the phenomenon observed on May 15 was due to a

stream with an unknown radiant. If we assume that the velocity of the

stream was 70 kra/sec, then the mass of the particles detected in the stream

was apparently ~5X10"w gm.

may be almost totally excluded. Explorer I

instruments also recorded sporadic increases

of the stream in this region. These increases

were about an order of magnitude higher than

the average impact rate. Of great importance

are the diurnal variations in the impact rate

which were also observed on Explorer I (Dubin,

1960).

According to Whipple (1961a; 1961b) there

is a dust envelope about the earth in which

Noch~li in a broad region from 100 to 100,000

km. As seen from the above considerations,

it is difficult at the present time to encompass
108 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

this entire range with a single relationship

between N and h. In the altitude range from

100 to ~2,000 km, we can write Ncchr1. From

2,000 km to higher altitudes, N decreases more

slowly. Future experiments will determine the

dependence of impact rate on height and latitude.

Several hypotheses have been suggested to

explain the existence of the dust cloud about

the earth; at the present time, however, no one

of these hypotheses can be regarded as final

(Moroz, 1962).

References

DUBIN, M.

1960. IGY micrometeorite measurements. In

Space research, H. K. Bijl, ed., pp. 1042-

1058. North-Holland Publishing Co.,

Amsterdam.

ISAKOVICH, M. A., AND Roi, N. A.

1960. An acoustical method for the measurement

of the mechanical parameters of meteorites. In Artificial earth satellites, L. V.

Kurnosova, ed., vol. 2, pp. 105-107

(transl. from Russian). Plenum Press,

New York.

KOMISSAROV, O. D.; NAZABOVA, T. N.; NEUGODOV,

L. N.; POLOSKOV, S. M.; AND RUSAKOV, L. Z.

1960. Micrometeorite studies using rockets and

satellites. In Artificial earth satellites,

L. V. Kurnosova, ed., vol. 2, pp. 68-74

(transl. from Russian). Plenum Press,

New York.

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, H. K. Bijl, ed., pp.

1033-1041. North-Holland Publishing

Co., Amsterdam.

LAVBENTYEV, M. A.

1961. The problem of piercing at cosmic velocities. In Artificial earth satellites, L. V.

Kurnosova, ed., vol. 3, pp. 85-91 (transl.

from Russian). Plenum Press, New

York.

MOBOZ, V. I.

1962. On the dust envelope of the earth. In

Artificial earth satellites, L. V. Kurnosova, ed., vol. 12 (transl. from Russian).

Plenum Press, New York.

NAZABOVA, T. N.

1961a. Results of a study of impacting of meteoric

matter by means of instruments mounted

on space rockets. In Artificial earth

satellites, L. V. Kurnosova, ed., vol. 5,

pp. 524-527 (transl. from Russian).

Plenum Press, New York.

1961b. Study of meteoric particles through instruments on the third Soviet artificial

satellite. In Artificial earth satellites,

L. V. Kurnosova, ed., vol. 4, pp. 402-410

(transl. from Russian). Plenum Press,

New York.

STANYUKOVICH, K. P.

1961. Elements of the theory of the impact of

solid bodies with high (cosmic) velocities.

In Artificial earth satellites, L. V.

Kurnosova, ed., vol. 4, pp. 292-333

(transl. from Russian). Plenum Press.

New York.

WHIPPLE, F. L.

1961a. The participate contents of space. In

Medical and biological aspects of the

energies of space, P. Campbell, ed., pp.

49-70. Columbia University Press, New

York.

1961b. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.
Cosmic Dust Showers by Direct Measurements

By M. Dubin,1 W. M. Alexander,2 and O. E. Berg

The cometary origin of meteor streams is

well established. During the process of disintegration of comets, particles are dispersed

along the heliocentric orbit, and it appears

reasonable to assume that the age of the meteor

stream is related to the uniformity in the

counting rate of shower meteors for annually

recurring meteor streams. The large number

of meteors observed in the Draconid display in

1946 is evidence of the recent formation of the

stream from the familiar comet GiacobiniZinner. Dispersion of dust particles in the

meteor stream from interplanetary forces resulting from the Poynting-Robertson effect,

corpuscular bombardment, and other radiative

forces, is expected to be increasingly pronounced

with decreasing dimensions of the dust particles.

The extension of the range of measurements of

meteoritic material to smaller masses by direct

measurements with satellites may, therefore,

improve our knowledge of the history and age

of meteor streams.

The number distribution of meteors as a

function of visual magnitude has been measured

by visual and optical methods. Similar distributions as a function of electron line density

along the trail have been determined by using

radar. Browne, Bullough, Evans, and Kaiser

(1956) determined such distributions for the

Perseids, Quadrantids, and the Arietids. For

the Perseids, for example, they found that

compared to the distribution of sporadic meteors

there was a depletion of the small meteors for

visual magnitudes greater than 7. Weiss

(1961) measured distribution functions for the

Geminids, the S Aquarids, and the 17 Aquarids,

as well as for the sporadic meteors. Although

the distribution function varied for different

meteor streams, only the daytime Arietids has

1

 National Aeronautics and Space Administration, Washington, D.C.

:O<x)dard Space Flight Center, Greenbelt, Mi!.

an "s" value (the exponent in the distribution

function indicating rate of increase in number

with decreasing mass) equal to 2.7 (compared

to "s"=2.0 for sporadic meteors). This is the

only shower with "s" greater than 2.0.

Direct measurements of micrometeorites or

interplanetary dust have been made in the

United States on a number of satellites, rockets,

and probes. Significant data on four satellites

have been obtained: 1958 Alpha, Explorer I,

launched February 1, 1958, perigee 355 km,

apogee 2550 km (Dubin, 1960a, b, 1961; and

Hibbs, 1961a, b); 1959 Eta, Vanguard III,

launched September 18, 1959, perigee 509 km,

apogee 3751 km (La Gow and Alexander, 1960);

1960 Delta, Explorer VI, launched August 7,

1959, perigee 186 km, apogee 39,000 km; and

1960 Xi, Explorer VIII, launched November 3,

1960, perigee 425 km, apogee 2300 km

(McCracken, Alexander, and Dubin, 1961, and

McCracken and Alexander, this Symposium,

p. 71).

The direct measurements of cosmic dust

refer to particle of mass less than 10~8 grams

or greater than +20 on the visual magnitude

scale. Daily variations in the flux of cosmic

dust particles greater than an order of magnitude are often observed. We have excellent

evidence that two cosmic dust showers or

streams have been detected by these direct

measurements. One of these dust streams,

detected on 1958 Alpha, permitted a determination of an approximate radiant; the other

has been detected on more than one occasion

and apparently is related to an annually

recurring meteor stream.

Results of Measurements

Cosmic dust shower, February 1958.—Evidence

of a cosmic dust shower from the data of 1958

Alpha was apparent for a 10-hour period begin109
110 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Impacts per station pass for Satellite 195S Alpha

February

date

2

2

2

2

2

2

2

2

2

2

:i

3

3

3

3

3

3

3

3

3

3

3

3

:i

3

3

3

Greenwich

time

1512

1833

1930

1933

2033

2139

2238

2338

2339

2340

0043

0132

0138

0139

0141

0142

0258

0334

0338

0344

0344

0349

0539

0750

0958

1200

1405

No. hits

2

5

2

1

4

2

2

5

11

7

7

2

4

5

12

2

3

4

]

1

2

1

7

2

2

0

5

Time of

pass

(sees)

087

159

233

09

787

221

691

192

366

174

832

213

259

187

261

7

180

213

120

71

192

—

338

142

527

952

663

Station

Santiago, Chile

Woomera, Australia

Quito, Equador

Fort Stewart, Ga.

Woomera, Australia

Fort Stewart, Ga.

Woomera, Australia

Ehrlick, Kansas City, Mo

Fort Stewart, Ga.

Havana, Cuba

Woomera, Australia

Temple City, Calif.

Blossom Point, Md.

Ehrliek, Kansas City, Mo

Fort Stewart, Ga.

Havana, Cuba

Woomera, Australia

Temple City, Calif.

Ehrlick, Kansas City, Mo

Fort Stewart, Ga.

Havana, Cuba

Antigua, B.W.I.

JPL, Calif.

Quito, Ecuador

Santiago, Chile

Santiago, Chile

Santiago, Chile

Hits/sec

X 103

2. 9

31. 0

8. 5

14. 5

5. 1

i). 1

2. •)

26. 3

30. 0

40. 0

8.4

9. 3

15. 5

26. 5

46. 0

286. 0

16.7

18. 7

8. 1

14. 0

10.4

20.8

7.0

3.8

0

7.5

Average impact rate, Feb. 1-Feb. 12, 12 days

Average impact rate, Feb. 5-Feb. 12, 8 days

1.5

0.43

ning on February 2, 1958. The detector was

a piezoelectric crystal with an average threshold sensitivity to micrometeoroid impacts of

2.5X10"3 dyne-seconds. This is equivalent to

detecting particles of mass 8XlO~10 grams and

greater with an average impact velocity of

30 km/sec. The data from Explorer I were in

real-time, recorded only while the satellite

was over a telemetry receiving station. Table

1 shows the data for each pass over a telemetry

station in the interval from February 2, 1512

hours, to February 3, 1405 hours, Greenwich

time. Impacts were recorded for every pass

but one during the interval of the cosmic dust

shower. The table includes the station location, the number of hits during each pass, the

time of each pass, and the number of hits per

second.

The impact rate from table 1 has been

replotted as a polar plot in figure 1 as a function

of time. The inner filled-in circle in the polar

plot is the zero level, or zero hits per second.

The next ring is the average impact rate of the

last 8 days of the 12-day experimental period,

i.e., 0.43 XlO"3 hits/sec. The average impact

rate over this period is shown by the next

circle, and was 1.5X10"3 hits/sec. The plotted

points are the real-time readout rates during

the shower period. It is quite evident that

the impact rates during the shower period

were nearly two orders of magnitude greater

than the average of the latter two-thirds of

the measurement period.

Except for Woomera, Australia, which is

represented by the squares, the circular points

in figure 1 represent the impact rate for all

stations in essentially the same time zone

covering about a three-hour period. The local

time for these stations in the United States and

South America during the maximum of the
METEOR SYMPOSIUM—DUBIN, ALEXANDER, AND BERG 111

GREENWICH TIME-HOURS

0

FIGURE 1.—Impact rate for Satellite 1958 Alpha, February 2-3,

Greenwich Time.

shower intensity was early evening. This

indicates a meteor stream in a direct heliocentric orbit. It is evident that the stream is

in the ecliptic since it was detected by receiving

stations in both the Northern and Southern

Hemispheres. The square-plot points represent

the impact rate from five passes over the

station at Woomera, Australia. They provide

further evidence of a direct heliocentric orbit;

the impact rate at Woomera as a function of

time is first high, then decreases, and then

increases again. This impact rate was near

a minimum when at the other stations it

was near a maximum. Since the longitude at

Woomera differs from other receiving stations

by nearly 180°, the earth should have shielded

the satellite from this stream. The apogee of

1958 Alpha at 2550 km was located near

Woomera on this date. Hence, the earth's

shield there would be incomplete. Figure 1

has been shadowed to suggest the extent of the

meteor stream, which appeared to have lasted

about 10 hours. There is no known meteor

stream which may be related to this cosmic

dust shower detected on 1958 Alpha.

Annually Recurring Cosmic Dust Shower in

November.—A cosmic dust shower has been detected with both satellites and sounding rockets

in November. It was first recognized from the

micrometeoroid data from 1959 Eta, although

it was first detected in 1955 from an Aerobee

rocket. Additional data from 1960 Xi are still

of a preliminary nature, but support the fact

that this shower recurs annually.

A number of rocket flights were carried out

by Berg in 1955 (Berg and Meredith, 1956) and

in 1960. He used a micrometeorite detector

which detected the impact-flash of light resulting from the hypervelocity impact of the

particle on an aluminum-coated lucite or quartz

surface.

Figure 2 describes the measurements on three

separate rocket firings. The first firing of

Berg's experiment was carried out on Aerobee

NRL^25 on November 17, 1955, at 0215

M.S.T. A 1P21 photomultiplier was used to

detect light flashes on impacts of an aluminized

lucite cone with a light sensitivity of 10~4

lumen seconds/m2. On the assumption that

0.002 percent of the impact energy is transformed into visible light, a detector would be

able to detect particles of mass greater than

10"13 grams. Berg found that 101 impacts

were observed on the telemetry record in the

84-second period while the rocket was above an

altitude of 85 km. Almost none were observed

below this altitude, and the distribution of

impacts on the upward and downward trajectory of the rocket was fairly symmetrical.

The area of the detector was 75 cm2, and the

impact rate was 1.6 X 102 impacts/m2/sec.

This rather high impact rate observed on
112 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

AEROBEE AEROBEE

NRL-25 t

r

 ~ <:>*

\ LUCITt ^ ^ OUAKTi ^ \ ^

& 0

F1.WS215

 fin* 13< 0

K... 17. 1»55 M-. M. IH »

\

\

OUARTZ

•m

JUPITER

AM-2E

OUADTZ

O f t

Fl»4 If 47

A

. . 25. 19W

» . • 1«5C»2

FIGURE 2.—Description of measurements on three separate rocket

firings.

NRLr-25 remained an anomaly for a number

of years. The experiment was repeated by

Lovering (1959) in Australia, and no impacts

were observed on a single rocket flight. In

1960 Berg repeated the measurement on

Aerobee NASA 4.12 and on Jupiter AM-28.

He used the 1P21 with lucite and with quartz

cones to check for Cerenkov radiation. Aerobee NASA 4.12 was fired on March 25, 1960, at

1340 E.S.T., with a 75 cm2 detecting surface

and with 1P21 and 6199 photomultipliers.

One impact was observed on the 1P21 and two

events were observed on the 6199. This is

equivalent to rate of 1.2 impacts/m2/sec and an

exposure area-time of 2.4 m2 sec. On NRL25 the exposure area-time was 0.64 m2

 sec.

Similarly, on Jupiter AM-28, fired on January 25, 1960, a space-oriented detector with

185 cm2 was exposed at 1947 E.S.T. The 6199

photomultiplier with a quartz cone was used.

Included also was a calibrated light source,

giving a 50 microsecond light pulse every 26

seconds. The experiment was known to be

working correctly, and the area-time of the

exposure was 2.4 m2 sec. Four events were

detected, giving an impact rate of 1.6 impacts/

m*/sec. Thus, of three separate rocket flights

similar to the earlier experiment not one could

confirm the 1955 results for the impact rate

within a factor of 100.

Although it was surmised that a dust shower

might explain the rocket data, Alexander,

McCracken, and LaGow (1961) provide rather

clear confirmation of this hypothesis with their

micrometeorite data from 1959 Eta. This

experiment consisted of four piezoelectric crystals with a threshold impact sensitivity of

1X 10~2 dyne-seconds. If we assume an average

impact velocity of 30 km/sec, particles of mass

greater than 3.3X10"9 grams could trigger the

counter on the satellite. Except in rare instances, real-time data were not obtained on

1959 Eta, although the sample was much greater

than on 1958 Alpha. Data were recorded for

78 days, with the total number of events approximating 5000 impacts.

Figure 3 is a plot of the impact rate (log of

the number of impacts per hour) as a function

of the date from November 10 through November 20: "C" is the average rate from September

18 through October 9; "B" the average from

November 10 to November 20; and "A" the

average from November 16 to November 18.

It is evident that from November 16 to 18

there are periods when the impact rate was two

orders of magnitude greater than the average

A AVERAGED 16 NOV. - 18 NOV.

B AVERAGED (0 NOV. - 20 NOV.

C AVERAGED 18 SEPT. - 9 OCT.

n II is is M s

FIGURE 3.—Impact rates during the November 1959

interplanetary dust particle event.
METEOR SYMPOSIUM—DUBIN, ALEXANDER, AND BERG 113

shown in "0" , and also than the average of the

78-day period. It is also interesting that there

were rapid fluctuations in the rate during the

period of the shower, and that several orbits

showed no impacts—or very few—even though

extremely high rates were observed for small

segments of the orbit. These rapid fluctuations

are probably real fluctuations in the spatial

density of interplanetary dust particles.

The Aerobee NRLr-25 was fired on November 17, 1955, at 0215, which was during the

same annual period as that of the intense impact

rate observed on 1959 Eta. Hence we arrive

at the hypothesis that both measurements

detected a shower, and that this cosmic dust

shower recurs annually and may possibly be

related to the Leonid meteor stream. Preliminary analysis of the data from the lightflash micrometeorite experiment using a 6199

photomultiplier with 1000 A evaporated layer

of aluminum on 1960 Xi indicates that an impact rate similar to that observed on NRL—25

was also observed in November 1960 during

approximately the same time period. The

analysis, however, has not been completed,

and it is still not possible to prove or disprove

the annual recurrence of this cosmic dust

shower. The piezoelectric experiment on Satellite 1960 Xi was so oriented as to be shielded

from the Leonid radiant; in fact, the microphone data of this spin-stabilized satellite did

not detect a shower at the time.

Discussion and conclusions

From the available data on direct measurements

of cosmic dust made with satellites and rockets

we have presented evidence of large fluctuations

in the flux of cosmic dust. In addition to daily

variations, which are often greater than an

order of magnitude, we have observed sets of

conditions which may be attributed to cosmic

dust streams. Large fluctuations are also

apparent in the streams themselves.

Although the total amount of data available

from direct measurements is still fairly small,

these two cosmic dust streams represent a large

fraction of the total number of impacts recorded

on all the satellites. The total number recorded on Satellite 1958 Alpha was 145, of

which nearly half may be associated with the

cosmic dust shower. Similarly, on 1959 Eta,

of approximately 5000 impacts, about 2800

occurred during the cosmic dust shower between

November 16 and November 18. Even if the

number of impacts so far recorded on 1960 Xi

and all other space vehicles were included, the

number of events occurring in these streams

represent a considerable fraction of this total.

By comparison, the number of meteors in

meteor streams observed optically, visually,

and by radar is only about 10 percent of the

number of sporadic meteors similarly observed.

On the other hand, Gallagher and Eshelman

(1960) have reported that a large fraction of the

meteors observed with their highly sensitive

radar equipment, capable of detecting meteors

of approximately visual magnitude +14, appear to be in streams. Does this perhaps support the hypothesis of a continuous generation

of dust by disintegration of conglomerates of

interplanetary material and a short lifetime of

the dust in interplanetary space? If so, it

would explain the relative unimportance of the

space or background density of sporadic dust

particles. On the other hand, if the rate of

dispersion of dust particles after disintegration

from a large conglomerate were rather rapid

and if the rate of removal of dust were slow,

the large majority of the dust particles would be

isotropically dispersed; then the variations in

the flux of cosmic dust as detected with satellites would be small, and the number of sporadic

dust particles would far outweigh the component of dust in showers. Additional measurements are certainly required to determine the

geueration and destructive characteristics of

interplanetary dust.

References

ALEXANDER, W. M.; MCCBACKEN, C. W.; AND LAGOW,

H. E.

1961. Interplanetary dust particles of micronsize probably associated with the Leonid

meteor stream. Journ. Geophys. Res.,

vol. 66, pp. 3970-3973.

BKHG, O. E., AND MEREDITH, L. H.

1956. Meteorite impacts to altitude of 103 kilometers. Journ. Geophys. Res., vol. 61,

pp. 751-754.

BROWNE, I. C ; BULLOUGH, K.; EVANS, S.; AND KAISER,

T. R.

1956. Characteristics of radio echoes from meteor

trails. II. The distribution of meteor

magnitudes and masses. Proc. Phys.

Soc. London, vol. 69B. pp. 83-97.
114 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

DUBIN, M.

1960a. Meteoritic dust measured from Explorer I.

Planetary Space Sci., vol. 2, pp. 121-129.

1960b. IGY micrometeorite measurements. In

H. K. Bijl, ed., Space research, pp. 1042-

1058. North-Holland Publishing Co.,

Amsterdam.

1961. Remarks on the article by A. R. Hibbs,

"The distribution of micrometeorites

near the earth." Journ. Geophys. Res.,

vol. 66, pp. 2592-2594.

GALLAGHER, P. B., AND ESHELMAN, V. R.

1960. "Sporadic shower" properties of very

small meteors. Journ. Geophys. Res.,

vol. 65, pp. 1846-1847.

HIBBS, A. R.

1961a. The distribution of micrometeorites near

the earth. Journ. Geophys. Res., vol.

66, pp. 371-377.

1961b. Author's reply to the preceding discussion

on the article, "The distribution of

micrometeorites near the earth." Journ.

Geophys. Res., vol. 66, pp. 2595-2596.

LAGOW, H. E., AND ALEXANDER, W. M.

1960. Recent direct measurements of cosmic dust

in the vicinity of the earth using satellites. In H. K. Bijl, ed., Space research,

pp. 1033-1041. North-Holland Publishing Co., Amsterdam.

LOVERING, J. F.

1959. Micrometeorite impacts to an altitude of

135 km. Planetary Space Sci., vol. 2,

pp. 75-77.

MCCRACKEN, C. W.; ALEXANDER, W. M.; AND

DUBIN, M.

1961. Direct measurement of interplanetary dust

particles in the vicinity of earth.

Nature, vol. 192, pp. 441-442.

WEISS, A. A.

1961. The distribution of meteor masses for

sporadic meteors and three showers.

Australian Journ. Phys., vol. 14, pp.

102-119.

Abstract

By means of rockets and satellites, direct measurements of cosmic dust over the past several years have yielded

two separate sets of data which indicate interplanetary dust showers consisting of particles of mass less than 10~*

grams. These cosmic dust showers were observed with micrometeorite detectors using piezoelectric crystals and

photomultipliers for detecting the light flash resulting from particle impacts. The Explorer I interplanetary dust

stream was detected for about a 10-hour period beginning on February 2, 1958. The peak rate of particles was

nearly 50 times the average impact rate over the remainder of the 12-day period of the experiment. From the limited

amount of data it may be shown that this stream was nearly in the ecliptic in a direct heliocentric orbit. The shower

does not correspond to a known annually recurring meteor shower.

The second stream of interplanetary dust, detected with satellites and from a sounding rocket, appears to recur

annually with a peak intensity on November 17. It was detected first in 1955 from an Aerobee rocket and recognized

in the November 1959 data from the Vanguard III satellite. Preliminary analysis of the Explorer VIII data indicates that it was probably also detected in 1960. The dust stream corresponds to the Leonids with a heliocentric

velocity of 72 km/sec. The data supporting the detection of these two interplanetary dust streams are presented and

discussed. The physical significance of these measurements is also reviewed. Although direct measurements from

satellites have been made over a period of about four months and during the time of other known meteor streams, so

far only these two interplanetary dust streams have been detected by direct measurements.
Discussion

F. L. Whipple.—I think that we should throw

the discussion open to all of the papers in this

session since they seem to be so intimately

related.

I have plotted the number of counts versus

the time since launch in a number of these

acoustic experiments and have found that this

drops off rapidly, so that it is possible that

some of these effects are due to noise.

M. Dubin.—This is not true for many of the

satellites.

I would like to comment on the paper by

R. Soberman and C. Hemenway. I believe

that there is a fundamental difficulty in relating

these results to the rocket and satellite experiments. The rocket in question was opened

below 90 km, where the particles have been

slowed down by the atmosphere. There is a

large uncertainty in the settling rate at these

altitudes, and I believe that where the exact

altitudes of collection are unknown in this

experiment, we should not place too much

faith in the flux calculations.

L. O. Jacchia.—I have seen some figures

quoted for dust at altitudes as high as 90 km

for the bright sunsets after the explosion of

Krakatoa in 1883; those bright sunsets are

said to have persisted for something like 3 or 4

years.

F. L. Whipple.—I don't feel that we can

accept the validity of those height estimates at

that time. Dr. Goody's work has shown that

you cannot make a reliable estimate of the

amount of material at high altitudes by the

sunset method. The fact that something was

seen after sunset at that altitude does not

prove, I think, that it wasn't secondary scattering. I don't see anything to hold larger particles up there.

E. L. Fireman.—One can go the other way

and say that these results should lead to a

tremendous concentration at the airplane collection altitudes. The relative settling rates

would predict an increase in concentration of

something like 107 at a 15-km altitude. Therefore, I am surprised that people haven't seen

many more of these particles in the aircraft

collections.

C. L. Hemenway.—We do find much higher

concentrations of these same types of particles

on aircraft collectors.

F. L. Whipple.—Some calculations made

from the aircraft collections are not completely

out of line with these other estimates of the

influx rate.

C. L. Hemenway.—I might interject that

when aircraft collections are made by the

filtering technique where the air expands

through a hole at subsonic velocities you don't

find the fluffy particles breaking up. On the

other hand, when you collect by the impactor

technique you find a large number of smashed

particles that look similar to the ones we have

shown today.

J. Manson.—We have been working on aircraft collections for some time. We think that

possibly the secondary precipitation mechanism

of forming sulfate particles at altitudes of about

20 km may hide some of these particles and

would certainly speed up their fall rate.

C. L. Hemenway.—I would support that. I

would say that the extremely small particles

that we have seen in aircraft collections and

have named nanometeorites for a convenient

label were found at U-2 altitudes only in

clumps. This would suggest that such a clump

had been brought down as a part of a larger

particle that partially evaporated under electron-beam bombardment.

C. Ellyett.—There is evidently some question

as to a possible particle increase at the time of a

meteor shower, thus associating the small particles with the larger meteoroids. You propose

to fire into a quiet period and a pronounced

shower period. I would like to suggest an

alternative method, that is, to fire in both the

115
116 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

northern and southern hemispheres at the same

time since we have an entirely separate set of

showers.

P. M. Millman.—I would like to remind the

audience of the evidence of the noctilucent

clouds and the trains left by large meteors, such

as the Tunguska fall, which tend to collect at a

preferred height due to the temperature profile.

One of the best theories to explain the noctilucent clouds suggests a possible increase in size

of these particles due to the formation of ice on

a very small solid nucleus. When one is talking about the possibility of particles being held

at certain levels I think that this evidence should

be carefully considered.

R. K. Soberman.—We deliberately opened

above the noctilucent cloud altitude, which I

believe is consistently in the 80 to 85 km altitude

region.

M. Dubin.—The estimates of particle concentration in noctilucent clouds (that is, 1 to 5

particles per cubic centimeter) give sufficient

numbers at about the altitude of opening to

account for your results, and this would explain

the low velocity. A higher altitude opening

would solve this question. Another point is

that Dr. Weiss mentioned in his paper that Dr.

Kaiser has measured the distribution of the

Arietids in the radio region and found an s number greater than 2.5, which would give a large

number of small particles at the time of that

shower.

C. W. McCracken.—Earlier Dr. Soberman

made the remark that his results from the two

satellites did not fit the mass-distribution curve

that we presented. I find that if I treat his

four datum points as I did the other data, then

those four points fall within an order of magnitude of the curve. Also the 300 particles per

square meter per second with diameters greater

than 3 microns, which he finds from the rocket

measurement, is within one order of magnitude

of an extrapolation of the mass-distribution

curve. Therefore, I don't see any tremendous

discrepancies that would lead one to conclude

that an appreciable geocentric concentration

has been measured.

F. L. Whipple.—Referring to the clusters that

Dr. Hemenway showed, I have been considering

how these particles can be spread out only over

a few microns. If they had fallen any distance

through the atmosphere they should have been

separated by meters at least. I might suggest

that as the rocket goes up there is a lot of degassing going on and the air density in the

vicinity of your collectors may be as much as

1000 times greater than ambient. It is quite

possible that the particles that survived entering

the atmosphere may have broken up when they

hit this much denser gas envelope.

M. Dubin.—Dr. Soberman said in his papers

that he did not trust the earlier rocket acoustic

measurements because he did not find any large

number of holes in the penetration experiments.

Evidence was presented that many of the particles do break up and may not be able to penetrate the mylar films. These particles would

still show up as a pulse on the microphone systems. There were cases where we observed

clustered pulses that we did not believe. This

may be the explanation. Therefore, I do not

feel that one can say that these experiments

rule out the validity of the earlier acoustic

measurements. The velocity of impact, I feel,

can still be questioned since the rocket did open

close to the so-called noctilucent cloud region.

R. K. Soberman.—With regard to noctilucent

clouds, there is a half hour per day at these

latitudes in which you could see the clouds if

they existed in this area. They have not been

observed this far south, let alone at 30° N.

F. L. Whipple.—But the dust that may form

the clouds may exist at all latitudes.

M. Dubin.—If these fluffy particles were to

strike a wire grid on a satellite, what would be

the result?

G. L. Hemenway.—I would say that the fluffy

particles have no chance of breaking the grid.

M. Dubin.—The microphones would still

detect them and you could develop a curve of

the type that McCracken has shown. But

because of the fluffy particles I don't think

you can compare the microphone data with the

wire-grid breakage rate.

E. L. Fireman.—If the statistics are as Dr.

Hemenway reported, then fluffy particles are

only about 12 percent of the total number.

R. K. Soberman.—This is pure speculation,

but these irregular particles which we observe

and which form the majority of the particles

may have been part of larger loose agglomerates.

C. L. Hemenway.—Because of our stringent
METEOR SYMPOSIUM—DUBEST, ALEXANDER, AND BERG 117

requirements and the difficulties in classification, I wouldn't trust the percentage breakdown too far. I would trust the size distribution

and the over-all numbers of particles per unit

area.

M. Dubin.—One more point. If you believe

the distribution function obtained by microphone systems is as McCracken presented it,

plus the fact that there are irregularities in the

flux of particles, then you do not have to impose

a dust belt to tie in the rocket and the satellite

data.

J. S. Greenhow.—I would like to show how

the measurements of radar rates extrapolate

to the micrometeorite measurements. Dr.

Weiss showed yesterday that with electron line

densities of 1014 to 1015 per centimeter, s is about

2.5. These are fairly reliable measurements.

I have extended this down to 10" with a value

of s of about 2.4. So over this range of electron

line densities s is of this order. If we look at

the absolute rate for a line density of 1012 per

centimeter, we find about 30 per 104km2per

hour. We only detect, of course, those at approximately right angles to us; in order to get

a true rate we have to multiply by a factor of

about 20. This line density corresponds to a

mass of about 10~2 gram. For micrometeorite,

I obtained from the previous graphs a rate of

about 10~3 per square meter per second for a

mass of 10"8 gram. If we take this range of

106 in mass and something like 5 x 107 in rate

when one puts in the various factors, we find

that the s value required to account for this

difference in rates is 2.4. So it seems reasonable

that we have an s value of about 2.4 all the

way from these large meteors that are about

zero magnitude and 10~2 gram down to 10~8

gram. It seems to me, therefore, that it would

be unreasonable to expect the slope to change

in the micrometeorite range and become something else.

A General Survey of Meteor Spectra

By Peter M. Millman

 l

The study of the spectra of meteors dates

from the 1860's when an English astronomer,

A. S. Herschel, commenced his visual observations with specially mounted direct-vision binocular prisms. For about 20 years observations were reported by a number of astronomers

including Herschel himself, A. Secchi, H. A.

Newton, and N. von Konkoly. For a bibliography of the subject during this period see

Millman (1932).

Through this early work it was realized that

in general meteors had bright-line spectra,

though sometimes the intense luminosity of

the meteor head caused the lines to blend into

each other giving the appearance of a continuous spectrum with a few predominant lines

superposed. The orange-yellow lines of neutral sodium and the green lines of neutral magnesium were correctly identified by these nineteenth century observers.

The first meteor spectrum photograph was

made on a Harvard patrol plate at Arequipa,

Peru, on June 18, 1897 (Pickering, 1897). The

first program of meteor spectro-photography

was carried out by S. Blajko (1907) at the

Moscow Observatory during the spring and

summer of 1904. However, at this time there

was no general activity in this field of astronomical photography, and by 1930, when I

first became interested in the subject, only

eight photographic meteor spectra were known.

Five of these had been photographed by chance

on programs conducted for other purposes.

During the last 30 years the number of photographic meteor spectra has grown slowly but

steadily and the world total now stands at

well over 400.

Even more important than the increase in

numbers of spectra has been the advance in

quality. This has been due chiefly to the de-

> National Research Council, Ottawa, Canada.

velopment of new photographic emulsions,

which are faster and cover a wider range of

wave length, and to the use of gratings instead

of prisms for the dispersing element. The original spectra were all photographed on bluesensitive plates. Fast plates sensitive to the

yellow-green became available in 1932 (Millman, 1935) and panchromatic plates sensitive

to the red in 1933 (Millman, 1934). By 1950

it was possible to use an infrared emulsion to

photograph meteor spectra (Millman, 1953).

It was also in 1950, on the Ottawa program,

that replica transmission gratings were first

successfully used. With a grating relatively

high dispersons are possible in some of the

orders, and lenses of longer focal length can be

employed without materially increasing the absorption of the dispersing element. Plates la,b

and 2a, b illustrate spectra photographed with

gratings on the Canadian programs.

The photographic observations have confirmed the fact that the luminosity of meteors

results primarily from a bright-line atomic

spectrum with a small percentage of the light

coming from simple molecules, and possibly a

continuous background in certain cases. Table

1 lists the multiplets that have been identified

with some reliability, the reference numbers

being those from the table by Moore (1945).

Multiplets found in some recent spectra of high

dispersion are included in table 1, while some

identified earlier on the basis of poor quality

prismatic spectra have not been included. An

attempt has been made to select only those

multiplets for which it is felt there is independent evidence of their presence. Since

meteor spectra as a whole give a consistent

picture, an analysis of a weak spectrum of poor

definition has been judged in view of what is

present in high dispersion spectra of good definition. In other words, the multiplets listed

119
120 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Multiplets identified in meteor spectra (reference numbers according to Moore, 1945)

(Bold face type indicates the most prominent multiplets; parentheses, those Identified with less certainty.)

H I

N I

O I

Na I

Mg I

Al I

Si I

Ca I

Cr I

M n I

Fe I

Co I

Ni I

N II

0 II

Mg II

Si II

Ca II

Fe II

Sr II

x2

1

1

1

1

1

1

(2)

1

22

1

2

1

19

38

(74)

350

522

(772)

1107

(28)

(1)

33

3

1

4

1

1

27

1

2

4

5

2

(5)

(3)

2

(23)

7

5

2

20

39

152

(352)

523

801

1146

(29)

(3)

(35)

5

2

(9)

2

2

28

1st positive group,

3

5

6

3

(9)

3

32

(9)

(6)

3

21

41

168

354

553

816

1150

(31)

5

(36)

8

(10)

3

37

8

9

(8)

9

(10)

4

(47)

22

16

4

22

42

169

355

558

965

1163

(34)

(6)

(52)

15

(20)

4

38

2d positive group.

16

10

(12)

11

(ID

5

(31)

5

23

43

207

357

559

984

1165

(150)

(17)

86

28

5

42

(20)

11

14

(16)

(9)

(40)

6

24

45

217

383

(597)

1062

1178

18

(8)

48

21

12

15

(17)

18

13

25

62

268

(385)

686

(1066)

(19)

(9)

49

(25)

14

19

15

26

68

278

409

(687)

1067

(20)

74

23

(20)

16

36

71

(280)

(476)

693

1092

(30)

3F

21

18

37

72

318

482

733

1094

(32)

represent my selection on the basis of a study

of all the observational data available to date.

There is no doubt that it will soon be possible

to add to the list a substantial number of additional multiplets.

Table 1 contains multiplets from 13 neutral

atoms and 7 singly ionized atoms, and band

systems from one molecule. The ionization

potentials of the upper levels involved are in

general low, particularly for the stronger, more

prominent multiplets. Over 80 percent are in

the range 2 to 8 eV and most of the remainder

are in the range 10 to 14 eV. Only the multiplets from N II and O II have excitation potentials above 20 eV.

Any trailing train luminosity of reasonable

strength will be photographed in the breaks of

the meteor track, produced by a rotating

shutter. Plate lb illustrates a good example

of this effect in a Perseid meteor. The train

or wake spectrum exhibits a similar character

to the spectrum of the meteor head, but the

low excitation multiplets and intercombination

lines are much stronger relative to the other

multiplets. Except for Ca II the ionized

elements are almost entirely lacking. Table

2 lists the multiplets reliably identified in

train or wake spectra. Their excitation potentials average 4 eV compared with an average

of about 6.5 eV for the multiplets in table 1.

The durations of the luminosity photographed

in meteor trains or wakes probably range from

a few hundredths of a second up to a second or

two. Unfortunately, the spectrum of a persistent or long enduring train has not yet been

photographed.
METEOR SYMPOSIUM—MILLMAN 121

Of particular interest in meteor trains is the

presence of the forbidden line of oxygen at

5577A (multiplet 3F of O I), often called the

auroral green line (see pi. 2b). This was first

identified by Halliday (1958) and has since

been found in at least 25 spectra including a

number photographed by Russell (1959, and

this Symposium, p. 171). This feature tends

to appear at greater heights than most of

the other meteor spectrum lines, and often

disappears before the rest of the spectrum has

reached maximum intensity. On the average,

this oxygen line is brightest between heights

of 110 km and 100 km, while the maximum

light of the remainder of the meteor spectrum

occurs at an average height of 90 km. The

green line appears chiefly in the spectra of

fast meteors, and this height of 90 km is typical

of the maximum light for the spectra of meteors

with velocities greater than 50 km/sec. Geminid spectra have the light maximum some 15

km lower on the average, and the spectra of

slow sporadic fireballs with velocities near

20 km/sec are brightest at a height of around

60 km. Giacobinid spectra, brightest near a

height of 90 km, are abnormally high for their

velocity of 23 km/sec.

Of the 318 photographic meteor spectra

listed up to the end of 1958 (Millman, 1959),

over 70 percent are from the well-known

meteor showers. Since meteors of this category

do not seem to fall as meteorites, meteor

spectra provide the only direct evidence of the

composition of these objects. The atomic

abundance of the elements in the largest class

of stony meteorites, the chondrites, has been

TABLE 2.—Multiplets in meteor train and wake spectra

(Bold face type Indicates the most prominent multiplets; parentheses,

those identified with less certainty.)

O I

N a l

M g l

C a l

Mn I

F e l

Call

N,

3F

1

1

1

2

1

21

1

2

2

2

(23)

2

3

3

3

41

( 9 )

18

4

42

(19)

5

43

(1st positive group.)

(21)

15 (16) 20

(268)

given by Urey and Craig (1953). Of the 15

abundant elements listed by these authors,

all except sulphur, potassium, phosphorus, and

titanium appear in table 1 above. Neither

sulphur nor phosphorus has good low excitation

lines in the observed region, and the position

of the potassium line in the far red is overlapped by first-order iron lines in the spectra

obtained up till now. Titanium, as a minor

constituent, is difficult to identify because of

the multiplicity of lines and the overlapping

with other elements. Three elements not common in meteorites—hydrogen, nitrogen, and

strontium—are listed in table 1. The occurrence of hydrogen in meteor spectra may

possibly indicate the presence of ices of some

form in the cometary meteoroids. Nitrogen

must certainly be contributed by the atmosphere, and it is not possible to say whether

any of it comes from the meteoroid itself.

Strontium, though not common, is found in

very small amounts in some meteorites. In

summary, it appears that tbe cometary

meteorites do not differ too markedly in general

composition from the stony meteorites. The

absence of sulphur and potassium from meteor

spectra and the presence of hydrogen are

probably the most significant indications of

possible differences.

Meteor spectra vary greatly in quality, from

faint records showing only a single line to high

dispersion spectra in which 100 or more separate items have been measured. In any statistical study of spectra it is important to

consider this feature, and the following quality

scale has been found convenient:

a - detail of 50 lines or more,

b - 20 to 49 lines,

c - 10 to 19 lines,

d - 9 lines or less.

Meteor spectra exhibit a fairly consistent

pattern with a few dominant characteristics,

and I proposed a simple system of classification

some years ago (Millman, 1935). A study of

all available data has indicated that this

original classification scheme is still useful and

it is summarized below, revised slightly to

adjust it to the panchromatic emulsions now

generally used. Classification of a spectrum

is based on its character at light maximum and

involves identification of the strongest features
122 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 3.—Classification of 259 meteor spectra

Meteor

Leonid (L)

Orionid (0)

Perseid (P)

Lyrid (Y)

Quadrantid (Q)

6 Aquarid (D)

Taurid (T)

Geminid (G)

Giacobinid (J)

Miscellaneous (N)

Vel

km/sec

72

66

60

]

> 31-48

J 35

23

12-70

Totals

a

9

1

1

1

12

Y

b

2

27

1

5

35

c

7

4

11

1

3

9

35

148

d

4

3

45

1

13

66

a

1

1

2

b

1

1

2

3

6

13

X

c

4

1

4

9

10

28

82

d

4

12

9

14

39

a b

1

2 5

2 6

Z

c

2

3

5

23

d

1

3

2

4

10

W

d

3

2

1

6

6

in two wavelength regions, the blue-violet

from 3500 to 4500 A and the orange-green

from 5000 to 6000 A. Four main types are

defined below:

Type Y: The H and K lines of Ca II are the strongest

features in the blue-violet.

Type X: If not as above, then either the D-lines of

Na I, or the lines near 5180A or 3835A

of Mg I, give the strongest feature in

either the orange-green or the blue-violet.

Type Z: If not as above, then the lines of Fe I, or

those of Cr I, give the strongest feature

in either the orange-green or the blueviolet.

Type W: Not as above.

This classification, though developed on a

strictly empirical basis, has some physical

significance since Type Y spectra are of higher

excitation than Type X. In Type Z spectra

most of the elements common in stony meteoroids are weak or absent, and hence a reasonable percentage of Type Z spectra must correspond to iron meteoroids. Type W will

include peculiar spectra and those too faint or

ill-defined to have other classification features.

Since spectrum quality has a direct bearing on

what can be identified, it is suggested that a

letter for the quality scale be prefixed to the

type. For example, a spectrum of 35 lines

showing very strong H and K of Ca II would be

classified as bY, one of 58 lines showing just the

iron multiplets would be aZ. If it should be

found advisable, numbers could be suffixed to

the type letters to indicate levels of excitation

within each type. It is suggested that these

should be used in the same sense as for stellar

spectra, that is, lower numbers referring to

higher excitations.

All the meteor spectra secured prior to 1959,

for which information is available, have been

classified in the above system. Their distribution in type, listed according to velocity, is

given in table 3. It will be noted that the fast

meteors are predominantly Type Y, meteors of

medium speed tend to be Type X though some

are of the other types, while slow meteors are

confined to Types X and Z. Giacobinid

spectra (see pi. \c) are good examples of what

we find in the light of very slow shower meteors.

In the miscellaneous group the Type Y

examples probably represent chiefly cometary

meteoroids, since asteroidal meteoroids as a

class are medium to low velocity objects

(Whipple and Hughes, 1955). In table 3

there are probably not more than 30 miscellaneous spectra produced by asteroidal meteoroids,

and at least two-thirds of these will be Types Y

and X, produced by stony meteoroids. Of

the miscellaneous spectra Type Z, it is likely

that not more than six represent iron meteoroids. Two examples which are probably in

this category are reproduced in plates Id and 2c.

These spectra exhibit very little other than

strong low level iron multiplets and sometimes

the ultimate lines of chromium.

A further insight into the relations among meteor spectra may be obtained by an examination
METEOR SYMPOSIUM—MILLMAN 123

100

o b c d a

Mgl + Si I + CaE + Fell

100

Fel

b e d

CrI + Mnl

b e d

Na I + Mg I + Ca I

FIGURE 1.—The frequency of identification of various elements in 259 meteor spectra

photographed prior to 1959, plotted against the spectrum quality from a to d. The

plot has been smoothed to show general trends and should not be used for quantitative values. Abbreviations: L, Leonid; O, Orionid; P, Perseid; G, Geminid;

J, Giacobinid; Sh, shower; N, miscellaneous.

of the frequency with which various atoms are

identified in any group. Figure 1 illustrates

some of these data. The observational material

used was the same as that included in table 3.

Percentage identification of the atoms is plotted

against spectrum quality. These curves are

smoothed averages and give qualitative information only and should not be used to give

quantitative values. They do, however, clearly

demonstrate the danger of drawing general

conclusions from spectra of low quality only.

The correlation of the appearance of the

ionized elements with the velocity of the meteor,

and the universal presence of iron in all spectra

of good quality, are quite evident features of

the plot. Another interesting point is that the

elements Ca, Na, and Mg are more frequently

identified in the shower meteors, while Cr and

Mn are found more frequently in the miscellaneous group which probably contains a significant percentage of nonshower meteors.

Another way of looking at meteor spectra

is to list the features which are strongest in

each example. Naturally, this will be greatly

modified by the wavelength sensitivity of the

grating or prism-lens-emulsion combination.

If we consider only the good quality spectra

studied here, ionized calcium is the strongest

feature in all Perseid spectra. The Geminid

spectra are roughly divided into four equal

groups with ionized calcium, neutral magnesium, neutral sodium, and neutral iron the

strongest in each group respectively. Magnesium is somewhat ahead of the other three

elements in frequency, suggesting the possibility

that this element is a significant constituent in

Geminid meteoroids. Giacobinid spectra are

about equally divided between sodium and iron
124 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

EXPLANATION OF PLATE 1

Meteor Spectrum No. 340, Type aY, a bright

Perseid photographed at the Newbrook Meteor

Observatory at 9h 27» 55« UT, August 13, 1959.

Lens, focal length 20 cm, aperture 7 cm; grating,

400 lines/mm; emulsion, Kodak Tri-X Aerecon;

dispersion in second order 60 A/mm, no rotating

shutter, meteor moving down in figure, observed

visually magnitude —7 or —8 with a persistent

train of 10-second duration. Halliday (1961)

has measured over 100 lines in the spectrum.

Note particularly the late appearance in the

burst of the low level iron multiplets Fe I 2

and 3 as compared to the higher level multiplets

Fe I 41, 42, 43, and the ionized elements. This

is a similar effect to that found by Russell (1960)

in the spectrum of the terminal burst of another

Perseid meteor.

Meteor Spectrum No. 272, Type aY, a bright

Perseid photographed at the Springhill Meteor

Observatory at 6h 20° 15', August 12, 1958.

Lens, focal length 15.0 cm, aperture 3.3 cm;

grating, 200 lines/mm; emulsion, Kodak 103 aF

spectrographic; dispersion in first order 320

A/mm, rotating shutter occulting 10/sec, open

to closed ratio Yt, meteor moving up in figure,

observed visually magnitude —7 or brighter

with persistent train duration 180 sec, photographic trajectory heights from 112 km to 83

km with light maximum at 90 km. Infrared

spectrum of this meteor, secured with another

camera, studied by Miliman and Halliday

d:

(1961). Note high relative strength of multiplets Fe I 1, 2, 3, Mg I 1, and Ca I 1 in wake

spectrum filling next to last shutter break.

Meteor Spectrum No. 86, Type bX, a Giacobinid

photographed at North Bay, Ontario, at 3h

51m 42» UT, October 10, 1946. Lens, focal

length 15.0 cm, aperture 3.3 cm, prism angle

30°, flint glass; emulsion, Kodak XXX-B

plate; mean dispersion H5—H-y 410 A/mm,

rotating shutter occulting 10/sec, open to closed

ratio Yi, meteor moving down in figure, observed

visually magnitude —2 with persistent train

duration 20 sec, photographic trajectory heights

from 109 km to 90 km, light maximum of sodium

line 102 km, of magnesium and iron lines 98

km. Note early appearance and disappearance

of sodium line.

Meteor Spectrum No. 24, Type aZ, nonshower

photographed at Flagstaff, Ariz., at 6h 35TM

23» UT, February 27, 1933. Lens, focal length

15.0 cm, aperture 3.3 cm, prism angle 30°,

flint glass; emulsion, Cramer Iso Presto; mean

dispersion Ha—Ry 410 A/mm, no rotating shutter, meteor moving down in figure violet end of

spectrum at left, observed visually magnitude

— 9 with train 2 sec duration. Visually determined heights of major bursts at 75, 73, 71,

69, 66, 65, 63, 59 km respectively. This spectrum has been studied by Miliman (1935).

Spectrum shows very little besides iron and

nickel.
MILLMAN PLATE 1

U

Fe 43 Fe 42 Fe 41

Fe 3 Fe 2

U I I I

Ca+ I Sr +l Ca I Mg+ 4

For explanation see facing page.
MILLMAN PLATE 2

For explanation see facing page.
METEOR SYMPOSIUM—MILLMAN 125

EXPLANATION OF PLATE 2

Meteor Spectrum No. 273, Type bY,& bright Perseid

photographed at the Springhill Meteor Observatory at 6h

 39" 25" UT, August 12, 1958. Lens,

focal length 20 cm, aperture 7 cm; grating, 200

lines/mm; emulsion, Kodak infrared aerographic;

no filter, dispersion in first order 240 A/mm,

rotating shutter occulting 12/sec, open to closed

ratio y%, meteor moving down in figure, observed

visually magnitude -5 with a persistent train

duration 30 sec, photographic trajectory heights

from 104 km to 79 km with light maximum at

84 km. First order infrared overlaps second

order violet. This spectrum has been studied by

Millman and Halliday (1961). Note the early

appearance of the O I line, and the increase in

relative strength of the Ca II lines towards the

end of the path.

Meteor Spectrum No. 294, Type dX, a Perseid

photographed at the Newbrook Meteor Observatory at 7h

 30" UT, August 15, 1958. Lens, focal

length 6.2 cm, aperture 8.7 cm; grating, 80

lines/mm; emulsion, Kodak I-D spectroscopic;

dispersion in first order 1950 A/mm, rotating

shutter occulting 11.6/sec, open to closed ratio %,

meteor moving up in figure, approximate heights

of photographic trajectory 120 km to 100 km.

This spectrum has been studied by Halliday

(1960). Note the auroral O I line at 5577A

which carries across all the shutter breaks,

indicating a minimum duration of an appreciably

fraction of a second. The sodium D-line appears

just to the right of the auroral line, and the

magnesium green line just to the left.

Meteor Spectrum No. 26, Type bZ, nonshower

photographed by the Texas Observers at Fort

Worth, Tex., at 7h 03- UT, August 12, 1933.

Lens, focal length 30 cm, aperture 7.5 cm; prism

angle 20°, flint glass; emulsion, Kodak Hyper

Press; mean dispersion H5—H7 333 A/mm, no

rotating shutter, meteor moving down in figure

violet end of spectrum at left, observed visually

magnitude —5 with train 1.5 sec duration.

Spectrum shows mainly low level multiplets of

neutral iron. Note similarity to Spectrum 24

(see pi. Id).

638805—«3 11
126 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

as the strongest feature. For the miscellaneous

group of spectra, sodium comes first, followed by

ionized calcium and neutral iron.

Several investigators, including myself, have

noted that the character of a meteor spectrum

frequently changes along the photographed

path. Usually this change is in the sense of

progressing to higher excitations, with the

associated greater relative strength of the

ionized atoms such as Ca II, Mg II, and Si II.

Bursts near the end of the path for bright

meteors of the faster showers demonstrate

particularly well this enhancement of the ionized

atoms (Russell, 1949). However, in the case of

slow nonshower fireballs it is quite possible for

the neutral iron vapor to show a lower excitation at the bursts (Millman, 1935).

Since a meteor generally increases in luminosity over most of the visible path, the change

in excitation will be correlated with luminosity.

The early part of the path of a fast, bright

fireball may show only the nitrogen bands,

sodium D-lines, and some iron. This will give

an intensity distribution strong in the red and

yellow. As the fireball brightens the lines of

ionized calcium and ionized magnesium, as well

as other features, become relatively stronger

and will tend to increase the intensity in the

blue and violet. It is found that spectra of

the faint meteors of high-velocity showers often

appear similar to the early parts of the paths

of much brighter meteors of the same shower.

This agrees with the observational results of

Jacchia (1957), Ceplecha (1959), and Davis

(this Symposium p. 233), which indicate a

higher color index, and therefore a redder color,

for the faint meteors. There are a few very

faint Perseid spectra that lack the strong lines

of Ca II, a characteristic feature of most

spectra of this shower. Cook (1955) has

suggested a two-parameter dependence of

ionization and excitation in meteor spectra, the

major controlling factors being meteor velocity

and the ratio of characteristic meteoroid

dimension to the mean free path of an evaporated atom. Since the fainter, and hence smaller

meteors, disappear higher in the atmosphere,

the above suggestion could explain some of the

observed correlations, but the situation is

probably somewhat more complex in many

cases.

In conclusion I express my thanks to I. S.

Astapovich, E. N. Kramer, and K.A. Liubarsky,

U.S.S.R.; Zd. Ceplecha and J. Rajchl, Czechoslovakia; I. Halliday, Canada; H. B. Ridley,

England; and J. A. Russell, U.S.A., all of whom

have provided me with unpublished details of

meteor spectra for this survey.

References

BLAJKO, S.

1907. On the spectra of two meteors. Astrophys. Journ., vol. 26, pp. 341-348.

CEPLECHA, Zd.

1959. On the colour index of meteors. Bull.

Astron. Inst. Czechoslovakia, vol. 10,

p. 39.

COOK, A. F.

1955. The nature of meteoric radiation. In T.

R. Kaiser, ed., Meteors, Spec. Suppl.

Journ. Atmosph. Terr. Physics, vol. 2,

pp. 8-15. Pergamon Press, New York.

HALLIDAY, I.

1958. Forbidden line of O I observed in meteor

spectra. Astrophys. Journ., vol. 128,

pp. 441-442.

1960. Auroral green line in meteor wakes. Astrophys. Journ., vol. 131, pp. 25-33.

1961. A study of spectral line identifications in

Perseid meteor spectra. Publ. Dominion

Obs. Ottawa, vol. 25, pp. 1-16.

JACCHIA, L. G.

1957. On the "color index" of meteors. Astron.

Journ., vol. 62, pp. 358-362.

MILLMAN, P. M.

1932. An analysis of meteor spectra. Ann.

Harvard Coll. Obs., vol. 82, pp. 113-146.

1934. Meteor spectra—list I. Journ. Roy.

Astron. Soc. Canada, vol. 28, pp. 279-281.

1935. An analysis of meteor spectra: second

paper. Ann. Harvard Coll. Obs., vol.

82, pp. 149-177.

1953. The typical Perseid meteor spectrum.

Nature, vol. 172, pp. 853-854.

1959. Photographic meteor spectra (appendix

7). Journ. Roy. Astron. Soc. Canada,

vol. 53, pp. 271-276.

MILLMAN, P. M., AND HALLIDAY, I.

1961. The near-infra-red spectrum of meteors.

Planetary Space Sci., vol. 5, pp. 137-140.

MOOBE, C. E.

1945. A multiplet table of astrophysical interest.

Contr. Princeton Univ. Obs., no. 20,

parts 1, 2.

PICKERING, E. C.

1897. Spectrum of a meteor. Astrophys. Journ.,

vol. 6, pp. 461-462.
METEOR SYMPOSIUM—MILLMAN 127

RUSSELL, J. A.

1949a. A composite spectrum of a Perseid

meteor of 1948. Pop. Astron., vol. 57,

pp. 187-192.

1949b. A note on revised wavelenths for a composite spectrum of a Perseid meteor of

1948. Pop. Astron., vol. 57, pp. 344-345.

1959. Some Perseid meteor spectra of the past

decade. Sky and Tel., vol. 18, pp.

549-551.

1960. A time-resolved spectrum of the terminal

burst of a Perseid meteor. Astrophys.

Journ., vol. 131, pp. 34-37.

UBBT, H. C, AND CRAIG, H.

1953. The composition of the stone meteorites

and the origin of the meteorites. Geochim. et Cosmochim. Acta, vol. 4, pp.

36-82.

WHIPPLE, F. L., AND Hughes, R. F.

1955. On the velocities and orbits of meteors,

fireballs, and meteorites. In T. R.

Kaiser, ed., Meteors, Spec. Suppl. Journ.

Atmosph. Terr. Physics, vol. 2, pp. 149-

156. Pergamon Press, New York.

Abstract

Over 400 meteor spectra have now been photographed at various observatories, with most of the data having

been obtained in three countries—Canada, the U.S.S.R., and the U.S.A. The range of wavelengths covered extends

from 3000A to 9000A. The bright-line emissions for roughly 200 multiplets have now been identified with some

certainty. These belong to 13 neutral atoms, 7 singly ionized atoms, and one molecule. The composition of cometary meteoroids does not seem to differ markedly from that of stony meteorites. The excitation in a meteor spectrum

depends chiefly upon the velocity of the meteor and its absolute magnitude. A simple system of meteor spectrum

classification is suggested, based on an earlier proposal made by the author in 1935.

Meteor Spectra with High Dispersion

By Zd. Ceplecha* and J. Rajchl*

This paper is based on the analysis of two

photographs of meteor spectra with high

dispersion obtained by transmission diffraction

gratings in the autumn of 1960 at the Ondfejov

Observatory (Rajchl, 1961). The cameras used

were provided with Tessar objectives having

focal ratios of 1:3.5 and 1:4.5 and focal lengths

of 30 cm and 36 cm. The first camera was

equipped with a transmission objective grating

with 600 grooves per millimeter, and the second

one with a grating with 400 grooves per millimeter. The photographic materials used were

Agfa Press plates 25° D with dimensions 18X24

cm. A shutter rotating approximately 450

times per minute was used with these cameras.

The method of wavelength determinations

Since a meteor spectrum photographed with

an optical transmission grating is usually off

the optical axis of the camera, the ordinary

method of wavelength determination is hardly

feasible. The diffracted ray falls in the plane

determined by the incident ray and the optical

axis when the spectrum passes through the

optical axis. On the other hand, when the

spectrum does not pass through the optical

axis, the diffracted rays lie on the surface of a

cone, the axis of which is parallel to the grooves.

The section of this diffraction cone made by

the focal plane is the diffraction hyperbola,

along which the spectral record is distributed.

Absolute wavelengths can be found from such

a spectrum if it includes the zero-order image.

A method based on Rowland's (1893) was

developed to exploit the full accuracy that

could be obtained. Complete details, with

equations, have been published (Ceplecha,

1961). We present here a brief description of

the principal features of the method.

1

 Astronomical Institute of the Czechoslovak Academy of Sciences,

Ondfejov, Czechoslovakia.

The spectral plate is measured with the y-axis

placed roughly parallel to the meteor motion,

thus leaving the x-coordinate of any one line

only slightly dependent on the position along

the track where it is measured. The coordinate

system for the whole plate is computed from

measurements of zero-order images of stars

(Ceplecha, 1951; 1954). The spectrum must be

photographed with a rotating shutter. The

measurements of one break in three different

lines then give the diffraction hyperbola, and

thus the connection between the coordinate

system of the plate and that of the grating.

The coordinate system of the grating directly

determines the wavelengths of individual lines

if we know the precise number of grooves per

millimeter and the direction cosines of the zeroorder image of the meteor. Identification of

one line will yield this precise number of grooves

per millimeter, and comparison with the number

of grooves specified by the manufacturer will

check the identification. Thus it is possible to

say that the wavelengths of all the lines are

computed without previous identification, and

that they are determined absolutely by the

measurements of angles. Of course, because of

optical distortions, the coordinate system, defined by zero-order images of three stars and by

their apparent spherical coordinates with corrections for atmospheric refraction added, is

less accurate than necessary for absolute determinations of wavelengths. It is possible, however, to correct the coordinate system established

from three stars at different places of the meteor

spectrum by using additional stars. For

example, with an undriven camera the intersection points of star images with the meteoric

spectral lines may be used for this purpose.

Since the directions of spectral lines in various

parts of the spectrum differ slightly, it is necessary to compute the point of intersection of

129
130 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

diffraction hyperbolae with each line, a somewhat laborious procedure, obviated in the case

of hundreds of lines only by the use of an

electronic computer. We used NE-803, completing our work on the two spectra in one hour

of computer time.

It is very interesting to note incidentally

that the dispersion can be chosen along an

ellipse, if the grating is inclined to the optical

axis of the camera. For our cameras the angle

of 54° is sufficient to photograph all meteor

spectra with dispersion along an ellipse. Such

an experimental arrangement might offer some

advantages for photography of meteor spectra.

Meteor spectrum S 6

This spectrum was photographed September 13,

1960, at 18* 59m UT. The spectrum of a single

bright flare was well exposed. The flare was

shorter than one break (the number of breaks

per second was about 15.2). The spectrum is

24 cm long and is near the longer edge of the

plate, with the hyperbolic form visible at first

sight. Some of the brightest spectral lines also

appeared three breaks before the flare. Thus it

was possible to determine that the angular

velocity was 6.9°/sec. A direct photograph of

this meteor is, however, not available since the

meteor flare was only 28° above the horizon at

azimuth 118°, where none of our direct cameras

was pointed. The spectrum begins with a part

of the second order and continues with the

third, fourth, fifth, sixth, and seventh orders.

The main order contained is the fourth, but the

orders overlap, as shown in figure 1. They are

on the opposite side from the "blazed" first

order. Thus the distribution of the intensity

of one line in different orders is relatively

smooth. The approximate dispersion, which

changes slightly with the place on the plate, is

presented in table 1. The dispersion in the

fourth order is about 19 A/mm. With such a

high dispersion, it is possible to compute the

wavelengths with relatively great precision.

TABLE 1.—Approximate dispersions of meteor spectrum

S6

Order 2 3 4 5 6 7

Dispersion A/mm 38 25 19 15 13 11

plate

-24 cm

FIGURE 1.—Overlapping of orders in meteor spectrum S 6.

n

30

20

10

-1.0 _•_. -0.5 + 0.5 -1.0 A

FIGURE 2.—Distribution of the deviations of measured

wavelengths from tabular wavelengths of 116 unblended

lines.

The disentanglement of the different overlapping orders was very laborious. The wavelengths were computed for every possibility,

and identifications of the individual lines

were sought in different orders. Some factors,

for example the different optical quality of the

image depending on the wavelength, simplified

the choice of the spectral order, but the most

important factor considered was the repetition

of one line with corresponding intensities

in all spectral orders. The results appear in

table 2, which contains 166 lines with their

identifications. It is interesting to note that

70 percent (116 lines) are not blended at this

high dispersion. The mean deviation of the

measured wavelength from the laboratory

wavelength for these unblended lines was only

±0.21 A. The distribution of the deviations is

given in figure 2.
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL 131

The basic spectral tables used for the identifications are the Russian tables of Zajdel et al.

(1952), from which the intensities 7tab presented

in table 2 are taken for the arc spectra of individual elements. The observed intensities 70bl!

of lines of the meteor spectrum were estimated

by eye (the scale is given with table 2). The

mean wavelengths of table 2 were calculated for

each line from wavelengths of different orders

by weighting with the number of the order.

The mean intensities were computed for the

intensity level of the fourth order. The intensities from other orders were reduced to the level

of the fourth order by multiplying by the factors

derived from comparison of observed intensities

of all lines in different spectral orders (the correction factors are given with table 2). Since

the spectral sensitivity of the plate was not

taken into account, the intensities are only

provisional values.2

The majority of the lines are iron lines belonging to 76 different multiplets. The multiplet numbers presented in table 2 are from

Moore's (1945) tables. The strongest lines are

Na doublet 1; Mg triplet 2; ionized Ca doublet

1; Ca line 4226.73; Fe lines 4375.93 of multiplet

2; 4383.55 of multiplet 41; 5328.37 of multiplet

15. Other elements observed are Mn multiplets 2, 4, 5, 6, 22, 23, 24; Ni multiplets 45,

86, 131, 143; Al multiplet 1; Cr multiplets 1, 7,

31, 96; and Co multiplet 34.

The elements usual in meteorites and air,

which are not observed in this spectrum, are

Cu, P, S, C, Si, K, N, O.

The quality of this meteor spectrum is well

demonstrated by the neighborhood of the Ca II

line 3933.67 A. The following lines are separated: Fe line 3927.92; Fe line 3930.30; weak Fe

line 3931.12; weak Fe line 3932.63; and Ca

II line 3933.67. This is the first instance in

which these iron lines were separated from the

Ca II line. The closest lines separated in this

spectrum are only 0.43 A apart.

The Ca II doublet in this spectrum is very

strong, although the meteor is slow.

As already indicated, direct double-station

photographs of this meteor are not available.

It is possible, however, to estimate that this

'The boloraetric intensities of lines will be published in Ball. Astron.

Inst. Czechoslovakia, vol. 14. no. 2, 1963.

meteor belongs to the Southern Taurid stream.

Then the radiant aR=5°, 5R=0°, which lies

on the great circle of the meteor, and an assumed velocity of 29 km/sec compared with the

observed angular velocity will yield 11° of

inclination to the horizontal plane and 76 km

for the height of the flare. This is quite acceptable. If the height of the flare is assumed to be

in the interval from 90 to 60 km, the velocity

lies within a short interval between 34 and 23

km/sec. In any case this meteor can be classified as slow.

Spectrum of meteor No. 27471

The meteor was observed October 27, 1960,

at 0h13m048 UT. Since double-station photographs are available, complete data on the

atmospheric trajectory and the orbit can be

presented. The detailed study of the velocity

changes of this meteor is discussed in a paper

by Ceplecha and Davies.3

The height of the beginning of this meteor

was 86.8 km with the original velocity of

»„,=25.95 km/sec, which was possible only if

the composition of the meteor was iron (Ceplecha, 1958). The observed radiant was a R =

39?09, 5R=10?87, and the elements of the orbit

were

a=2.08 a.u.,

6=0.759,

2=0.501,

co=98? 64,

Q=33?44,

i = 4?89.

This orbit is identical with the association

No. 85 observed by Jacchia and Whipple (1961).

The brightness of the meteor increased from

—0*5 at the beginning to the maximum light

of — 5*5 at height 65 km, where the velocity

of the meteor was 25.5 km/sec. This part of

the trajectory was composed of a series of

individual pulsations, the last of which was the

maximum itself. After the maximum there

were several pulsations; then a relatively long

part of the trajectory exhibited almost constant

brightness between —3m and —4m. The end

of the trajectory occurred quite suddenly at

the height of 41.1 km. The velocity measured

at the end was 13.2 km/sec.

» Zd. Ceplecha and J. Q. Davies, "On the Change of the Heat-Transfer

Coefficient of Bright Meteors," to be published in Bull. Astron. Inst.

Czechoslovakia.
132 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6

[EXPLANATION: Scale of observed Intensities I»bi: 0, not observed; 0.5, weakest lines; 1, very weak; 2, weak; 3, medium

intensity; 4, strong; 5, very strong; 6, strongest lines. The correction factors for the level of intensities of the 4th order

were derived from comparison of observed intensities in different orders of all observed lines:

Order: 2 3 4 5 6 7

Correction factor: 0.7 0.8 1.0 1.5 2.0 3.3

The symbol + means that the line was observed but that it was not measured because it was too weak (or not sharp

enough) or because it blended with another line. The column headed "Mult." gives the number of multiplet according

to Moore (1945). The figures In the last column (ev) represent the energy of the upper excitation level.]

Line observed

No. Order

1. 4

5

6

7

Mean:

2. 4

5

6

7

Mean:

3. 4

5

6

7

Mean:

4. 4

5

6

7

Mean:

5. 4

5

6

7

Mean:

6. 4

5

6

7

Mean:

7. 4

5

6

7

Mean:

lohn

1

1

0. 5

1

1. 7

0

2

0

0

Xob.

3644. 27

3643. 62

3644. 87

3644. 75

3644- 44

3681. 60

(0.8) (3681.60)

1

1

0

0

0.6

1

0. 5

0

0

0.4

1

0.5

0

0

0.4

o

1

1

0

1.4

1

1

2

0

/. 6

+

3696. 99

3696. 99

3700. 72

+

3700. 72

3705. 25

+

3705. 25

3719. 95

3720. 09

3719. 94

3719. 99

3733. 93

3733. 79

3733. 86

3733. 86

Blended

with line

No. Order

/158 3

\ll9 4

160 3

^tmb

3644. 41

3682. 23

3679. 92

3683. 06

3697. 43

3696. 57

3701. 09

3705. 57

3719. 94

3734. 87

3733. 32

Identification

/,.b

200

400

500

200

100

100

300

700

1000

1000

400

C a l

F e l

F e l

F e l

F e l

Mn I

F e l

F e l

F e l

F e l

F e l

Mult.

9

772

5

5

389

24

385

5

5

21

5

ev

5.30

6. 91

3. 36

3.41

6.35

6. 23

6.35

3.39

3.32

4. 18

3.43
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

133

Line observed

No. Order 7ob8 Xob«

8. 4 2 3737. 27

5 2 3737. 97

6 1 +

7 0

Mean: 1. 8 3737. 66

9. 4 1 3743. 00

5 0

6 1 3743. 48

7 1 3743. 37

Mean: 1. 6 3743. 32

10. 4 2 3745. 72

5 0. 5 +

6 1 3745. 01

7 1 3745. 17

Mean: 2. 0 3745. 24

11. 4 2 3749. 20

5 1 -f6 1 3749. 64

7 1 3749. 81

Mean: 2. 2 3749. 61

12. 4 1 3816.06

5 0

6 0

Mean: 0. 3 3816. 06

13. 4 1 3820. 36

5 0

6 0

Mean: 0. 3 3820. 36

14. 3 1 3822. 41

4 1 3823. 14

5 0.5 +

6 0

Mean: 0. 6 3822. 83

15. 3 2 3824 37

4 2 3824. 68

5 1 +

6 0

Mean: 1. 3 3824. 55

16. 3 0

4 1 3826. 27

5 0

6 0

Mean: 0. 2 3826. 27

Blended

with line

No. Order

128 3

129 3

Identification

Xt«b /tab Mult, ev

3737. 13 1O00 Fe I 5 3. 35

3743.36 200 Fe l 21 4.30

3745. 56 500 Fe I 5 3. 39

3745.90 150 Fe l 5 3.43

3749. 49 1000 Fe I 21 4.22

3815. 84 700 Fe I 45 4. 73

3820.43 800 Fe l 20 4. 11

3823. 51 75 Mn I 6 5. 38

3823. 89 50 Mn I 6 5. 40

3824.44 150 Fe I 4 3. 24

3825. 88 500 Fe I 20 4. 16

6SSS05—63- 12
134 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order /Ob» \>b«

17. 3 0

4 1 3827. 78

5 1 3828. 11

6 0

Mean: 0.6 8827.96

18. 3 0

4 1 3829. 36

5 1 3829. 91

6 0

Mean: 0. 6 8829. 67

19. 3 1 3831. 69

4 1 3832. 40

5 0

6 0

Mean: 0.4 8832. 10

20. 3 0

4 1 3832. 93

5 0

6 0

Mean: 0. 2 8832.98

21. 3 1 3834.04

4 1 3834. 10

5 1 3834. 96

6 0.5 +

Mean: 1. 1 8834. 44

22. 3 0

4 1 3836.49

5 1 3837. 04

6 0

Mean: 0.6 8886.80

23. 3 1 3837. 86

4 1 3838. 19

5 0.5 +

6 0.5 +

Mean: 0. 9 8888. 05

24. 3 0

4 1 3839. 36

5 0

6 0

Mean: 0.2 8889. 86

Blended

with line

No. Order

Identification

Xtab 7tl>b Mult, ev

3827. 82 200 Fe I 45 4. 79

3829. 35 10 Mg I o 5. 94

3832.31 250 Mg I 3 5. 94

3833. 31 100 Fe I 221 5. 79

(3834. 36 75 Mn I 6 5.39)

(3833. 86 75 Mn I 6 5.41)

3834. 22 400 Fe I 20 4. 19

3836.33 100 Fe I 664 6.53

3838. 29 300 Mg I 3 5. 94

3839. 26 100 Fe I 529 6. 27
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

135

Line observed

N o. Order

25. 3

4

5

6

Mean:

26. 3

4

5

6

Mean:

27. 3

4

5

6

Mean:

28. 3

4

5

6

Mean:

29. 3

4

5

6

Mean:

30. 3

4

5

6

Mean:

31. 3

4

5

6

Mean:

32. 3

4

5

6

Mean:

/obi

0

1

1

0

0.6

0

1

0

0

0.2

0

1

0

0

0.2

1

1

1

0

0.8

0

1

0

0

0.2

(3)

3

2

0

2.0

(3)

1

1

0

0.8

3

3

2

1

^obs

3839. 77

3839. 80

S8S9. 79

3840. 62

SS40. 62

3841. 21

3849. 83

3850. 32

3850. 27

S850. 18

3852. 28

3852. f S

3856. 52

3856. 80

3856. 68

3858. 38

3858. 63

3858. 52

3859. 79

3859. 97

3859. 69

+

3859. 81

Blended

with line

No. Order

32 3

32 3

^tab

3839. 78

3840. 44

3841. 05

3849. 97

3850. 82

3852. 58

3856. 37

3958. 30

3859. 91

Identification

^tab

100

400

500

500

200

150

500

800

1000

Mnl

Fel

Fel

Fel

Fel

Fel

Fel

Ni I

Fel

Mult.

6

20

45

20

22

73

4

32

4

ev

5.41

4.22

4.83

4.23

4.21

5.99

3.25

3.63

a 2i
136

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6— Continued

Line observed

No. Order

33. 3

4

5

6

Mean:

34. 3

4

5

6

Mean:

35. 3

4

5

6

Mean:

36. 3

4

5

6

Mean:

37. 3

4

5

6

Mean:

38. 3

4

5

6

Mean:

39. 3

4

5

6

Mean:

40. 3

4

5

6

Mean:

/obs

2

1

1

1

1.5

3

(5)

2

0

1. 8

4

3

1

0. 5

2.2

1

1

1

0.5

1. 1

1

1

0.5

0

0.6

1

1

1

0.5

1. 1

2

2

(3)

1

1. 9

1

1

(3)

0.5

0.9

Xoba

3872. 15

3872. 58

3872. 55

+

3872. 46

3878. 21

(3877. 47)

8878. 21

3886. 39

3886. 47

3886. 66

+

3886. 53

+

3892. 34

3891. 47

+

3891. 86

(3894. 17)

3893. 40

+

3893. 40

(3894. 17)

3894. 06

3894. 12

+

3894. 09

3895. 94

3895. 76

(3897. 01)

+

3895. 84

3898. 07

3897. 83

+

3897. 93

Blended

with

No.

133

165

38

135

37

166

/ 39

\166

line

Order

3

3

3

3

3

3

5

3

Xtab

3872. 50

3878. 02

387S. 58

3886. 80

3886. 28

3891. 93

3S93. 39

3894. 07

3895. 66

3897. 90

Identification

/tab

300

400

300

125

600

100

100

1000

400

100

F e l

F e l

Fe I

Cr I

Fe I

F e l

F e l

C o l

F e l

F e l

Mult.

20

20

1

23

4

733

430

34

4

280

ev

4. 19

4. 16

3. 28

4. 19)

3.24

6.60

6. 13

4.23

3. 29

5.87
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

137

No.

41

42

43

44

45

46

47

48

Line observed

Order

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

3

4

5

6

Mean:

Job.

3

2

2

1

2

2

1

0

i. S

2

1

0. 5

0. 5

1. 1

2

3

0.5

0

1.3

3

3

2

1

2. 6

(6)

3

1

(6)

9 9

(5)

3

1

(6)

2. 2

(5)

0.5

0. 5

0

0.4

^obs

3899. 82

3899. 73

3899. 37

_j_

3899. 60

3902. 91

3903. 11

3903. G3

3903. 28

3905. 47

3906. 52

+

+

3906. 07

3920. 46

3920. 26

+

3920. So

3922. 97

3922. 85

3922. 97

+

3922. 93

3927. 90

3927. 74

3927. 81

3930. 34

3930. 49

3930. 42

3931. 66

+

3941. 66

Blended

with line

No. Order

137 3

139 3

156 2

156 4

50 3

157 4

/50 3

\47 3

Xt»b

3S99. 71

3902. 95

3906. 48

3920. 26

3922. 91

3927. 92

3930. 30

3931. 12

Identification

A«b

500

500

300

500

600

500

600

35

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Mult.

4

45

4

4

4

4

4

565

ev

3.26

4.73

3.28

3. 28

3.21

3.26

3.24

6.42
138 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order

49. 3

4

5

6

Mean:

50. 3

4

5

6

Mean:

51. 3

4

5

6

Mean:

52. 3

4

5

6

Mean:

53. 3

4

5

6

Mean:

54. 3

4

5

6

Mean:

55. 3

4

5

6

Mean:

56. 3

4

5

6

Mean:

lob*

(5)

0.5

0.5

0

0.4

5

4

3

3

4.6

1

0.5

0.5

0

0.5

0.5

1

0

0

0.6

1

1

1

0.5

/. 1

5

4

3

3

4.6

1

0.5

0

1

0.8

2

2

1

0

1.3

Xoba

3932. 63

+

3932. 63

3933. 64

3933. 71

3933. 54

3933. 55

3933. 60

3944. 25

+

+

3944. 25

+

3956. 33

3956. 33

3961. 20

3961. 51

3962. 29

+

3961. 76

3968. 45

3968. 51

3968. 38

3968. 08

3968. 32

+

+

3984. 68

3984. 68

4005. 38

4005. 18

+

4005. 27

Blended

with line

No. Order

/50 3

\47 3

145 3

^tab

3932. 63

(3933. 61

3933. 67

3944. 01

3957. 05

3957. 03

3956. 68

3956. 46

3961. 52

3969. 26

3968. 47

3985. 39

3983. 96

4005.25

Identification

7,

80

200

600

2000

80

50

150

100

3000

600

500

125

200

250

>b

F e l

F e l

Call

A l l

C a l

F e l

Fe I

F e l

A l l

F e l

Call

F e l

F e l

F e l

Mult.

/280

\652

/(488

\ 562

1

1

6

562

278

604

1

43

1

661

277

43

ev

5.85

6. 40

6.22)

6.42)

3. 15

3. 14

5.02

6.40

5.80

6.37

3. 14

4.59

3. 12

6.41

5.83

4. 65
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

139

Line observed

No. Order

57. 3

4

5

6

Mean:

58. 3

4

5

6

Mean:

59. 3

4

5

6

Mean:

60. 3

4

5

6

Mean:

61. 3

4

5

6

Mean:

62. 3

4

5

6

Mean:

63. 3

4

5

6

Mean:

64. 3

4

5

6

Mean:

hbs

3

3

2

0.5

2. 1

2

2

2

0.5

/. 5

2

2

2

0. 5

1.5

(4)

1

0

0

0.3

4

3

2

1

2.8

3

2

1

0

1.6

1

1

1

0

0.8

3

3

0.5

0.5

1.8

Xob,

4030. 78

4030. 73

+

4030. 75

4032. 97

4033. 13

+

4033. 06

4034. 46

4034. 41

+

4034. 43

4042. 55

4042. 55

4045. 97

4045. 85

+

-f

4045. 90

4063. 69

4063. 68

4064. 05

4063. 84

+

4066. 21

4065. 33

4065. 72

4071. 71

4071. 86

-f

+

4071. 80

Blended

with

No.

/58

\59

/57

\59

/57

\58

61

line

Order

5

5

5

5

5

5

3

Xtab

(4030. 50

4030. 76

4033. 07

4034. 49

4041. 36

4045. 82

4063. 53

4063. 60

4066.60

4066. 98

4071. 74

Identification

/

120

500

400

250

100

400

100

400

40

100

300

tab

F e l

M n l

M n l

M n l

?

M n l

F e l

M n l

F e l

F e l

F e l

F e l

Mult.

560

2

2

2

5

43

5

43

424

358

43

ev.

6.26)

3.08

3.08

3.08

5. 18

4 55

5. 21

4.61

6.03

5.87

4.65
1 4 0 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order 7ob. Xob8

65. 3 1 4105. 13

4 1 4104. 90

5 0. 5 +

6 0

Mean: 0. 6 4105. 00

66. 3 1 4127. 82

4 0. 5 +

5 0. 5 +

6 1 4126. 33

Mean: 1. 0 4126. 83

67. 3 2 4132. 02

4 1 4132. 11

5 (5)

6 0. 5 +

Mean: 1. 2 4132.07

68. 3 (3)

4 1 4143. 31

5 (2)

6 (1)

Mean: 1. 0 4143. 31

69. 3 3 4143.80

4 3 4143. 67

5 2 4143. 96

6 1 4144.07

Mean: 2. 6 4143. 91

70. 3 1 4154. 46

4 0. 5 +

5 0

6 0

Mean: 0. 3 4154. 46

71. 3 1 4199. 12

4 1 4198. 99

5 0

6 0

Mean: 0. 4 4199.05

72. 3 3 4202.02

4 2 4201. 82

5 1 +

6 1 +

Mean: 2. 0 4201. 91

Blended

with line

No. Order

161 4

132 4

69 3

69 5

69 6

Identification

Xtab /tab Mult, ev

4104.13 100 Fel (j£J J *

4126. 19 80 Fe I 695 6. 34

4127. 61 100 Fe I 357 5. 86

4132.06 300 Fe I 43 4. 61

4143.42 200 Fe I 523 6. 03

4143. 87 400 Fe I 43 4. 55

4153.91 120 Fe I 695 6. 38

4154. 81 100 Fe I 694 5. 81

4154.50 100 Fe I 355 6. 35

(4199.97 - Fe I 3 3. 03)

4198. 31 250 Fe I 152 5. 35

4199. 10 300 Fe I 522 5. 99

4202.03 400 Fe I 42 4. 44
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

141

Line observed

No. Order Job8 \ohs

73. 3 1 +

4 1 4206. 87

5 1 +

6 0

Mean: 0.8 4206.87

74. 3 1 4210. 66

4 1 4210. 21

5 (5)

6 1 4210. 42

Mean: 1. 3 4210. 41

75. 3 1 4213. 42

4 0. 5 4213. 82

5 (5)

6 0. 5 4213. 73

Mean: 0. 8 4213. 69

76. 3 3 4216.02

4 2 4216. 24

5 (5)

6 1 +

Mean: 2. 1 4216. 15

77. 3 5 4226. 74

4 4 4226. 78

5 3 4227. 00

6 3 4226. 98

Mean: 4. 6 4226. 90

78. 3 1 +

4 1 4242. 69

5 0.5 +

6 1 4242. 91

Mean: 1. 1 4242. 82

79. 3 1 +

4 1 4245. 09

5 0. 5 +

6 0.5 +

Mean: 0. 9 4245.09

80. 3 1 +

4 1 4247. 19

5 0.5 +

6 1 4247. 51

Mean: 1. 1 4247. 88

Blended

with line

No. Order

143 4

143 4

143 4

Identification

*tab /tab Mult. ev

(4207. 13 80 Fe I 352 5. 77)

4206. 70 125 Fe I 3 3.00

4210. 35 300 Fe I 152 5. 42

4213.65 100 Fel 355 5.78

4216. 19 200 Fe I 3 2.94

4227. 43 300 Fe I 693 6. 25

4226. 73 500 Ca I 2 2.93

1

4246. 09 80 Fe I 906 6. 56

4245. 26 80 Fe I 352 5. 77

4248. 23 150 Fe I 482 5. 98

4247.43 200 Fe I 693 6. 29
142 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order 7ob9 Xob3

81. 3 (2) +

4 (2) +

5 0.5 +

6 1 4249. 73

Mean: 1. 4 4249. 73

82. 3 (2) +

4 (2) +

5 1 4251. 13

6 1 4250. 92

Mean: 1.8 4251.02

83. 3 3 4254. 48

4 2 4254. 43

5 1 4254. 33

6 1 4254 42

Mean: 2.0 4254. 41

84. 3 1 +

4 1 4268. 96

5 1 4269. 07

6 1 4268. 76

Mean: 1. 3 4268. 92

85. 3 4 4271. 30

4 3 4271.80

5 3 4272. 20

6 2 4271. 67

Mean: 3. 7 4271. 78

86. 3 3 4274.33

4 2 4274. 68

5 2 4275. 03

6 1 4274. 70

Mean: 2.4 4M4- 73

87. 3 1 4282. 23

4 1 4282. 47

5 0

6 0

Mean: 0. 4 4282. 37

88. 3 1 +

4 1 4285. 92

5 0

6 0

Mean: 0. 4 4285. 92

Blended

with line

No. Order

82 3

82 4

81 3

81 4

Identification

Xt.b Jtab Mult, ev

4250. 13 250 Fe I 152 5.38

4250. 79 400 Fe I 42 4.47

4254. 35 5000 Cr I 12 . 91

4268. 74 30 Fe I 649 6. 20

4267. 83 125 Fe I 482 6.01

4271. 16 400 Fe I 152 5. 35

4271. 76 1000 Fe I 42 4.39

4274.80 4000 Cr 1 1 2.90

(4283. 01 40 Ca I 5 4. 78)

4282.41 600 Fe I 71 5.07

4285.45 125 Fe I 597 6. 12
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

143

Line observed

No. Order

89. 3

4

5

6

Mean:

90. 3

4

5

6

Mean:

91. 3

4

5

6

Mean:

92. 3

4

5

6

Mean:

93. 3

4

5

6

Mean:

94. 3

4

5

6

Mean:

95. 3

4

5

6

Mean:

96. 3

4

5

6

Mean:

/ob,

3

2

1

0.5

/. 7

3

2

1

1

#. 0

1

1

0.5

0

0. 6

1

1

1

0

0.8

1

1

0

0

0.4

3

3

2

2

3. 1

0

0

1

0

0.4

1.5

1

(4)

0

0.5

Xob»

4289. 64

4289. 71

4289. 81

+

4289. 73

4293. 94

4294. 20

4294. 09

+

4294- 09

4299. 89

4299. 93

+

4299. 91

+

4302. 48

4301. 64

4302. 01

+

4305. 16

4305. 16

4308. 25

4307. 90

4307. 96

4308. 03

4308. 02

4312. 70

4312. 70

+

4314. 95

+

4314- 95

Blended

with line

No. Order

/97 3

\98 3

148 4

Xt.b

(4289. 36

4289. 72

4294. 13

4299. 24

4302. 53

4302. 19

4305. 46

(4307. 74

4307. 91

4312. 55

4315. 09

Identification

/

35

3000

700

500

50

50

100

45

1000

100

500

*

Cal

Crl

Fel

Fel

Cal

Fel

Fel

Cal

Fel

Mnl

Fel

Mult.

5

1

41

152

5

520

476

5

42

23

71

ev

4.77)

2.89

4.37

5.29

4.78

5.92

5.89

4.76)

4.44

5.81

5.07
144 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order

97. 3

4

5

6

Mean:

98. 3

4

5

6

Mean:

99. 3

4

5

6

Mean:

100. 3

4

5

6

Mean:

101. 3

4

5

6

Mean:

102. 3

4

5

6

3/ean:

103. 3

4

5

6

Mean:

104. 3

4

5

Mean:

/obs

1 . 0

1

(4)

0

0.5

1. 5

1

(4)

0

0.5

4

3

2

1

2.8

0

0. 5

0.5

1

0.8

5

4

3

3

5

4

3

3

4. £

0. 5

1

1

(4)

1.0

1

1

1

A /

+

4317. 98

+

4317.98

+

4319. 31

-f

4319. 31

4326. 07

4325. 66

4325. 58

4325. 96

4325. 81

+

+

4374. 78

4374- 78

4376. 56

4376. 08

4375. 96

4376. 00

4376. 10

4383. 74

4383. 51

4383. 53

4383. 60

4383. 68

4.

4392. 79

4393. 72

-f.

4393. 31

+

4401. 48

+

4401. 48

Blended

with line

No. Order

/96 3

\ 9 8 3

148 4

/96 3

\ 9 7 3

148 4

143 5

^tab

4318. 65

4320. 59

4319. 64

4325. 76

4374. 95

4375. 93

4383. 55

4393. 45

4401. 55

Identification

60

125

100

1000

150

500

1000

20

1000

»b

C a l

C r I

C r l

F e l

Mn I

F e l

F e l

1

N a l

N i l

Mult.

5

96

06

42

2

41

17

86

ev

4.77

5.76

5.75

4.47

5.69

2.83

4.31

4. 92

6.00
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

145

Line observed

N o. *i)rder

105. 3

4

5

Mean:

106. 3

4

5

Mean:

107. 3

4

5

Mean:

108. 3

4

5

Mean:

109. 3

4

5

Mean:

110. 3

4

5

Mean:

111. 3

4

5

Mean:

112. 3

4

5

Mean:

113. 3

4

5

Mean:

114. 3

4

5

Mean:

IobS

3

3

3

3. 3

2

1

0.5

1. 1

1

0. 5

0

0.4

2

(6)

2

2. 3

1

(6)

1

1. 2

3

3

4

3.8

0.5

0. 5

1

0.8

1

1

0

0.6

2

3

3

3.0

0.5

1

1

1.0

Xob8

4404. 14

4404. 64

4404. 72

4404. 55

4406. 58

4407. 43

+

4407. 07

4409. 10

4409. 47

4409. 31

4414. 88

+

4415. 29

4415.14

4421. 81

+

4421. 90

4421. 87

Mil. 50

4427. 31

4427. 37

4427. 38

+

+

4456. 11

4456.11

+

4458. 31

4458. 31

4461. 39

4461. 72

4461. 58

4461. 58

+

4466. 44

4466. 23

4466. 32

Blended

with line

N o. Order

156 3

157 3

^tab

4404. 75

4407. 72

4408. 42

4414. 88

4415. 12

4422. 57

4427. 31

4455. 89

4459. 12

4461. 65

4466. 55

Identification

/

1000

100

125

150

600

300

500

100

400

300

500

tab

Fel

Fel

Fel

M n I

Fel

Fel

Fel

Ca I

Fel

Fel

Fel

Mult.

41

68

68

22

41

350

2

4

6S

2

350

ev

4.37

4.99

5.01

5.69

4.42

5. 64

2.85

4.68

4.95

2. 86

5.60
146 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order /ob. Xob»

115. 3 0. 5 +

4 1 4471. 81

5 0

Mean: 0. 5 4471.81

116. 3 0. 5 +

4 1 4475. 49

5 0

Mean: 0. 5 4475. 49

117. 3 1 4481. 65

4 2 4481. 71

5 2 4482. 21

Mean: 1. 9 4481. 90

118. 3 0

4 1 4578. 59

5 0

Mean: 0. S 4578. 59

119. 3 1 +

4 2 4601. 81

5 1 +

Mean: 1.4 (4601.81)

120. 3 1 4829.32

4 1 4828. 87

5 0. 5 4828. 97

Mean: 0. 8 4829. OS

121. 3 1 +

4 1 4891. 23

5 0

Mean: 0. 6 4891. 23

122. 3 0

4 1 4902. 60

5 0

Mean: 0. 3 4902. 60

123. 3 0. 5 +

4 1 4957. 32

5 0. 5 +

Mean: 0. 7 4957. 32

124. 3 0. 5 +

4 0. 5 +

5 1 4965. 99

Mean: 0. 8 4966. 99

Blended

with line

No. Order

/l58 3

\ 2 5

Identification

Xt,b /t»b Mult, ev

4472. 79 100 M n I 22 5. 72

4476.02 500 Fe I 350 5. 61

4481. 33 100 Mgll 4 11. 63

4482. 17 150 Fe I 2 2. 82

4578. 56 80 Ca I 23 5. 23

4602. 94 300 Fe I 39 4. 18

4829. 38 200 Cr I 31 5. 11

4829.03 300 Ni I 131 6. 10

4891. 50 70 Fe I 318 5. 38

4890. 76 100 Fe I 318 5.41

4903. 32 500 Fe I 318 5.41

4957. 60 300 Fe I 318 5. 31

4957.30 100 Fel 318 5.35

4966. 10 300 Fe I 687 5. 82
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

147

Line observed

N o. Order

125. 3

4

5

Afean:

128. 3

4

5

Mean:

127. 3

4

5

Afean:

128. 3

4

5

Afean:

129. 3

4

5

Afean:

130. 3

4

5

Afean:

131. 3

4

5

Afean:

132. 3

4

5

Afean:

133. 3

4

5

Afean:

134. 3

4

5

Afean:

/„

1

0.

1

0.

1

1

1

* •

0.

2

1

1.

2

1

1

1.

1

1

1

1.

1

2

1

1.

(3)

1

0

0.

5

5

3

4-

5

5

3

4-

5

5

3

-4-

bs

5

5

3

4

1

4

5

5

5

5

Xob.

4984. 41

-f

4984.24

4984. SO

5005. 96

5005. 96

-|-

5005. 96

+

5012. 14

5011. 91

6012. 01

+

5098. 87

5098. 87

+

5101. 89

5102. 37

5102. 16

5109. 93

5110. 30

5110. 39

5110. 24

+

5142. 21

5142. 21

+

5167. 33

5167. 38

6167. 36

+

5172. 64

5172. 66

5172.65

+

5183. 72

5183. 60

6183. 65

Blended

with line

N o. Order

15 4

16 4

30 4

133 3

132 3

4984. 13

4983. 86

5006. 13

5005. 72

5012. 07

5098. 70

5102. 24

5110. 41

5142. 54

5141. 75

5142. 93

5167. 49

(5166. 29

5167. 32

(5171. 60

5172. 68

5183. 60

Identification

500

200

300

200

300

200

SO

300

100

100

125

700

125

100

300

200

500

ab

Nil

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fe I

Fel

Fel

Fel

Fel

Mgl

Fel

Mgl

Mgl

Mult.

143

1066

318

984

16

66

65

1

/1092

\1090

114

16

37

1

2

36

2

2

ev

6.29

6.59

5.31

6.36

3.33

4. 61

4.63

2.42

6.64

6.68

4.83

3.36

3. 89

2.40)

5. 11

3.88)

5. 11

5. 11
148 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

N o. Order

135. 3

4

5

Mean:

136. 3

4

5

Mean:

137. 3

4

5

Mean:

138. 3

4

5

Mean:

139. 3

4

5

il/ecm:

140. 3

4

5

Mean:

141. 3

4

5

Mean:

142. 3

4

5

Mean:

143. 3

4

5

Mean:

144. 3

4

Mean:

145. 3

4

Mean:

/ob*

1

1

1

1. 1

1.5

1

2

1.7

2

2

1

1. 7

1

2

1

1.4

1

2

1

./. A

1

1

0

0.(5

3

3

2

2

1

1

1.4

5

5

4

5.0

5

5

2

2

f. «

Xobs

5191. 25

5191. 42

5191. 35

5195. 20

5195. 25

5195. 15

5195. 20

5204. 21

5205. 20

5204. 53

5204- 64

5205. 76

5206. 34

5205. 63

5205. 90

5208. 71

5208. 44

5208. 28

5208. 44

+

5216. 28

5216. 28

5227. 03

5227. 25

5227. 13

5227. 14

5229. 48

5228. 92

5228. 87

5229. 04

5269. 42

5269. 54

5269. 49

5269. 49

5328. 75

5328. 08

5328. 37

5339. 98

5340. 04

5340. 01

Blended

with line

No.

37

99

42

43

56

Order

4

6

4

4

4

5191. 46

(5195. 47

5194. 94

5204. 58

5204. 52

5206. 04

5208. 60

5208. 44

5216. 28

5226. 87

5227. 19

5229. 86

(5270.27

5270. 36

5269. 54

5328. 53

5328. 04

5339. 94

Identification

/

400

100

200

125

400

500

200

500

300

200

400

200

20

400

800

150

400

200

ab

Fe

Fe

Fe

Fe

Cr

Cr

Fe

Cr

Fe

Fe

Fe

Fe

Ca

Fe

Fe

Fe

Fe

Fe

I

I

I

I

I

I

I

I

I

I

I

<

I

I

I

I

I

I

Mult.

383

1092

36

1

7

7

553

7

3G

383

37

1090

553

22

37

15

37

15

553

ev

5.42

6.61)

3.95

2.47

3.32

3.32

5.62

3.32

3.99

5.41

3.93

6.56

5.63

4.88)

3.96

3. 21

3.87

3.23

5.58
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

149

Line observed

No. Order Job, Xob.

146. 3 1 5341.08

4 (3) +

Mean: 0. 8 6341. 08

147. 3 3 5371.26

4 4 5371.40

Mean: 3. 2 6371. 34

148. 3 3 5397. 07

4 4 5397. 10

Mean: 3. 2 5397. 09

149. 3 3 5405.59

4 4 5405. 87

Mean: 3. 2 5405. 75

150. 3 4 5430. 11

4 4 5430.02

Mean: 3. 6 5430. 06

151. 3 2 5434.42

4 3 5434.41

Mean: 2. 3 6434- 41

152. 3 4 5447. 19

4 4 5446.97

Mean: 3. 6 5447. 06

153. 3 3 5455.83

4 3 5455. 77

Mean: 2. 7 5456. 80

154. 3 0. 5 +

4 1 5497. 71

Mean: 0. 7 5497. 71

155. 3 0. 5 +

4 1 5615. 63

Mean: 0. 7 5615.63

156. 2 6 5890. 15

3 6 5889.95

4 6 5889. 95

Mean: 5. 0 5889.99

157. 2 6 5895. 66

3 6 5895. 92

4 6 5895. 97

Mean: 6. 0 5895.88

Blended

with line

N o. Order

85 5

Identification

*t«b /t«b Mult, ev

5341.06 200 Mn I 4 4.44

5341. 03 200 Fe I 37 3.91

5371.49 700 Fe I 15 3. 26

5397. 13 400 Fe I 15 3. 21

5405.78 400 Fe I 15 3.28

5429. 70 500 Fe I 15 3. 24

5434. 53 300 Fe I 15 3. 29

5446.92 300 Fe I 15 3. 25

5455. 61 300 Fe I 15 3. 28

5497. 52 150 Fe I 15 3. 26

5615.65 400 Fe I 686 5.54

5889.95 9000 Na I 1 2.11

5895. 92 5000 Na I 1 2. 10
1 5 0 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Observed wavelengths and identifications of meteor spectrum S 6—Continued

Line observed

No. Order

158. 2

3

4

Mean:

159. 2

3

4

Mean:

160. 2

3

4

Mean:

161. 2

3

4

Mean:

162. 2

3

4

Mean:

163. 2

3

4

Mean:

164. 2

3

4

Mean:

165. 2

3

4

Mean:

166. 2

3

4

Mean:

/obs

1

(2)

1

0.8

1

0

1

0. 6

1

(2)

1

0.8

1

0. 5

1

0. 7

(3)

1

1

0.9

(3)

1

0

0.4

1

1

0.9

3

2

1

/. 6

2

(3)

1

1.2

X *

6137. 79

6136. 80

6135. 77

<S;S0. 5(5

+

6154. 11

6154. 11

6162. 56

6162. 34

4-

6162. 43

6191. 10

4-

6190. 17

6190. 48

+

6411.96

6411.36

6411. 62

6430. 24

6430. 24

6437. 87

6437. 60

6437. 72

6462. 22

6462. 39

4-

6462. 32

6495. 37

6494. 98

6495. 15

6495. 14

Blended

with

No.

/119

\ 2

:i

66

86

89

/ 8 9

\ 9 0

34

39

line

Order

4

r

f>

6

3

3

3

3

5

5

6137. 70

6136. 62

6154. 23

6162. 17

6160. 76

6191. 19

6191. 56

6411. 66

6430. 85

6439. 07

6462. 57

6494. 98

Identification

>

100

100

500

40

500

500

100

100

100

150

125

400

lab

Fe I

Fe I

Na I

Ca I

Na I

Ni I

Fe I

F e l

F e l

?

C a l

Ca I

F e l

Mult.

•JO 7

169

5

3

5

45

169

SI 6

62

18

18

168

ev

4. 61

4.47

4. 12

3. 91

4. 12

3.67

4.44

5. 58

4. 11

4. 45

4.44

4.31
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL 151

The spectrum of this meteor was photographed

in the zero order, in the first order with dispersion of 72 A/mm, and in the blue part of

the second order with 36 A/mm. [The dispersions given by Rajchl (1961) are those of

the spectograph and not of the meteor spectra.]

The spectral lines of the Na doublet are the

most intense lines and are separated one from

another in the first order. The beginning of

these lines is almost the same as the beginning

of the meteor trail photographed by normal

cameras. The whole spectrum is photographed

in the height interval from 85 km to 56 km.

The spectral lines were measured at the maximum brightness at the height of 65 km, and the

wavelengths were computed by the method

briefly described in this paper. The wavelengths of all 99 measured lines are given in

table 3.

The majority of the lines are iron lines

belonging to different multiplets. The strongest lines are: Na doublet 1; Mg triplet 2; Fe

lines 3720 of multiplet 5; 3856 of multiplet 4;

3860 of multiplet 4; 4045 of multiplet 43;

4383 of multiplet 41; 5269 of multiplets 15 and

37. Other elements observed are Ca I and

Ca II, Mg I, Ni I, Cr I, Mn I. The presence

of Co I and Si I is questionable. The elements

usual in meteorites and air but not observed in

this spectrum are: Al, Cu, P, S, C, K, N, O.

The iron line 3930.3 is well separated from

the Ca II line 3933.7. This Ca line, in comparison with spectrum S 6, is relatively weak, a

fact that may be connected, as previously

indicated, with the iron composition of the body.

A feature of this Ca II line is quite different

from the other lines. It is observable in the

maxima of brightness only. In comparison

with the others the changes of brightness of

this line are very strong. The Ca II doublet is

present in this spectrum, although the meteor

can be classified as slow.

Artificial spectra of meteoritic material using

shock tubes (Nicholls, et al., 1959) also show

the Ca II doublet at velocities less than 10

km/sec. Thus it is possible to conclude from

all these experimental results that the Ca II

doublet is emitted not only by high-velocity

meteors but also by slow meteors.

TABLE 3.—Spectrum of meteor No. 27471

[The lines with numbers from 1 to 22 are present in the second order only.

The lines with numbers from 23 to 33 are present in the first and second

order. If one measured wavelength only is presented, it refers to the

first order. All other lines from Nos. 34 to 99 are present in the first order

only. The dispersion of the meteor spectrum in the first order is approximately 72 A/mm and In the second order 3d A/mm. The intensity scale

is the same as is used in table 2.]

Line observed

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

/ob.

1

1

1

1

1

1

1

4

1

1

2

3

1

3

2

1

1

2

2

1

2

1

3

3

4

2

4

4

1

1

1

2

2

3

3

1

1

2

1

2

1

1

Xobs

3679. 6

3681. 1

3683.5

3686. 8

3689. 6

3705. 4

3707. 3

3721. 3

3724. 1

3734. 7

3736. 1

373R 4

3743. 0

3746. 8

3749. 8

3816. 6

3818. 8

3821. 3

3825. 4

3830. 1

3833. 1

3835. 0

3838.9 1

3839. 2 J

3856. 5 1

3857. 0 J

3860. 8 1

3860. 6 J

3866. 4 1

3865. 5 J

3868. 2

3878. 0 1

3879. 0 J

3885. 6 1

3887. 2 j

3891. 5

3894. 4

3899. 2 1

3900. 2 J

3905.2 1

3905.9 J

3913. 1

Identification

^t»b

3679. 9

3682. 2

3683.0

3687. 5

3689. 5

3689. 5

3705. 6

3707. 8

3719. 9

3722. 6

3733. 3

3734. 9

3737. 1

3743. 4

3745. 6

3745. 9

374a 3

3749. 4

3815. 8

3816. 2

3817. 8

3818. 5

3820.4

3825. 9

3824. 4

3829. 4

3832. 3

3834. 2

3838. 3

3856. 4

3859.9

3858. 3

3865. 5

387a 0

387a 6

3886. 3

3886. 8

3891. 9

3895. 7

3894. 1

3899. 7

3906. 5

3905. 5

3913. 6

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Crl

CrI

Crl

Fel

Fel

Fel

Mgl

Mgl

Fel

Mgl

Fel

Fe I

Nil

Fel

t

Fel

Fel

Fe I

Crl

Fel

Fel

Co I

Fel

Fe I

Si I

Fel

Mult

5

772

5

21

369

386

5

5

5

5

5

21

5

21

5

5

5

21

45

40

40

40

20

20

4

3

3

20

3

4

4

32

20

20

4

4

23

733

4

34

4

4

3

120
152 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 3.—Spectrum of meteor No. 27471—Continued TABLE 3.—Spectrum of meteor No. 27471—Continued

Line observed

No.

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

/ob.

3

3

3

1

3

1

2

4

1

1

1

3

3

1

1

2

1

1

1

1

2

1

3

1

1

3

1

1

3

1

1

1

3

4

1

2

2

2

Xob.

3921. 3

3928. 4

3932. 8

3948.9

3967. 7

4004. 5

4032. 0

4045. 2

4052. 2

4056. 6

4058. 4

4063. 1

4070. 8

4078. 4

4131. 6

4143. 2

4200. 4

4216. 6

4227. 0

4250. 7

4254. 5

4260. 8

4271. 6

4290. 0

4294. 2

4308. 3

4320. 4

4323. 0

4325. 8

4332. 9

4368.2

4371. 3

4376. 5

4383.3

4395. 4

4404. 5

4414. 6

4427. 8

Identification

Atab

3922. 9

3920. 3

3927. 9

3930. 3

3933. 7

3933. 6

3933. 6

3948. 8

3968. 5

3969. 3

4005. 2

4030. 8

4033. 1

4034. 5

4045. 8

4055. 0

4056. 5

4058. 0

4059. 4

4063. 6

4071. 7

4076. 6

4078. 4

4080. 2

4132. 1

4143. 9

4143. 4

4198. 3

4199. 1

4202. 0

4216. 2

4226. 7

4227. 4

4250. 1

4250. 8

4254. 4

4260. 5

4261. 4

4271. 2

4271. 8

4289. 7

4294. 1

4307. 9

4307. 7

4319. 6

4320. 6

4322. 7

4325. 8

4331. 6

4367. 9

4369. 8

4371. 3

4375. 9

4383. 6

4404. 8

4415. 1

4427. 3

Fel

Fel

Fel

Fel

Call

Fel

Fel

Fel

Call

Fel

Fe I

M n I

M n I

M n I

Fe I

?

Fel

Fel

Mn I

Mn I

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fe I

Fel

Fel

Cal

Fe I

Fel

Fel

Crl

Fel

Crl

Fel

Fel

Crl

Fe I

Fel

Ca I

Crl

Cr I

Fe I

Fel

Ni I

Fel

Fe I

Crl

Fel

Fel

?

Fel

Fel

Fel

Mult

4

4

4

4

1

488

562

604

1

43

43

2

2

2

43

218

320

29

29

43

43

558

217

558

43

43

523

152

522

42

3

2

693

152

42

1

152

96

152

42

1

41

42

5

96

96

215

42

52

41

518

22

2

41

41

41

2

Line observed

No.

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

lob*

2

1

1

1

1

1

1

1

1

4

4

4

1

1

4

1

1

2

1

1

1

1

1

1

1

5

4

Xobs

4462. 2

4482. 5

4835. 6

4878. 4

4932. 6

4942. 0

4989. 6

5011. 9

5132. 5

5168. 2

5172. 4

5183. 8

5206. 7

5227. 1

5270. 0

5319. 6

5321. 4

5327. 9

5396. 3

5405. 9

5542. 3

5572. 0

5622. 2

5681. 1

5882. 8

5889. 9

5896. 2

Identification

Xt»b

4461. 6

4482. 2

4481. 3

4481. 1

4878. 2

4878. 1

4989. 0

4988. 0

5012. 1

5133. 7

5168. 8

5167. 5

5167. 3

5172. 7

5171. 6

5183. 6

5208. 4

5206. 0

5204. 5

5204. 6

5227. 2

5270. 4

5270. 3

5269. 5

5322. 0

5328. 0

5328. 5

5397. 1

5405. 8

5572. 8

5569. 6

5623. 6

5682. 6

5889. 9

5895. 9

Fel

Fel

Mgll

Mgll

?

Fe I

Cal

?

?

Fel

Col

Fel

Fe I

Fel

Fel

Mgl

Mgl

Fe I

Mgl

Crl

Crl

Crl

Fel

Fel

Fe I

Cal

Fel

?

Fel

Fel

Fel

Fel

Fel

?

Fel

Fel

Fel

Nal

?

Nal

Nal

Mult

2

2

4

4

318

35

1066

16

1092

1

37

2

2

36

2

7

7

7

1

37

37

22

15

112

15

37

15

15

686

686

625

6

1

1

A wave feature in some spectral lines was

observed in both spectra. It reaches up to

about 1 A in the spectrum of meteor 27471,

and up to about 0.3 A in the spectrum S 6.

We have previously observed the wave-feature

of some spectral lines in the low dispersion

spectrograms of meteors where it reached up to

several Angstrom. A provisional explanation

of this phenomenon may lie in the blending

of very narrow lines, when one line and another

change places as a result of local variations in

microsensitivity of the photographic emulsion.

The spectrum of meteor No. 27471 is suitable

for study of spectral changes during the trajec-
METEOR SYMPOSIUM—CEPLECHA AND RAJCHL 153

tory. We know accurately the changes of velocity during the trajectory of this meteor. As

a result, we have a dynamic determination of

the heat-transfer coefficient and of the mass

ablation. Thus it will be possible to determine

the monochromatic luminosity coefficients.

This is a preliminary report on the subject.

Detailed data will be published in Bulletin of

the Astronomical Institute of Czechoslovakia.

References

CEPLECHA, Zd.

1951. The centre of a plate. Bull. Astron. Inst.

Czechoslovakia, vol. 2, pp. 105-106.

1954. Meteor photographs. III. A reduction

method of meteor negatives. Bull. Astron. Inst. Czechoslovakia, vol. 5, pp.

9-13.

1958. On the composition of meteors. Bull.

Astron. Inst. Czechoslovakia, vol. 9, pp.

154-159.

1961. Determination of wavelengths in meteor

spectra by using a diffraction grating.

Bull. Astron. Inst. Czechoslovakia, vol.

12, pp. 246-250.

JACCHIA, L. G., AND WHIPPLE, F. L.

1961. Precision orbits of 413 photographic meteors. Smithsonian Contr. Astrophys.,

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

MOOHE, C. E.

1945. A multiplet table of astrophysical interest.

Contr. Princeton Univ. Obs., no. 20,

parts 1, 2.

NICHOIXS, R. W.; WATSON, M. D.; and PARKINSON,

W. H.

1959. The laboratory excitation of meteoritic

spectra in shock tubes. Journ. Roy.

Astron. Soc. Canada, vol. 53, pp. 223-

231.

RAJCHL, J.

1961. Two meteor spectra with high dispersion.

Bull. Astron. Inst. Czechoslovakia, vol.

12, p. 167.

ROWLAND, H. A.

1893. Gratings in theory and practice. Astron.

and Astrophys., vol. 12, pp. 129-149.

ZAJDEL, Z. N.; PBOKOFEV, V. K.; and RAJSKIJ, S. M.

1952. Tables of spectrum lines. Moscow.

(English translation published by VEB

Verlag Technik, Berlin, 1961.)

Abstract

Analysis of photographs of two meteor spectra with dispersions from 72 A/mm to 11 A/mm is presented in this

paper. The method of reduction is briefly described. Absolute wavelengths were computed without previous

identification of any line, and the zero order of stars for determination of the coordinate system was used. The

mean deviation of computed wavelengths from the wavelengths of identified lines is only ± 0.2 A in the case of spectrum S 6. The lines of neutral iron predominate in both the meteor spectra.

A Short Note on Meteor Spectra With Low Dispersionl

By J. Rajchl2

Up to the present, 16 spectra of meteors

with low dispersion (about 200 A/mm in the

blue region, and about 800 A/mm in the red

region of the spectrum) have been photographed at the Ondfejov Observatory. It is

evident from these spectra that the emissions

of ionized Ca and Mg for some meteors are

visible from the beginning of the meteor.

For others, these emissions are absent, although

as is shown from rocket explorations, ionized

Ca and Mg atoms of meteoric origin are present at heights of about 100 km (Istomin, 1961).

From direct photographs it was possible to

determine the fundamental dynamical and

physical characteristics for three spectra of this

collection. Using the mass determined from

the photometry and the decelerations, we

calculated the diameter of the meteoroid on

the assumption that the density of meteoric

material is 3.5 gm/cm3. Following Baker

(1959), we determined the parameter B (i.e.,

the ratio of meteor-body diameter to the mean

free path of the emitted molecules with respect

to the oncoming molecules), and the flow conditions of the interaction between meteoric

body and the surrounding atmosphere. The

Ca II and Mg II emissions appear when the

flow conditions change from transition flow to

slip flow. In the case when the slip-flow conditions are already valid from the beginning of

meteor light emission, then the ionized emissions

occur from the beginning. This is fulfilled for

the meteors we investigated in the height interval from 96 to 100 km.

It is interesting to compare this result with

my recent finding (Rajchl, 1960) that the slipflow conditions are also present when a sudden

increase in meteor brightness (flare) occurs;

1

 Details of this paper will be published in Bull. Astron. Inst.,

Czechoslovakia.

1

 Astronomical Institute of the Czechoslovak Academy of Sciences,

Ondfejov, Czechoslovakia.

and it is a well-known fact that in flares the

emission of ionized Ca and Mg atoms prevails.

For example, in our spectral material there are

photographs of two meteors that emit light

only in the red region of the spectrum. But

when a flare occurs, very strong Ca II emission

is observable.

Thomas and White (1953) reported that the

Ca II emission is absent in the spectra of

Giacobinids, and connected this with the low

velocity of the shower. Let us suppose, as the

highest limit, the same meteoroid diameter for

Giacobinids as for our meteors, and let us use

the end heights determined for Giacobinids.

Then we find that these meteors emit light

above the region of slip flow, where transitionflow conditions prevail, and thus according to

our results it is impossible to observe Ca II

emissions. Similarly, for Super-Schmidt meteors also emitting light above the slip flow, i.e.,

in transition or free-molecule flow, it is possible

to admit from our point of view that the principal blue emissions Ca II and Mg II must be

absent and the faint meteors show redder.

This fact was recently pointed out by Ceplecha

(1959), and was photoelectrically observed by

J. Davis (private communication). It is interesting to point out that the height interval at

which ionized atoms begin to emit light is the

same as that found by Jacchia (1949) for a

slight increase of brightness shown by some

photographic meteors, and explained by the

possible influence of the flayer.

We may conclude that Baker's parameter B

is the more important one, governing the processes of light emission and its efficiency T,

and perhaps is more important than the meteor

velocity itself. But it must be emphasized

that our results are only preliminary and more

observational material is required for confirmation.

155
156 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

References

BAKER, R. M. L., Jr.

1959. The transitional aerodynamic drag of meteorites. Astrophys. Journ., vol. 129,

pp. 826-841.

CEPLECHA, Zd.

1959. On the colour index of meteors. Bull.

Astron. Inst. Czechoslovakia, vol. 10,

p. 39.

ISTOMIN, V. G.

1961. Nitrogen ions in the earth's upper atmosphere and nighttime ionization in the

E layer. Dokl. Acad. Sci. U.S.S.R., vol.

137, p. 1102.

JACCHIA, L. G.

1949. Photographic meteor phenomena and

theory. Harvard Coll. Obs. Reprints,

ser. 2, no. 31.

RAJCHL, J.

1960. A note to the problem of meteor flares.

Bull. Astron. Inst. Czechoslovakia, vol.

11, pp. 33-34.

THOMAS, R. N., and WHITE, W. C.

1953. The physical theory of meteors. IV.

Inquiry into the radiation problem—a

laboratory model. Astrophys. Journ.,

vol. 118, pp. 555-567.
Spectrographic Observations of Meteors in

U.S.S.R. in 1957-1960

By E. N. Kramer,1 K. A. Liubarsky,2 and V. I. Ivanikov'

The first photographs of meteor spectra

were obtained at the Moscow Observatory by

S. N. Blajko in 1904. After this only amateurs

were engaged in meteor spectrography. However, some good spectra were obtained by

K. P. Staniukovich and G. O. Zateishchikov in

1934, G. O. Zateishchikov in 1936, V. M.

Chernov in 1939, and K. A. Liubarsky in 1950.

During the IGY comparatively powerful spectral patrols came into operation at some

observatories.

In the Astrophysical Laboratory of the

Physical-Technical Institute, Academy of Sciences of Turkmenian S.S.R., Ashkhabad,

U.S.S.R., the patrol consisted of 8 cameras

(D:F=1:2.5, F=250 mm) and 2 cameras

(D:F=1:5, F=500 mm) with objective

prisms made of flintglass, angle 20°, diameter

120 mm. In the Astrophysical Institute,

Academy of Sciences of Tadjik S.S.R., Doushanbe, the patrol was designed under the

direction of L. A. Katasev and was fully completed in 1960. It consisted of 6 cameras

(D:F= 1:2.5, F=250 mm) with objective

prisms made of flintglass, angle 25°, diameter

250 mm. The calculation of the prisms was

published by Ivanikov (1957). The cameras

were equatorially mounted and clock driven.

The Odessa Astronomical Observatory ran a

patrol of four cameras (D:F= 1:4.5, F=125

mm) with objective prisms, angle 17°, and

diameter 45 mm.

At the meteor station4 of the Simferopol

section of VAGO, the patrol consisted of six

cameras of different types (D:F=1:2, F=125

i Odessa Astronomical Observatory, U.S.S.R.

1

 Astrophysical Laboratory, Ashkhabad, U.S.S.R.

* Astrophysical Institute, Doushanbe (formerly Btalinabad),

U.S.8.R.

• All Union Astronomical Geodetical Society, U.S.S.R.

638805—63 13

mm; D:F=1:4.5, F=250 mm; D:F=1:4.5,

F=135 mm) with objective prisms, angles

16°, 18°, 30° and diameters 45 and 30 mm. All

the stations used panchromatic films.

In the period 1957-1960, 95 spectra were

obtained, as follows: 32 in Ashkhabad (Liubarsky), 10 in Odessa (Kramer), 25 in Doushanbe

(formerly Stalinabad) (Ivanikov), and 28 in

Simferopol (Pushnoy).

The catalog of the spectra with the number

of lines n > 5 is given in table 1 and is a partial

continuation of the list published by Astapovich (1958).

The dispersion on all the spectra is small. In

the blue region of the spectrum it is equal to

100-200 A/mm, and for the Simferopol spectra

as high as 1000 A/mm. Some of the meteors

have a small angle between the direction of

the dispersion and the meteor trail. As a

rule, the stars of spectral type A0-A5 do not

appear on the negative near the meteor spectrum, and the irregular distortion of the wideangle objectives do not permit the use of these

stars for purposes of comparison. This is the

reason why the stations in Ashkhabad and

Odessa, independently of each other, used the

method of the construction of the dispersion

curve on the base of some line in the meteor

spectra, which may be easily identified on the

negative. The fact that the identification is

correct has been checked by means of the

interval coordination of the identification of

the other lines (Liubarsky, 1961). For this

purpose the list of the most widespread lines

in meteor spectra was employed. This method

was used partially in Doushanbe.

In Ashkhabad and Doushanbe the method

of control based on the multiplets was used;

if we identify any line of a multiplet in a

157
158 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Meteor spectra with the number of lines n >5

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

•

1957

1958

1959

1960

Date

Aug.

Aug.

Sept.

Oct.

Aug.

Mar.

June

Aug.

Oct.

6

7

12

13

13

7

8

8

9

21

22

6

11

12

12

12

13

13

13

13

28

17

18

26

3

13

21

See P. Millman, Journ.

Shower

Sporadic

?

?

Perseid

Sporadic

Sporadic

?

Sporadic

Sporadic

Orionid

Orionid

Perseid

Perseid

?

Perseid

Sporadic

Perseid

Cassiopeid

Perseid

Sporadic

Sporadic

Sporadic

Sporadic

Sporadic

Perseid

Cassiopeid

?

No.

lines

10

10

54

11

8

29

12

10

18

28

8

7

5

31

5

7

9

8

7

7

5

6

33

10

6

12

25

Astron. Soc. Canada, vol. 53

World

List*

No.

255

264

279

281

280

297

298

299

307

308

Observatory

Odessa

Doushanbe

Doushanbe

Odessa

Odessa

Ashkhabad

Doushanbe

Odessa

Odessa

Ashkhabad

Ashkhabad

Ashkhabad

Simferopol

Doushanbe

Simferopol

Simferopol

Simferopol

Odessa

Simferopol

Simferopol

Ashkhabad

Ashkhabad

Ashkhabad

Odessa

Ashkhabad

Odessa

Doushanbe

, pp. 271-276, 1959.

spectrum, the other weaker lines of this multiplet must also be in this spectrum. The

Ashkhabad station used the method of selection of spectral lines according to the order of

their appearance in comparison with the

potentials of excitation.

One spectrum in Odessa was reduced by

obtaining the mercury spectrum under conditions that are closest to the condition for

obtaining the meteor spectrum (Kramer, 1959).

The Doushanbe station began the study of

the dispersion as a function of the point in

the field of view, with the purpose of establishing the standard dispersion curves for

every point. In all spectra the lines of neutral and ionized metals were identified: iron,

calcium, magnesium, sodium, manganese, cobalt, and chromium. In the spectra of the

fast meteors the lines 6340-6350 A are frequent

and strong. They are identified by Cook and

Millman (1955) as Si II. This identification,

however, is very strange as this line often

appears earlier than the D Na I, and the H

and K Ca II lines, but the ionization and excitation potentials of silicon are very large

(about 20 ev). Neutral silicon is not identified.

Meanwhile any other identifications of this

line were not found.

In some spectra the presence of the line

near the well-known green line of oxygen

(forbidden 5577 A) was noted. The identification of this line as O I may be erroneous as

in this region there is a fairly strong line of

neutral calcium Ca I (23).

Most of the spectra show a strong unresolved

system N2 1 P.G. According to Liubarsky the

intensity of the nitrogen bands depends less

on the variations of the brightness of the

meteor than does the intensity of the metal

lines. The Ashkhabad station (1960, June 18)

obtained the meteor spectrum in which, except

for N2 1 P.G., there is a strong system Na 2

P.G. Fourteen bands are resolved in this

system.

The Doushanbe station (1961, February 9)

obtained a spectrum without atomic lines.
METEOR SYMPOSIUM—KRAMER, LIUBARSKY, AND IVANIKOV 159

This spectrum consists of three unresolved

systems of bands; one of these systems may be

identified as N2 1 P.G., but the other two are

unidentified.

The Odessa station (1956, October 8) obtained the spectrum of a — 12m

 bolide (Kramer,

1958) with cyclical pulsating brightness. The

pulsations continued through the bright bursts;

the bursts are independent of the pulsations.

The cycles of the pulsations begin from sharp

double maxima, which are followed by intervals

of constant brightness. The brightness increases and falls very rapidly. Toward the

end of the trail the intervals between the

components of the double maxima as well as

between the maxima are shorter. A continuous

spectrum appears in the maximum.

Kramer explains these pulsations by arranging a cyclical regime at certain values of the

velocity and sizes of a meteor body. Near

the boiling point, when the vapor pressure

and external pressure are equal, a secondary

shock wave arises from the surface of the body

and the melting layer instantly evaporates.

The bolide flashes up for a second time after

the departure of the secondary shock wave.

The Ashkhabad station (1958, September 7)

obtained the spectrum of the — 9m bolide.

According to the visual observations of Astapovich, the height of the final point is 20 km

and the velocity is about 30 km/sec. The

bolide has a metallic spectrum only and the

lines of the ionized elements are absent. N2

1 P.G. is very strong. The bolide showed 14

flares separated by regular intervals. As Liubarsky notes, there are no spectral changes in

the flares; the flares may perhaps be due to

rotation, but they are not due to the variations

in temperature.

For one spectrum (Odessa, 1958, August 12),

Komarov tried to find the relative intensities

of the lines on the assumption that the density

is proportional to the logarithm of the intensity

in the density interval 0.4-1.4. He found that

in the flares the maximum intensity is displaced

toward the blue region of the spectrum and

hence the temperature rises. He also found X^,

(the color of the meteor) by using the comparison star a Lyrae.

Liubarsky noticed the strong asymmetry of

the profiles of certain lines (for example, H and

K Ca II). The asymmetry may perhaps be

caused by the presence of these lines in the

meteor train and by drift of the train. It is

unlikely that the blending of faint lines may

cause such an asymmetry for the H and K lines,

but for the weaker lines we must take this

possibility into account.

References

ASTAPOVICH, I. S.

1958. Meteor phenomena in the earth's atmosphere. Publ. House for Physical and

Mathematical Literature, Moscow.

COOK, A. F., AND MILLMAN, P. M.

1955. Photometric analysis of a spectrogram of a

Perseid meteor. Astrophys. Journ., vol

121, pp. 250-270.

IVANIKOV, V. I.

1957. The choice of an objective prism for meteor

spectrophotometry. Bull. Stalinabad

Astron. Obs., no. 20.

KRAMER, E. N.

1958. The spectrum of a bolide from October 8,

1956. Astron. Circ, Acad. Sci. U.S.S.R.,

no. 195.

1959. Spectra of three bright meteors. Proc.

Odessa Astron. Obs., vol. 5, no. 1.

LIUBARSKY, K. A.

1961. Spectral observations of meteors. Bull.

Comiss. Comets and Meteors, Acad.

Sci. U.S.S.R., no. 5.

Diffusion Effects Observed in the Wake Spectrum

of a Geminid Meteor

By Ian Halliday1

The spectrum of a spectacular Geminid

meteor was photographed on the night of

December 12/13, 1960, at the Meanook Meteor

Observatory (^=54°37'N, X=113°21/W).

This is one of two meteor observatories operated

by the Dominion Observatory in northern

Alberta. The spectrum exhibits interesting

peculiarities.

The meteor was photographed with a converted Kl9 aerial camera, focal length 12 inches,

focal ratio f/2.5, using Kodak Spectroscopic

I-D emulsion on glass plates 8 by 10 inches.

A Bausch & Lomb replica transmission grating

with 300 lines per mm was mounted immediately in front of the camera objective. The

camera was occulted 12.5 times per second by a

rotating shutter with a closed-to-open ratio of

2:1.

The meteor was not observed visually but

was recorded on an exposure that began at

3

h

32m U.T. and ended at 4b05m U.T., December 13, 1960. The meteor was initially outside

the field of view of the camera, but the zeroorder image entered the field before peak

luminosity was attained, while the first- and

second-order spectra entered the field at progressively lower heights.

The spectrum is reproduced in plate 1. The

meteor moved from upper right to lower left.

The right-hand edge of the photograph is the

edge of the original plate. The first segment

of the zero order at the top of the photograph is

the sixth segment that appeared on the plate,

while the lower end of the zero order (beyond

segment 13) has been omitted at the left. The

segment numbers are shown opposite each

segment of the spectrum along the right-hand

edge. Segments 20 and 21 are detectable only

i Dominion Observatory, Ottawa, Canada.

in the first-order image of the Na D lines. A

small portion of the first- and second-order

spectra of Vega appears in the lower left corner

of the photograph.

Height and velocity measures

Since the meteor was photographed from only

one station, no direct measures of height or

velocity are possible. Reasonably accurate

heights may be obtained, however, by assuming

a radiant position and velocity for the Geminid

shower and then determining ranges and hence

heights from the observed angular velocity.

A standard Geminid radiant at a=113°,

8= +32°, was assumed (Millman, 1954) since

the meteor appeared within an hour of the peak

of the shower (solar longitude 261°.l). This

assumed radiant was displaced to allow for the

effect of zenith attraction. It was then found

that the observed trail passed through the

apparent radiant shortly before the end of the

exposure, which gave a computed time for the

appearance of the meteor of 4h01m U.T.

A plot of the observed angular velocities

along the trail indicated a marked deceleration

in the latter half of the observed trail. The

angular velocity at the bottom of segment 4 was

assumed to correspond to a meteoric velocity of

36.0 km/sec, and other heights and velocities

were based on this assumption. The meteor

was 90° from the radiant near the end of segment 10, at a minimum range of 106.0 km from

the camera. Table 1 lists the computed heights

(corrected to sea level) and corresponding

velocities at the lower ends of selected segments.

Errors in the assumed meteoric velocity, radiant

position, and speed of shutter rotation could

result in the heights and velocities of table 1

161
162 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

being in error by as much as 3 to 5 percent.

There is no doubt, however, that the meteor

penetrated to unusually low heights in the

atmosphere.

TABLE 1.—Heights and velocities

TABLE 2.—Measured emission lines in the Geminid

spectrum—Continued

Segment

1

5

9

13

15

17

19

21

Height of

bottom of

segment

(km)

72.9

67.2

61.5

55.9

53.3

50.7

4& 5

46. 6

Veloeii

(km/te

36. 1

36.0

35.4

33.7

32.3

30.3

26.7

The meteor spectrum

The dispersions of the first and second orders of

the meteor spectrum were found to be 95 and

46 A/mm, respectively. Atomic emission lines

indentified in this spectrum are shown in table

2. A total of 95 features are identified. The

spectrum appears normal for a meteor of this

velocity except that the lines of ionized magnesium, calcium, and silicon are relatively

strong compared to those in the spectra of

fainter meteors with the same velocity. Almost

all the lines in table 2 were also identified in a

recent study of Perseid spectra (Halliday, 1961).

The only significant addition is the pair of lines

of Al I at 3944 and 3961 A. These are barely

detectable by sighting along the lines in a

30 X enlargement of the strongest segment of

the second order. The much greater relative

strength of the H and K lines for fast meteors

makes the detection of faint lines in this

spectral region very difficult for Perseid spectra.

TABLE 2.—Measured emission lines in the Geminid

spectrum

3683.1

3705. 4

3719. 9

3735. 6

3747. S

Atom or ion

F e l

F e l

F e l

F e l

F e l

F e l

F e l

F e l

F e l

Mutt.

5

21

5

21

5

5

21

5

21

Xld>

3679. 9

3683. 1

3687. 5

3705. 6

3707. 8

3709. 2

3719. 9

3737. 1

3734 9

3745. 6

3748. 3

3749. 5

Xtoras

3797. 1

3815. 9

3821. 0

3825. 1

3832. 8

3839. 1

3856. 4

3859. 7

3878. 2

3886. 5

3900. 3

3905. 5

3921. 4

3933. 6

3943. 6

3960. 6

3968. 8

3997. 2

4005. 0

4030. 8

4033. 5

4046. 1

4063. 4

4071. 7

4132. 4

4144. 4

4155. 5

4200. 9

4217. 3

4226. 6

4250. 9

4253. 6

4260. 6

4272. 1

4274. 2

4282. 2

Atom or ton

F e l

F e l

Fe I

Fe I

F e l

M g l

F e l

M g l

F e l

Si II

Fe I

F e l

F e l

Fe I

F e l

F e l

Fe I

Ca II

A l l

A l l

Ca II

F e l

F e l

F e l

F e l

Mn I

Mn I

F e l

F e l

F e l

Sill

F e l

F e l

F e l

F e l

F e l

F e l

F e l

F e l

Fe I

Ca I

F e l

F e l

F e l

Cr I

F e l

Fe I

F e l

Cr I

F e l

C a l

Mutt.

21

45

20

20

45

3

20

3

4

1

4

4

20

4

4

4

4

1

1

1

1

43

276

278

43

2

2

43

43

43

3

43

43

523

354

355

42

152

522

3

2

693

42

152

1

152

42

152

1

71

5

Xub

3795. 0

3798. 5

3799. 5

3815. 8

3820. 4

3825. 9

3827. 8

3829. 4

3832. 3

3834. 2

3838. 3

3856. 4

3856. 0

3859. 9

3878. 6

3878. 0

3886. 3

3899. 7

3906. 5

3920. 3

3922. 9

3933. 7

3944. 0

3961. 5

3968. 5

3969. 3

3998. 1

3997. 4

4005.2

4030. 8

4033. 1

4034. 8

4045. 8

4063. 6

4071. 7

4130. 9

4132. 1

4143. 9

4143. 4

4156. 8

4154. 5

4202. 0

419a 3

4199. 1

4216. 2

4226. 7

4227. 4

4250. 8

4250. 1

4254. 3

4260. 5

4271. 8

4271. 2

4274.8

4282. 4

4283.0
METEOR SYMPOSIUM—HALLIDAT 163

TABLE 2.—Measured emission lines in the Geminid

spectrum—Continued

TABLE 2.—Measured emission lines in the Geminid

spectrum—Continued

XmtM

4290. 2

4307. 6

4314. 2

4325. 8

4353. 1

4376. 1

4383. 6

4404 8

4415. 9

4427. 1

4461. 6

4481. 4

4530

4920. 4

4955. 1

5008. 9 »

5041. 3

5108. 5

5146. 1 »

5169. 4

5183.6

5207. 2

5227. 2

5269. 5

532a 5

5341. 8

5370. 5

Atom or ion

Crl

Cal

Fel

Fel

Cal

Fel

Fel

Mgl

Fel

Fel

Fel

Fel

Fel

Fe I

Fe I

Mgll

Fel

Fel

Fe I

Fel

Fel

Fel

Fe I

Fel

Fel

Fel

Fe I

Fel

Fel

Nal

Mgl

Fe I

Fel

Fel

Mgl

Crl

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

Fel

MuU.

1

5

3,41

42

5

71

42

14

71

2

41

41

41

2

2

4

2

68

318

318

16

318

16

36

1

16

36

16

383

8

2

1

36

37

2

7

37

383

15

37

383

15

37

37

15

Xl.b

4289. 7

4289. 4

4291. 5

4307. 9

4307. 7

4315. 1

4325. 8

4351. 9

4352. 7

4375. 9

4383. 5

4404. 8

4415. 1

4427. 3

4461. 7

4481. 1

4481. 3

4482. 2

4528. 6

4919. 0

4920. 5

4957. 3

4957. 6

5012. 1

5006. 1

5041. 1

5041. 8

5110. 4

5107. 5

5107. 6

5142. 9

5150. 8

5139. 5

5148. 8

5153. 4

5167. 3

5172. 7

5166. 3

5168. 9

5171. 6

5167. 5

5183. 6

5204. 5

5206. 0

5208. 4

5227. 2

5226. 9

5232. 9

5269. 5

5270. 4

5266. 6

5328. 0

5328. 5

5341. 0

5371. 5

5402. 8

5429. 8

5448. 8

5456. 9

5499. 0

5528. 3

5573. 2

5587. 2

5615. 5

5685. 8

5712

5892. 9

5980. 2

6063

6105

6121. 9

6139

6157. 0

6162. 7

6229

6251

6347. 1

6369

6397. 8

6438

6461

6494.4

Atom or ion

Fe l

Fe l

Fe l

Fe l

Fe l

Mgl

Fe l

Fe l

Fe l

N a l

Fe l

Mgl

N a l

Sill

F e l

Ca l

Ca l

F e l

F e l

N a l

Ca l

F e l

F e l

Sill

Sill

F e l

F e l

Ca l

Fe l

Ca l

F e l

MuU.

15

15

15

15

15

9

686

686

686

6

686

8

1

4

207

3

3

169

207

5

3

207

169

2

2

168

816

18

168

18

168

Xl.b

5397. 1

5405.8

5429. 7

5446. 9

5455. 6

5497. 5

5501. 5

5506. 8

5528. 4

5572. 9

5586. 8

5615. 5

5682. 6

5688. 2

5709. 4

5711. 1

5890. 0

5895. 9

5979. 0

6065. 5

6102. 7

6122. 2

6136. 6

6137. 7

6154.2

6160. 7

6162. 2

6230. 7

6252. 6

6347. 1

6371.4

6393. 6

6400.0

6439. 1

6462. 7

6462.6

6495. 0

• Feature noticeably broad.

Variation in luminosity

The photograph in plate 1 indicates that this

meteor maintained approximately peak luminosity from segments 6 to 16, inclusive, an

atmospheric path length of 27 km. Before

segment 6, the zero order is considerably

weaker, while the spectral lines are fading

noticeably by segment 17 and drop abruptly

in intensity at segment 19. Peak luminosity

appears to occur at about segment 11, near a

height of 59 km. The lines in the blue region

of the first-order spectrum appear stronger here

than in subsequent segments, although the

variation between segments 11 and 14 is quite

small.
164 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

To estimate the peak luminosity the zeroorder image of the meteor was compared with

zero-order star trails. The meteor trail is

definitely weaker than the trail of Vega and

appears to match the zero order of a Cygni.

The meteor image trails across the plate at

a rate 5,820 times greater than does the image

of a Cygni, corresponding to a difference of

9.4 magnitudes. The apparent magnitude of

a Cygni is +1.3, from which the meteor magnitude is estimated at —8. This is a "panchromatic" magnitude, which may be influenced by

such factors as emulsion sensitivity and the

blaze of the grating. In other cases (Cook

and Millman, 1956; Milhnan and Cook, 1959),

it proved to be only slightly different from

photographic magnitudes.

The meteor exhibits a rapid flickering superimposed on the gradual rise and fall in overall

intensity. The frequency of the flickering was

estimated in each segment by measuring the

fraction of a complete segment occupied by the

largest number of complete cycles observed

within the segment. The results were converted to cycles per second and are shown

plotted in figure 1.

Over most of the observed trail the flicker

is within the range of 100 to 300 cycles per

second. In a sense, it follows the general

light curve with a gentle rise to maximum

and a steeper decline. The peak of the fre360 r

320

280

,240-

"200 -

160-

i20r

801-

4 0 -

8 10 12

SEGMENT

16 18

FIGURE 1.—Frequency of the flickering plotted against

position along the trail as indicated by segment numbers.

quency curve occurs about two segments

after the peak of the light curve. From segments 9 to 12 the frequency is fairly constant

near 150 cps, but jumps suddenly at segment

13 to about 320 cps and then declines, only

slowly, for another two segments. The amplitude of an individual fluctuation reaches a

maximum near segments 10 to 12, resulting

in a more pronounced fluting of the spectrum

here than at other places.

The periodic flaring might be interpreted

as indicating the repeated crumbling or fragmentation of minor amounts of material from

the main meteoroid in the form of solid fragments. The increased surface area exposed

to ablation would then account for the increased

luminosity at each minor flare.

Alternatively, the phenomenon might be

closely associated with rotation of the meteoroid. If the meteoroid is quite irregular in

shape and rotates in such a manner that it

alternately presents a large side and a smaller

end to the oncoming atmosphere, then the

amount of material ablated, in gaseous form,

would vary in a periodic manner. The light,

of course, is produced by the hot ablated gas

and not by the solid surface.

A third possibility, suggested by Dr. L. G.

Jacchia, is based on laboratory studies of

ultraspeed pellets by Rinehart (Rinehart,

Allen, and White, 1952). A flashing phenomenon was observed for the pellets and explained by an oscillation of the pellet during

its flight. The luminosity will be low if there

is a leading edge of the object, and high when

a whole face of the object is exposed to ablation.

For a meteor at relatively low heights where

continuum flow occurs, as is expected for this

Geminid, an oscillation may be set up that

would lead to a flickering phenomenon. Sudden jumps in the frequency of the flicker, such

as are observed near segment 8 and again just

before segment 13, could indicate a tumbling

of the meteoroid to oscillate about a new axis.

On the rotation hypothesis these changes

might be interpreted as a fracturing of the

object into two or more pieces with an accompanying increase in rotational velocity for

each piece. It is noted, however, that no

general increase in luminosity accompanies

these changes in the period of the flicker,
HALLIDAY PLATE 1

10

I I

13

16

17

18

A Geminid meteor spectrum showing parts of the zero order (at left), and first- and second-order spectra.

Segment numbers are indicated at right.
HALLIDAY PLATE 2

Greatly enlarged portion of the meteor spectrum showing the split wake-lines of H and K in segment IS

of the second-order spectrum.
METEOR SYMPOSIUM—HALLIDAY 165

which suggests that the effective exposed

area is not greatly changed. This would

appear to favor the oscillation hypothesis.

The wake spectrum

The zero-order image shows a slight wake in

the gap between the segments, beginning at

segment 6. The D lines of Na I show a strong

wake where they enter the field of the camera

at segment 11, and the wake is observable as

far as segment 19. Peak intensity of the wake

occurs at segment 15, where the following multiplets can be detected in the wake: Na I, 1;

Mg I, 2, 3; Ca I, 2; Ca II, 1; Mn I, 2; Fe I, 1, 2,

4, 5, 15, 20, 21, 41, 42, 43.

Most of these multiplets have been listed in

earlier studies of wake spectra (Halliday,1958),

although the manganese lines near 4030 A

have not been listed previously. The wake

spectrum shows the usual preference for lines of

low excitation potential, but it is less pronounced than in most other cases. The line of

Mg I, 2 at 5183.6 A is moderately intense in

the wake, whereas its presence was quite doubtful in most earlier wake spectra. The H and K

lines of Ca II are strong in the wake and persist

essentially as far back into the gap as the other

wake lines, in contrast to some spectra in which

the H and K lines decay much faster in the wake

than the low-excitation Na I and Fe I lines.

The most significant feature of this spectrum

appears to be a clear splitting of the stronger

wake lines into two components. It is observable in the second-order spectrum from segments

14 to 18. The H and K lines show the splitting

most distinctly because of their strength, but

other lines in which it is also observable are:

X 4045 of Fe I, 43; X 4226 of Ca I, 2; and X 4383

of Fe I, 41. For the Na D lines, in the firstorder spectrum, the situation is complicated by

the fact that the splitting is in general comparable to the separation of the two D lines. In

segments 18 and 19, however, the separation due

to the splitting effect is large enough to show in

spite of the duplicity of the spectral feature.

For the remainder of the wake lines the intensity in the wake is either too low or the resolution of individual lines is too poor to identify

both components of the wake lines.

The two components of one wake line may

be considered as "red" and "violet" compo638805—63 14

nents; i.e., displaced to longer or shorter wavelengths compared to the position of the main

spectral line in the adjacent segment of the

normal meteor spectrum. The flickering effect

can be detected in the wake, although in some

cases only one component appears to strengthen.

The individual components show distinct curvature in places with little correlation between

the two components. In some instances the

wake components can be traced down the trail

well into the following segment of the meteor

spectrum.

Individual descriptions of the components

of the H and K lines, in the second order, are

given below for segments 14 to 18.

Segment 14-—The red component is the

stronger, shows some curvature, and appears

to fluctuate more due to flickering than does

the violet component. The images are within

1 mm of the extreme edge of the plate, which

limits the value of this segment.

Segment 15.—A large-scale reproduction of

this region is shown in plate 2. The red component is strong near the main segment and

can be traced back farther than the violet one.

The effects of flickering are more evident in the

violet component. Both components show

some minor kinks, particularly near the main

segment.

Segment 16.—The red component is very

strong in the lower portion of the wake, while

the violet component is weak. The violet

line strengthens considerably at an earlier flare

in this segment of the wake. The red component may be detected higher than the violet

one, and also continues about two-thirds of the

way through the main part of segment 16.

With decreasing height within the segment, the

red component approaches the main line but

fades out before actually joining the main

spectral line.

Segment 17.—The violet component is much

the stronger in this segment. Just above the

main segment the splitting is quite large, while

the violet line bends over toward the red component a little farther up in the wake.

Segment 18.—The wake is now quite weak,

with the violet component stronger than the

red component. The splitting of the two components is larger than in earlier segments.
166 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

In the first-order Na D lines the two components are not clearly resolved until segment 18.

Faint double wake-lines are also detectable in

segment 19 for Na D, with an even wider

separation than in segment 18.

Interpretation of the double lines

One obvious explanation to consider for the

doubling of the spectral lines in the wake is a

physical splitting of the meteoroid into two

pieces. This has been observed for some

meteors; for example, in spectrum 132 (Millman

and Cook, 1959). A splitting of the meteoroid

was suggested as one possibility to account for the sudden jump in the frequency of the flicker at segment 13. While this

may have occurred it is not the explanation

for the double wake-lines, since the wake-lines

are generally converging near their lower ends

in each segment, while a splitting of the meteoroid would lead to diverging fragments. In

segment 16 the red component can be traced

for a total distance equivalent to half a complete segment, whereas the exposure time is

only one-third of a segment; i.e., the red component is not an exposure on a trailing fragment.

The two components are not due to Doppler

effects of an expanding column. The observed

splitting would correspond to a relative expansion, transverse to the direction of meteor

motion, of about 600 km/sec. This is a most

unreasonable value when the initial velocity

of the meteor was only 36 km/sec.

The best interpretation is that the wake

represents a time exposure of the expanding

column of meteoric gas, taken while the luminosity is decaying. Meteor spectrographs are

slitless spectrographs, which produce a broad

image of a broad source even in monochromatic

light. The two wake components apparently

represent a side view of a hollow luminous

column that shows two well-defined edges

because the effective thickness of the luminous

portion is small compared to the thickness of the

entire column. Note that in comparing the two

components at a particular point on the trail,

one should compare two points on a line perpendicular to the direction of meteor motion,

rather than two points on a line parallel to the

spectral dispersion.

Figure 2 shows three computed curves for the

intensity profilo plotted along a radius of the

column from x=0 at the center to a;=1.0 at the

outer edge. The three curves correspond to an

effective thickness t of the luminous portion of

the column of 0.05, 0.15, and 0.40, in units of the

column radius. The resolution of the plate is

insufficient to rule out very small values of t,

but the components are sharp enough to indicate

that the effective value of t is not much greater

than 0.15.

One complete segment corresponds to 0?080,

made up of an exposure of 0*027 and an occulted

interval of 0?053. The wake is observable

approximately halfway across an occulted portion, from which it follows that the effective duration of the luminosity is considerably less than

one shutter break. For all points within the

gap, the total exposure is the same, 0?027, but the

"age" of the column when the exposure starts is

different for each point. A point at the lower

end of a normal wake, where the main meteor

spectrum segment is starting, receives an exposure from age t=QH) to tf=0?

027. For a point in

the middle of the gap, the exposure runs from

<=0?027 to *=0?054. This is about the last

observable point in most segments; i.e., there is

insufficient luminosity emitted after t—0?03 to

record on the plate.

FIGURE 2.—Computed intensity profiles for three values of t,

the effective thickness of the luminous column.
METEOR SYMPOSIUM—HALLIDAY 167

As noted earlier, some of the wake lines, particularly the red components, can be traced

down into the following segment. For different

points within the segment itself, all exposures

start at t=0 but have different durations. The

durations decrease linearly with distance down

the segment from a maximum exposure of 0?027

at the top to 0?000 at the bottom (where the

shutter occults the camera for the next 0?05).

In segment 16, it was noted that the red component was observable two-thirds of the way

through the segment; i.e., for any exposure

duration longer than 0*009.

Magnitude of the splitting

Once it is known that the split lines correspond

to a physical separation of material in the

meteor column, it becomes of interest to determine the magnitude of the splitting. The

separation of the two components was measured

at frequent intervals in each segment of the

wake, and the results were plotted. The scales

were converted to diameters of the column, in

meters, by allowing for the plate scale and the

range of the meteor corresponding to each

segment.

The results are presented in table 3, where the

curves have been read at equal intervals corresponding to 0*004 of meteor travel. For

example, a time of $=0*012 indicates a point hi

the occulted portion from which it took the

meteor 0*012 to reach the point at which the

shutter reopened to begin the next segment of

the main spectrum. (The entire gap corresponds to 0*053, and although the wake can

sometimes be detected at least halfway through

the gap, both components are seldom observable for more than one-third of the gap.) The

mean splitting within each segment is shown at

the bottom of the table.

TABLE 3.—Diameters of the column (meters)

t

(tee) 0.000

0.004

0.008

0.012

0.016

0.020

Mean

H

37

42

40

15

31

34

39

45

37

16

49

49

44

49

53

49

n

69

73

61

54

64

18

78

82

85

83

77

77

80

In segments 15 and 16, the red components

can be traced into the main segment. They

begin with separations from the main spectral

line (corresponding to a radius of the column)

of about 24 meters. One-third of the way down

through the segment the separation is about 16

meters, and this is maintained for another third

of the dash, until the line fades out as noted

previously. At the lowest observable points

these red components are displaced about 16

meters from the main column, recorded in an

exposure which lasted for only 0?009.

In all cases where separations for lines of Ca

I or Fe I could be measured, the observed

points fell quite well on the corresponding curve

derived for the H and K lines of Ca II.

The splittings within one segment of the wake

are fairly constant; i.e., the red and violet components are nearly parallel. The mean values

for the five segments show a curious dependence

on height: the splitting increases with decreasing height and may be represented quite well by

the linear relation

<Z=550-9.41 h,

where d is the diameter in meters at a height of

h km. The relation is derived from observations between heights of 50 and 55 km.

From the observed rates of expansion, one

may compute an equivalent diffusion coefficient.

Opik (1958) has shown that an effective radius

R at time t may be denned by R*=ZIH. For

the lowest observed points on the red components, £=0*009, R=16 meters, from which

Z>=9.5X107 cm2/sec. The effective value of t

should really be smaller, or D should be somewhat larger. For a typical point in the wake,

#=3 0 meters, and an effective value of * is

about 0*03, from which Z)=1.0X108 cm2/sec.

Opik tabulates normal diffusion coefficients for

these heights of about 2X102 cm2/sec; i.e., the

observed expansions exceed those predicted

from normal diffusion by a factor of 5X106.

Discussion

At the low heights of this meteor one should

expect a shock front to form around the moving meteoroid. The observed wake luminosity,

however, is produced by meteor atoms of calcium, sodium, and iron, not by atmospheric

particles. An effective front of expanding me-
168 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

teoric material appears to exist inside the heated

volume produced by the shock front. Violent

collisions at the surface of this meteoric front

continue to excite the meteoric atoms for intervals up to about 09

03. As shown earlier, the

sharpness of the two components of the strong

wake lines indicates that the effective thickness

of the luminous portion of the meteor column

is not more than about 15 percent of its radius,

or else the lines would appear more diffuse.

The wake components indicate a diffusion of

meteoric material into the atmosphere, but the

effective diffusion coefficients are so large as to

suggest the phenomenon is essentially explosive. During the initial stages the diameter of

the column is observed to expand at a rate in

excess of 3 km/sec. It is not surprising that

the expansion should be very rapid compared

to normal diffusion since the amount of material deposited by such a bright meteor is so

great as to constitute a major change in local

density along the meteor trajectory. The rate

of diffusion of meteoric material in this case is

so great that it seems reasonable to infer that

much fainter meteors, perhaps any meteor

brighter than 0 magnitude, will also give rise

to appreciably more rapid diffusion than is observed by radar for faint meteors. Great care

should be taken, then, that normal diffusion

coefficients are not considered as a known quantity in calculations involving the gas columns

left by bright meteors.

It is of considerable interest to note that the

ion column of Ca II ions expands at the same

rate as the atom column of Ca I or Fe I. This

is not normally considered to be the case, at

least for radar observations, which, of course,

are for meteors about 10 magnitudes fainter than

this Geminid. Manning (1958), for example,

quotes Loeb (1934) to support a statement that

the ion column will diffuse only one-fifth as

fast as the atom column. Loeb's results are

based on experiments in which ions were allowed

to diffuse through an electric field. He states

(p. 548): "the velocity gained from the field

between impacts is further supposed small

compared with the thermal velocities of agitation." It is not clear that these results are

applicable to the meteor case, where the presence of an electric field is unlikely and the

systematic velocity of the meteor particles is

very large compared with thermal velocities.

Manning mentions that the ion column for a

bright meteor may be larger than for a faint

one if ionization can still be accomplished during

the expansion of the atom column. For calcium, 6.09 ev are required for ionization, which

is higher than the excitation of any wake line.

This makes it more likely that an ion of Ca II,

which emits H or K radiation 0?03 after the

passage of the meteor, survived nearly all of

that interval as an ion, and was then excited

with an additional 3.1 ev to radiate, rather than

that the ion was formed from a Ca I atom and

excited to radiate by any collision occurring

later than perhaps 0?002 after the atom left the

meteoroid.

Rapid rotation or oscillation for this meteoroid is suggested by the regularity of the

flickering phenomenon and is supported to some

extent by the split wake-lines. The variation

in relative intensity between the red and violet

components could arise from either mechanism,

since varying amounts of material would be

ejected from the meteoroid in a manner which

is not radially symmetrical. This could also

account for some of the curvature observed in

the wake lines.

One Perseid spectrum is known which shows

a similar but much less pronounced splitting

of the wake-lines. It is spectrum 223 in Millman's (1958) list of meteor spectra. The splitting is evident in one segment of the H and K

lines, but it is confined to a very short path

length near a bright flare. The fact that the

phenomenon is so pronounced for the Geminid

meteor may be associated with its low height

in the atmosphere. The much smaller mean

free path may tend to localize the zone where

appropriate collisions may occur and effectively

shield the inner portion of the wake column,

giving rise to the hollow-tube effect.

References

COOK, A. F., AND MILLMAN, P. M.

1956. Photometric analysis of a spectrogram of a

Perseid meteor. Astrophys. Journ., vol.

124, pp. 476-477.

HALLIDAT, I.

1958. Meteor wakes and their spectra. Astrophys. Journ., vol. 127, pp. 245-252.

1961. A study of spectral line identifications in

Perseid meteor spectra. Publ. Dominion

Obs. Ottawa, vol. 25, pp. 1-16.
METEOR SYMPOSIUM—HALLIDAY 169

LOEB, L. B.

1934. Kinetic theory of gases. Ed. 2. McGrawHill Book Co., New York.

MANNING, L. A.

1958. The initial radius of meteoric ionization

trails. Journ. Geophys. Res., vol. 63,

pp. 181-196.

MILKMAN, P. M.

1954. A provisional list of the major meteor

showers. Journ. Roy. Astron. Soc.

Canada, vol. 48, pp. 193-195.

1958. Photographic meteor spectra (appendix 6).

Journ. Roy. Astron. Soc. Canada, vol. 52,

pp. 275-276.

MlLLMAN, P. M., AND COOK, A. F.

1959. Photometric analysis of a spectrogram of a

very slow meteor. Astrophys. Journ.,

vol. 130, pp. 648-662.

OPIK, E. J.

1958. Physics of meteor flight in the atmosphere.

Interscience, New York.

RINEHART, J. S.; ALLEN, W. A.; AND WHITE, W. C.

1952. Phenomena associated with the flight of

ultra-speed pellets. Part 3. General features of luminosity. Journ. Appl. Phys.,

vol. 23, pp. 297-299.

Abstract

A study is made of an unusual Geminid meteor spectrum, photographed between heights of 73 and 47 km.

Peak luminosity, estimated at magnitude —8, occurred near 59 km. The meteor exhibited a pronounced flicker,

with a frequency varying from 50 to 300 cycles per second. The flicker may be associated with rotation or oscillation of the meteoroid.

A prominent wake spectrum was photographed between 50 and 55 km, consisting of lines of Na I, Mg I, Ca I,

Ca II, Mn I, and Fe I. The stronger lines are split into two distinct components attributed to a hollow luminous

column rather than splitting of the meteoroid or Doppler effects. The diameter of the column varies from 40 to

80 meters, but shows no variation from one atom or ion to another. Diffusion coefficients computed from the observed rate of expansion exceed the normal values at these heights by a factor of more than 10s

. The expansion in

this case might be considered as explosive.

On the Frequency of Occurrence of the

Auroral Green Line (5577 A) in Perseid Spectra

By John A. Russell *

In a note announcing his identification of the

forbidden line of O I at 5577 A in the spectra

of three meteors, Halliday (1958) pointed out

the difficulty of explaining why the line had not

been detected previously. In a subsequent

study of old spectra, Millman (1960) located a

number of appearances of the auroral line,

including one in a spectrum from the 1933

Harvard Leonid campaign and one obtained in

1950 by the author. This latter spectrum, No.

121 on the World List (Millman, 1952), had not

been reduced at the time of Millman's identification because of its mediocre quality.

Spectrum No. 121 is one of five Perseid

spectra (World Nos. 118-122) obtained in a

31-hour interval with the same instrument: a

30° prism, f/5.6 lens of 130-mm focal length,

and Super XX roll film. It is evident that

these spectra should provide some information

on the consistency with which the green line

appears under similar instrumental and atmospheric conditions. Spectrum No. 118 contains

only the H and K lines of ionized calcium. In

spectrum No. 122 the H and K lines were

strong, but the remainder of the spectrum was

very weak. In neither of these spectra could

the 5577 line be detected. Spectrum No. 120

was reproduced in an earlier paper (Russell,

1953). It was well exposed, but suffered from

a poor orientation of the path with respect to

the prism edge, from foreshortening as the result

of the proximity of the meteor to the radiant,

and from the location of the spectrum in the

very corner of the photographic film. When

the original negative was enlarged and the contrast increased by two successive printings on

contrast lantern slide plates, the green line

1

 Department of Astronomy, University of Southern California, Los Angeles, Calif.

appeared briefly at the beginning of the trail.

Spectrum No. 119 was reproduced in a general

paper on Perseid spectra (Russell, 1959) as an

example in which the H and K lines, though

present, were not dominant. When this spectrum was treated photographically by the process used on No. 120, the auroral green line also

became evident.

More recently the presence of the auroral

line in two additional spectra, Nos. 103 and

107, obtained in 1948 and 1949 with the same

instrument, was detected by careful reexamination of the negatives. This brought the green

line identifications to five out of the seven

spectra photographed with the same equipment

during three consecutive Perseid showers.

We note that the auroral line was not found

in the spectrum that showed only the H and K

lines, or in the one which showed little besides

strong H and K lines. A correlation between

the strength of the green line and that of the

H and K lines was originally suggested by a

Perseid spectrum, No. 198, obtained with different apparatus (Russell, 1959). This was the

first Perseid in the author's experience that

failed to show H and K lines or that exhibited

strongly the O I line, the density of which in

this spectrum was second only to that of the

sodium D-lines. The extent of this possible

correlation was investigated in the following

manner. From estimates made visually outside of noticeable bursts, the plates were

arranged in order of increasing density of the

K line relative to the blend at 3830 A, and

numbered from 1 to 7. The plates were then

arranged in order of increasing density of the

O I line relative to the D lines and again numbered consecutively. The results are illustrated

in figure 1.

171
172 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

To the extent that so small a sample can be

relied upon, the correlation appears to be real.

Spectrum No. 198 (photographed 1956) and

Halliday's spectrum No. 302 (photographed

1958), which consists solely of the green line,

would extend the graph linearly toward the

lower right. Why a correlation such as this

should exist is not clear. As most of the data

plotted in figure 1 are from meteors observed

within a period of 31 hours, it may be necessary

to explain some of the differences in the spectra

as the result of differences in the meteoroids

rather than as exclusively the effect of variable

atmospheric conditions. Of possible significance is the observation that the strength of

the green line is almost entirely unaffected by

bursts (Halliday, 1960), whereas the strength

of the H and K lines is most strongly influenced

by them (Russell, 1950).

ORDER

OF

K

3830

7-

6-

5-

4-

3-

2

1-

e

e

•

0

•

e

0

1 2 3 4 5 6 7

ORDER OF 5577/ D

FIGURE 1.—K-line density versus density of 5577 in seven

Perseid spectra.

Halliday (1960) finds some evidence for a

correlation between the occurrence and depth

of penetration of the green line, on the one

hand, and geomagnetic and solar activity, on

the other. Milhnan (1960), however, points

out that the Leonid spectrum in which he

found the green line was photographed at the

depth of the sunspot minimum of 1933. The

geomagnetic activity and solar activity during

the Perseid showers of 1948-1950, 1956, and

1958 are indicated in table 1. The data are

taken from the "Summaries of Mount Wilson

Magnetic Observations of Sunspots," which appeared regularly in Publications of the Astronomical Society of the Pacific until 1959. No

consistent pattern is evident relating the green

line to solar activity, although the absence of

extreme solar conditions during the period

1948-1950 makes the negative result inconclusive. The atmospheric depth to which the green

line penetrates relative to the other lines is remarkably uniform. It generally appears concurrently with the blend of iron lines at 3830 A

and fades about the time that the iron blend

at 3740 A becomes visible. As all of these

spectra are of meteors with a common high

velocity, they can provide only partial support

of Halliday's evidence that the green line is

exclusively a high-velocity feature.

TABLE 1.—Relation of auroral line emission to geomagnetic and solar activity

World

number of

spectrum

103

107

118

119

120

121

122

198

274

Date

8/12/48

8/13/49

8/12/50

8/12/50

8/12/50

8/13/50

8/13/50

8/11/56

8/12/58

Auroral

line

Geomagnetic

activity

Weak Great

Weak None

Missing Moderate

Weak

Weak

Weak None

Missing

Strong Great

Missing Not great

Number

tunspot

groups

that

day

10

6

6

9

14

Aug.

number

suntpot

groupt

that

month

12.4

8.6

7.0

13.5

14.8

When spectra taken with other instruments

and emulsions are considered, a broader though

less homogeneous base is provided for studying

correlations. In 1951, by which time solar

activity was below average, a shutter-chopped

Perseid, No. 124 (Russell, 1959), which strongly

showed H and K lines and the first positive

group of nitrogen bands, failed to display the

green line. A low-dispersion but fairly wellexposed spectrum of a Geminid, No. 140,

obtained in 1953 shows no green line. This

absence fits both the low-velocity and the solaractivity correlation. A sporadic meteor of

unknown velocity, No. 148, photographed in

1954, showed very strong H and K lines but no

green line. Both spectrum No. 198 (1956)

and a similar but much fainter spectrum

obtained the next night with the same instru-
METEOR SYMPOSIUM—RUSSELL 173

ment show a relatively strong green line but no

H and K lines. Table 1 indicates that a great

magnetic storm was in progress at the time and

that general solar activity was high.

If general solar activity is a factor in producing the green line, no spectrum obtained by the

author should show it better than the Perseid

photographed in 1958 with the 18-inch Schmidt

at the Mount Palomar Observatory (Russell,

1960). This spectrum, No. 274, shows very

strong N2 bands in the red and 40 measurable

features. In the region of the spectrum where

the green line would normally appear, there is

a broad, amorphous darkening that is a little

sharper on one side than on the other. The

sharper boundary is close to 5577 A. This

feature was not included in the published discussion as no lines are seen in it under the

microscope. It differs from the green line's

customary behavior in that it does not appear

sooner than the other lines; actually, the N2

bands appear first, much farther back along

the trail. If this feature were produced by the

forbidden O I line, blurred by winds during the

brief period of radiation, a minimum wind

velocity of 5 km/sec would be required to account for the breadth of the line. A. F. Cook

(private communication) suggests that this

feature is produced by additional, unresolved

N2 bands. The conclusion that the green line

is not involved in this spectrum seems strongly

justified. Although general solar activity was

higher in 1958 than in 1956, no great magnetic

storm was in progress at the time of the 1958

shower.

Conclusions

The seven Perseid spectra obtained with the

same instrument over the 3-year period 1948-

1950 indicate that (1) there appears to be an

inverse correlation between the strength of the

H and K lines and the strength of the auroral

green line at 5577 A; (2) the spectra consistently show the green line except where its

absence would be expected in the light of statement (1); (3) the position of the green line

relative to the rest of the spectrum was consistently similar. A consideration of several

other spectra indicates that (1) any correlation

between general solar activity and the occurrence of the green line appears weak, at best; (2)

there is no violation of Halliday's findings that

the green line is not found in the spectra of lowvelocity meteors.

References

HALLIDAT, I.

1958. Forbidden line of O I observed in meteor

spectra. Astrophys. Journ., vol. 128, pp.

441-442.

1960. Auroral green line in meteor wakes.

Astrophys. Journ., vol. 131, pp. 25-33.

MILLMAN, P. M.

1952. Photographic meteor spectra. Journ. Roy.

Astron. Soc. Canada, vol. 46, pp. 121-

125.

1960. The auroral green line in a Leonid spectrum.

Journ. Roy. Astron. Soc. Canada, vol.

54, pp. 189-192.

RUSSELL, J. A.

1950. Intensity variations in the spectrum of a

Perseid meteor. Contr. Meteorit. Soc,

vol. 4, pp. 250-254; Pop. Astron., vol.

58, pp. 134-138.

1953. Asymmetrical lines in the spectra of

meteors. Meteoritics, vol. 1, pp. 103-

105.

1959. Some Perseid meteor spectra of the past

decade. Sky and Tel., vol. 18, pp. 549-

551.

1960. Molecular nitrogen in the spectra of two

Perseid meteors. Publ. Astron. Soc.

Pacific, vol. 72, pp. 291-295.

Abstract

A reexamination of seven Perseid spectra, obtained with the same instrument, has revealed five instances in

which the auroral green line of O I at 5577 A is visible. All of the seven spectra were photographed during the

showers of 1948-50, five of them within a 31-hour period.

An inverse correlation appears to exist in these spectra between the strength of the auroral line and that of the

H and K lines of ionized calcium. The points of appearance and disappearance of the auroral line relative to those of

other lines were consistently similar.

A consideration of several other meteor spectra indicated little if any correlation between the occurrence of the

green line and general solar activity. There is, however, no evidence contrary to Halliday's findings that the green

line appears only in the spectra of high-velocity meteors.

638805—63 15

Negative Ions and Luminosity in Meteor Trains

By T. R. Kaiser

 x

The work reported here forms part of a theoretical study of the processes of dissipation of

ionization in meteor trails and, as it is hoped

to report this more fully elsewhere, the relevant

parts of the theory are given only in outline.

The main causes for decay of volume electron density in a meteor trail are diffusion

(molecular and eddy), electron-ion recombination, and negative ion formation. The latter

is complicated somewhat through the competing processes of electron detachment and mutual

neutralization of positive and negative ions.

Both recombination and mutual neutralization

can contribute to the meteor train luminescence

through the processes

A

+

-\-e-*A+hv (radiative recombination), (1)

(2)

where the primes denote excited states. The

positive ions will be the products of collisional

ionization and the negative ions will be O2 and

0", produced by electron attachment. In the

meteor height region molecular oxygen is predominant.

Formulation of the problem

The expressions for the rate of change of volume

density of the various ionic species are:

^

^ —a3nen+—

(3)

(4)

(5)

(6)

where nt, n_ and n+ are the volume densities

of electrons, negative and positive ions respectively. The diffusion coefficient D is treated

as a constant, identical for all species. While

this will be essentially true in the absence of

heavy negative ions, it is only an approximation in the general case. However, from a generalization of the theory of ambipolar diffusion

(Kaiser, 1953), it seems that it is not likely to

vary by more than a factor of two. The terms

ai, a?, 03, and a4 are the rate coefficients for

attachment, detachment, recombination, and

mutual neutralization, respectively; ax will be

proportional either to molecular density n cm"3

for radiative attachment, or to n

2

 for threebody attachment in which the excited negative

ion is stabilized by collision; a^ will be proportional to n for collisional detachment or constant for photo-detachment; a3 will be constant

since recombination appears to be radiative

(Kaiser and Greenhow, 1953; Kaiser, 1953).

The contribution of recombination to train

luminosity has been discussed by Kaiser (1955).

A reassessment of this process suggests that it

may be significant for the brightest meteors

but that generally it is likely to be less important than mutual neutralization. In the present analysis, therefore, we will neglect it and

put 03=0.

The most important quantity for radio meteor studies is the electron line density, ae cm"1

.

The corresponding quantities for the other species are a+ and <x_. Since, if a3=0, positive

ions can disappear only by neutralization with

heavy negative ions, the total train intensity

is given by the expression,

L

~

 2 dt (7)

1 University of Sheffield, England.

If we take g as the mean number of photons

produced in reaction (2), / will be measured

in photons per second per cm length of train.

175
176 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Solutions to equations 3 to 6 ( a3=0)

We will assume the trail is formed with negligible radius at time t—0.

(i) O2=0.

Equation (3) becomes

(8)

(9)

n<=£m°xv(-TTu) ao)

with the solution (Kaiser, 1953)

where

and OQ is the initial electron and positive ion

line density. This solution has been used to

derive values of ai from long enduring radio

echoes (Kaiser, 1953; Davis, Greenhow, and

Hall, 1959a, 1959b).

Equations (4) and (5) contain the non-linear

neutralization terms and are not amenable to

exact analytic solution.

(ii) at=0.

This is not directly helpful for the train

problem since it gives 7=0 ; however, it is

capable of exact solution which may be of

value in radio-echo studies and is helpful in

obtaining an approximate solution when a« is

sufficiently small (see below). The solutions

are:

ct.—:— -(a,+o,)0j, (11)

[l-exp(-(a1+oa)0]. (12)

a+=a0= constant

For all ionic species

4*Dt*xp\~WiJWhen t becomes large compared with(a1-f-o2)"1

,

The form of the electron and negative ion

decay is illustrated in figure 1.

(iii) a^Q.

Approximate solutions have been found for

extreme cases of slow and rapid neutralization.

Here at (a) and a_ are given ap-

 X4=

7r-ri

proximately by solutions (11) and (12), with

a+ decreasing with time:

1 (13)

Aa,ia0(l—e~r

)

dt

a1

(14)

where

and

The train luminosity will follow equation

(14) and will have decayed significantly when

T~1 , i.e., tf~ (ai+e^)"1.

The initial intensity 70 is, from equations (7)

and (14):

(15)

(b) a?4»l. In this case the negative ion

volume density rises rapidly (instantaneously

for zero initial radius) to n-^di/di and maintains this value throughout the region of

the column of ionization where w«/w_ exceeds

<hl<i\', beyond this limit it is proportional to

\

/

/

X

^ * - — "--• "

_

a,*«2

FIGURE 1.—Variation of electron and negative ion line

density for a«=0. Solid line, a«/ao; broken line, a-fa^.
METEOR SYMPOSIUM—KAISER 177

If also

I — da+

~di Oil0e-a

ih (16)

(17)

we get

where equation (16) remains valid to

If x^>\ but z4a1/(a1+a2)

<

^l (which requires

a^ai) the initial intensity is still approximately as given by equation (17) but the decay is more rapid and it is estimated that

the intensity will fall to a fraction of its initial value in a time

tar1- (18)

The significance of the above is that, provided

x^>l, negative ions are initially mopped up

by neutralization before detachment can operate and, unless a% is extremely large compared with au this will continue to £>af \

In the limiting case, a?=0, it is possible

to interpolate graphically to obtain solutions

for intermediate values of xt; these are given

in figure 2.

Interpretation of experimental data

Hawkins and Howard (1959) have analyzed

in detail the decay of luminosity in a train

photographed with a Baker Super-Schmidt

camera, over the atmospheric height range 84

to 93 km. They find the decay to be exponential with a duration which increases with

height (i.e., with decreasing atmospheric

density). They have also estimated the rate

of train decay for a long enduring train observed

by Liller and Whipple (1954), which suggests

that the duration is a maximum at about

92.5 km and decreases above this height.

They infer that the decay of light from both

normal and long-enduring trains follows an

exponential law and that the rate of decay

is a well-defined function of height. The

decay constants obtained by Howard and

Hawkins are plotted in figure 3 as a function

of height and atmospheric molecular density

ncm~3, the latter as given by Nicolet (1959).

The decay constant is defined as dM/dt, where

M is the train magnitude.

These results strongly suggest that below

92.5 km the decay obeys equation (16) (equation (15) with xt

 <d, will be shown to lead to

too low a value for the initial intensity).

Liller and Whipple suggest that the increasing

decay constant (decreasing duration) at greater

heights is due to diffusion. This would imply

that the trails become resolved and hence

surface brightness rather than total intensity

is recorded.

For an unresolved train, equation (16) gives

dM

dt = 1.09a,; (19)

FIGURE 2.—Decay of train intensity for various values of

hence ax can be deduced directly from experiment. The theoretical initial decay rate for

a finite resolving power has been evaluated

on the assumption that the camera records

a line source as having a brightness profile

exp (—TP/XI2), where x is measured along the

normal from the axis of the image. It is

further assumed that D<xn~l and the two

extremes of radiative and three-body attachment are considered separately.

(a) Radiative attachment,

dM

dt -1.09a,,

(b) Three-body attachment,

dM m M_ IY n V , o n*"»T

i./ n J

JL+^V (20)

(21)
178 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

• HAWKINS t HOWARD

O LILLER t WHIPPLE

IOO

I

3O 31 32 33 In fit cm3)

FIGURE 3.—Train decay rate, dM/dt magnitude sec"1, as a function of atmospheric density and height. The theoretical curves, which are discussed in the

text, are derived for three-body (a) and two-body (b) attachment.

where the subscript "min" refers to the values

corresponding to minimum dM/dt. The result

of fitting the formulas (20) and (21) to the

experimental results is illustrated by the curves

plotted in figure 3. It is clear that the experimental data strongly support three-body attachment, at least below 92.5 km. In fitting

formula (21) we obtain at min=6X10"2

and hence

n

2

sec~1 (22)

for the relation between attachment coefficient

and total molecular density. The result also

implies that a2 > at and xi ^ 1 up to 92.5

km. If we take Z>=5X10* at this level

(Greenhow and Lovell, 1960) and note that

trains have been observed for meteors as faint

as magnitude +2.5 (Hughes, 1959) for which

«0~1013cm~1 (Kaiser, 1953) we obtain a limit

for the mutual neutralization coefficient, namely,

at > 10~7 cm3 sec"1* (23)

Substituting the above values we get a;i~9

meters, which implies a resolvable train diameter of the order of 20 meters. This agrees

well with Whipple's estimate of the order of

30 meters for the Baker Super-Schmidt cameras

(Liller and Whipple, 1954).

In spite of the above, the explanation of

the increasing decay constant above 92.5 km

as due to diffusion is not completely convincing,

particularly if one considers in more detail the

form of the decay in surface brightness with

time. However, although one could speculatively suggest additional explanations, this

is hardly justified until more experimental data

are available.

The relation between meteor and initial

train magnitude

If the meteor produces p photons through

collisional excitation for each electron and we

ignore any difference between meteor and

train spectral distribution, then, for

In deriving expression (21) we obtain a

relation for the camera resolution, characterized

by*,:

Xi=(DmJalm^. (24)

~2.5flog,o(p/2)-logio(aiT)], (25)

provided ai!T<l. T is the instrumental integrating time and Mte.lo is the initial train
METEOR SYMPOSIUM—KAISER 179

magnitude. If the ionizing and luminous

efficiences are assumed to be of the same order

(Kaiser, 1953), then p/q will be of order unity

and

5M 2.5 log10 {axT). (26)

Thus, for instance, with T=0.5 second for

the first train exposure we expect 8M to be

about zero at 82.5 km, + 3 at 90 km, and

+ 7 at 100 km. These values might be optimistic at the lowest height due to the finite

delay in operating the camera; generally they

appear to be quite reasonable in order of magnitude. They do imply that slow neutralization (Xi<gil) would produce much fainter

trains than are observed.

It should be noted that for p/q~l, the integrated train intensity, I / dt, will be of the

Jo

same order as the meteor intensity.

Discussion

It is suggested that the train decay observed

with the Harvard cameras is due to negative

ion formation followed by mutual neutralization, leaving the resultant atoms in excited

states. The attachment appears to be a threebody reaction and to determine the train decay

constant below 92.5 km; at greater heights the

increased decay constant may be controlled by

diffusion, due to the finite resolving power of

the instruments. It would clearly be very

useful in future experiments to arrange that

the trains remain unresolved at all heights in

order to avoid the latter complication. According to Dr. J. Davis (private communication), photoelectric recording of trains is

feasible and has some desirable features as

compared with the photographic technique,

particularly as in principle it can be used to

record directly the total light emitted from a

small section of a train as a function of time.

A comparison between the integrated train

intensity Sldt and the meteor intensity

would lead to an estimate for the ratio p/q.

Finally, the attachment coefficient arrived at

here may be compared with the values estimated from very long-enduring radio echoes.

It is interesting to note that the former is

associated with the decrease of da+fdt (which is

approximately equal to dajdt) with time,

whereas the lifetime of the echoes is dependent

directly on the decrease of a, with time. The

importance of attachment in radio echo studies

of meteors was pointed out some years ago by

the author (Kaiser, 1953) and a value was

found for the coefficient which corresponds,

in the present terminology, to Oi ~ 0.03 sec"1 at

95 km height. Recently Davis et al. (1959a,

1959b) have derived coefficients for the same

height which range between 0.015 and 0.025

sec"1. In comparison, the relation (22) gives

ai=0.026 sec"1 at 95 km height.

Note added October 1962

Further consideration has suggested an alternative (or additional) mechanism to explain the

increasing decay constant above 92.5 km in the

observations of Liller and Whipple (fig. 3).

It arises if the quantity Xidil (fli-\-(h) is less

than unity even though ?<>1, which may occur

on the rising portion of the meteor ionization

curve if, as suggested, axocn2 while a2ocn.

The minimum decay constant (maximum train

duration) will be found near the height at which

(27)

At greater heights, the train duration, from

equation (18), becomes

t> (28)

Hence, since Dccn l and Ojocw, we obtain

focoo; i.e., on the rising part of the ionization

curve the duration will decrease with increasing

height. Since, from intensity considerations,

we still require a?4>l, equation (27) enables a

lower limit to be set for the detachment coefficient 02, namely, a2>6X10~2

 sec"1 at 92.5 km,

and generally O2>10~I8n.

References

DAVIS, J.; GKEENHOW, J. S.; AND HALL, J. E.

1959a. Combined photographic and radio echo

observations of meteors. Proc. Roy.

Soc. London, ser. A, vol. 253, pp.

121-129.

1959b. The effect of attachment on radio echo

observations of meteors. Proc. Roy.

Soc. London, ser A, vol. 253, pp.

130-139.
180 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

GBEENHOW, J. S., AND LOVELL, A. C. B.

1060. The upper atmosphere and meteors. In

Physics of the upper atmosphere, J. A.

Ratcliffe, ed., pp. 513-549. Academic

Press, New York.

HAWKINS, G. S., AND HOWARD, W. E.

1959. Decay of light from a meteor train.

Astrophys. Journ., vol. 130, pp. 1003-

1007.

HUGHES, R. F.

1959. Meteor trains. Smithsonian Contr. Astrophys., vol. 3, no. 8, pp. 79-94.

KAISER, T. R.

1953. Radio echo studies of meteor ionization.

Advances in Physics (Phil. Mag.

Suppl.), vol. 2, pp. 495-544.

1955. Meteors. Spec. Suppl. Journ. Atmosph.

Terr. Physics, vol. 2. Pergamon Press,

New York.

KAISER, T. R., AND GREENHOW, J. S.

1953. On the decay of radio echoes from meteor

trails. Proc. Phys. Soc. London, vol.

66B, pp. 150-151.

LlLLER, W., AND WHIPPLE, F. L.

1954. High-altitude winds by meteor-train photography. In Rocket exploration of

the upper atmosphere, R. L. F. Boyd

and M. J. Seaton, eds., pp. 112-130.

Interscience, New York.

NICOLET, M.

1959. The constitution and composition of the

upper atmosphere. Proc. Inst. Radio

Eng., vol. 47, pp. 142-147.

Abstract

The decay of meteoric ionization due to the combined effects of diffusion, electron attachment and detachment,

and mutual neutralization of positive and negative ions, has been studied theoretically. It is proposed that the

excited neutral atoms resulting from mutual neutralization produce meteor train luminosity. Interpretation of

experimental data, in the light of the theory, leads to values for the electron attachment coefficient which agree

reasonably with those obtained from radio observations and suggests that attachment occurs through a three-body

process.
Luminosity from Large Meteoric Bodies

By H. Julian Allenl and Kenneth K. Yoshikawa

 l

It is usual in meteor theory to ascribe the

origin of the luminosity of meteors to collisions

of air molecules with, the surface molecules of

the meteoric body. In this case the rate of

removal of mass from the surface is directly

proportional to the luminosity, which affords a

most convenient means for analysis of meteor

flight. It seems not to be generally appreciated that the above procedure must be

restricted to meteoric bodies which experience

free-molecule flow—that is, to those bodies

which are small compared to the mean free

path of the air molecules.

For meteoric bodies in continuum flow,

wherein the body is large compared to the air

mean free path, the air molecules approaching

the body enter into a highly compressed layer

of gas which precedes the body itself. Lindemann and Dobson (1923) aptly called this layer

the "protective gas cap." The most energetic

collisions in the case of such flow occur between

the air molecules in the atmosphere and in this

gas cap. The resulting luminosity from the

gas cap is not a consequence of mass-loss rate

of surface molecules, but the radiation from it

may be a principal source of aerodynamic

heating of the meteoric body and thus cause

removal of mass by ablation. Plate 1 gives an

illustration of gas-cap radiation from a body as

photographed in a shock-tube wind tunnel at

Ames Kesearch Center. The airspeed is only

4.3 km/sec with the ideal gas temperature in the

shock layer at about 4500° K, yet the luminous

gas cap near the bow of the body and near the

control surface for this simulated space vehicle

is clearly evident. It should be noted that at

the instant this photograph was taken, no

ablation of the surface of this metal model was

occurring.

i National Aeronautics and Space Administration, Ames Research

Center, Moflett Field, Calif.

Gas-cap radiation

During the development of long-range ballistic

missiles and, more recently, of space vehicles

intended to enter the atmosphere of earth or

other planets, the problem of gas-cap radiation

was readily recognized (see, e.g., Allen and Eggers,

1958) by aerodynamicists as one that would

require considerable study if satisfactory heat

shields were to be designed for such vehicles.

An intensive effort, both theoretical and

experimental, has been made to understand the

phenomenon (Kivel and Bailey, 1957; Kivel,

1959; Armstrong, 1959; Hochstim, 1957;

Ziemer, 1960; Meyerott, Sokoloff, and Nicholls,

1960; Yoshikawa and Wick, 1961; Camm,

Kivel, Taylor, and Teare, 1959). The phenomenon is a complex one and far from well

understood. The experimental studies, moreover, have not been carried into the speed

regimes of most meteors. Thus, in the following paragraphs concerning gas radiation it must

be constantly borne in mind that the description

of the phenomenon is probably incomplete, and

the magnitudes discussed are extrapolations of

our present knowledge.

When continuum air is compressed on entering a gas cap of a meteoric body, it is drastically

slowed down relative to the body. The high

kinetic energy of the stream is then almost

entirely converted to heat. The translational,

rotational, and vibrational modes of the molecules are first excited. At meteor speed the

energy is sufficient, moreover, to dissociate and

ionize a large fraction of the air in the cap.

These atomic and molecular species become the

sources of the radiation. In addition, time is

required to establish equilibrium between the

gas species during and following the compression transient so that the amount of the radiation is a function of this time of relaxation.

The whole process then can be visualized as

181
182 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

FIGURE 1.—Variation of pressure, temperature, and radiation

in air following shock compression.

shown in figure 1. During the initial compression ("A") the temperature attains values

approaching that corresponding to an ideal

molecular gas; it then decreases as energy is

diverted to dissociate and ionize the molecules

and to form interim molecules until chemical

equilibrium is established. The level of radiation takes somewhat longer to subside to an

equilibrium value. The radiation intensity

received by the body surface therefore depends

upon the position of the surface relative to this

time-dependent process. If the air density in

100 -

the gas cap is low, the time scale is such that

the body surface may be in the position relatively close to the start of the original compression, as at "B" (fig. 1). The radiation will

then be principally from "out-of-equilibrium"

air. On the contrary, if the gas-cap density

is high, the whole of the transient behavior

will occur in a much shorter time and hence

effectively farther from the body. In this case

"C" may represent the position of the body so

that the radiation received may be well approximated by the equilibrium value as the integrated mean, provided the density is not so

high that reabsorption occurs within the layer.

Where reabsorption occurs, the radiation, of

course, becomes limited.

Using the results of Yoshikawa and Wick

(1961), we have calculated the radiative heattransfer coefficient in equilibrium flow \aB,

which the body receives from the gas cap.

For this purpose it was assumed that the total

volume of the radiating cap is the product of

the frontal area of a sphere of radius r and the

thickness of the gas cap. The results are shown

in figure 2.

The out-of-equilibrium effects were obtained

by extrapolating data from AVCO (Camm,

Kivel, Taylor, and Teare, 1959) and Ames

Research Center (e.g., Allen, 1961) with the

assumption that the total gas-cap radiation is

limited to about 15 percent of the total energy

as a maximum since body size or reabsorption

within the gas would limit further losses.

(Note that the "black body" limit was far

above this.) The results are shown in figure 3.

0 2 4 6 8 K) 12 M 16 18 20

Velocity, v, km sec"'

FIGURE 2.—Radiative heat-transfer from the gas cap of a sphere for

air in chemical equilibrium
METEOR SYMPOSIUM—ALLEN AND YOSHIKAWA 183

FIGURE 3.—Radiative heat-transfer coefficient for air out of chemical equilibrium.

Thereon \o is the radiative heat-transfer coefficient for the air out of chemical equilibrium,

and p is the ratio of the ambient air density

p at altitude h to that at sea level, po. The

ratio XG/XGB will be less than unity for large

values of ~j>r when reabsorption becomes

important.

Theory for meteors, including continuum

flow

The equations for acceleration and mass loss

rate for all meteor air flow regimes are given

in the following. The notation used is that of

Jacchia (1948).

The equation of motion, which relates the

acceleration of the meteoric body to its mass

and to the drag it experiences in flight, is the

familiar one

input to the body surface must appear as

ablation of the surface. Thus

dm

dt~~ (2)

where f is heat of ablation (thejheat energy

absorbed by a unit mass of the body during

ablation), and X is the heat-transfer coefficient.

On the other hand, it is well known that the

ablated mass from meteoric bodies in freemolecule flow emits radiation (see, e.g., Opik,

1958). For continuum flow it is again to be

expected that a fraction of the total radiation

resulting from ablation can be related to the

time rate of change of mass by the equation

dm

dt (3)

dv

m

1/3 (1)

where v is velocity, m is mass, p is air density,

y is drag coefficient, and Ami/3 is the effective

cross-sectional area.

The time rate of change of mass may, in

principle, be obtained in two ways: On the

one hand, since for meteoric bodies of all but

the smallest in size, (1) the heat radiated from

the body is negligible compared to the heat

transferred to it, and (2) the rate of heat transfer to the surface is so large that the interior

temperature is essentially unchanged during

the descent through the atmosphere, heat

where / is the total radiation, Ia is the gascap radiation, and r0 is the luminous efficiency factor.

In the determination of mass loss for meteoric

bodies in free-molecule flow (which constitute

nearly all of the observed meteors), it has

been customary to put all of the reliance on

equation (3) rather than equation (2). The

reasons for accepting equation (3) are:

(i) The gas-cap radiation (/<?) must be

zero for free-molecule flow.

(ii) The luminous efficiency can be calculated

from rather well-established physical principles.

The reasons for rejecting equation (2) are:

(i) In free-molecule flow, the heat-transfer
184 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

coefficient X is dependent upon the accommodation coefficient which is a relatively

unknown quantity at this time. It is true

that the drag coefficient y is also a function

of the accommodation coefficient, so it might

be thought that in some artful way knowledge

of X could be obtained from its relation with

y. Such a course does not appear profitable

because a change in the accommodation coefficient to produce a change in y from one to

about two is sufficient to change X all the

way from one to zero.

(ii) Only the upper limit for f (i.e., that

corresponding to vaporization) can be established. The lower limit is uncertain. If no

flaring is observed so that the lower limit

can be assumed to be that corresponding

to ablation as a liquid, the value of f may

fall as low as one-sixth that for vapor ablation.

If flaring occurs (and this is commonly the

case), the ablation may have occurred in the

solid state (by crumbling due to aerodynamic

forces and thermal stress), so f could conceivably be but a small fraction of the value

for vaporization.

For meteors in continuum flow, it is our

opinion that the order of preference may well

be reversed, particularly in the case of slow

meteors, which are commonly meteors of

asteroidal origin.

There is less reluctance to accept equation (2)

for the following reasons:

(i) The heat-transfer coefficient, which is dependent on both the radiative and the convective heating, is often far better known than it is

for free-molecule flow. This is particularly true

if the flow in the boundary layer is laminar,

and if the gas-cap radiation is close to that for

chemical equilibrium. However, as will be

discussed later, lack of knowledge of the shape

of the meteoric body introduces important

uncertainties in the heat-transfer coefficient.

(ii) If care is exercised to exclude as a necessity integration through those trajectory points

which, through evidence of flares or observed

physical breakup, are suspect as regards the

ability to fix f within the limits of vaporization

and fusion, the uncertainty in f is thereby

reduced. However, this uncertainty still remains a serious objection to the use of equation

(2).

Perhaps the most important argument for

accepting equation (2) is that equation (3)

is an even less attractive one for the following

reasons:

(i) The value of the gas-cap radiation will

generally be a modest-to-large fraction of the

total radiation emitted by the meteor, but the

gas-cap radiation depends upon the size of the

meteor since the gas-cap volume is a direct

function of size. Equation (1) can be used to

find mass but not size unless the meteor mass

density is known, and this is not the usual case.

Again, the unknown shape is a complicating

factor.

(ii) Values of TO, while presumably fairly

well known for fast meteors in free-molecule

flow, are not too well known even for slow

meteors in free-molecule flow. In continuum

flow it is to be expected that T0 would be much

reduced, but by an unknown amount. However, it is clear from laboratory firings in

ballistic ranges that TO is not zero.

Certainly in time the situation will become

a less pessimistic one for equation (3). Improvements in ground laboratory measurements

should give fair estimates of T0 as well as more

precise gas-cap radiation values. For observed

meteors for which the meteorites are found,

the knowledge of the final mass and shape, and

the characteristics of the materials of which

they are composed should allow considerably

more reliance to be placed on both equations

(2) and (3) as means for calculating the instantaneous mass along the trajectory.

Application of theory to Meanook Meteor 132

Millman and Cook (1959) analyzed (by

equations for free-molecule flow theory) the

flight of a bright meteor observed in Canada

at the Meanook and Newbrook stations. The

data for this meteor are given in table 1, and

the observed radiation is indicated by the solid

curve in figure 4. These data were of particular

interest to us since, as will be demonstrated,

this meteor actually experienced continuum

flow during the observed portion of its descent

through the atmosphere.

To analyze these data it is necessary at the

outset to assume a shape for the meteoric body.

Allen (1960) indicated that a sphere should

approximate a body in most cases for the follow-
ALLEN AND YOSHIKAWA PLATE 1

Gas-cap radiation from an entry body.

METEOR SYMPOSIUM—ALLEN AND YOSHIKAWA 185

,.- i __

3 iff"

FIGURE 4.—Meanook meteor luminous intensity and comparison with gas-cap radia*

tion for spherical bodies

ing reasons. If the body on entering the atmosphere is tumbling fairly rapidly, the mean

drag force experienced will be that of a sphere.

When the initial tumbling rate is low, it can be

shown that the body will generally stop its

rotation and, instead, oscillate about an attitude

for which it is aerodynamically stable. Now it

should be noted that stable attitudes are not

those for which streamline flow would result.

Thus rodlike or platelike shapes will assume an

attitude for which the largest dimensions are

perpendicular to the direction of motion. Such

bodies in their high-drag attitude have approximately twice the drag coefficient of a sphere.

As an opposite extreme, a right circular cone

will fly with its apex forward only if the total

cone angle is greater than about 40° of arc.

In this case the drag is about one-fourth that for

a sphere, but it should be noted that for such a

shape the conical point will promptly ablate and

hence the drag will be increased. On the average, then, we expect that the assumption of a

spherical shape would give an error in the drag

coefficient most probably less than a factor of 2.

Under the assumption that the meteor is spherical, then

For a sphere in continuum flow

7=2- (5)

thus equation (1) can be solved for the radius

opo / pV \ ,a\

r=—^— I -7-777 I * \y)

Of course the meteor density is not known,

a priori, and must be determined. Table 1

gives six values of v (not counting the extrapolated value for vm given by Millman and Cook)

and five of acceleration as a function of k.

These data can be used to obtain a general

series expression for v in the following way:

Allen and Eggers (1958) have shown that when

no mass is lost

v*=t?m(F, (7)

where k is a constant (negative). When mass

is lost during descent, as is the case for meteors,

then k must be a function of altitude—or,

more conveniently, p. Thus we may express

the velocity as

m=-irri

Pm

o ,

where pm is the meteor density.

638805—63 16

In v

8

=

so that

dtf/dh

v

2

 ''

(8)

- ••>!• «
186 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Observed data for Meanook Meteor 132 *

Epoch (t)

seconds

0

.317

.538

.980

1.0

1.157

1.4

1.423

1.732

1.8

1.909

2.0

2.042

2.086

2.2

Altitude (A)

meters

67. 59X103

52. 71X 10s

47. 12 X 10s

42. 11X103

39. 98X103

38. 21X 10s

Speed (v)

m sec"1

17. 42X103

16. 58X103

15. 45X103

13. 10 X 10s

11. 28X103

9. 16 X 10s

Luminous

intensity

253. 7

363. 1

478.5

824.0

847.5

1038. 0

1087. 0

1057. 0

602.5

501.5

353.2

240.0

310.4

405.5

37.35

Acceleration

(dv/dt) m sec~2

- 1 . 88X10»

- 4 . 02X103

- 8 . 78X103

- 9 . 97X103

-11.21X10*

•Additional observations: Two pronounced flares observed at f=0.8 sec and i=2.08 sec (fig. 4); meteoric body

observed to break in two pieces at t —1.75 sec (A=42.63X 10s m); velocity at entrance to atmosphere from extrapolation by Millman and Cook, »oo = 17.59X10I

 m sec"1.

Deduced data: entry angle Zfi=29.8° (cos ZR=0.868). Radiant power conversion: one zero-magnitude luminous intensity equals 2.73 X10"" kilowatts-m-J

.

But since the density is very nearly an

exponential function of h, that is,

(10)

where /3 varies slightly with h, then

and equation (9) becomes

(12)

Now we note that since the flight path is

essentially straight so that the vertical velocity

IB

then

so that

dh „

—=—v cos Zfi,

dv_dv dh_ 1 dv2

dt dh dt 2 dh

(13)

(14)

(15)

Thus between equations (8) and (15) one

may find the values of as many of the C coefficients as one has values for v and dvjdt, given

the variation of density with altitude. In the

calculations of this report, the 1959 AKDC

atmosphere (AFCRC, 1959) was used for p and

p+h(dp/dh). Our first attempt to find the C

values using an IBM-704 computer was unsatisfactory because severe oscillations of the

functions became evident for low altitudes. It

was surmised that this difficulty arose because

we had required equations (8) and (15) to have

continuity through the altitude 42,630 meters

(corresponding to Epoch 1.75 sec) where the

body was observed to break into parts. Accordingly, we tried employing two sets of these

equations: one above the altitude of the break

and one below. These results are reasonably

satisfactory, but it was necessary to reduce v*

from 17.59 km per second (Millman and Cook

extrapolation) to 17.54 km per second to avoid

having the radius decrease with increasing altitude at the highest altitudes. The coefficients

in equations (8) and (15) in the two altitude

regimes are:
METEOR SYMPOSIUM—ALLEN AND TOSHIKAWA 187

for h >42,630 m

(70= 0.9772322 X 10

O, =-0.5223564 X 10s

O2=-0.8908289 X 105

<73= 0.6952320 X 108

Ct= -0.3252341 X 10"

C6= 0.8007179 X 1013

C6= -0.8640033 X 10lfi

for &<42,630 m

<?o=— 0.9705839 X 10

<?,= 0.3809221 X 105

C2= -0.3075595 X 108

<78= 0.1302624 X 10"

<?4= -0.3065301 X 1013

<?6= 0.3800107 X 1015

C,=-0.1940589 X 1017

(16)

(17)

Oscillations occur also with these functions,

and it would probably be best to have allowed

similar discontinuities at the altitudes corresponding to the two observed flares (at Epochs

t—O.S sec and <=2.08 sec). However, the results obtained with the above coefficients are

certainly adequate for yielding the variation of

radius with altitude to evaluate gas-cap radiation Io and heat transfer X to be given later.

The calculated values of v, dv/dt, and the

product pmr are given in table 2 as a function

of altitude (along with the values of (3+h(df}/dh)

used), and are shown in figure 5. The observational data of table 1 are also shown as the

circled points for comparison. The calculated

product pmr shows a decrease of about 20 percent at the observed altitude of breakup.

The data of table 2 were used to determine the

radius as a function of altitude for values of

meteor density from 10,000 to 50 kg m~8. The

gas-cap radiation was then evaluated in accordance with the method indicated earlier. The

calculated values of Io are plotted on figure 4

along with the total luminous intensity observed

for the meteor. If T0 were zero, then Ia would

constitute all the radiation, and the indicated

density for the meteor would He between 1,000

and 500 kgm~3 representing one limit. To

evaluate the other limit, it was assumed that

Jacchia's (1948) value of log T O = —18.19 (in his

units) was applicable to the ablated mass-loss

rate for this meteor. From the calculated

variation of the product pmr, the time rate of

Velocity , v , km-sec"1

Deceleration,-dv/dt , km-sec'1

O IO 20 30 40 50 60 70 80

Meteor density - rodius product, fmr , kg m"f

FIGURE 5.—Observed and calculated characteristics for

Meanook meteor.

mass loss was calculated for the various assumed

densities and the luminous intensity, from the

ablated mass evaluated from the equation,

dm (18)

The sum of IQ-\-IA is plotted along with observed luminous intensity / in figure 6. This

limit indicates the meteor density to lie between

2,000 and 1,000 kgm~3. Comparing these two

limits we chose water density (1,000 kgm~8) as

the most appropriate value, and evaluated the

radius and mass as a function of altitude along

with the corresponding Knudsen numbers

(ratio of air mean-free-path to body radius)

and the Reynolds numbers (the product of the

diameter, density, and velocity divided by the

absolute viscosity). From the calculated Knudsen numbers (table 2) it is clear that the

meteor experienced continuum flow throughout

the observed part of the descent. The Reynolds numbers are so low that the flow in the

boundary layer must be laminar. With this
188 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

I I I H

I I I O

on Q H t-.* w o\vo Jt

NS o tn en d f^ nof -

HHOOHHCVIr?> tn

B

1

?

•NO ONOO IAiAIArnrj o o\c-vo t- w jo-* A ONC-VO IAIAIPINO t-ON-* evi c-rj

oooooo ooooooooooooooo

8 8 88888 88 88 8888^8 88888 888 8888888

1

T3

•a i

li IfNlA lf\NO VQNO t-t^a o ONO\O\ ONOO ON ON00 lf\

:8888888888888888888 8:

9

C\ t^ ON d

oo iTiSjo

rn en

1

 *-?

OO t— t^NO NO ITwt <n 00 Oi H

SSmuMAmIAuStnifNUMTN

t- I A co H ON t-vo IA co

- * - * - * - * CO CO CO CO CO

!£!5ScH^S

8lft«»sl8l3Sd

Q>oo cow co rH O\ t— NO t—oioaocooiAOe o IACOCO- * ON NO NO H CO.* CO H o\co

IA CTvOO CO OJ ON CVJ -* - * CU CV1 CK IA CVli?\qNOHON>HCOHpNlAr-|IAQONHCOCOH

CV1 IA ON-* ON-* HCONO tAlTNlAI^p IA3 ; O ON H CO t - Q P-^t H CO IA CO IA Oi ON O

cvl cvj e\i co co^t I A IAN 2 r-co ON O OJ COIACO O- * t-HvooNOcoHCUO N t—co V- w

HHHHHOICMdlro (n j - * irsNO I—00 oo ON O f

S- CO t— ONCO CO IA CO t— 1ACO -=»• co^t- t— H - * ON t~-NO CO IA O NO CO C—-* 1ANO ON CO ON <

tA-4; CM Q CO NO CO O NO CU C- CM VO ON >-{ CO CO r-l C— H CO CU Q> H CO Q\-* p iH O O 5-N.

-*-*-*. * COCOCOCOCVlOJi-lrHO ONONOO t—NO 4 rtH ON NO -=t OvDCVlF-OCUcOHO
METEOR SYMPOSIUM—ALLEN AND TOSHIKAWA 189

Time , seconds

FIGURE 6.—Meanook meteor luminous intensity and comparison with sum of gas-cap

and maximum ablative radiation for spherical bodies.

knowledge it is possible to estimate two limiting

values for the ratio

corresponding to ablation by vaporization on

the one hand, and fusion on the other. The

heats of ablation used were 8X106 m2 sec"2

and 1.4X109 m2sec~2 (usual values for stone),

respectively, and again y of % was employed.

The value of the heat-transfer coefficient has

two contributions, one due to radiative heating

from the gas cap and the other due to the convective heating resulting from the shear in the

laminar boundary layer. The radiative component, X<7, was calculated from the total gascap radiation as previously discussed assuming

an absorptivity of unity for the surface. This

value applies if either fusion or vaporization is

the process of ablation. This is in contrast to

the convective heating, since the convective

component for ablation by fusion, \,r, differs

markedly from that for ablation by vaporization, \,y, as discussed by Adams (1959).

For ablation by fusion, the convective heattransfer coefficient is that which would occur

for a solid body. If Lees' (1957) estimate is

used (or see Chapman, 1959),

When ablation by vaporization occurs, the

vapor which is pushed into the boundary layer

partially fends off the hot air from the surface,

thereby reducing the shear and hence the heattransfer coefficient. The ratio of convective

heat transfer for vapor ablation to that for

liquid ablation may be obtained (Adams, 1959)

as

(20)

where for the constant K a value of 0.3 is a good

average.

In table 2 values for Xcy, \?F» and X© are given,

and are appropriately combined to give the

expected limits for X/yf for ablation by vapor

run-off and liquid run-off. The latter quantities are plotted in figure 7.

Finally, the value of X/yf can be inferred

directly from the experimental data by use of

equations (2), (4), (5), and (13):

16pw cos ZR/dr

pv2 \dh (21)

0.000216

(19)

Since r varies somewhat erratically with h, the

derivative was evaluated at any altitude k by

dividing the value of r at A+1000 m less r at

k—1000 m by the AA=2000 m. The resulting

computed values from equation (21) are given

in table 2 and plotted in figure 7. Even with

the smoothing the computed values do not pro-
190 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

tib

O .5 1.0 1.5 2.0 25 3.0 3.5

Heot transfer factof.-jj xlO7, sec' m'*

FIGURE 7.—Calculated and experimental values of the heat-transfer factor for

Meanook meteor.

duce a smooth variation, but clearly it is evident that the values are reasonably close to the

computed limit for vapor ablation. It should

be noted, however, that this does not mean that

a substantial loss of surface material in the

liquid state or even the solid state does not

occur, for, as has been shown by Dean R.

Chapman in a yet unpublished work on the

ablation of tektites, even a small fraction of

ablation by vaporization serves to depress the

heat transfer by convection.

Discussion

Light.—It is clear, in the present case, that

equation (3) for the calculation of mass cannot

be used since the appropriate value of r0 and its

variation to velocity probably bear no relation to the values and variations suggested

by Opik and Jacchia. In any event, T0 would

be expected to be much less than that for the

free-molecule regime and, since even using

Jacchia's value gives the relative proportion of

ablation light to gas-cap light as low as 35 percent as shown in figure 8, the difference between

the total radiation and the gas-cap radiation

must be so small that no precision from equation (3) could be expected.

There is a disturbing trend of the gas-cap

light as compared with the observed luminous

intensity shown on figure 6, since, if we match

the two at any given point, the calculated gascap light exceeds the observed lumination at

the higher speeds, but is less than at the lower

speeds. A possible reason for this is that T0

might vary as a negative power of velocity, but

the required variation appears far more than

can be considered reasonable, particularly since

the ablation radiation in the present case must

1=0

2 A .6

Gas cap radiation fraction.

FIGURE 8.—Gas-cap radiation as a function of maximum

possible total radiation.

be much smaller than we have assumed. There

is no doubt that there can be a considerable

error in our estimates of the gas-cap radiation,

for, as noted earlier, the actual meteor body

may not be near spherical in shape and no

doubt changes in shape in the course of descent.

Also, the gas cap is well out of chemical equilibrium over most of the range, and the meteor

velocities here are beyond those for which we
METEOR SYMPOSIUM—ALLEN AND YOSHIKAWA

I si i

191

FIGURE 9.—Equilibrium gas temperature as a function of altitude and velocity.

1

1.23,000 •»

n -1

ft

11

/

r

 n

/ jj

J

J

1— i —

^ T . 12,000 V

1

n !

—

! ,-

J

h Hi i

—i

1

.4 .5

Wow lt*9U>, p. , o

FIGURE 10.—Power spectral density of gas-cap radiation for equilibrium air.

have obtained data for gas radiation, so that

the ^results given had to be extrapolated

extensively.

However, it should be noted that errors in

assessment of the gas-cap radiation may not be

the principal cause for the observed differences,

but rather the observed intensity interpreted as

the total radiation emitted may be in considerable error itself. This can be seen from the

following: In figure 9 are shown the gas-cap

temperature and density as a function of

velocity and altitude for equilibrium flow. The

heavy dashed curve shows the trajectory of

the Meanook meteor expressed in these variables. It is seen that even for equilibrium flow

the gas temperature would vary from about

17,000° K early in the entry down to about

8,000° K or less near the end of the flight.

For the actual gas flow, which is well out of

chemical equilibrium, the maximum temperature would be considerably higher. Figure

10 shows the theoretical estimates of the

power spectral density for the gas-cap radiation

in equilibrium for 8,000° K and 12,000° K

(Meyerott et al., 1960), and for 23,000° K

(Armstrong, 1959) for a gas-cap density appropriate for the Meanook meteor. This figure

shows that for wavelengths well into the
192 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

ultraviolet important contributions exist, particularly when the velocity is high. However,

the observed intensity for the meteor was

obtained from measurements essentially in the

range from 0.3 to above 0.6 micron. Thus the

observed luminous intensity approximates the

total radiation emitted only near the end of the

flight when the speed is low. In the early

portion of the flight, when the speeds are high,

the total radiation emitted must be much

larger than is indicated by the plot in figure 4.

In consequence, the disagreement may not be

as real as the present evidence indicates. In

any event, the density of the meteor is probably

less than our analysis has indicated.

Data reduction.—It was noted earlier that a

better analysis of the series solution for v and

dvjdt would have been to break the solution

(to avoid the necessity for continuity) at the

altitudes corresponding to the two observed

flares. The data, as presented by Millman

and Cook, are insufficient to allow such a

procedure. It would clearly be valuable to

attempt to reanalyze this meteor using the

original unfaired data from as many points as

there were shutter breaks on the original films.

However, the analysis presented gives results

that, in general, agree with the observed

behavior of the meteor. In particular, as

noted on figure 5, the computed values of the

radius-density product show an increase in

negative slope at the altitudes corresponding

to the flares, as would be expected. Moreover,

it was noted by Millman and Cook that when

the breakup of a meteor occurred, a small

piece was kicked forward ahead of the main

body. This could account for the unexpected

slope observed for the density-radius product

at altitudes just below the altitude for breakup.

Heat-transfer factor, X/7f.—It is of interest

to note that the experimental values for X/7f

are consistent with the observations of the

flares in that an increase in X/yf is noted near

the altitudes corresponding to the flares. However, there are several other increases noted at

altitudes where no flares were observed, but

these may result from the fact that in the

analysis the velocity function was forced to be

continuous at the flare points. The required

continuity promotes residual oscillations at

many points if it is called for at the altitudes

corresponding to the flares.

The relation of the computed vapor ablation

and liquid ablation values to the experimental

values of the heat-transfer factor looks reasonable. The actual heat-transfer factor is expected to be more nearly allied with the vapor

case even though a sizable fraction of the

ablated material is liquid, or even solid, since

the vapor blowing in the boundary layer

greatly reduces the convective-heat transfer;

thus the heat-transfer coefficient is well approximated by the calculated vapor value.

Future prospects

It is to be expected that future research in our

ground laboratories will prove very useful to

the meteor astronomer by providing better values for the total gas-cap radiation and its

power spectral density. Moreover, it should

be possible to better understand the nature of

the radiation from the ablated mass in the

future. Future work should also permit much

better estimates for the effect of blowing due

to vaporization in the boundary layer on the

convective-heat transfer. The principal limitations of the ground laboratory work in the

past have resulted from the fact that it was

not possible to reach even the lowest of meteor

speeds in the laboratory. Recently, however,

we have managed to enter the meteor speed

regime, and have made measurements of gascap radiation and ablation radiation up to

speeds of 13 kilometers per second. We do

not expect ever to be able to reach the highest meteor speeds, but we will probably improve

the present situation materially.

Dr. McCrosky recently suggested the construction of a series of optical stations in the

Mississippi Valley to track fireballs. The purpose of this system would be primarily to expedite finding the meteorites so that their radioactivity could be analyzed soon after their

arrival on earth, thus improving our knowledge of cosmic origin and environment. The

system McCrosky proposes could also, in our

opinion, provide useful tracking data to obtain

a better understanding of the heating of meteors. The analysis of Meanook Meteor 132 is

very encouraging in this respect. Clearly, the
METEOR SYMPOSIUM—ALLEN AND TOSHIKAWA 193

present methods are capable of giving the velocities and altitudes and the flight path with

about the precision required for such analyses.

Examination of the meteorite shape, mass, and

material properties would play a very important

part in such heat-transfer analyses. However,

it is evident that not only should McCrosky's

system be designed to give the best coverage

for trajectory evaluation, but also the cameras

themselves should be designed to give radiation response on the plates for a wide enough

range of wavelengths. Also, adequate spectrographic equipment should be provided. In

this way very valuable information on gas-cap

and ablation radiation would be obtained for

speeds far higher than we will probably be

able to obtain in the laboratory.

References

ADAMS, M.C.

1959. Recent advances in ablation. Journ. Amer.

Rocket Soc, vol. 29, pp. 625-632.

AIR FORCE CAMBRIDGE RESEARCH CENTER

1959. Abbreviated English tables of the ARDC

model atmosphere. Geophysics Research Directorate, Air Force Cambridge

Research Center, ARDC.

ALLEN, H. J.

1960. On the motion and ablation of meteoric

bodies. In N. J. Hoff and W. G.

Vincenti, eds., Aeronautics and astronautics, Proc Durand Centennial Conference, pp. 378-416. Pergamon Press,

New York.

1961. Problems in atmospheric entry from parabolic orbits. Journ. Japanese Soc.

Aeron. Space Sci., vol. 9, no. 85, pp.

43-50.

ALLEN, H. J., AND EGGERS, A. J., JR.

1958. A study of the motion and aerodynamic

heating of ballistic missiles entering the

earth's atmosphere at high supersonic

speeds. Report 1381, NACA.

ARMSTRONG, B. H.

1959. Mean absorption coefficients of air, nitrogen, and oxygen from 22,000 to 220,000°

K. Report LMSD 49759 (July 15),

Lockheed Aircraft Corp.

CAMM, J. C; KIVEL, B.; TAYLOR, R. L.; AND TEARE,

J. D.

1959. Absolute intensity of non-equilibrium radiation in air and stagnation heating at

high altitudes. Research Report 93,

Avco-Everett Research Laboratory.

CHAPMAN, D. R.

1959. An approximate analytical method for

studying entry into planetary atmospheres. Report 11, National Aeronautics and Space Administration.

HOCHSTIM, A. R.

1957. Gas properties behind shocks at hypersonic

velocities. I. Normal shocks in air.

Convair Zph(GP)-002.

JACCHIA, L. G.

1948. Ballistics of the upper atmosphere. Harvard Coll. Obs. and Center of Analysis,

Massachusetts Inst. Tech., Tech. Rep.

No. 2.

KIVEL, B.

1959. Radiation from hot air and stagnation

heating. Research Report 79, AvcoEverett Research Laboratory.

KIVEL, B., AND BAILEY, K.

1957. Tables of radiation from high temperature

air. Research Report 21, Avco-Everett Research Laboratory.

LEES, L.

1957. Recent developments in hypersonic flow.

California Inst. Tech. Publ. 428; also,

Jet Propulsion, vol. 27, pp. 1162-1178.

LlNDEMANN, F. A., AND DOBSON, G. M. B.

1923. A theory of meteors and the density and

temperature of the outer atmosphere to

which it leads. Proc. Roy. Soc. London, ser. A, vol. 102, pp. 411-437.

MEYEROTT, R. E.; SOKOLOFF, J.; AND NICHOLLS, R. W.

1960. Absorption coefficients of air. Report

LMSD 288052, Lockheed Aircraft Corp.

MlLLMAN, P. M., AND COOK, A. F.

1959. Photometric analysis of a spectrogram of a

very slow meteor. Astrophys. Journ.,

vol. 130, pp. 648-662.

OPIK, E. J.

1958. Physics of meteor flight in the atmosphere.

Interscience Publ., New York.

YOSHIKAWA, K. K., AND Wick, B. H.

1961. Radiative heat transfer during atmosphere

entry at parabolic velocity. Technical

Note D-1074, National Aeronautics and

Space Administration.

ZlEMER, R. W.

1960. Extended hypervelocity gas dynamic charts

for equilibrium air. Space Technology

Labs., Inc., TR-60-0000-09093.

Preliminary Notes on Some Results of Photographic

Multiple Meteorite Fall of Pfibram

By Zd. Ceplecha1

This paper is based on the double-station

photographs of the meteorite fall of Pfibram.

The details of this first photographic meteorite

fall have been published (Ceplecha, 1961).

Ten plates are available of the fall, which was

photographed from two stations 40 km apart;

the four stony meteorites that were recovered

belong to different photographed trajectories

of individual fragments.

The photographs allow the determination of

the end heights of the individual fragments into

which the meteorite was split. The velocity at

the end point can also be found by computing

the invisible ("dark") part of the trajectory.

Thus it seems to be of great importance to

derive theoretically the connections among

different parameters at the end of the visible

("light") trajectory of a large body. This is

simpler than studying the visible trajectory

itself, because its end can be taken as the beginning point of the invisible trajectory.

The end height of the visible trajectory

The thickness of the meteorite crust is usually

very small relative to the dimensions of the

body itself. Thus we can solve the problem by

assuming a semi-infinite space full of meteorite

mass, the boundary of which is a plane. Air

of density p moves with velocity v perpendicularly to the surface of this boundary plane.

Let the fraction A of the total kinetic energy

of the moving air be transferred through the

boundary plane into the body. Thus A is the

heat-transfer coefficient. The energy in the

body itself can be transferred to the air only by

heat conduction. The radiation from the sur1

 Astronomical Institute of the Czechoslovak Academy of Sciences,

Ondfejov, Czechoslovakia.

face is negligible in the range of temperatures

under consideration.

We measure the distance x from the boundary

plane into the body, and make x=0 on the

boundary plane. Let T be the temperature of

the body in the atmosphere as a function of

the time t and the distance x. Let To be the

temperature of the whole body after a very

long time; To is, of course, equal to the temperature of the undisturbed air. We can then

define the temperature T according to the

equation

T=T0+r. (1)

If X is the heat conductivity, 8 the density, and

c the specific heat of the body, we can define

the coefficient /8 by the equation

V

(2)

Then we can formulate our problem by the

well-known equation of heat conduction:

I

dz2 (3)

It is useful to choose the zero point of the

time at the moment when the light trajectory

ends; then

tB=0. (4)

The initial condition for r can then be written in

the form

rjr, (5)

where rB is the temperature at the surface when

the light trajectory ends. The end condition,

from equation (1), is then

T(«,x)=0. (6)

195
196 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

The boundary condition is given by the

equation

This is the complete mathematical formulation of the problem. The complete solution

of equation (3) with the additional conditions

in equations (5), (6), and (7) is not possible in

analytical form. But it is possible to solve

these equations exactly in analytical form if

we are satisfied with a solution at one point only.

This point will be the point E, where the light

trajectory ends.

The value pi? in equation (7) is an unknown

transcendental function of time. An analytical

function of time can be substituted on the

assumption that both these functions are

identical in their values and first derivatives.

Then the whole problem can be solved by analytical functions.

Let us take

(8)

where the subscript E denotes values on the

surface of the body at the end of the light

trajectory, and A: is a coefficient which must be

determined. If we use the exponential law of

the air density

p=Poe~ M, (9)

then the condition of equal values and derivatives together with the drag equation will yield

for k the equation

k=bvB cos zB—3T — pBvB. (10)

m

Here m is the constant mass and s the constant

area of the cross-section; T is the drag coefficient,

and zB the zenith distance of the radiant. Now,

if we replace the right-hand side of equation (7)

by equations (8) and (10), then equations (3), (5),

(6), and (7) can be solved. Without going into

details of derivation, I write the solution directly

_ 2\(-Ar)1/2'

(11)

where k is given by equation (10). This is the

exact solution, but it is valid for one point only.

However, we are nor interested in solutions at

other points. Equation (11) contains the numerical factor 2, which originated from equation (7), under the assumption of a plane boundary. The energy in this case goes in only one

direction. In reality, the energy is distributed

over all directions in space. We shall assume

uniform distribution of the energy. This

assumption is supported, for the jEJ-point, by

the fact that there was no difference in the

thickness of the crust between the front and the

back of the Velka meteorite (one of the Pfibram multiple fall). Then the numerical

factor 2 in equation (11) will be four times

greater and we arrive at the equation

_ | _

8\(-k)1/2'

(12)

which is valid if we can neglect the curvature of

the meteorite surface as a factor in the concentration of the heat conducted inwards. This

is possible, because the dimensions of the crust

of the Pfibram meteorites are smaller by three

orders of magnitude than the dimensions of the

bodies. Numerical computations of the heattransfer coefficient presented in the following

section are based on equation (12).

The solution of the problem contains the

term (—k)m, which of course must be real.

This is possible only if the equation

P*>

b cos z (13)

3rm

is valid. Equation (13) is a very good criterion for testing whether a meteorite of mass

m can follow a fireball that ends at a height

hB. The numerical values obtained from equation (13) are presented in table 1.

TABLE 1.—Critical and end heights (km) of a fireball.

When h E of the fireball is less than the presented value,

a stony meteorite of mass m can follow (for iron meteorites the heights are S or 4 km lower)

COS ZB

1

0.5

0.1

mass m

100 gr

37

42

55

l k g

32

36

48

10 kg

27

31

42

100 kg

23

27

37

1,000 kg

17

22

32
METEOR SYMPOSIUM—CEPLECHA 197

The heat-transfer coefficient

Equation (12) can be used for the computation

of the heat-transfer coefficient A, if other

values are known. In the case of the Pfibram

meteorites, we have pB and b from the end

height Us which was directly measured from

the double-station plates. The zenith distance

of the radiant zR was also measured directly.

The end velocity vB can be computed from the

dark-flight distance of meteorites, but the value

is only provisional at present, because the

wind-tunnel measurements have not yet been

completed. The same holds true for the product r— (Ceplecha, 1961). The surface ternTYh

perature at the beginning of the light trajectory

of a meteor was computed by Levin (1956).

It is evident that this value, giving the limiting

conditions for the rapid evaporation, is the

same for the end of the light trajectory. The

density of the meteorites was measured, but

the measurements of the heat conductivity are

not yet finished. The heat conductivity X is of

course the main factor in equation (12), and

strongly determines the numerical results. We

have not yet obtained values for the heat conductivity from direct measurements, and therefore use the mean value for stony meteorites

as given by Opik (1958). Thus the numerical

values given in tables 2 and 3 must be taken as

provisional, and are accurate to an order of

magnitude only.

TABLE 2.—Computed end-point velocity VE (kmfsec).

From equation (12), with the following constants:

TE =2.1X10 S; X=2X105; c=lX107; 5 = 3.6; cos

zR=0.683

Meteorite

Luhy

Velkii

HojSin

Draikov

Heat-transfer coefficient A

0.01

4.0

5.2

5.8

6.5

0.005

5.3

6.9

7.7

8.5

0.002

7.6

9.9

11.1

12.3

0.001

10.1

13.1

14 6

16.3

TABLE 3.—Computed thickness d of the meteorite crust

(m=1.5X10s, A = 0.002)

Meteorite d(cm)

Luhy 0. 011

Velkii . 009

HojSin . 006

DraJkov .015

Equation (12) was used to compute the end

velocity vB, with different values of A, shown

in table 2. The end velocities of the same

meteorites can be estimated from the computed

and the observed dark-flight distances. The

end velocity for the Luhy, Velkfi, and Hojgfn

meteorites was provisionally estimated to be 7

km/sec, and for the DraJkov meteorite to be 11

km/sec. Thus it is evident from table 2 that

the heat-transfer coefficient at the end of the

light trajectory was about 0.002 or 0.003.

The thickness of the meteorite crust

The solution of equations (3), (5), (6), and (7)

can be presented in a more general form if we

are not interested in the surface temperature

alone. If r(x) is the temperature in the body

at the distance x from the surface, then the

equation

T(x)=rJfexp[-(-A:)1/2x/i8] (14)

is valid. If we use the temperature of the

melting point rm, the thickness d of the meteorite crust follows from equation (14):

d=

0 log I*j

0.434 (-£)1/2'

(15)

The theoretical thickness of the crust for

A=0.002 is about 0.1 mm for all the meteorites

of the Pffbram fall. The numerical data are

presented in table 3. The measured thickness

of the crust for the Velka meteorite is between

0.18 mm and 0.29 mm—about twice or three

times the theoretical value. This agreement

is quite good, as many provisional values were

used in the computations.

References

CEPLECHA, Zd.

1961. Multiple fall of Pffbram meteorites photographed. 1. Double-station photographs

of the fireball and their relations to the

found meteorites. Bull. Astron. Inst.

Czechoslovakia, vol. 12, pp. 21-47.

LEVIN, B. J.

1956. The physical theory of meteors and

meteoric matter in the solar system.

Publ. House Acad. Sci. U.S.S.R., Moscow.

OPIK, E. J.

1958. Physics of meteor flight in the atmosphere.

Interscience, New York.
198 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Abstract

The theory presented in this paper can be applied to meteorite falls. The heat-transfer coefficient at the end

point of the light trajectory and thickness of the meteorite crust can be computed. The preliminary value of the

heat-transfer coefficient at the end points of four Pfibram meteorites was estimated to be about 0.002 or 0.003. The

definitive numerical values will be published in the Bulletin of the Astronomical Institute of Czechoslovakia in a

series of papers entitled "Multiple Fall of Pffbram Meteorites Photographed."
Results from an Artificial Iron Meteoroid at 10 km/sec

By R. E. McCrosky* and R. K. Soberman2

The results described in this paper are derived

from a successful attempt to produce a meteor

in the upper atmosphere with a body of known

mass and composition. This was accomplished

by accelerating a small pellet of stainless steel

by an air cavity charge attached to the nose of

a high-speed re-entry rocket. The experiment was made possible only through the

cooperation of a number of organizations.

The test vehicle was a Trailblazer I rocket,

developed by the Applied Material and Physics

Division of the National Aeronautics and

Space Administration at Langley Field, Va.,

for use in a re-entry research program conducted

by the Massachusetts Institute of Technology

Lincoln Laboratory. The optical observations

described were made by the Harvard Meteor

Project with considerable technical assistance

from Lincoln Laboratory. The air cavity

charge was constructed and tested by the Air

Force Cambridge Kesearch Laboratories.

The primary purpose of the experiment was

the determination, to within narrower limits

than previously available, of the efficiency with

which the kinetic energy of a meteoroid is

transformed to luminous energy in the photographic region. From a simple inspection of

meteor spectra, one can ascertain that a great

majority of the meteor luminosity is produced

by the excitation of the meteoric atoms, particulary for the luminosity in the photographic

(3500 to 5000 A) region. Whether the ablation is by direct vaporization, melting, or

fragmentation, the meteoritic material must be

vaporized before appreciable luminosity is

produced. The vaporized atoms are then

excited by collision. The instantaneous intensity of a meteor must be related to the rate of

• Harvard College Observatory, and Smithsonian Astrophyslcal Observatory, Cambridge, Mass.

> Geophysics Eesearch Directorate of the Air Force Cambridge Research Laboratories, Bedford, Mass.

mass loss. Presumably the velocity of the

meteor will also influence the rate of luminous

energy production. As a minimum statement

of the problem one can write:

dm

(1)

where / is the instantaneous intensity, m the

meteoric mass, and /(») some function of the

velocity. The data obtained from observations of natural meteors are consistent with an

expression of the form

/=TU ~

or

T T0 dm ~

I=-^-dt*'

(2a)

(26)

where T0 is the luminosity coefficient and T=T0 V

is the ratio of the observable luminous energy

to the kinetic energy.

Certainly other factors besides the mass loss

and velocity also influence the luminosity,

notably the composition of the meteoroid and

its aerodynamical properties. But at the

present time one must be content, generally,

with the simplified theory implicit in equation

(2). The considerations of additional factors

must await a determination of such basic

parameters as the meteor mass and density.

Equation (2b) may be integrated to give

m=mp=— I -5 dt- (3)

Since / and v are observable quantities, the

mass of the meteor can be determined if T0 is

known. Masses determined from the observed

luminosity are referred to as photometric

masses (mp). A number of estimates of this

or related quantities are available (Whipple,

199
200 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1943; Cook, 1955; Opik, 1955; McCrosky, 1961;

Cook, Jacchia, and McCrosky, in this symposium

(p. 209); Lazarus and Hawkins, in this symposium (p. 221). However, the scatter in the

values is extreme; a factor of more than 10a

separates the highest from the lowest estimate

and this uncertainty, or more, enters essentially into all mass determinations of meteors.

The mass of a meteoroid can also be determined, in principle, from the observed deceleration. The drag equation,

de_ rAd~2/3pv

2

dt~ m

1

'

3

 ' (4)

includes as unknowns the drag coefficient T,

the mass, and a shaped factor A. Here

AS~2/3=Am~m, where A is the presentation

area and 8 the density of the meteoroid. The

atmospheric density p is known to sufficient

precision at meteor heights. In view of the

large uncertainties of m and 5, one is prompted

to assume reasonable values for T and A and

solve equation (4) for the unknown:

If the meteoroid density were known, one

could determine a "dynamic mass" (md) from

equation (5). There is considerable evidence

(e.g., see Whipple, 1955; McCrosky, 1955;

and Jacchia, 1955) that the majority of

meteors, those of cometary origin, are extremely

fragile. The weak structure may be associated

with bodies of low density and one cannot

safely assume that the density of these meteoroids is that of meteoritic stone. Until independent measures of meteor densities are

made, and this is not immediately likely,

equation (5) is of limited value in making estimates of masses.

If the mass can be determined from equation

(3), it would appear that the density can be

derived from equation (5). However, some

caution is required here. The dynamical mass

represents the mass of the major meteoroid

body, whereas the photometric mass refers

to that portion of the entire meteoroid that has

not yet produced appreciable luminosity (i.e.,

that part which is not yet vaporized). If the

entire mass consists partly of a parent body and

partly of solid or liquid fragments, these two

masses should not agree and are not interchangeable. If fragmentation were the only

important factor, the photometric mass would

never be smaller than the dynamic mass and

equation (5) would yield a lower limit on the

density. Unfortunately, however, mp may

be underestimated. We have assumed in

equation (3) that the entire mass has been

vaporized by the end of the trajectory. This

condition is reasonably well met for highvelocity meteors, but for low-velocity meteors

there may be a substantial terminal mass

that is not accounted for in mp. For this

reason, md may exceed trip if fragmentation

is absent, and the derived value of 8 would be

an upper limit.

To summarize, observations of natural meteors have not yet yielded reliable data on the

luminous efficiency, meteor masses, or meteor

densities. The present experiment was intended to supply a reliable value of the luminous

efficiency of one meteoric element, iron.

The experiment

The Trailblazer I rocket (see pi. 1) is normally

a 6-stage vehicle; the first three stages hit a

velocity package (the final three stages) to an

altitude of approximately 300 kilometers and

these three stages fire downward in sequence.

The last, or sixth stage, is a 5-inch spherical

rocket motor which, after burnout, enters the

atmosphere at 6 or 7 km/sec and serves as a

test object for re-entry studies. In the case

of the Trailblazer I used for the meteor experiment, an air cavity charge was mounted on

the 5-inch rocket motor as a seventh stage of

propulsion (see pi. 1). This explosive projectile accelerator is shown in plate 2. It

consists of a chemical delay fuse, a "tetryl"

booster and a cylindrical charge of plastic

bonded RDX molding explosive. The air

cavity in the RDX is sealed by a 5.7-gram

pellet of Stainless Steel 304. When ignited,

a plane detonation wave—utilizing the air

in the cavity as a buffer—propels a portion of

the steel pellet forward with a velocity of about

4 km/sec. These projectiles have been recovered intact in the laboratory to determine

their mass. Such a recovered projectile is

shown, next to an unfired pellet, in plate 2.
McCROSKY AND SOBERMAN PLATE 1

Left, Trailblazer I-G 7th-stage rocket. Right, 6th-stage spherical rocket engine and 7th-stage gun.
Top, 7th-stage pellet before and after detonation. Bottom, Disassembled 7th-stage gun showing test pellet.
METEOR SYMPOSIUM—McCROSKY AND SOBERMAN 201

BEFORE

EXPERIMENT

AFTER

EXPERIMENT

I 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4 7 4.8 4 9

VELOCITY (KM/SEC)

FIGURE 1.—Velocities achieved by air cavity charge during

ground tests.

The resultant velocity and mass of these test

projectiles are shown in figures 1 and 2. All

the charges referred to in these figures, as well

as the charge utilized in the experiment, were

fabricated in an identical manner from the

same batch of materials

In producing the artificial meteoroid, the

air cavity charge was to be fired shortly after

burnout of the 5-inch rocket motor at an altitude of 195 kilometers.

The seven-stage Trailblazer was fired at 00h

56m 20' E.S.T. on April 21, 1961. The re-entry

of the steel pellet was observed visually at

01h 02m 00B by many observers. It was photographed by the Super-Schmidt meteor cameras

at the Arbuckle Neck, Va., and the Eastville,

Va., stations of the M.I.T. Lincoln Laboratory; and also by smaller cameras operated by

the National Aeronautics and Space Administration at Eastville, Va., and at Coquina

Beach, N.C. The re-entry of the sixth stage

was also observed visually and photographically.

Since it was conceivable that the meteor

would be near or below the observable threshold, duplicate observations were made whenever possible. For this reason we relinquished

the chance of spectrographic observations

with the Super-Schmidt equipped with a prism.

Observational results

Trajectory.—The probability that the observed

meteor was of natural origin and not the result

of the experiment is small but must be con638805—63 17

8EF0RE

EXPERIMENT

AFTER

EXPERIMENT

2.1 2.2 2.3

MASS (GRAMS)

FIGURE 2.—Post-detonation masses of air cavity charge pellet

determined from ground tests.

sidered. The submeteoric velocity (see table

1) of the pellet, although not intentional, is

virtual proof of the origin of the body. Furthermore, an upward extrapolation of the

trajectories of the sixth and seventh stages

indicates a coincidence of these objects in space

and in time that agrees, to within the accuracy

of the observation, with the position and time

at which the seventh stage was intended to

fire. The photographs certainly refer to the

seventh stage pellet.

The photographs were reduced by the standard precision method described by Whipple and

Jacchia (1957). The summary of the results

are given in table 1. We followed the usual

meteor analysis procedure and, by least squares,

fitted the observed distances D along the trail

by an equation of the form

D=a+bt+cekt. (6)

The values of the constants, and their probable

errors, are included in table 1. D and t take

the value zero at the beginning point.

Photometry.—The same photometric techniques described by Whipple and Jacchia have

been used to determine the meteor light curve.

Each dash (shutter opening) of each SuperSchmidt trail was compared with trailed images

of stars in the Harvard Standard region at

5= + 15°, a=75°. The comparison film had

been obtained earlier in an excellent (New

Mexico) sky. In addition to the usual corrections for reciprocity failure, the relative trailing

rates of star and meteor, and the distance of
202 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Trajectory data derived from Super-Schmidt

photographs of re-entry pellet

Duration

Maximum Mv,

Velocity at beginning

Beginning height

End height

Beginning range

End range

Zenith distance at midpoint

Radiant (1950)

Zenith distance of radiant, ZR

Constants of equation (6)

a= 0.012±0.020 km

6= 9.787 ±0.046 km/sec

c= 2.8X10-«±0.3X10-*km

k= 12.5 sec"1

0. 77 sec

-0. 4

9. 8 km/sec

69. 4 km

62. 6 km

254 km

254 km

76°

a=204?5

5= 37?5

15°

the meteor, very considerable absorption corrections were also indicated. The sky conditions at the time of the experiment were

particularly good for the locale, but the observations were made at a low elevation. Calibration photographs of the re-entry region were

made, with each Super-Schmidt camera, within

minutes after the event to provide for these

absorption corrections. The cameras were

kept stationary for these exposures. About

20 star trails on each Super-Schmidt calibration

film were compared with star trails on the

comparison film. The calibration stars were

chosen at about the re-entry azimuth and at

zenith distances from 48 to 85 degrees. True

apparent photographic magnitudes for these

stars were taken from the Henry Draper

catalogue, and the apparent absorption values

were fitted by least squares to the equation

(7)

where Z is the air mass above sea-level at the

zenith distance of the star. The observed

values fit the equation over the entire range of

the zenith distance with a mean scatter of 0.3

magnitude. Some of this scatter is certainly

due to errors in the Henry Draper magnitudes.

We obtained the following values for the two

stations:

a b

Arbuckle Neck 0. 17 0. 30

Eastville 0.77 0.24

The nonzero values of the constant a can be

interpreted as a difference in the film sensitivities

between the comparison and the calibration

films. However, the value of the air mass

coefficient is surprisingly low for a sky at sea

level on the east coast. Perhaps this should

be attributed, along with the nonzero value of

a, to a nonuniform sky that was relatively poor

near the zenith because of local haze but

degrading less rapidly than normal at increasing zenith angle. The cause of this slightly

anomalous behavior, whatever it might be,

does not concern us. The re-entry film and

comparison film were identical emulsions exposed on an identical sky. The photometric

measures of both re-entry and calibration

films were made against the same comparison

film. Thus our "absorption" measures represent corrections that must be applied to the

re-entry film whether these departures result

from actual absorption or from changes in

system sensitivity.

The corrected measures are plotted in figure

3. The agreement between the results from

the two stations is generally excellent. The

free-hand curve drawn to the points has been

taken to be the true light curve for the remainder of this analysis.

Luminous efficiency

Equation (3) gives the luminous efficiency as

T JL dt> (8)

where T is the duration of the meteor. We

will assume at the outset the mass to be 2.2

grams, realizing that the terminal mass may

not be negligible for this pellet and that,

therefore, the luminous efficiency derived will be

a lower limit. The intensity / is given by the

light curve. We have included in the integrated intensity those extrapolated regions at

the beginning and the end of the light curve

when the meteor was fainter than film limit.

The intensity as used here is defined by:

MM =-2.5log/. (9)

The velocity at the end of the trajectory is

rapidly decreasing and not particularly well

determined. The formal solution of the trajectory suggests a velocity of 5 km/sec at T=

0.75 second. If this velocity is accepted,
METEOR SYMPOSIUM—McCROSKY AND SOBERMAN 203

the contribution to the integral in the region

from 0.7 to 0.9 second becomes inordinately

large and unrealistic because of the uncertain

extrapolation of the light curve and the poorly

determined velocity. If one arbitrarily sets

the velocity at 6 km/sec whenever the formal

solution yields a lower value, one obtains

To=8.6X10~19

 (cgs and MPg). If instead of a

limiting velocity of 6 km/sec, one chooses

8.5 km/sec (the point on the descending branch

of the light curve for which the contribution of

I/i? first exceeds that of the previous integration step), then TO=6.6X1O"19

 (cgs and

Mpg). We will take

T0=8X10-16(cgs and Mpt) (10)

as the observed value in our discussion.

One must clearly recognize the limitations

attached to this value. It is a lower limit to

the efficiency of stainless steel at velocities of

about 10 km/sec. In attempting to derive

other values from this, one must enter areas of

speculation. In the following sections we will

investigate three corrections that are necessary

to convert the value in equation (10) to a luminosity coefficient valid for meteoric material at

10 km(sec. The corrections cannot be derived

without assumptions. We offer the following

analysis as a "best estimate" for those who may

require it. If the mass-luminosity problem

of meteor physics is to be solved by the present

experimental techniques, observation of a

number of materials at several velocities will

be necessary.

Correction jor the composition of the pellet.

—The choice of pellet material was dictated by

the physical properties rather than by the

chemical composition of the metal, and for

this reason the pellet composition does not

match either meteoritic iron or the metallic

components of meteoritic stone. A comparison

of the major constituents of these materials

relative to the iron content is given in table 2.

TABLE 2.—Composition of various materials relative to

Fe

Cr

Ni

Mn

their Fe content

Stainless

304

100

28

15

3

Met.

stone

100

1

5

1

Met

iron

100

trace

9

-0. 5

0

0.5

1.0

-

-

S 1 I

c

o

/

 + \

/ \

1

+ SS

o SK

\

\

\

0 .1 .2 .3 .4 .5 .6 .7 8 .9

t (tec)

FIGURE 3.—Light curve of the artificial meteor.

The contribution of both Ni and Mn to the

luminosity is certainly small and, in any case,

is probably comparable to the contribution of a

similar mass of iron. However, the gross discrepancy in the relative abundance of Cr is a

matter for concern. To derive a value for the

luminous efficiency of iron alone, one must

first know the ratio of the efficiency of Fe to

that of Cr. A few Cr I lines are seen in the

best spectrum of a low velocity meteor. They

are generally blended with the iron lines which

are far more prevalent. If one accepts that the

Cr/Fe ratio found in chondritic meteorites or

in cosmic material generally (^1%) is also

valid for cometary meteoroids, then the available data on meteor spectra and on the absolute oscillator strengths of the important

spectral lines of the two elements suggests that

the luminous efficiency of Cr does not differ

enormously from that of Fe. For the present,

we prefer the assumption that T0(Cr)=T0(Fe),

and that the value given in equation (10)

for the steel pellet is representative of pure

iron. If, instead, we assume as probable

extremes either that T0(Cr)=l/10r0(Fe) or

To(Cr) = 10T0(Fe), then the corresponding values for ro(Fe) become 1.0X10"18

 and 2.9X10"19,

respectively.

Correction jor terminal mass.—The rate of

mass loss from a nonfragmenting meteoroid is

proportional to the energy flux and inversely

proportional to some energy of ablation f (heat

of vaporization or fusion), and is given by

dm (ID
204 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

where A is the heat-transfer coefficient. Dividing equation (11) by equation (4) and integrating one obtains

%=m0 exp I —| (fljj—vtyl (12)

where <r= K^Z &Q& the subscripts refer to conditions at two points on the trail. Let m0, v0

refer to the beginning of the trail, and TO/, vf

to the time when all sensible vaporization has

ceased. Then the unvaporized terminal mass

is given if vf and a are known. The correction

to T0 (Fe) can be appreciable if A is as low

as 0.3, or if vr is as high as 7 km/sec. We require estimates of both of these quantities.

The estimates will necessarily be rough, and in

making the estimates we will lean towards an

underestimate of the terminal mass. The corrected luminosity coefficient, therefore, will

remain a lower limit.

Vaporization of natural meteors is known

to occur at velocities as low as 8 km/sec, and

probably continues at still lower velocities.

Some estimate of the minimum velocity vf can

be obtained by requiring a balance between

the collisional heating and the radiation loss.

We have

(13)

or, since the equilibrium temperature term To*

is negligible,

where /9 is the emissivity and this a is the

Stefan-Boltzmann constant. It appears that

the expression is independent of the body size

but, in fact, A varies with the flow regime and

is a function of the body size and of p. Anticipating a later result, we will assume a body

radius r = 1 mm and compute A at the end point

altitude of 62.6 km (p=2.6XlO~7 gm/cm3) from

the relationship given by Probstein and Kemp

(1960),

'

2

(15)

where L is the mean free path in air. From

equation (15) we obtained A«0.7.

Levin (1956) suggests that intense vaporization will occur at temperatures above 2000°—

2800° K. We will assume the higher figure as

a conservative value for our purpose. Handbook values for the emissivity of liquid steel

are about 0.28. From equation (14), vf=3.5

km/sec. If instead we take T=3500° K, the

vaporization temperature of iron, vf=4.7 km/

sec. The distinction between these two values

is hardly noticeable in equation (12). Let us

take »/=4 km/sec.

The determination of an appropriate value

for <r is more critical and not as straightforward as the determination of vf

 for two reasons.

First, the heat-transfer coefficient A is not well

known. Second, since our concern is with the

unvaporized remainder, we must investigate the

vaporization history of any droplets removed

from the pellet—the mass loss of the pellet

itself will not necessarily represent the amount

of material vaporized. With the aid of several plausible assumptions it is possible to surmize the general mass-loss history of this particular pellet. In addition, some observational

verifications of aspects of the presumed history

are available and will be summarized at the

end of this section.

We suppose the following sequence of events:

(1) The sixth stage of the Trailblazer has a

spin about the flight axis of 36 rps. The pellet

partakes of this motion plus any perturbation

introduced by the detonation wave of the

seventh stage. These latter effects have not

been adequately observed, but they are thought

to be small. We assume that the most likely

configuration for the pellet is a spin-stabilized

motion about the flight axis (a stable position

for supersonic flight even without spin) and

therefore about the minor axis of the pellet.

(2) The pellet is heated, to an unknown

extent, by the ejection process. In the ground

tests, only a minute fraction of the material

on the rear surface showed signs of melting;

the front surfaces were essentially unaffected.

However, the material has been "worked" and

some modest temperature rise (100° C?) must

occur at this time.

(3) Free molecular flow prevails from ejection to an altitude of about 85 kilometers.

In this region the heat-transfer coefficient A

is near unity and the body is heated further.
METEOR SYMPOSIUM—McCROSKY AND SOBERMAN 205

It acquires about 10 percent of the energy

needed to melt entirely. Conduction prevents

any melting of the front surface. Radiative

cooling is negligible.

(4) The major heating occurs in the continuum flow regime below 85 kilometers. Some

melting must occur before the onset of luminosity. This melt may be spun off, blown off,

collect at the edge, or creep to the rear surface.

Complete melting is conceivable if sufficient

heat is transferred to the rear surface by the

flow. It is more likely that melt collecting on

the edge begins to be removed by drag and

centrifugal forces. The mass-area ratio of

these nearly spherical drops will be similar to

the major body, and little differential deceleration will occur.

(5) Eventually complete melting must occur.

Whether the remaining liquid mass is stable or

not depends on the drag load, the angular

momentum, and the restoring force of surface

tension. The drag load increases through the

first half of the trajectory but, in compensation,

the angular momentum decreases and the surface tension increases as the body sheds droplets.

(6) If the body is stable, mass loss by melting

will cease and the body, after an interval of

further heating, will begin to vaporize strongly

until the velocity is sufficiently reduced. If

the body is unstable, it will break into droplets

which will continue to vaporize until the

velocity vf is reached by each droplet.

The beginning of luminosity must be accompanied by either (a) vaporization from the

surface of the pellet, (b) vaporization from

small droplets thrown off from the pellet, or

(c) fragmentation of the pellet into some very

small particles. We discard (c) as improbable.

If (b) is important, (a) does not occur appreciably; for if the pellet is losing mass efficiently

by melting, its temperature cannot approach

that necessary for vaporization. To demonstrate that (b) is a possible mechanism, we

must show both that the surface can have

melted and that there was sufficient force to

remove droplets against surface tension. The

geometry of the pellet is a determining factor

for each of these conditions.

The shapes of pellets recovered on the firing

range are roughly that of one-half an oblate

spheroid with the plane surface leading. The

major axes are of the order of 12 mm and the

semi-minor axes about 3 mm. The body may

also be reasonably well characterized as a

cylinder 12 mm in diameter and 2.5 rcym thick.

Consider a hemispherical drop, of radius r,

on the edge of a cylinder, of radius a, spinning

at a rate «. This drop will be thrown off when

the centrifugal force exceeds the surface tension

force, or when

(16)

where S is the surface tension. For steel

(8=1.2Xl& dynes/cm and 5=7.9 gm/cm3) the

limiting value of r is about 1 mm. That is,

the droplet need have a diameter only comparable to the thickness of the pellet to be

unstable against centrifugal force. Spraying

will certainly occur whenever molten material

reaches the edge. In addition, the drag force

on the drops will enhance the spraying process.

The conduction of heat inward from the

leading surface will delay melting for a time.

The solution for the heat transfer within a

cylindrical meteor entering an exponential atmosphere has been given by Levin (1956), and

is applicable here. For a thin cylinder of thickness D and conductivity X, with the major

area presented to the air stream, one finds the

temperature to be

e2x/x°+1

where W(t)——£— is the heat flux per unit area

at time t, and

depth given as

is a characteristic heating

8cv cos

/3 is the scale height of the atmosphere, c is the

specific heat of the material, and ZR is the

zenith distance of the radiant. For Stainless

Steel 304, X=2XlO6 ergs/cm sec degree and

c=5XlO8 ergs/gm degree.

Using these values, one finds that if A=0.3,

sufficient energy to raise the surface to the

melting temperature will have been introduced

by the time the pellet becomes visible. Since
206 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

A is almost certainly considerably larger than

0.3 (equation (15) gives a value of A«0.5 at

70 km), some melting must have occurred. We

deduce that initial mass loss is due to melting

and spraying. The droplets are small enough

to be nearly in free-molecular flow and are subject to a heat-transfer coefficient of near unity.

This form of spraying may continue until

the pellet is completely melted, or until sufficient angular momentum has been shed with

the droplets. Various attempts to describe

the mass-loss phenomena in sufficient detail

to distinguish between these two events have,

not unexpectedly, been unsuccessful. However,

the observed light-curve offers a clue, which

although indefinite, cannot be ignored. At

t=OA second (see fig. 3) the intensity subsides

temporarily. This is seen on Super-Schmidt

films taken from stations separated by 50

kilometers. The decrease is certainly real and

not the effect of uneven atmospheric absorption.

Compared to the light curves of natural meteors,

it is a most unusual event. We suspect that

this represents the time when spraying ceased

or decreased markedly, and that the delay in

the light-curve represents the time required

to melt the remaining solids. At this time,

at least half of the initial mass remains in the

pellet since half of the luminosity is yet to be

produced. An approximate analysis suggests

that the molten mass might be stable against

the flattening brought on by the rotation, but

it certainly will not be stable against distortion

by drag. Applying the results of an analysis

given by Opik (1958) on the deformation of

liquid droplets, one finds that a one gram mass

of liquid iron will initially be flattened to an

oblate spheroid of semi-minor axis

=0.04 cm, (19)

and semi-major axis

a=(3m/4ir5&)l/2=0.9 cm. (20)

In these computations we have used the value

of 0.5 for the drag coefficient and the atmospheric density at 65.7 km (1.8X10"7

 gm/cm3).

Opik suggests also that if a/6>4, the droplet

will be unstable and a breakup into droplets

of dimension a/b=2 will occur, where b is given

by equation (19). This formulation predicts

that the droplet disintegrates into about 102

pieces of a=l mm. Assuming that these particles act independently from the incoming

air stream, equation (15) gives A«0.8. In

all probability the effective body size for each

of the particles is larger than its physical

dimension since the cluster of droplets will

act on the air stream in concert to some extent.

But since this value of A is an upper limit, it

will yield a lower limit in the correction to the

luminous efficiency, which is what we seek here.

From the above discussion we arrive at the

following best estimate for the terminal mass:

(1) The first half of the mass is introduced

as small droplets by spraying at essentially

the initial velocity of the meteor and ablates

with A« l (o-=7X10-12) until the velocity

of vr is reached. For this computation we

have used the heat of vaporization of iron,

6.4X1010 ergs/gram plus the energy required

to raise the melt from 1800° to 3500° K,

1.1X10"10 ergs/gram. We have presumed free

molecular flow and therefore have used F=l.

Less than 1 percent of the mass remains at

4 km/sec.

(2) For the droplets formed by the disruption

of the liquid body we have used A=0.8 and

F=0.5 as characteristic values for continuum

flow. Then <r=lX10~". For this portion

of the original mass, the terminal mass is again

negligible.

No significant correction for the value of

luminous efficiency given in the preceding

section is necessary. The above analysis is

dependent on the assumption of a specific

and unusual form of mass loss, but one which

can be defended in its broad outline. We give

here, without computations, four observations

that tend to substantiate the assumptions:

(1) We have already shown that the beginning height of this meteor is consistent with

the assumed re-entry geometry. We believe

that, without the rapid rotation, the beginning

point would have been delayed appreciably.

Our estimates of the beginning point of the

visible trajectory before the experiment were

based on an observation (Halliday, 1960) of

a natural iron meteoroid. The rotation was

ignored. We used an empirical law (McCrosky,

1955) for the beginning height of meteors

Pbe« inconstant, and scaled from Halliday's
METEOR SYMPOSIUM—McCROSKY AND SOBERMAN 207

example (altitude, 69.4 km.; velocity, 13.4

km/sec) to obtain the estimate of the beginning

point. In fact, the natural and simulated

meteors appeared first at the same altitude

in spite of a difference factor of 2 in the fl3

term.

(2) We have assumed that half of the mass

is ablated at t=0A second. This assumption

is found to be in good agreement with equation

(15) if it is supposed that the body loses mass

from both the front surface and the edges in

such a fashion as to keep constant the shape

factor, A. If, as extreme alternatives, it is

assumed that the body loses mass only at the

edges, or only from the front surface, equation

(15) is reasonably well validated.

(3) The duration of the dip in the light curve,

about 0.15 second, is comparable to the time

required to liquefy one gram of the material if

it is near the melting point and if the heat

transfer coefficient is correctly given by equation (15).

(4) The velocity near the end of the trail is in

general agreement with that expected from

droplets of 1 mm radius introduced into the

atmosphere at £»0.5 second.

Correction for composition of meteoroids.—

Spectra of low velocity meteors show that most

of the luminosity observed on a blue-sensitive

emulsion arises from iron line emissions,

particularly from the

 5D-6D° and 6D—8

F°

transitions. Thus, a determination of the

luminous efficiency of iron leads directly to a

determination of the luminous efficiency for

meteoritic material if the relative iron content

of the meteoroid is known. The abundances

in iron and stony meteorites are, of course,

known. But no reliable information exists on

the composition of the most common body, the

cometary meteoroid. It is plausible that the

heavier elements and oxygen occur in the same

ratio as in stony meteorites and, therefore,

approximately in the same relative abundances

as in the sun; but these may well be diluted by

some lighter elements, particularly H, C, and N.

The luminous efficiency of each of these latter

elements is certainly very low, and the absence

of appreciable luminosity from these in meteor

spectra is not necessarily an indication of their

rarity. However, unless Fe is excluded in a

highly selective fashion in the formation of

comets, it seems unlikely that the iron abundance can be less than 1 percent by weight.

In table 3, we list provisional values for the

luminous efficiency based on the iron abundances stated in the table, the luminous

efficiency for iron TO (Fe)=8X10~19 as determined from the above results, and the assumption that all the luminosity in the range 3500-

5000 A produced by meteors at 10 km/sec

results from iron line emissions. Since other

elements will contribute to the luminosity, the

values given will be lower limits; the more so

for those cases where the iron abundance is low.

TABLE 3.—Provisional values of the luminosity coefficient

for meteoric material at 10 km/sec.

Cometary meteoroids

Irons Stones (extreme estimates)

Fe abundance 93% 15% 1% 20%

TO 7.4X10-" 1.2X10-" 8X10-" 1.6X10-"

In addition to the uncertainties imposed by

the composition of the meteoroids, differences

in velocity between the simulated meteor and

natural photographic meteors (mean velocity

«25 km/sec) may introduce appreciable errors

if our result is extrapolated to these higher

velocities. The velocity function we have

employed (see equation 2), although compatible

with meteor observations generally, must

certainly fail at sufficiently low velocities.

There is some evidence (Jacchia, 1949) that the

luminous efficiency is decreasing more rapidly

than suggested by equation (2) for meteors of

«<16 km/sec. In any case, there is no reason

to expect an increase in the efficiency at low

velocities and, therefore, extrapolations of our

result to higher velocities will give upper limits

for the masses of natural meteoroids.

Acknowledgment

The research reported here and accomplished

at Harvard College Observatory was performed

under subcontract to Lincoln Laboratory, a

technical center operated by Massachusetts

Institute of Technology, with support from the

U.S. Advanced Research Projects Agency

under Air Force Contract AFl9(604)7400

(ARPA Order 13-61).

Many individuals from National Aeronautics

and Space Administration, Lincoln Laboratory,

A.D. Little, Inc., Harvard College Observatory, and
208 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Air Force Cambridge Research Laboratories

contributed to this program. We attribute its

success, in large part, to the splendid personal

efforts of Mr. Lawrence Prugnarola of Lincoln

Laboratory and to Messrs. Stanley Chrest,

Thomas Ryan, and Anthony Mandile of Air

Force Cambridge Research Laboratories in the

preparation of ground observation facilities and

the air cavity charge.

References

COOK, A. F.

1955. On the constants of the physical theory of

meteors (abstract). Astron. Joum., vol.

60, pp. 156-157.

HALLIDAT, I.

1960. The spectrum of an asteroidal meteor

fragment. Astrophys. Journ., vol. 132,

pp. 482-485.

JACCHIA, L. G.

1949. Photographic meteor phenomena and

theory. Harvard Meteor Project Technical Report No. 3, Harvard Coll. Obs.

Reprints, ser. 2, no. 31.

1955. The physical theory of meteors. VIII.

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

vol. 121, pp. 521-527.

LEVIN, B. J.

1956. The physical theory of meteors and

meteoric matter in the solar system.

Publ. House Acad. Sci. U.S.S.R., Moscow.

MCCROSKY, R. E.

1955. Fragmentation of faint meteors (abstract).

Astron. Journ., vol. 60, p. 170.

1961. Observations of simulated meteors. Smithsonian Contr. Astrophys., vol. 5, no. 4,

pp. 29-37.

OPIK, E. J.

1955. Meteor radiation, ionization and atomic

luminous efficiency. Proc. Roy. Soc.

London, ser. A, vol. 230, pp. 463-501.

1958. Physics of meteor flight in the atmosphere.

Interscience, New York.

PROBSTEIN, R. F., AND KEMP, N. H.

1960. Viscous aerodynamic characteristics in

hypersonic rarefied gas flow. Journ.

Aero. Space Sci., vol. 27, pp. 174-192.

WHIPPLE, F. L.

1943. Meteors and the earth's upper atmosphere.

Rev. Mod. Phys., vol. 15, pp. 246-264.

1955. On the mass-luminosity relation for meteors

(abstract). Astron. Journ., vol. 60, pp.

182-183.

WHIPPLE, F. L., AND JACCHIA, L. G.

1957. Reduction methods for photographic

meteor trails. Smithsonian Contr. Astrophys., vol. 1, no. 2, pp. 183-206.
Luminous Efficiency of Iron and Stone Asteroidal Meteors

By A. F. Cook,1 L. G. Jacchia,1 and R. E. McCrosky

 l

We shall give a detailed discussion of theory

and observation for three meteors, one iron and

two stone. The first is known to be a pure iron

from its spectrum. The other two yield results

consistent with those of the first if they are

assumed to be composed of meteoritic stone.

Finally, a satisfactory comparison is made with

the observed re-entry of an artificial iron meteor.

The result is a determination of the luminous

efficiency law for iron and solid stone meteors

valid in the range of velocity from 9 to 21 km

sec"1.

Iron meteors

It is convenient to approach the problem of the

luminous efficiency of meteors by starting with

objects made of meteoric iron or pure iron.

One meteor showing the spectrum of an iron

without stone inclusions has been reported by

Halliday (1960).

We expect that initially the meteoroid conducted all the heat received at its surface to the

interior. The surface temperature must then

have been determined by the rate at which heat

was received earlier along the trajectory. If

the meteroid were not rotating, the part of the

surface normal to the direction of flight would

have received a heat flux

rF=- 2 (1)

where A is the heat-transfer coefficient, pa

the atmospheric density, and V the velocity.

Since very little change in velocity was observed

over the trajectory, we may assume that V

is constant in equation (1).

Two possibilities will be considered. The

first is that the meteor may have been near or in

free molecular flow; in both cases A will be a

1

 Smithsonian Astropbyslcal Observatory, and Harvard College Observatory, Cambridge, Mass.

638805—63 l g

constant. For a rough unpolished surface

we may expect this constant to approach unity

(Opik, 1958, pp. 52-54). The second possibility

is that the meteor may have been in viscous or

laminar continuum flow. In that case we expect

that (Probstein and Kemp, 1960)

A~(1.6Z/r)1/2, (2)

where I is a mean free path in air and r is the

radius of the meteroid, assumed to be a sphere.

Since

(3)

for I in cm, pa in gm cm"3 (Minzner, Champion,

and Pond, 1959), we have

and

A~1.14X10-*(rPa)-1/2, (4)

F~5.7 X10"V" "WF3. (5)

Let us make the further approximation that

pa~Pa exp [- (h-ho)/H], (6)

where His the scale-height defined by

HJ%rlnpXl

 (7)

and h denotes height above sea-level. The

approximation of equation (6) amounts to the

assumption that the scale-height of equation

(7) is a constant independent of h. We now

note that

h—A«= — («—s0) cos Zs, (8)

where s is the distance along the trajectory

from an arbitrary zero point, s0 is the value

of s corresponding to the height h$, and ZB is

the zenith distance of the radiant. Furthermore,

s— (9)

209
210 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

according to the approximate assumption of

constant velocity. Substitution of equation

(9) into equation (8), substitution of the result

into equation (6), and substitution of that

result into equation (1) (with A~l) and into

equation (5) yields

exp [(VIH) cos ZR(t-Q], (10)

or

X exp [i (V/H) cos Z«(*-*o)]» (H)

where we adopt the smaller value as correct.

Equations (10) and (11) can be written as

F=Foexp[(t-t0)/T],

where for equation (10) we have

cos ZB),

(12)

(13)

and for equation (11) we have

F0=5.7XW-ir1/2f&Vi,T=2H/(y cos ZR). (14)

Levin (1956) has shown that for a flux of the

form given in equation (12) extending back to

t=—», the following temperature distribution

is expected in a semi-infinite medium at negligible initial temperature bounded by a plane

surface at x=0,

T(x,t)=T0(t) exp (-x/xj, (15)

(16)

(17)

where x is the distance from the surface, F(t)

is given by equation (12), K is the conductivity,

cv the specific heat, pm the density, and k the

thermometric conductivity of meteoric iron.

As soon as To= 1800 °1£ is reached (the melting

temperature, Opik, 1958, pp. 156-158), molten

ron will start to flow. To form an idea of

the conditions required to remove molten iron

from the meteoroid, we must consider the

problem of flow of the melt.

Flow of molten iron

We consider a convex meteoroid with axial

symmetry about the direction of flight. Let y

be perpendicular to the surface outward, r

the radius of curvature in the xy-plane, and

r2 the radius of curvature in the plane normal

to the local x-direction. Let 6 denote the

angle between the y-direction and the direction

of flight. The equation of continuity takes

the form

(18)

r2 sin

- £- (r2u sin 0)+ ^

9 bx v by

where u, v are the x and y components of velocity

of the iron. The equation for the conduction

of heat takes the form

bT. dT , b2T

ox oy Oy2 (19)

where a steady state has been assumed and only

the dominant term in the Laplacian of the

temperature has been kept on the right-hand

side. The equation of the transport of the ucomponent of momentum is

bu bu d / bu\ dp /onN

The dynamic viscosity is taken to have the form

of a step function of temperature:

7>1800°K, M=« ,

T<1800° K, M=2X10~ 2 gm cm"1 sec"1,

(21)

as given by Opik (1958, pp. 156-158).

We begin by linearizing equation (20) in u, v,

whence

and we denote the rate of flow of shearing

momentum across the boundary y=0 by T0,

whence

(22)

by n nbxy>

u(v)= ^p_V . (23)
METEOR SYMPOSIUM—COOK, JACCHIA, AND McCROSKT 211

We next assume that u(bT/bx)<g; v(bTjby),

whence the equation for the conduction of heat

(19) yields

h

2T bT

k^4-v^-=Q. (24)

by2 by

Let ym denote the value of y at which T= Tn

= 1800° K, the melting point. Then in the range

0 > y > ym we have

by (25)

where we remember that y is negative below the

liquid surface. In the range ym ^>y^> —

 m

 we

have v=vw, a constant, and

In (bT/by) =lim In (bT/by) + ^ (y-ym). (26)

v<vZ

The conservation of conducted energy requires

that

k lim (bT/by)=k lim

»>»- V<Vm

where fr is the heat of fusion. Then we have

lim I?-lim &?

V<Vm V>Vm

(27)

From equation (25) we have in the range

0>y>ym,

In (bT/by)=\n [{bT/by)]v.^£vdy'. (28)

The combination of all these results yields

bT bl

and

. . bT FbT

ym>y>— °°, ->-=\ -^r

(29)

=o exP (j

(30)

By substituting equation (21) into equation

(23) we obtain

o>y>ym, ^(

ym>y>— <*>,u(y)=o,

(31)

(32)

where the condition (eq. 32) corresponding to

infinite viscosity of the solid has been imposed

at the solid-liquid interface, y=ym, and where

Ho denotes the dynamic viscosity at the surface

of the liquid. Substitution of equations (31)

and (32) into the equation of continuity (18)

yields

1

sin 0 bx

[r2 sin d X ( r o - | (33)

In free molecular flow the shear transfer to

the surface will be

T O = A ' paV

2

 sin 6 cos 6, (34)

where A' is a constant which we shall call the

shear-transfer coefficient. In analogy with the

heat-transfer coefficient we shall take it to be

unity. In viscous and laminar continuum flow

we may make the approximation (Probstein

and Kemp, 1960)

A'~(0.84r/Z)"2, (35)

whence from equation (3)

A '~8.3X 10"

 5(rPa)1/2

 (36)

8.3X 10-br1'

i

p

1

J

2

V

2

 sin 9 cos 6. (37)

and

In free molecular flow the dynamic pressure

upon the surface is

V&— P<y2 cos 2 9. (38)

We make the approximation that this relation

still holds in viscous and continuum flow. The

pressure due to surface tension is

pt=st(l/rl+l/r2), (39)

where st is the surface tension which, according

to Opik (1958, pp. 156-158), is 1200 dyne

cm"1. The sum of the gradients of these

two pressures is

_ S / (l|j + l|i \ (40)

\rf bx A da;/
212 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

An additional effective component is added to

this pressure gradient by the acceleration of

the meteor,

;=-p m ^sin0 , (41)

where we take for the deceleration the standard

form

dV . PaV

2

a I pm 7ii

(42)

where r is the drag coefficient, A is a shape

factor (1.208 for a sphere), and m is the mass

of the meteoroid. It then follows that the

inertial component (41) of the pressure gradient may be written

sin d. (43)

The sum of equations (40) and (43) is the

total pressure gradient to be used in equation

(33),

QP=-PaV

2

 sin 0 [- cos e-TA(pJmy/3~\

ox t_rx J

*' \ ^2 >\~ I Z3 ~>TZ ) ' (44)

As x approaches zero, 6 approaches zero and,

by axial symmetry, r2 approaches r, and the

z-derivatives of ru r2, and ym approach zero.

In this region equation (33) may be integrated

to yield

r i

' (y-ymy-tfm

L J

;lim ^snm r2.

x-»0 x->0

(46)

By substituting y—ym we obtain the fl-component of velocity at great depths:

Hm p ^

r-X> 6 r

(47)

The velocity distribution (eq. 45) enables us

to integrate the equations for the temperature

gradient (29) and (30) whence, imposing the

conditions

we find

(48)

X

X(yt3-5ymy"-5y!ny

t

-5ys

m)

]}*'•

(49)

We assume that all the terms in the exponential

are sufficiently small so that equation (49) may

be replaced by

where

— ^0+^ (Zf+CpTjpnVny,

(50)

Thus we have

0>y>ym,T^Tm+^Ur+cpTm)Pmvw{y-ym) (51)

and

ym>y>-m,T^=Tm exp I y (y—yTO) •

Equation (47) may be expressed in the form

^ y (53)

We now assume that vaporization is negligible, i.e., #0=0, and we obtain

^ y (54)
METEOR SYMPOSIUM—COOK, JACCHIA, AND McCROSKY 213

This is a cubic equation in yjr. The solution

of this equation must then be substituted into

equation (50) to find To. Next, the assumption that vaporization is always negligible must

be verified by computing the rates of loss of

mass and heat by vaporization at To. Finally,

the assumption that the argument of the exponential in equation (49) is small must also be

verified.

Before the computation near x=0 can be

undertaken we must return to equation (33)

and ask where on the surface the second term

on the right-hand side might vanish. At such

a point melt would presumably flow past, as

it is neither removed nor accumulated by the

flow field. At smaller z the flow field would

remove melt, at greater x it would accumulate

melt. On our assumptions the excess accumulation plus the local ablation would be removed

by vaporization. If flow of melt without ablation continues past this critical value of x, it

can only do so if u(bT/bx) at y=0 dominates

over v(bT/by). We ignore the trivial case of

T0<C.Tm, i.e., when the surface is still solid and

Mo=°°, and near such a point we expect ym to

attain a local minimum, whence it follows that

|.{ r , sin »[r.-| | f »„]}=<>.

 (55)

The surface tension may be expected to be

near a maximum here, and we may thus drop

the last term in equation (44).

We now consider the special case of a spherical meteoroid (ri=r, x=r&), for which we have

be (56)

By substituting equations (33) and (44) into

equation (56) we obtain

sin0|6(A'- 4 y*\ cos2

 6+9T ^ cos 0

- 2 (A'-4^)]=0 . (57)

The root sin 0=0 is extraneous on account of

the division by sin 0 which occurs in equation

(33). We assume that ym/r<g.l, whence we obtain the roots

(58)

and by retaining the first root as the only nonextraneous value, we have the result that

0~54°7. Melt will begin to flow past here as

soon as To, by conduction alone according to

equation (16), reaches Tm. If r is sufficiently

large the melt will blow off as droplets, otherwise the surface temperature will rise until

vaporization removes the iron. The criterion

for the former process is (Opik, 1958, pp. 83-86)

7.6s,

TPaV

(59)

In free molecular flow r^l . In continuum

flow with negligible shear transfer the dynamic

pressure (eq. 38) alone contributes to the drag,

and if we integrate over the exposed hemisphere,

we find from the local contribution pd cos2 0,

f*r/2

T~21 sii

Jo

We then estimate that in viscous flow

sin 0 cos3 0d6=~-

(60)

We also note that the flux is a function of 0,

and is not given by equation (1) but by

F = | A.F3 cos 0. (61)

The computation was made for free molecular

flow with 0=54!7, »c=4X 106 ergs cm"1 sec"1 deg,

cp=6.91X108 ergs gm"1 deg-1, and pn=7.8

gm cm"3. These constants are the same as

those adopted by Opik (1958, pp. 156-158).

The ARDC 1959 model atmosphere (Minzner,

Champion, and Pond, 1959) was also used.

Equation (13) was used for T, equation (61)

for F, and equation (16) for T0=Tm, and we

obtain

^PJry'2(r/Vy, (62)

at the onset of ablation. For Halliday's

meteor, V=1.32X108 cm sec"1, and cos ZB=

0.48. A trial value of H yields T from equation

(13) and pa from equation (62), whence h is

found and, from the model atmosphere, an
214 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

improved value of H. The process converged

rapidly to predict a beginning height somewhat

below 74.1 km. This value is too high compared with the observations.

The alternative is to adopt h > 69.2 km,

whence 2?<6.38X105 cm, and to compute an

upper limit on T from eq. (14) and then to solve

equation (16) for F:

F=(KCpPjT)mTo. (63)

Then with To= Tm we find a lower limit for F.

Finally equation (5) may be solved for r, whence

an upper limit is obtained:

- (*

(64)

This upper limit is a radius of 1.54 cm.

We also consider a second model in rapid

rotation about an axis perpendicular to the

direction of flight. If the period of rotation is

short compared with r, then we may use an

average flux. At points where the normal to

the surface is parallel to the direction of flight

at some orientation during rotation, we have

for the average flux

T=tpaV3' (65)

From the computation for free molecular flow

this flux, with A^l, gives an upper limit for

the beginning height of 72.2 km, only 3.0 km

above the photographed beginning height.

This model is valid only for r<0.53 cm (from

A=l in eq. (2)). We also require that r>x0

by equation (17) otherwise the surface temperature will be higher than by equation (16) and

ablation will begin at a greater height. We

have k=0.004 cm2 sec"1 for meteoric iron from

k=-

CpPm

(66)

whence, in viscous or continuum flow, x0<0.39

cm, and in free molecular flow with rapid rotation XQ=0.27 cm. r must lie in the range of

about 0.3 to 0.5 cm in order that this latter

model should be a valid physical picture.

For the nonrotating model, r must be sufficiently large so that A<1 at a height of 74.1

km in order to prevent the onset of ablation

at that height. Thus r>0.23 cm. In this case

the controlling limit becomes r>x0 for viscous

or continuum flow, a condition safely satisfied

by r>0.39 cm. The radius for the model varies

from about 0.4 to 1.5 cm. Opik's criterion

(eq. 59) for the shedding of droplets is 0.23 cm

at this height for r=1.54 cm. At r=0.37 cm it

is 0.15 cm, which is smaller due to the increase

in r. We see that for this meteor this criterion

is just satisfied and no more.

Next, for the nonrotating model, we must

verify the assumption that vaporization is not

important near x=0. The highest surface temperature obviously occurs for the largest radius,

which exhibits the slowest rate of removal of

melt by divergence of the flow field. For a

spherical meteoroid we have

(67)

(68)

Equation (54) becomes

where A is given by equation (4), A' by equation (36), T by equation (60), and f by

y—-Q y _i_ y _i_£ f'j1 y \ (69)

where cp$ is the specific heat of the solid, fr

the heat of fusion, and cPi the specific heat of

the liquid. Opik (1958, pp. 156-158) gives cP,=

6.91 X106 ergs gm"1 deg-1, f,=2.69X109 ergs

gin"1, cp,= 6.66X106 ergs gm"1 deg-1. We

assume that the beginning of ablation occurred

at A=69.2 km. Then the result is yjr~—3.2 X

10~3 for 7o^TOT=18000K, and the final results are yjr=— 3.1X10"3

, 7T

0=1874°K. It

may easily be shown from the vaporization

law given by Opik (1958, pp. 156-158) that

rates of removal of both heat and mass by

vaporization are smaller by three orders of

magnitude compared with the rates due to

flow of molten iron. Also the characteristic

depth of heating is

—=0.15 cm,

and the depth of the molten layer is —ym=4.8X

10~8 cm, which is about l/20th of the depth of
METEOR SYMPOSIUM—COOK, JACCHIA, AND McCROSKT 215

heating. This circumstance makes the exponential in equation (49) nearly unity, and validates the use of equation (50).

Photometric mass and end point from the

light curve

The light curve has the appearance of a standard

light curve (Opik, 1958, pp. 63-65) collapsed in

duration. In the approximation where the

scale height is constant, equation (6) may be

used. If constant velocity is also assumed, the

standard light curve takes the form

(70)

where pe is the ambient atmospheric density at

the end point of the trail. Then pa is given by

equation (6), h by equation (8), and s by equation (9), which completes the conversion of the

independent variable to time. From equation

(6) we have

Pa=exp[-(h-he)/H]. (71)

We now propose to alter H from its true value

to one that will fit the observed light curve.

We do so for two purposes: to measure the total

photographic light emitted by the meteor;

and to extrapolate from the observed end point

to the true end point of the meteor.

Halliday (1960) gives beginning and end

heights determined by the threshold of the

emulsion. On such a short trail we assume the

threshold to be unchanged from beginning to

end. Let us denote the intensity of the meteor

at these points by IB,E- Then the density at

maximum intensity Pmax is given by

Pmax

Pe

1

(72)

and from equation (71) we have

=_<*. [Yl - £ *

Pmax LA Pe

where pB, PB are the densities at the observed

beginning and end points. By substituting

equation (72) into the above expression we

find

27 / (73 )

A series of values of IB.BI/max may be selected

and PB!P« and pshe found by solving equation

(73). For these values we obtain

Pma*

PB

PE __r> PE

3 p B Pmax

From equation (71) these ratios yield

hB—hm*z==H In (Pmax/PB)>

l-hB=H In

(74)

(75)

(76)

where hB, Am,,, hs are the observed height of

beginning, maximum intensity, and end, respectively. We now eliminate the scale height H

by obtaining the ratio ^from equations (75)

and (76):

(77)

=

x—hit In

The first form is an observed quantity, the

second a computed quantity from equations

(73) and (74). Thus the computed value

must be matched with the observed value to

find IB,B/IIMLX- Then equation (75) or equation (76) yields the effective scale-height for

the light curve,

(78)

(Pmax/ps) In

where the ratios have been computed from

equation (74). Then from equations (71)

and (72) the true end height (complete ablation of the meteoroid) is

he=hmtix—H In (p«/pmax)=^max—H In 3. (79)

The total light emitted up to the disappearance

of the meteor at te is

x. (80)
216

The photometric mass introduced by Millman

and Cook (1959) is

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Fdt=\ exp jj COS ZR(t — te) dt

F

4

 cos Z,

(81)

where the terminal mass is neglected.

From the spectrogram, Halliday (1960) gives

^s=68.3 km, ^«=64.9 km, and from the direct

photograph, &B=69.2 km, ^=64. 7 km. From

his figure 1, the ninth of thirteen visible segments of the spectrogram is seen to be the

brightest. The corresponding value of Amax is

66.0 km. Then the two values of & are 2 and

2%, respectively, which in turn yield H=1.56

and 1.62 km, and A«=64.3 km in both cases.

Finally, he gives the maximum brightness in

panchromatic light as absolute magnitude —4.2.

The spectrum of a slow meteor is overwhelmingly due to iron, except for the D-line of

sodium and the first positive group of nitrogen

bands (Milhnan and Cook, 1959); hence, except

for these two emissions, the reduction from

panchromatic to photographic magnitude

should be the same. The contribution of the

D-line may safely be neglected, but the first

positive group of N2 is not seen in Halliday's

spectrogram, and hence the reduction found by

Millman and Cook for a slow cometary meteor

of +0.2 magnitude should probably be altered

by an unknown negative quantity. It seems

best to make no correction at all, hence the

intensity at maximum brightness was

in units of a zero magnitude star. From

equation (81) the photometric mass was

^=1.2 X 10~17 0 Mag cm~3 sec4,

where H=1.59 km is adopted as the effective

scale-height of the light curve. This photometric mass and the end height of 64.3 km are

our two fundamental observed quantities.

Limits on mass from end height

For the nonrotating model we can set an upper

limit on the mass by putting A= 1 in equation

(1). Then the total heat input to the end

point of the trajectory will be given by

2 cos ZR

where we have substituted equations (6), (8),

and (9), and integrated. For an upper limit

on the diameter we neglect conduction of heat

in directions other than the direction of flight,

and use T0=Tm in equation (69) for f. We

then obtain

d<

2£pm cos

(82)

since all the heat input must ultimately be used

for melting. The limit from equation (82) is

2.3 cm, so that the upper limit on the radius is

1.2 cm. A lower limit on the radius can be

established by assuming equation (1) to be

valid when A= l until equation (5) predicts a

lower value, and then by using equation (5)

with r fixed therein at its initial value. For a

given value of r the two fluxes are equal when

pa=-

1.297X10"8

whence we have

=^PeV

3

r explj cos

Jr

(83)

dt

exp

[2HCOsZ'

t(t-te)~jdt,

where

H

We now find, with d=2r, that

1 PeV

2H 1.297X10"8

2 cos ZR i

+1.14X10"4

1/2T/2Z7

{l 1

then

4fP(BcosZfi

r

1/2

 cos ZR

-[1.297X10-8/(rp.)]^}=2fPmr,

.297 X10~8 2.28X10"4

{ I / „ \ 1 /O

1.297X

rpe

114X1Q-4
METEOR SYMPOSIUM—COOK, JACCHIA, AND McCROSKY 217

and if we put

1.14X10-* /1.297X1Q-V2

% m ^ " m

 )

1Q-V2

 fQA.

. ) ' (84 )

we obtain

tt«-2it»+5.19X10-«

 rpw

2T?rf g

=0- (85)

The last term in equation (85) has the value

0.0526, and we find r>0.61 cm. This is,

however, a closer limit than the upper limit

previously found.

For the rotating model, an upper limit can

be found as above by putting A=l, but using

equation (65) instead of equation (1). The

limit obtained is a limit on r rather than on d

and is expressed by

-

< Pe

-2ir{pm COS ZR

(86)

which establishes the limit r<0.74 cm.

A lower limit can be established as above but

with the left-hand side divided by v for averaging the flux over a rotation and the right-hand

side divided by 2, since the radius rather than

the diameter sets the limit. The result is

r. 1-297X1Q-8

2ir COS ZR p,

, 1.14X10"*

I" /1 .

r

m

 cos ZR

297X10"8V

/

and then

n_

= 0 . (87)

The last term in equation (87) has the value

0.083, whence we find r>0.44 cm.

From the above analysis we may estimate

0.5<r<0.9 cm. The corresponding range for

the mass is from 4 to 24 gm. For r=0.7 cm,

the mass is 11 gm.

Coefficient in formula for luminous efficiency

The coefficient in the law for luminous efficiency, the mass, and the photometric mass

are related as follows (Millman and Cook,

1959):

9 9 J/

mf =^ (88) m

whence we find T O =6X1O~1 8 to 10~18 0 Mag

gm"1 cm"8 sec* as r varies from 0.5 to 0.9 cm.

For r=0.7 cm, we have T O =2X1O~1 8 0 Mag

gm"1 cm"3 sec4.

On the other hand, McCrosky and Soberman

(see this symposium, p. 199) find that, from a reentering iron pellet of known mass, TO=8X1O~W

0 Mag gm"1 cm"3 sec*. If we now use the

logarithmic mean, we obtain

log T0= —17.70 for spectrum no. 210,

log T O = —18.10 for re-entering pellet,

log TO= —17.90 adopted pro tempore.

Iron

For low velocity meteors the spectrum in the

photographic region is almost exclusively dominated by iron lines (Millman and Cook, 1959).

Hence we should be able to derive the luminous

efficiency of meteoric stone in photographic

light from that of iron by multiplying the

luminous efficiency of iron by the fraction of

the mass of meteoric stone due to iron. According to Opik (1958, pp. 159-162) this fraction is 0.154, from which we deduce that

log TO= 18.71 for stone.

Coefficient in deceleration equation for stone

The deceleration equation usually appears in

dV_ 1 PaV

2

dt~ K^?l<*'

the form

where K is an observable quantity,

(89)

(90)

In terms of physical parameters, it takes the

form

(91)

where A is a shape factor. For a sphere we have

vt=(9ir/16)1/3= 1.208.

If we insert into equation (91) this value of A

and the value of T0 for stone found above, then

i£=3.4X10« for r=l , and 8.1X106 for r=l/2 .

The corresponding values of the logarithm are

log isT=6.61 and 6.91, respectively. These

expected values for stony meteors may be contrasted with log .K~6.29 observed for cometary

638805—63 -19
218

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Observed data for meteor No. 1242

(Beginning height, 74.9 km on FA 8808; maximum light, 47.1 km on FA 8808 and AI 39336; end height, 38.0 km on FA 8808, 36.6 km on RH 12890;

cos ZR=0.632.)

Epoch

t(sec)

1. 0526

1.6842

2. 3158

2. 9474

3.5790

4. 2105

Height

i(km)

62.56

57.78

53. 10

48.61

44.38

40.57

Velocity

F(km/sec)

11.93

11.81

11.48

10.94

10. 13

8.87

Acceleration

dV/dt (km/sec2)

- 0 . 185

- 0 . 389

- 0 . 660

- 1 . 024

- 1 . 505

- 2 . 23

Air density*

pa(gm/cm3)

2. 58X 10~7

4. 49X10-'

7. 49X10-7

1. 278X l0-«

2. 195X10-'

3. 698 X 10-«

Jt-JL

O Mag cm"3 sec4

7. 56X10-18

6. 69X10-18

5.64X10-18

4.07X10-18

2. 432X10-18

0. 885X10-i»

I I

O Mag

3.0

3.3

4.8

4.3

4.0

2. 1

(smoothed)

O Mag

3.0

3.3

4.0

4.0

3.3

2. 1

• According to Minzner, Champion, and Pond (1959).

TABLE 2.—Reduced values of parameters on assumption that 1/K and a are constant for last three epochs

Epoch t

sec

I. 0526

1.6842

2. 3158

2. 9474

3. 5790

4. 2105

Photometric mass ^/i

0 Mag cm"3 sec

 4

10. 09 X 10-18

9.22X10-18

8. 17X 10-"

6. 60 X 10-"

4. 96X 10-18

3.42X10-18

f 1/K

0 Mag

 I/3

 gm"1 cm sec4/3

1.087X10-7

1.303X10-7

1. 347X lO-7

1. 266X10-*

1. 140X10-7

1. 155X10-7

a/K

O Mag

 I/3

 gm"1 cm3sec-J/3

8. 41X10-i»

6. I6XIO-19

5. 75X10-i»

5. 19X10-i»

4. 78 X 10-i»

5. 15X10-i»

TABLE 3.—Deduced values of parameters on assumption that 1/K is constant over trajectory

(The values of a are computed using the mean VK deduced for computation of the masses.)

Epoch t

sec

1. 0526

1. 6842

2. 3158

2. 9474

3. 5790

4. 2105

Photometric mass ^

O Mg cm"3 sec *

1.710X10-17

1.623X10-17

1.518X10-17

1.361X10-"

1. 197X10-'7

1.042X10-17

' 1/K

0 Mag

 m gm~i cm sec4/3

1.285X10-7

1.573X10-7

1.656X10-7

1.598X10-7

1. 529X10-7

1.676X10-7

a/K

0 Mag

 xt% gm"1

 cm3

sec -

2/3

5. 92X10-i»

4.23X10-1'

3.81X10-1'

3. 20 X 10-i»

2. 66X 10"i»

2. 45X10-"

a

cm2 sec"2

3.6X10-12

2. 6XIO-12

2.3X10-12

2. 0X10-12

1.6X10-12

1. 5X10-12

meteors. Two such meteors with anomalously

large log K have been well photographed in the

Harvard Program, and will be discussed in turn.

Meteor No. 1242

Meteor No. 1242 was photographed on February 6, 1945, from Harvard College Observatory in Cambridge, Mass., on plate no. AI

39336, and at the Oak Kidge Station (now

Agassiz Station) in Harvard, Mass., on plates

nos. FA 8808 and RH 12890. The meteor

appeared at 5h 12m 17" UT. Table 1 lists the

pertinent data from the reductions.

The method of Millman and Cook (1959) is

used to determine that~^=2.5X10~18 from the

last three points. The results are given in

table 2. These results are not satisfactory

since neither 1/if nor a is constant.

We next assume that 1/K alone is constant

From the reciprocal of the cube of equation (90)

we have

(92)

•D J

The coefficient of ^//e and the entire last term

are observed quantities. The equation is to be

solved for ^ t and 1/K3 as unknowns. We do

so by grouping the first three epochs and the

last three epochs and using average values for

each. The results are 1/K= 1.628 X10"7 0 Mag

gin"1 cm sec,logii:= 6.79, and

0 Mag gm~3 sec* (see table 3). We estimate

that r~l/ 2 since we are presumably far from

free molecular flow, and hence log TO= — 18.36.
METEOR SYMPOSIUM—COOK, JACCHIA, AND McCROSKY 219

TABLE 4.—Observed data for Meteor No. 19816

(1/K(obs)=value computed from eq. (90); 1/K(corr)-1/K(obs) corrected for presence of two equal fragments; beginning height, 91.1 km (SK); minimum

light, 60.1 km; end height, 47.1 km(SL); cos Z«=0.716.)

.Jt-Jt, I 1/K(obs)

Camera

SK

SL

SK

SL

SK

SL

SK

SL

t

sec

0.764

1. 135

1.860

2.038

2.425

2.623

2.824

3. 124

h

km

80. 13

74.02

64. 16

61.06

56.49

53. 75

51.87

48.92

V

km/sec

20.67

20.57

19.87

19.27

17.85

16.36

14.63

10.77

dV/dt

km/sec2

- 0 . 158

- 0 . 416

-2.02

-2.75

-5.92

-8.45

-9.67

-8.90

Pa

gm/cm3

2. 117X10-8

5.739X10-8

2. 123X10-'

3. 105 X10-7

5. 178 X10"7

6. 935X10"7

8.662X10-'

1. 23lX10-«

O Mag cm-3 O Mag OMag1/3gm-' 1/K(corr)

sec4

6. 60X10-"

6. 07X10-"

4. 43X10-"

3. 87X10-19

2. 71X10-19

2. 05X10-"

1. 14X10-"

0. 32X10-"

1.2

1.3

2.5

2.5

1.9

1.9

1.3

cm sec4/s

1. 52X10-'

1. 45X10-'

1. 84X10-'

1. 74X10-'

2. 32X10-'

2. 68X10-'

2. 53X10"'

0.23 1. 98X10-'

1. 52X10-'

1. 45X10-'

1. 84X10-'

1. 38X10-'

1. 84X10-'

2. 13X10"'

2. 01X10-'

1. 57X10"'

cm2 sec"2

6. 0X10-12

2. 9X10-'2

1. 8X10-"

1. 7X10-'2

1. 2X10"12

1. 5X10"12

2. 6X10-12

6. 0X10"12

Smoothed magnitudes are used at some

epochs, primarily because oscillations appear on

the FA and AI plates near maximum light.

A very short period flicker is found on the RH

plate. The following model may be used to

represent the observed behavior. The meteoroid is assumed to have been in rapid rotation

upon entering the atmosphere. After free

molecular flow was left behind, a torque depending upon orientation developed and became

stronger. First, the angular velocity of rotation was diminished at all orientations except

those for which no torque occurred, and restoring torques were met on either side of these

null orientations. The period lengthened until

rotation ceased and oscillation began about an

equilibrium orientation. This change occurred

around maximum light. Thereafter the period

of oscillation became progressively shorter.

Next, we consider the shape bounded by two

right circular cylinders of equal diameter with

axes intersecting perpendicularly. We then

make the axis of rotation perpendicular to the

axes of the cylinders. Finally, we orient the

axis of rotation perpendicular to the direction

of flight. Such a model does not really deviate

much from a sphere, and yet it can be shown

that the torques produced upon it are about

equal to those required to fit the observed

periods. This model can also be made to fit

an observed proportionality of the period of

oscillation to the inverse square root of the air

density along the lower part of the trail.

Meteor No. 19816

This sporadic meteor was photographed with

the Super-Schmidt meteor cameras (SL 12537

and SK 9821) at the Sacramento Peak and

Organ Pass meteor stations in New Mexico.

The meteor appeared at 0Sh 50ra 13s UT on

December 8, 1958. The entire trajectory of

62 km was photographed on at least one of the

cameras, but the initial 12 km and the final

4 km were photographed at only one station.

The light curve is particularly smooth, exhibiting only one brief flare of 0.2 magnitude.

During the final portion of the trajectory, two

particles are in evidence, and it is likely that the

flare represents the time of splitting of the

original body. The deceleration history of the

separate particles indicates that they have

nearly comparable masses. The lifetimes and

the total luminosity of each particle are similar.

In the following analysis we have made the

approximation that the masses and area of the

particles are exactly identical although, in fact,

some difference between them must exist for

differential deceleration to be observed. Apart

from this single fracturing, there is no evidence

of unusual wake or terminal blending that

frequently is visible in meteor trails formed by

fragmenting cometary bodies.

The data for this meteor is given in table 4.

Four deceleration solutions were made for each

trail. The values for K'1 are generally lower

for the later solutions, presumably due to the

presence of the two fragments. In the penultimate column of table 4, we increased K~l

 by

2

1/3

 for those solutions where two fragments

existed. The corrected values show no significant trend with time. It appears that the terminal mass is negligible, as would be expected

for a meteor with an initial velocity of 21 km/

sec. Assuming the same values for A, T, andpm
220 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 5.—Orbital elements of asteroidal meteors

Meteor

Iron Meteor

Meteor No. 1242

Meteor No. 19816

Pribram Meteorite

Corr. rad.

a

332T0

3?0

70!5

191!5

S

+ 73!2

+ 59?2

-0?2

+ 17!7

sec)

13.4

12.2

20.7

20.9

a

1.05

1.33

2.24

2.42

e

.117

.262

.662

.674

.928

.984

.756

.790

1.173

1.68

3.72

4,05

247?5

172? 1

65?4

241?6

Si

219?1

317?1

75!7

17?1

i

13!3

6?9

12?6

10?4

r-u+Q,

106?6

129?2

141?1

258?7

as were used for meteor no. 1242, we find log

T O = —18.24. These two values are in excellent agreement.

Optimum values of the luminous efficiency

factor for iron and stone

Spectrum no. 210 yields, on reduction for

the abundance fraction of iron in stone,

log TO= —18.51 for stone. For the above two

meteors log r o= —18.36 and —18.24. The

mean of the three values is

log TO= —18.37 for stone.

Application of the reduction for the abundance

fraction of iron yields log TO= — 17.56 for iron,

while McCrosky and Soberman (see this symposium, p. 199) find log r o= —18.10 for a reentering iron pellet of known mass. This discrepancy corresponds to a deviation in the shape

factor (larger than for a sphere) by the antilogarithm of 0.18, or of about 1.51. If we adopt

this new corresponding value of the shape

factor we have

.4=1.83, log r 0= — 18.10 for iron, and

— 18.91 for stone. (93)

Orbits of asteroidal meteors

The meteors discussed in this paper are of

unique value because their physical characteristics indicate that the objects are of asteroidal

origin. These meteors, together with the

Pffbram meteorite that was photographed in

flight (Ceplecha, 1961), represent a new source

of data on the orbits of asteroidal material with

small perihelion distance. The information is

collected in table 5. Three of the orbits have

been published previously (Halliday, 1960;

Whipple, 1954; and Ceplecha, 1961).

It is apparent in the table that these four

meteors represent two distinct classes of orbits.

However, an inspection of the orbits of the

asteroids with small perihelion distance indicates

that this is probably a chance grouping.

References

CEPLECHA, Zd.

1961. Multiple fall of Pffbram meteorites photographed. Bull. Astron. Inst. Czechoslovakia, vol. 12, pp. 21-47.

HALLIDAT, I.

1960. The spectrum of an asteroidal meteor

fragment. Astrophys. Journ., vol. 132,

pp. 482-485.

LEVIN, B. J.

1956. The physical theory of meteors and meteoric matter in the solar system. Publ.

House Acad. Sci. U.S.S.R., Moscow.

(German translation published by Akademie-Verlag, Berlin, 1961, pp. 47-49.)

MlLLMAN, P. M., AND CoOK, A. F.

1959. Photometric analysis of a spectrogram of

a very slow meteor. Astrophys. Journ.,

vol. 130, pp. 648-662.

MINZNER, R. A.; CHAMPION, K. S.; AND POND, H. L.

1959. The ARDC model atmosphere. Air Force

Surveys in Geophysics, No. 115, Geophysical Research Directorate, Air Force

Cambridge Research Laboratories.

OPIK, E. J.

1958. Physics of meteor flight in the atmosphere.

Interscience, New York.

PBOB8TEIN, R. F., AND KEMP , N . H.

1960. Viscous aerodynamic characteristics in

hypersonic rarefied gas flow. Journ.

Aerospace Sci., vol. 27, pp. 174-192.

WHIPPLE, F. L.

1954. Photographic meteor orbits and their

distribution in space. Astron. Journ.,

vol. 59, pp. 201-217.
Meteor Ionization and the Mass of Meteoroids

By Donald M. Lazarus1 and Gerald S. Hawkins:

The excitation and ionization observed in

meteor trails have long been assumed to result

from inelastic collisions of meteor atoms with

those of the atmosphere after their ablation from

themeteoroid surface. This assumption is based

on the premise that the surface temperature of

meteoroids is inadequate to cause excitation and

ionization. Unfortunately, meteor velocities

are such that the quantum mechanical calculation of excitation and ionization cross sections

is difficult because neither the high-energy

Born approximation nor the assumption of

adiabatic collisions is really valid. In addition,

the complex electronic structure of the meteor

constituents and the atoms of the atmosphere

make the form of their interaction mathematically unwieldy. Lastly, suitable analytical

wave functions are not available for most of

the atoms in question.

However, it is possible to make reasonable

approximations to the form of the interaction

and to the wave functions. The problem of

wave-function distortion in the case of near

adiabatic collisions is not so easily handled,

but its expected effect is discussed in our

analysis of the predictions of various crosssection calculations.

The ionization cross section

Inelastic atomic collisions are most conveniently

classified by the ratio of the duration of the

collision to the period of the internal motion

of the electron to be excited (Massey, 1949).

This ratio is conveniently given (Bates and

Massey, 1954) by the expression

T

T

(1)

1

 Yale University, New Haven, Conn.; and Harvard College Observatory, Cambridge, Mass.

' Boston University, Boston, Mass.; Smithsonian Astrophysical Observatory, Cambridge, Mass.; and Harvard College Observatory, Cambridge, Mass.

where / is the atomic radius in units of a^; AEis

the energy of the transition in ev; Mx is the

mass of the incident atom relative to the proton

mass; and E the impact energy in ev. For

fast collisions, T/T<O, and the Born approximation is valid. When TJT>\, the encounter

is said to be near adiabatic. For AE=5 ev,

T/T varies between 12 and 7 for velocities

between 35 and 60 km/sec. Bates and Massey

(1954) have pointed out that in this instance

it is necessary to treat the colliding atoms as

a quasi-molecule. The perturbed stationarystate method (Massey and Smith, 1933) could

then be applied, taking into account the effect

of the interaction on the wave functions during

the collision. Unfortunately, this treatment is

not a useful one in practice as the wave functions and potential energy curves for the pseudomolecule are generally neither known nor

readily calculable. However, if the interaction

does not produce a near crossing of the potential

energy curves of the atoms in the initial and

final states in question, then a result similar

to a Born approximation calculation would be

found (Mott, 1931), except for the fact that

a reduction of the cross section at low energies

occurs because of distortion. If, however,

there is a near crossing of the potential energy

curves, an adiabatic transition becomes more

probable. The probability for this type of

transition has been calculated by Landau

(1932), Zener (1932), and Stueckelberg (1932),

and applied to transitions into the continuum

by Bates and Massey (1954) with the result

that the cross section for ionization is given

approximately by the relation,

'=(- E

lJ2t 0 (2)

when the expression in parentheses is small

compared with unit}. The symbol g is the

221
222 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

ratio of the statistical weight of the initial

state to all other possible initial states; Rx is the

internuclear distance at which the separation

of the initial and final states of the potential

energy curves is a minimum; and t is the lifetime for auto-ionization of the quasi-molecule.

The formulation used in this paper is that

of the variation of parameters (Schiff, 1955,

chap. 8, sec. 30), which in first order gives the

same result and has the same range of validity

as the first Born approximation.

The interaction, i.e., the electric potential

due to the atmospheric atom at the positions

rti of the electrons of the sodium atom, is taken

to be the screened coulomb potential,

(3)

where rx is the internuclear separation, rt

the position of the i01 electron of the sodium

atom relative to its nucleus, and a and A are

interaction parameters. We assume that the

electron wave-functions can be separated, and

that removal of the 3s electron does not appreciably change the wave function of the inner

electrons. With these approximations, the

matrix element for the transition to the continuum becomes

H'=L~ ,(r2)—<

r

\2

(4)

where ^*'(r2) and fa (r2) are the ionized and

initial state functions, respectively, and L3 is

the volume in which the atoms are normalized.

As usual, ko and k are the initial and final

propagation vectors for the interaction potential

in center of mass coordinates, and rl2=\ rx— rt\.

Any sophistication in the choice of the analytical wave functions tfv(r2) and \p0 (r2) leads to

a matrix element that is totally unwieldy for

calculation. The functions were therefore taken

to be

(5)

for the ejected electron; with k'=mv'l%, the

electron momentum divided by Planck's constant over 2x,

(6)

for the normal state, where (L')~312 and B are

the usual normalizing factors, and b is a constant parameter. The lack of orthogonality

of the initial and final state functions has been

investigated. It can be shown that adding an

orthogonalizing term to equation (5) by the

Schmidt process affects the matrix element only

slightly. This term vanishes as r2—>«, so

that the asymptotic form of ^jt'fo) is not

affected.

By integration with the usual substitution

-»->- •

K=ko—k, the matrix element becomes

H

r

=L-\L'Y

(7)

If we define K'=K—k', equation (7) becomes

The probability for the ejection of the valence

electron with wave number k' in the direction

9',<p', accompanied by the scattering of the

atmospheric atom with wave number k in the

direction 8, <p, is given by the expression

sin sin

where ok>(6<pdf<p'k') is the differential cross

section for the process; p. the reduced mass so

-* -> -> -* -» ->

that kii=nvo/fi and k=nv/h where v0 and v are

the intial and final relative velocities, respectively; and p(k) and p{kf

) the densities of states

in the vicinity of k and k', respectively.

densities are

uL3

=j^r-3 k sin 6ddd<p,

The

(10)

so that the total cross section for ionization

from the ground state is given by the expression,
METEOR SYMPOSIUM—LAZARUS AND HAWKINS 223

O/W =

contribution to the integral is for small values

olK.

sin Odtkk sin O'dO'dv'dk' (11) Fo r sma U value g o f ^

sin edddip sin e'dd'd<p'dk'. (12)

Transforming from angular to momentum

variables, we obtain

and

k sin OdO=^ dK;

K'2=K2+k'2-2Kk' cos B',

Kk'sw0'dB'=K'dK'.

(13)

(14)

Substituting equation (8) in equation (12) and

carrying out the integrations over <p and <p\ we

obtain

dK r*'"" d¥ r°+k

The first integral is easily evaluated:

_2b*f 1 1

~ 7 \[62+(.K:-fc')2]

7

 [&2+(#+fc')2]

7

3 \{b2+{K-k')2]*

I

The lower limit ko—k for the second integration

is determined by applying the principle of the

conservation of energy:

(16)

where Ex is the ionization energy. The upper

limit is taken as infinity since the greatest

(17)

(18)

If we retain the first two terms in equation (18)

and the leading term in equation (17) and

introduce the notation,

It is therefore possible to expand:

^<4- 1 ~i I ZiZAlC I ~T (19)

the cross section becomes

„ , 9X2nirmn2b

2A2B2

(20)

The coefficients S, R, Q, and P are functions

of a, 6, k0) and A:'. The interaction parameters

A and a were chosen to give the best possible

fit to the oxygen potential determined by the

numerical integration of the radial charge

distribution obtained from the Hartree (1957)

numerical wave-functions. The value of b was

take from the Slater (1951, app. 13, p. 476)

screening constants.

The numerical integration of equation (20)

was performed for several values of k0 and the

resulting cross section is plotted in figure 1.

The ionization probability

The probability of ionization of an atom with

wave number kt in one collision is

(21)

where <ro(k{) is the elastic scattering cross

section; and 2<rB(kt) is the sum of all possible

excitation cross sections. The elastic scattering

cross section for a single charged particle

encountering a screened coulomb field is, in the
224 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

VELOCITY v km/sec

FIGURE 1.—The dependence of ionizing cross section on

velocity.

first Born approximation (Schiff, 1955, chap.

7, sec. 26),

If I <72-4 _4

(22)

h

2

where a——271/3' e represents the electronic,

and Ze the nuclear charge. In the energy

range under consideration, <ro(&<) is much

greater than <ri{ki), and it will be assumed also

to be much greater than 2<rB(kt). Therefore,

(23)

If we let Pt be the probability that ionization

will result from the Ith collision, it is easily

seen that

(24)

.*{:

f>k 4=1

i-1 "^

The possibility of ionization from an excited

state has been neglected because the lifetimes

of excited states are much less than the average

time between encounters in the upper

atmosphere.

Since /3<<^1, it is possible to simplify the last

of equations (24) to the expression

Pi«ft, (25)

so that the total probability for the ionization

of an evaporated meteor atom becomes

(26)

Let 77, be the fraction of the velocity lost in

an elastic collision with an atmospheric atom.

By combining the equations for conservation

of momentum and energy, we can then give

[cos 0<±(M!/M?— sin2

(27)

where MI is the mass of a meteor atom, 0, the

angle of scattering of the meteor atom, and /z2

the mass of the atmospheric atom. The

average of t}t over the normalized angular

distribution in the approximation k^a^l is

(28)

M1+M2

In the range of meteor velocities, the ionization cross section given in figure 1 can be

approximated by the expression,

(29)

Inserting equations (22) and (29) into equation

(23) and retaining only the two leading terms

in kt (the other two terms give a negligible

contribution), we obtain

if the w

tb

 collision is the last one in which

sufficient energy is available for ionization.

However,

(31)

so that

The elastic scattering cross section used in

the calculation of /3 is subject to the same criti-
METEOR SYMPOSIUM—LAZARUS AND HAWKINS 225

cism as the ionization cross section; i.e., it gives

too large a cross section at low energies because

distortion is not taken into account. Since /3

involves the ratio of the cross sections, it is

likely that the effect of neglecting distortion

will be reduced. The effect on the inelastic

cross section is generally greater than in the

elastic collision so that /3 will remain an overestimate.

From the cross section given by equation (2),

which results from the near crossing of potential

energy curves, we obtain for this process an

ionization probability of

(33)

V 1-v ) °J

The velocity dependence of the probability

resulting from curve crossing appears to be in

better agreement with radio-meteor measurements than with the Born approximation result.

Nevertheless, it is doubtful whether this type

of collision would be prevalent in the majority

of encounters between meteor and atmospheric

atoms.

The Born approximation cross section appears to be more compatible with the great

majority of experimental results (Massey and

Burhop, 1952, ch. 7). Moreover, the manner

in which the Born approximation is expected to

fail in low-energy collisions (Massey and Smith,

1933; Mott and Massey, 1949, ch. 11; Mott,

1931) is well known, and has been discussed

above. It has been used with considerable

success to derive the range-energy relations for

alpha particles and protons.

One of the assumptions made in applying

these conclusions to meteor phenomena is that

the upper atmosphere is monatomic. This assumption, of course, is not precisely correct

although it is true for the majority of atmospheric atoms at 100 km. Those diatomic molecules present in the upper atmosphere will tend

to reduce /3 because of the large cross section

for rotational excitation. This competing process may lead to a term 2aB(kt) in equation (21)

which is comparable with <re(kt). The calculated j8 must therefore be considered an upper

limit. Processes in which excitation of the

meteor atom and the atmospheric constituent

occur during a single collision have been neglected because such events are much less

probable than single-excitation collisions.

Application to meteoroids

The number of ions produced in an infinitesimal

volume of a meteor trail is related to the mass

of ablated meteor material in that volume by

the equation

a

dQ—-=- dmo>

Ml

(34)

where m is the average mass of a meteor atom

and /3 is the ionization probability. The calculation of /3 enables one to determine the mass

of a meteor by the integration of equation (34).

If the velocity is constant, the number of ions

per unit length of trail is related to the visual

magnitude M at that point by the equation

(35)

which is derived in the appendix (p. 227).

Making use of the relation between trail

length x and height H, where f is the zenith

angle, we find that

dx= dH,

cos f '

(36)

and equation (35) can be written in the form

6

 J—l—dH.

cos f (37)

The variation of magnitude M along the

trail is given by the normalized light-curve

(Whipple and Hawkins, 1958, sec. 3, p. 525)

which, for 360 measured meteors, is closely

approximated by the parabolic form

Ho

(38)

where Ho is a two-value parameter. We take

Hn=Hb for the portion of the light curve between the beginning and the maximum, and

He for the portion between the maximum and

the end. From the experimental data, Hb=

3.5X103 meters, and i7e=2.0Xl03 meters.
226 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Thus

>

 (39 )

which is readily integrated to give for equation

(34) the value

In r_ I T i TT PWo—Afnj.il

(40)

Let us assume for the moment that the meteoroid consists en tirely of sodium. For a sodiumoxygen collision ^=0.42, and the following

values of /3 are obtained: for a Perseid of velocity 60 km/sec, /3=1.6X10"2

; and for a Geminid

of velocity 35 km/sec, 0=2.7 X10~8. Hawkins

(1956) has shown that M0=40.75 for a Perseid

and 38.89 for a Geminid. The mass m0 is obtained with these radar values for meteors of

maximum magnitude, Mmax =0 . Thus for the

Perseid, m0=0.212(l/cos f) gm, and for the

Geminid, Wo=0.620(1/cos f) gm.

These results do not, of course, represent the

mass of a meteoroid since the calculations were

performed for sodium-oxygen collisions. The

oxygen may be considered a reasonable approximation to the average atmospheric atom, but

the properties of the other meteor constituents

may lead to different masses than those obtained

for the above "sodium meteor." The proper

approach (determining an average J8 and £i) is

to evaluate the ionization cross sections and the

respective ionization probabilities for each constituent, and weight each by its abundance in

meteoroids. Since the calculations of the cross

sections for all meteor constituents is not feasible, and since their velocity dependence is

expected to be similar to that of sodium, the

following rough approximation will be used to

obtain some idea of the effects of these elements

on the calculation of meteor masses.

The average atomic mass is easily evaluated

from the cosmic abundances of the elements

(Brown, 1949). If the ionization probabilities

for the various elements have the same form,

they will differ only in magnitude. The magnitude of the cross section is inversely proportional to a high power of the energy required

for ionization, and directly proportional to the

reduced mass of the particles.

It is not unreasonable to assume that the

ionization cross section varies as ET~

6

, where

ET is the ionization energy (Bates and Griffing,

1953). In addition, it is necessary to multiply

the cross sections by n, the number of valence

electrons available for ionization. Thus the

relative ionization probabilities are related by

the ratios of n(^-6\ Table 1 gives these

factors and the abundances.

TABLE 1.—Total ionizing

Element

Na

Mg

Al

Si

Ca

Fe

Inert

Number of

atoms per

100

0.8

14.6

1.4

16.2

1. 1

6.2

59.6

Estimated

0(Na=l)

1.000

. 198

1.518

.288

.972

.384

.000

Mean /3 per atom

probability

Weighted contribution

per atom

0.0080

.0290

.0213

.0468

.0106

.0238

.0000

. 1323/S(Na)

The average ionization probability 0 is 0.1323

/Sjva, and the average mass of a meteor atom

is 3.72 X10"28 gm. The insertion of these values in equation (40) gives mo=1.66 (1/cosf)

gm for the Perseid, and 4.85(l/cos f) gm

for the Geminid. There are additional uncertainties in these figures due to the assumption

of the cosmic mix, and the sodium-like behavior of all atoms. Unfortunately, this uncertainty cannot be adequately assessed.

Using the radio meteor values for Mo given

by Hawkins, one readily obtains an upper

limit for the luminous efficiency from equation

(7) of the appendix. For a meteor of visual

magnitude 0,

and

W,8=3.194X10-3 for «=60 km/sec,

T//3=3.295X10~2 for r=35 km/sec,

so that the upper limits are

T=8.9X10~ 6 for »=35 km/sec
METEOR SYMPOSIUM—LAZARUS AND HAWKINS 227

and

T=5.1X10" 5 for 0=60 km/sec,

with the computed values of /3.

Appendix

The luminous efficiency T is defined by the

relation between 7, the visible energy produced

per second, and the rate of ablation:

1 dm0

2 dt (1)

By dividing equation (34) by dx=—vdt, we

obtain

dm0

dx v

(2)

and eliminating

and (2) gives

/dt between equations (1)

(3)

Opik (1937) obtained the luminosity relation

M=7.1-2.5log1 0 7 (4)

from the standard fluxes of established stars.

Combining equations (3) and (4), we find for

the visual magnitude

M=7.1-2.5 log10 Q UIOBU^ .

(5)

Finally, for constant velocity, the second term

in equation (5) is a constant and can be combined with the first term to yield

where

(6)

(7)

Acknowledgment

The research in this paper was supported

jointly by the U.S. Army, Navy, and Air Force,

under contract with the Massachusetts Institute of Technology.

References

BATES, D. R., AND GRIFFING, G.

1953. Inelastic collisions between heavy particles.

I. Excitation and ionization of hydrogen

atoms in fast encounters with protons

and with other hydrogen atoms. Proc.

Phys. Soc. London, vol. 66A, pp. 961-971.

BATES, D. R., AND MASSEY, H. S. W.

1954. Slow inelastic collisions between atomic

systems. Phil. Mag., ser. 7, vol. 45,

pp. 111-122.

BROWN, H.

1949. A table of relative abundances of nuclear

species. Rev. Mod. Phys., vol. 21, pp.

625-634.

HARTEEE, D. R.

1957. The calculation of atomic structures. John

Wiley & Sons, New York.

HAWKINS, G. S.

1956. Meteor ionization and its dependence on

velocity. Astrophys. Journ., vol. 124,

pp. 311-313.

LANDAU, L. D.

1932. Theory of superconductivity. Phys. Zeitschr. Sowjetunion, vol. 2, p. 46.

MASSEY, H. S. W.

1949. Collisions between atoms and molecules at

ordinary temperatures. Phys. Soc., Rep.

Progr. Phys., vol. 12, pp. 248-269.

MASSEY, H. S. W., AND BURHOP, E. H. S.

1952. Electronic and ionic impact phenomena.

Clarendon Press, Oxford.

MASSEY, H. S. W., AND SMITH, R. A.

1933. The passage of positive ions through gases.

Proc. Roy. Soc. London, ser. A, vol. 142,

pp. 142-172.

MOTT, N. F.

1931. On the theory of excitation by collision

with heavy particles. Proc. Cambridge

Phil. Soc, vol. 27, pp. 553-560.

MOTT, N. F., AND MASSEY, H. S. W.

1949. Theory of atomic collisions. Ed. 2. Clarendon Press, Oxford.

OPIK, E. J.

1937. Researches on the physical theory of meteor

phenomena. III. Basis of the physical

theory of meteor phenomena. Publ.

Obs. Astron. Univ. Tartu, vol. 29, no. 5.

SCHIFF, L. I.

1955. Quantum mechanics. Ed. 2. McGrawHill, New York.

SLATER, J. C.

1951. Quantum theory of matter. Ed. 1.

McGraw-Hill, New York.

STUECKELBERG, E. C. G.

1932. Theorie der unelastischen Stosse zwischen

Atomen. Helvetica Phys. Acta, vol. 5,

pp. 369-422.
2 2 8 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

WHIPPLE, F. L., AND HAWKINS, G. S. ZENER, C.

1958. Meteors. In Handbuch der Physik, S. 1932. Non-adiabatic crossing of energy levels.

FlQgge, ed., vol. 52, pp. 519-564. Proc. Roy. Soc. London, ser. A, vol. 137,

Springer-Verlag, Berlin. pp. 696-702.

Abstract

An upper limit for the ionizing probability /3 is obtained for sodium atoms that have evaporated from the surface

of a meteoroid entering the atmosphere, and the result is generalized to apply to the other meteor constituents. Comparison of this result with radio meteor measurements leads to a meteor mass which suggests an upward revision

of the meteor mass scale. An upper limit for the luminous efficiency is also obtained. The lower limit for the mass

of a zero-magnitude Geminid meteor incident at 45° is found to be 6.86 gm, and the mass of a zero magnitude Perseid

is 2.35 gm.
Statistical Verification of the Physical

Theory of Meteors

By B. J. Levin1 and S. V. Majeva1

Hawkins and Southworth (1958), using the

photographs of 360 meteors obtained with

Baker Super-Schmidt cameras, compared their

light curves (for three points—beginning, maximum light, end) with the theoretical curve

for nonfraginenting meteor bodies. They

showed (see fig. 5 of their paper) that almost

all measured points lie within the theoretical

light curve. The same is true if, instead of

taking a curve for n= % as was done by Hawkins

and Southworth, we take a curve for ju— %

which gives a shorter path length. The

parameter n characterizes the relation between

the changes of the frontal cross-sectional area

S and of the mass Mot the meteor body according

to the formula S^M" (Levin, 1956, formula

3.24). The rising branches of these curves

are similar, but the descending branch for

n=% is much steeper than for fi=%, and even

steeper than the curve drawn by Ananthakrishnan (1960) according to the hypothesis that

the luminosity factor r~vp (instead of the

conventional r~t;).

Jacchia (1955) noted that the observed path

length of meteors is shorter than the theoretical

one, and he ascribed this to fragmentation of

meteor bodies. More convincing evidence in

favor of the fragmentation theory can be

obtained by comparing the positions of beginning and end points (relative to the point of

maximum light) for the same meteor. This

was done by using the data of Hawkins and

Southworth. Moderate deviations of points

from the theoretical curves were not taken into

account, and only those beginning or end points

were regarded as anomalous for which HB—HML

or HML—HB were less than a half of correspond1

 O. Schmidt Institute of Physics of the Earth, U.S.S.R. Academy of

Sciences, Moscow.

ing values for M=K for the same value of

Am=mnm—mML. Only 13 meteors (3.5 percent)

have anomalous position of both points, i.e., a

very short path; this means that only a flare

was photographed. For seven meteors (2 percent) the approximately normal position of the

beginning point is accompanied by the

anomalous position of the end point; this means

that the meteor ended in a terminal flare or

shortly after a flare.

In spite of a very liberal classification of

beginning and end points as "normal," only 117

meteors (33 percent) have approximately normal positions of both points. At the same time,

for 221 meteors (62 percent) the position of the

beginning points is anomalous, i.e., they lie too

close to the points of maximum light, while the

end points He more or less normal. Such

deviations from theoretical light curves indicate the fragmentation of meteor bodies. If

we are to regard as normal only those beginning

points which lie in the region of theoretical

light curves for different values of n, i.e., those

which lie to the upper left from the straight

line corresponding to M=0 , then 87 percent of

meteors become anomalous. For them the

mean increase of light intensity is greater than

the maximum theoretical value for meteors

produced by nonfragmenting bodies.

Levin (1956) used the data on 140 meteors

photographed at Harvard by conventional

cameras to obtain a statistical verification of

two basic formulas for the physical theory of

meteors. Below are given the results of an

analogous verification of these formulas using

the data for 337 meteors photographed by

Super-Schmidt cameras. Hawkins and Southworth kindly sent us their unpublished data on

the masses of meteor bodies. These masses

229
230 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

were obtained by the photometric method (by

integrating the light curve) and are expressed

in the Opik-Jacchia scale. They are averages

of values found for each film of a pair. Southworth informed us that there is frequently a

large difference between these individual values.

According to nonfragmentation theory, the

air density at the height of maximum light pML

can be represented by the formula (Levin,

1956, formula 3.40)

cosc Z,

and if the drag coefficient and the heat-transfer

coefficient are constant, a=0.33, b=2, and

e=l. The data for 116 "normal" meteors and

for 221 meteors produced by obviously fragmenting bodies were analyzed separately with

the theoretical values of a, b, c given above, the

dispersion e of the reduced HML is 4.7 km for

"normal" and 4.8 km for fragmenting meteors.

The least-squares solution leads to a marked

reduction of dispersion and gives the values of

the parameters shown in table 1. It remains

TABLE 1.—Observed parameters in the equation pML

a

b

c

t

"Normal"

meteors

0. 32 ±0. 05

0. 89 ±0. 18

0.85 ±0.21

± 3. 6 km

Fragmenting

meteors

0. 15 ±0.05

1. 9 ±0. 14

0. 55 ±0. 15

±3.9 km

unclear why the value for b for "normal"

meteors is about half the theoretical value,

while the values for a and c are close to theory,

and why for fragmenting meteors the reverse

is true.

The analogous verification was done for the

maximum light formula

/ar-A/gflg COS* Z

(Levin, 1956, formula 3.60). The values a=l,

0=4, and 7=1 correspond to the theoretical

basis of the photometric method for the determination of masses of meteor bodies. However,

since the masses are obtained by integration of

the light curve which for real meteors deviates

from the theoretical one, the least-squares solution gives somewhat different values for a

The reduction of the observed maximum

magnitudes mML, with theoretical values for

a, 0, 7, gave for "normal" meteors a dispersion

e=0*29, and for fragmenting meteors e=0*64.

The least-squares solution is given in table 2.

TABLE 2.—Observed parameters in the equation for

"Normal"

meteors

a 0.86±0.08 0. 73±0.03

0 3. 67±0.08 2. 67±0. 10

7 0. 72±0.09 0. 46±0. 10

±0*49

Fragmenting

meteors

For meteors produced by obviously fragmenting bodies, the values for a, /3, 7 are

substantially smaller than the theoretical ones.

This probably shows that the fragmentation

masks the dependence of mML on Mo, v0, cos Z.

For "normal" meteors, a, 0,7 have intermediate

values, probably also because of fragmentation

in a more moderate form.2

The least-squares solution also gives values

of (mML)i0, the maximum absolute magnitude

of a meteor produced by a body with Mo= 1 gm,

flying vertically into the atmosphere at a

velocity of »0=10 km/sec. We obtain

for "normal" meteors: (mAfi)io= + lf?2

and

for fragmenting meteors: (mafI,)i0=-|-0'74.

These values are expressed in photographic

magnitudes. If we convert them to a visual

scale and, in spite of some doubts, use the same

correction +1*8 as for meteors photographed

by conventional cameras, we obtain the values

+3*0 and +2*2, respectively. The first

value (for "normal" meteors) is close to the

previously obtained value +2*86 (Levin, 1956).

Accordingly, meteor bodies that produce a

meteor of zero visual magnitude during vertical

motion with initial velocity po=4O km/sec must

have initial masses 0.062 gm and 0.030 gm,

respectively (instead of Mo=0.055 gm obtained

in 1956). It is clear that fragmentation decreases the path length of a meteor and at the

same time increases its brightness; therefore

> Note added in March 1962. Further Investigation showed that after

a simple allowance for fractlonation, the theoretical values of a, 0, y give

a good representation of all observations together with a dispersion +0»16;

i.e., even better than a least-squares solution for "normal" meteors.

(Levin, in press.)
METEOR SYMPOSIUM—LEVIN AND MAJEVA 231

a smaller initial mass is needed to produce a

meteor with a given maximum magnitude.

The manner in which the fragmentation influences the estimates of the masses of meteor

bodies and of the amount of meteoric material

accreted by the earth deserves further

investigation.

References

ANANTHAKBISHNAN, R.

i960. Light curves of meteors. Nature, vol. 187,

pp. 675-676.

HAWKINS, G. S., AND SOUTHWOBTH, R. B.

1958. The statistics of meteors in the earth's

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

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.

LEVIN, B. J.

1956. The physical theory of meteors and meteoric matter in the solar system. Publ.

House Acad. Sci. U.S.S.R., Moscow.

On the Color Index of Meteors

By John Davis

 1

A comparison of photographic and visual

meteor magnitudes reveals an interesting relationship. Jacchia (1957) has compared the

meteor color index, defined as the difference

between the photographic magnitude and the

corresponding visual magnitude, with the maximum intrinsic brightness of a meteor as

measured with a photographic system. The

photographic system used was a Super-Schmidt

camera (Whipple and Hawkins, 1958) with

blue-sensitive film corresponding approximately

to the International Photographic system

(Allen, 1955), and the visual magnitudes were

the direct estimates of an observer. Jacchia

found that the color index showed very little

variation with meteor velocity but a large

variation with maximum photographic brightness, the ratio of "photographic" to "visual"

light decreasing with maximum meteor brightness. The author has confirmed Jacchia's

results during the combined photographic and

radio-echo meteor program at Jodrell Bank

(Davis, Greenhow, and Hall, 1959; Davis, 1959).

The results of both Jacchia and the author

are shown in figure 1, where color index has

been plotted against visual magnitude in order

that comparison may be made with results

obtained with a photographic system of different spectral sensitivity. Jacchia has divided

the observations of 294 meteors into four

groups according to absolute photographic

magnitude, and deduced the mean color index

for each group. The two points given by

Jacchia for the brightest meteors were derived from the observations of 45 meteors

made with the Harvard small cameras. It

is possible that color indices derived from small

cameras may differ from those from Schmidt

cameras due to differences in their relative

< Nuffield Radio Astronomy Laboratories, Jodrell Bank, England.

Now at School at Physics, University of Sydney, Australia.

spectral transmission curves. The author has

reduced his data in the same way as Jacchia,

but only 53 meteor observations were available,

and the larger errors associated with the mean

points in figure 1 can be accounted for by the

difference in the number of observations.

The variation of color index with brightness

has been explained by Jacchia in terms of the

PurkynS effect. He suggested that the variation is a spurious physiological effect due to the

difference in the spectral sensitivity of the eye

for bright and faint sources (photoptic and

scotoptic vision).

Ceplecha (1959) has made a similar study

with the difference that he used panchromatic

film, sensitive to approximately 6700 A, to

obtain his "photographic" magnitudes. He

thus obtained a panchromatic index which

he found to increase as the maximum brightness

of the meteor decreased. This is shown in

figure 1 for comparison with the color index.

The quite different results obtained with blue

and with panchromatic systems have been

suggested by Ceplecha to originate in real

spectral changes of the meteor light with a

previously unsuspected high emission in the

red becoming relatively predominant in fainter

meteors.

All the observations described have been

based on subjective estimates of visual magnitudes, and these are suspect. Systematic

differences up to 0.5 magnitude between experienced observers have been found, and it

appears that a single visual magnitude estimate

has a standard deviation of the order of ±0.8

magnitude. Inspection of the data included

in figure 1 shows that the standard deviation

of a single visual estimate is ±0.8 from the

author's observations. Jacchia's results give a

standard deviation of ±0.6 magnitude, but

since the majority of his results are based on

233
234 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Colour Indei

Ponchromolic

Index

-4 -2 O +2 +4

Visual Magnitude

FIGURE 1.—The variation of meteor color index with meteor

brightness. X, The results of Jacchia obtained with a

blue photographic system; Q, results of Davis obtained

with a blue photographic system; O, results of Ceplecha

obtained with a panchromatic photographic system.

the mean of two visual-magnitude estimates,

these figures are in good agreement. They

suggest that the main cause of scatter in color

index can be ascribed to the inaccuracy of the

estimates of visual brightness. Objective

measurements of visual magnitudes are therefore very desirable in this kind of work.

Two photomultipliers with Tri-alkali cathodes of 5-inch diameter have been used in a

study of this problem. They have been set up

with a screen above them to define a zenithal

field of 50° diameter and with Chance glass

filters to provide the required spectral responses. One tube has been fitted with an

OBlO filter to give a spectral sensitivity corresponding approximately to a blue photographic system, and the other has an OGr2

filter to give a response corresponding to a

mean visual observer (mean photoptic and

scotoptic). The relative spectral responses

of the photocathode-filter combinations are

shown in figure 2. The relative spectral

sensitivities of the photocathodes and the

spectral transmission of the filters have been

measured at the National Physical Laboratory,

Teddington, England. The relative spectral

sensitivity curve of the photographic system

(Davis, in preparation) is shown in figure 2 for

comparison with the blue photoelectric system.

The spectral transmission curve for the Royal

Society Meniscus Schmidt camera has been

computed from data supplied by Chance

Brothers Ltd. The transmission of the lenses,

reflection at mirror and at alTglass-air surfaces

have been taken into account in the calculations. The results have been combined with

the spectral sensitivity curve of the Kodak

photographic emulsion (V6010) to give the

relative spectral sensitivity curve of the cameraemulsion combination. Spectral sensitivity

curves for the normal and dark-adapted eye

(Allen, 1955) are also included for comparison

with the green photoelectric system. Common

filter glasses have been used; nevertheless, a

reasonably good match has been obtained,

particularly in the case of the blue system.

The varying components of the photomultiplier

outputs over a bandwidth of 1/10 to 20 c.p.s.

have been recorded with a Siemens high-speed

pen recorder.

The amplitudes of meteor signals from the

blue (OBlO) and green (OGr2) channels have

been converted to arbitrary magnitude scales

which correspond to the photographic and

visual magnitude scales respectively, except

for the addition of constants which at this

stage have not been determined. In figure 3,

green magnitudes have been plotted against

the author's direct visual estimates of meteor

magnitude. The broken line represents a

linear, 1:1 relationship between the two magnitude scales, whereas the full line has been

derived from figure 1 for the hypothetical case

of a constant color index with the observed

Meniscus Schmidt

Pnologrophic

Blue Photoelectric

^ Nornol Eye

A \ \ .-.Dork Adopted Eye

Photoelectric

O3 OS O7 Ot

WAVELENGTH IN MICRONS

FIGURE 2.—The relative spectral sensitivity curves of the

three photocathode-filter combinations.
METEOR SYMPOSIUM—DAVIS 235

+ 1

+2

u +4

Constant Colour

Index—observed

variation due to

the Purkyne effect

O 2 4 6

2-5 Loo G

FIGURE 3.—A comparison between visual magnitudes and

the green photoelectric brightness.

variation being due to the Purkyne" effect.

A total of 24 meteors has been used in this

diagram. Since the major error lies in the

estimate of visual magnitude, the data have

been divided into four groups according to

their value of 2.5 log G, and the mean values

of visual magnitude have been derived (G is

the amplitude of the "visual" photoelectric

signal on an arbitrary scale and is proportional

to the incident light intensity). The diagram

shows clearly that it is not possible to explain

the variation in terms of the Purkyne" effect

alone. This conclusion is further supported

by figure 4 in which the photoelectrically

determined color index is plotted against blue

magnitude. Some 40 meteors have been used

in this diagram and, since the error in 2.5 log

B/G is the greater, the data have been divided

into five groups according to their values of

2.5 log B, and mean values of 2.5 log B/G have

-O- 5

O

J-t-OS

' + IO

+• 1-5

•I-2-O

IO 6 4

2-5 Log B

-6 -4 - 2 O +2

Photographic Magnitude

FIGURE 4.—The variation of photoelectric color index (2.5

log BIG) with meteor brightness. O, Points representing

the mean of 8 meteors; -f, point representing a single

bright meteor.

been derived (2? is the amplitude of the blue

photoelectric signal on an arbitrary scale).

An absolute calibration of the blue magnitude

scale has been made from fifteen meteors

photographed and recorded photoelectrically.

The photographic magnitude scale is indicated

in figure 4 alongside the blue scale, the uncertainty in the calibration being ±0.1 magnitude.

The curve representing the variation in color

index with meteor brightness determined from

visual and photographic observations, which is

shown in figure 1, has been transposed to

figure 4. It must be noted that the color

index given in figure 4 is not absolute but

gives only the relative change in index with

meteor brightness. Owing to the uncertainty

in the calibration of the blue and the green

magnitude scales against the photographic

and visual scales, it is not possible to fix the

position of the curve relative to the ordinate

of figure 4 with sufficient accuracy for comparison with the photoelectric color indices. Therefore the position of the curve relative to the

ordinate scale has been chosen arbitrarily to

give the best fit to the points. It will be seen

that a good fit is obtained, thus supporting the

conclusion drawn from figure 3. The implication is that the variation is due to a real change

in the meteor spectrum. The Purkyne" effect

has a much smaller influence on the results

than was envisaged by Jacchia.

Another series of observations has been

made in which the OGr2 filter was replaced by

an OR2 filter to give a response from approximately 6000 to 7000 A with the peak sensitivity

from 6100 to 6500 A. The relative sensitivity

curve of this photocathode-filter combination

is shown in figure 2. A red index, which is

defined as the difference between blue (OB 10)

magnitude and red (OR2) magnitude, has

been plotted against blue magnitude in figure

5, in which 44 meteors have been used. The

data have been treated in the same manner as

for figure 3, being divided into five 2.5 log B

groups, and mean values of 2.5 log B/R have

been derived. Again the index is only relative,

but it shows clearly that faint meteors are

relatively redder than bright meteors. A

smooth curve has been drawn through the

points in figure 5 to indicate the trend of the

results.
236 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

-OSOs

• +O-5

+ I-O

+ 1-5

+2-O 6 4

2-5 Log B

-6 -4 -2 O +2

Photographic Magnitude

FIGURE 5.—The variation of the photoelectric red index (2.5

log BfR) determined photoelectrically with meteor brightness. Each point represents the mean of 8 meteors.

Approximately half of the meteors observed

in the photoelectric program have been Geminids, and the remainder sporadics. No significant difference has been found between meteors

of the Geminid shower and sporadic meteors.

The preliminary examination has shown that

Ceplecha's proposed explanation of the observed variation of color and panchromatic

indices with meteor brightness in terms of a

changing spectrum is correct. If the total

light from a meteor is considered, faint meteors

have relatively greater emission in the green

and red regions of the spectrum than bright

meteors. The transition in the emission spectrum over the range of visual magnitudes from

—2 to +3 is apparently a gradual one.

Dr. Peter Milhnan (personal communication)

has pointed out that the spectra of bright

meteors exhibit changes along the meteor trail.

The great majority of all spectra containing

sufficient detail show an increasing ratio of blue

to red light as the meteor passes from the faint

beginning, through maximum brightness, to the

lower end of the trail. Millman suggests that

faint meteors may exhibit a spectrum similar to

the faint early parts of bright meteor trails. If

this is so, changes in color index along the light

curve of a bright meteor should be observable

with the photoelectric system. No evidence to

support this has been found so far, but the

problem is being investigated further.

I am grateful to Sir Bernard Lovell for his

encouragement in this work and for the research facilities at Jodrell Bank. I also thank

Messrs. Turner and Newall for a research

fellowship.

References

ALLEN, C. W.

1955. Astrophysical quantities. Athlone Press,

London.

CEPLECHA, Zd.

1959. On the colour index of meteors. Bull.

Astron. Inst. Czechoslovakia, vol. 10,

p. 39.

DAVIS, J.

1959. Simultaneous photographic and radio echo

observations of meteors. Thesis, University of Manchester.

DAVIS, J.; GREENHOW, J. S.; AND HALL, J. E.

1959. Combined photographic and radio echo

observations of meteors. Proc. Roy.

Soc. London, ser. A, vol. 253, pp. 121-

129.

JACCHIA, L. G.

1957. On the "color index" of meteors. Astron.

Journ., vol. 62, pp. 358-362.

WHIPPLE, F. L., AND HAWKINS, G. S.

1958. Meteors. In S. Flugge, ed., Handbuch

der Physik, vol. 52, pp. 519-564.

Springer-Verlag, Berlin.

Abstract

Objective measures of meteor color indices have been made with a two-channel photoelectric apparatus. Photocathode-filter combinations giving spectral responses corresponding to a Super-Schmidt photographic system and a

mean visual observer have been used. The results show a variation of color index with meteor brightness in agreement with the subjective results of Jacchia and Davis. However, the variation can no longer be accounted for in

terms of a physiological effect alone as proposed by Jacchia. It must arise from a real change in the meteor spectrum

with meteor brightness as Ceplecha has suggested. This interpretation is further supported by the observations

made with blue and red sensitive photoelectric channels.
SPALDING, COLTER, ET AL. PLATE 1

a, The electronic equipment, b, Three motion-picture sequences of Perseid meteors.

I I! i
SPALDING, COLTER, ET AL. PLATE 2

a, Perseid meteor photographed in August 1960. b, Photograph of a bright meteor.
Image-Orthicon Photographs of Meteors

By J. Spalding,1 G. Colter,2 C. L. Hemenway,3 J. A. Cole,3

and J. F. Dugan3

The function of this brief communication is

threefold: First, to show some image-orthicon

photographs of meteors; second, to make sure

that the characteristics of image-orthicon techniques are understood by the scientists interested

in the study of meteors; and third, to seek

advice for the best possible means of exploiting

the capabilities of these techniques for meteor

research.

The most important characteristic of imageorthicon techniques for the study of meteors

is their very high sensitivity, which ranges

from 200 to 400 times that of the fastest

photographic films. This high sensitivity permits good time resolution at the expense of some

loss in spatial resolution. Typical resolution for

meteor studies is of the order of 10 lines per millimeter. The photo cathodes presently available

are approximately 1.75 inches in diameter. The

readout from such equipment is extremely

rapid, and 30 pictures per second can be

recorded with little difficulty. Image orthicons

are available with different spectral sensitivities.

There are tubes sensitive in the ultraviolet, in

the infrared, and in the visual. Images can be

stored on an image-orthicon target if desired.

In fact, we have stored an image of stars for a

half-hour without refrigeration and found that

the image brightness decayed by less than a

magnitude. By pulsing the cathode to target

potential, one can take exposures as short as a

millisecond without difficulty.

The operational characteristics of the system,

as used this past summer for motion picture

photography of meteors, are as follows:

Objective: 50 mm. fl, f/1.4

Tube: GE Z5396 (visual sensitivity)

> General Electric Company, Schenectady, N.Y., and Dudley Observatory, Albany, N.Y.

1

 General Electric Company, Schenectady, N.Y.

1

 Dudley Observatory, Albany, N.Y.

638805—63 20

Equivalent speed: ASA 1,000,000

Operating mode: 500 lines, non-interlaced

Limiting magnitude: ^>6OT.O for 1/30 sec exposure.

Plate la is a photograph of the electronic

equipment employed. The image-orthicon

camera is not shown and is outside the building

directed toward the sky. This system has the

advantage that the observer is in a comfortable,

heated room. The recording technique that

we have used is direct photography of the

monitor screen. The video tape technique

suggested by D. W. R. McKinley * offers a

number of advantages.

Plate 2a is a picture of a 3d-magnitude

Perseid meteor that we obtained in August

1960; the meteor motion is effectively "frozen,"

and the meteor wake is clearly separated from

the meteoroid. Thus it is possible to study

separately the time and spatial development of

the meteor, and its wake and train phenomena.

Plate 26 shows what happens when a bright

meteor comes into view. Although this —1

magnitude meteor overloaded the system, the

meteor wake can still be distinguished. Note

that this system has sufficient speed to photograph a weak aurora (below the meteor) in

l/30th of a second.

Plate 16 shows three motion-picture sequences of meteors taken at l/8th of a second

intervals during the last Perseid shower. The

first sequence shows a faint meteor with a

short-duration train. The second and third

sequences show meteors that fragmented, and

the spatial developments of the associated

flares are seen along with longer-duration

trains.

In summary, faint meteors, wakes, and

trains can readily be studied by image-orthicon

• Meteor Science and Engineering, McGraw-Hill, New York, 1961.

237
2 3 8 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

techniques. We note that the magnitudes of We welcome comments and suggestions for

meteors can be measured by direct comparison the exploitation of this equipment. We have

with the stars since short-duration exposures already obtained low-resolution spectra of

are used. The equipment is suitable for taking meteors and trains with an objective prism

motion pictures, which permit study of time coupled to this equipment. A transmission

and spatial development of meteors and their grating spectrograph has been constructed and

spectra. will be in use shortly.
Meteoritic Erosion in Space

By Fred L. Whipplex

Recently developed techniques in meteoritic

astronomy now enable us to determine upper

limits, or rough evaluations, of the erosion rates

on the surfaces of meteoroids moving in orbits

about the sun.

Successive sections of this paper discuss the

observational data on erosion rates, the theory

of high-velocity cratering, the deduced mean

density of the interplanetary dust component

and evidence for a dust cloud about the earth,

general physical effects on meteoroids in space,

and effects that meteoroids may have on space

vehicles.

Evidence for erosion of meteoroids in space

When cosmic rays penetrate solids in space,

they produce a number of transmutation or

spallation products in the material of the solidSome of the atomic species so produced are

stable against radioactive decay, while others

have a half-life that may be short or long. A

measurement of a stable isotope so produced

establishes the integrated effect of cosmic rays

over the period of exposure, while a measurement of a short-lived isotope provides the

cosmic-ray spallation rate over a recent, short

interval of time. After correction for spallation

cross sections, the ratio of the observed abundances of two such isotopes in a recovered meteorite provides a determination of the exposure

age.

The penetrating powers of cosmic rays are

definitely limited. One may assume that the

cosmic-ray rate has been statistically constant

in the past and conclude that the exposure age

represents the interval of time since the individually recovered meteorite was separated

from a larger body. Whipple and Fireman

(1959) showed that an alternative interpreta1

 Smithsonian Astrophystcal Observatory, and Harvard College Observatory, Cambridge, Mass.

tion of exposure age leads to a determination

of an upper limit to the rate of erosion acting on

the meteorite while it was in space. The actual

erosion rate experienced by the meteorite

may well have been smaller, depending upon

the unknown time at which the meteorite was

separated from a larger parent body.

Suppose, as an example, that in a recently

fallen meteorite the quantity of the stable

argon isotope A38 is measured, as well as that of

the isotope A39, which has a half-life of some 325

years. Since the relative cross sections for

average cosmic-ray spallation are known for

these two isotopes, the A39 measurement

provides a determination of the average rate

of production of A38 over some 100 revolutions of the meteoroid in orbit about the sun

and over a large number of sunspot cycles (the

latter in case the cosmic-ray activity is dependent upon solar activity).

Let us assume that the measurements are

made somewhere near what was the center of

the meteoroid before it was ablated and broken

by atmospheric passage, and that the meteoroid was roughly spherical, of radius R. Let

L be the distance through which the cosmicray spallation effect is reduced by a factor of e.

Then the measured A39 content leads to the

rate of production of A38 given by the equation

(1)

where C is the constant determined by the

measurement.

If we postulate a statistically linear erosion

rate of the external surfaces by all causes while

the meteoroid was in space, the accumulated

A

38

 will amount to

3

*=C fT exp [-{R+tt)IL]df

Jo

(2)

239
240 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

where T' is the interval of time since the

meteoroid was exposed to cosmic rays,

presumably by separation from a parent body.

The usually defined exposure age T follows

from a constant rate of production by cosmic

rays producing the A38; from equation (1) the

accumulated A38 is given by

A

3

»=CTexp(-R/L). (3)

On integrating equation (2) and equating

the values of A38 to that given by equation (3),

we find

If we assume that T is very great compared

to T, we obtain an upper limit to the erosion

rate by the simple expression,

e=L/T. (5)

Eventually our knowledge of the breakup

of asteroids in the formation of meteorites may

be adequate to enable us to put in a significant

value of T' in equation (4). At present, the

upper limit to the erosion rate given by equation (5) represents an adequate statement of

our knowledge.

For the Sikhote-Alin nickel-iron meteorite

Fireman (1958) found T=5X108 years by a

measurement of the decay rate of A39 and

an evaluation of the A38 content from the He3

measured in that meteorite. Whipple and

Fireman (1959) adopted a shielding constant

Z=72 cm on the basis of spoliation measures

in a high-energy accelerator, and thus derived

an upper limit to the erosion rate of a nickeliron meteorite as «=1.5X10~7

 cm yr"1. Fisher

(1961) has criticized this determination; he

prefers a value based upon Ne21 measurements

in the Grant meteorite leading to a value

«=1.1X1O~8 cm yr"1. A detailed critical discussion of the pros and cons concerning meteorite exposure ages by various isotopic measurements would become too involved for the

present paper and probably would not result

in any definitive conclusions in the present

state of the art. Measurements of 17 iron

meteorites giving exposure ages by A39 or Cl3a

rates are listed by Anders (private communication) and average about 3.4 X108

 years. The

five oldest average about 6 X108 years. I shall,

therefore, adopt as a significant estimate,

probably correct to within a factor of 2, an

upper limit to the erosion rate of nickel-iron

meteorites in space, e=1.2X10~7 cm yr"1, to be

used in the present discussion.

The fact that the exposure ages by the argon

method and by similar methods have consistently come out much smaller for stony

meteorites than for iron meteorites has been a

subject of considerable interest for several

years. Fireman and DeFelice (1960) suggested

that the difference results from the physical

weakness of stones as compared to irons, resulting in a more rapid etching of the stones, a

major assumption of this paper. In a summary

of argon measurements for various stony meteorites, Fireman and DeFelice (1961) find that

for nine chondrites the A39 decay rate ranges

only from 5 to 12 kg~* min"1. The exposure

ages and the A38 contents are similarly confined

in range (e.g., A38 only from 1 to 2X10~8 sec

gm"1). Typical exposure ages by the argon

method and also by similar methods for chondrites generally are less than 10s

 years. Until

more definitive results are available, I shall

adopt the typical exposure age of 4X107 years

determined for the Bruderheim meteorite by

Fireman and DeFelice, and a shielding constant

Z=70 cm, suggested by these authors. The

upper limit to the erosion rate for typical stony

meteorites then becomes e=1.7X10~8 cm yr"1.

Again the uncertainty may be comparable to a

factor of 2.

For photographic meteoroids, Jacchia and

Whipple (1961) find semi-definitive evidence

that the lifetime of photographic meteoroids

in space is relatively short, of the order of

10,000 years or perhaps less. Some 60 percent

of the precisely reduced photographic meteors

can be assigned to streams or associations; also

there is no tendency for meteors having aphelion

distances within the perihelion distance of

Jupiter to have their lines of apsides aligned

with those of Jupiter, as is so conspicuous for

the asteroids.

Since so many of the meteor orbits cross that

of Jupiter and are subject to relatively great

perturbations by that planet, the tendency to

streaming among photographic meteors indicates a relatively short lifetime. Over
METEOR SYMPOSIUM—WHIPPLE 241

periods of time adequate for the PoyntingKobertson effect to reduce the aphelia appreciably, Jupiter perturbations should cause

most of the stream identities to become unrecognizable. The lack of systematic alignment of the apsides among the meteors of

smaller aphelion distance again indicates that

Jupiter perturbations have not had time to

play an appreciable role for these meteoroids.

More precise evaluation of the time scale involved is under study by S. Hamid at the

Smithsonian Astrophysical Observatory, but

for the moment, an estimate of 10* years appears to be reasonable, although perhaps too

long.

Destructive forces are thus clearly at work

among the cometary meteoroids. Barring

totally destructive collisions, an erosion rate

should fairly describe the destructive processes.

Thus, to determine the erosion rate for the

photographic meteoroids, we need a determination of the meteoroid dimensions. Again, to

provide an upper limit, let us assume that the

104-year period of destruction applies to a zeromagnitude meteor with an entry velocity of 30

km sec"1. Until the luminous efficiency factor

or the ionizing efficiency factor has been theoretically or experimentally determined for

photographic meteoroids, we have available for

dimensional determination primarily the drag

measurements in the Harvard photographic

meteor program. These measurements provide

the following relation between meteoroid radius

R and density p, for a 0th magnitude meteor at

velocity 30 km sec"1:

i?p=0.23 (cgs). (6)

I am indebted to Allan F. Cook and Luigi G.

Jacchia for this evaluation, which is probably

significant to 20 or 30 percent. The largest

uncertainty rests in the assumed shape factor

of the meteoroid, which was taken to be 1.66,

and the drag coefficient, taken as (7d=2.0; both

enter linearly on the right side of the equation.

Accepting a time of 10* years for total

erosion, we estimate for the erosion rate in

equation (6),

c(phot. met.)=2.3X10"5/p (cm yr"1). (7)

This value may be taken as a rather high

estimate since we might well have chosen a

third-magnitude meteor as representative of

the fainter limit of the photographic determinations. This assumption would reduce the value

in equation (7) to a rate of approximately 10~5/P

cm yr"1. However, the determinations for

iron and stony meteorites are both upper limits,

and tentative indications suggest that the

photographic meteoroids may, indeed, be destroyed in a shorter mean time than 10* years

in the inner region of the solar system typical

of the orbital paths expected for recovered

meteorites. No clearcut information is yet

available concerning the density p to be applied

in equation (7). The lowest mean value is

p=0.05 gm cm"3 suggested by Cook and

Whipple (Whipple, 1955), but based upon a

rather unreliable method of mass determination

that depends upon the forward motion in the

incoming train of a bright photographic meteor.

There is little question but that some stream

meteoroids may average densities even smaller

than this, for example, the Giacobinid stream

of 1946, but average values for more typical

photographic meteoroids may more probably

lie near 0.3 gm cm"3. This problem of meteoroid density is under continuous investigation;

better values will be obtainable when more

definitive examples of stony meteors have been

investigated by photographic meteor techniques. We have clearcut evidence, particularly that by McCrosky (1955), that photographic meteoroids are weak structures and

that many of them crush under dynamic pressure of the order of one-third atmospheric

pressure, approximately 10~* dyn cm"2. Opik

(1955) previously deduced such a crushing

strength from less definitive observational data.

The basic assumption of this paper, that the

erosion rates calculated above for iron, stony,

and cometary meteoroids are actually measures

of space erosion, is an ad hoc assumption for

which no great affirmatory evidence can be

amassed. Its chief raison d'etre rests on the

fact that the values increase sequentially as

we go from materials of stronger to weaker

structural strength, or better, from greater to

lesser crushing strengths. Also there seems

little reason to believe that etching processes

such as ionic sputtering would be highly sensitive to strength of materials. The binding in

crystalline structures is not so vastly variable
242 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

from one material to another (see, for example,

Reiffel, 1960). Crater formation, however,

where there is no gravitational or other mechanism for retaining crushed material, should

increase markedly as the target material

becomes weaker structurally.

Anders (private communication) carefully

discusses the pros and cons of the erosion concept for irons and stones, and questions the

conclusion severely on the following grounds:

(a) Some of the harder stones have short exposure ages, while the "friable" Norton County

has an age of 2 to 5X108 years, (b) Macroscopic strength cannot be the major factor in

cratering by dust, only the microstructure; the

mechanical strength of iron and stone crystals

do not differ much; also from Buddhue's (1942)

measures of crushing strength even the macroscopic strengths of some stones are comparable

to that of the Descubridora, Mexico, iron (Om),

3.7X109 dyn cm"2, (c) Strong clustering of

ages occurs for the chondrites near 22X106

years versus much shorter ages; clustering also

occurs for the irons near 3X108 years and

6X108 years; the hexahedrites seem to show

shorter life times than the medium octahedrites.

Some of these objections are also voiced by

Eberhardt and Hess (1960).

The shorter derived exposure ages, whether

for irons or stones, whether for hard or soft

material, whether or not clustered in time,

really do not bear on the erosion problem.

There is every reason to believe that collisions

and breakage among meteoroids must occur.

Thus the shorter exposure ages (when not due

to leakage of gas) are reasonably interpreted

in the now classical fashion as measuring some

mean time since a breakup or breakups.

The great age for the Norton County

achondrite presents a problem. Edward L.

Fireman has permitted me to express his opinion

as follows: "The exposure age of Norton County

is more uncertain than that of other meteorites

because its Fe content (~1 percent) is the

lowest of any meteorite. Thus argon is produced mainly from Ca and K; the He may be

produced by a high Li6 content. Some Li and

target measurements in Norton County are

necessary to put its exposure age on a firmer

basis." Until these experiments have been

done, and until complete measures on single

samples are made, the problem does not appear

damning to the erosion concept.

It is quite clear, as Anders points out, that

pure compressive strength is not the vital

quantity that should measure the cratering

efficiency of high-velocity impact. Some numerical measures of malleability or of brittleness

should enter the cratering formula. Everyone

knows that violent shock on a meteorite will

break more stone than iron. The volume of

displaced material is mostly determined by

whether the material breaks when compressed

violently as the exposure shock wave spreads

and attenuates. The iron in most chondrites

is usually not adequate by volume (5 to 10

percent), and is too poorly distributed to offer

major protection to the stony material against

crushing and shattering. Undoubtedly it does

offer appreciable protection in some chondrites,

but the stronger crystals in the stone will fall

apart when the softer matrix is worn away by

cratering impact.

The questions raised by Anders cannot be

ignored and suggest a number of experiments

and measurements that must be made to

finally clarify the situation. I prefer for the

moment, however, to adopt the erosion concept

as a working hypothesis applying to the older

exposure ages, and to pursue the consequences

of this hypothesis.

Cratering by high-velocity impact

No definitive theory or experiment yet defines

the laws of crater formation by high-velocity

impact. Indeed, the broad dependence of the

phenomena upon velocity or nature of the

materials is not yet established. Rapid progress, however, is now being made in this area

of research, both in theory and in experiment.

The only theory that appears broad enough to

cover the types of target materials of interest

in meteoroids is by Opik (1958). He calculates

that a projectile (or meteoroid) of mass ft,

striking a large solid surface of density p, and

compressive strength S, at a meteoric velocity

v, will crush and displace a mass M, according

to the equation

M

where k is a dimensionless constant that depends
METEOR SYMPOSIUM—WH1PPLE 243

upon the shape and nature of the impinging

body. He derives values of k=4.7 for iron

impinging on stone, and k=4.3 for stone on

iron. Fireman and DeFelice (1960) apply his

theory to the problem of erosion rates and

meteoritic collision in space.

From effects of surface nuclear bursts, S.

Glasstone (1957, par. 5.8) adopts a scaling law

in which the linear dimensions of the displaced

earth vary as the cube root of the energy E.

Thus, the volume or mass of the earth displaced

and brecciated varies as the energy of the

explosion (with dependence upon the scaled

depth of the explosion). His constants lead

to an energy per unit mass of dry earth displaced

equal to about 1X109 erg gm"1.

Shoemaker (1960), in his calculations of the

mass that produced the Arizona Meteorite

Crater (Barringer Crater), adopts Glasstone's

scaling law and uses constants equivalent to

2.3 X108 erg gm"1 for displaced earth at an

impact velocity of 15 km sec"1. He also uses

the scaling law (E)1/3i, which would further

reduce the required ergs per gram for microscopic particles. I used the energy-scaling law

and a constant of 1.2 X1010 erg gm"1 for aluminum (Whipple, 1957).

Opik's relation (eq. 8) produces a volume of

displaced material proportional to the momentum rather than to the energy of impact. Thus,

at #=15 km sec"1, he calculates the impacting

mass of the Arizona iron meteoroid to be some

20 times greater than does Shoemaker (1.5 X1012

gm vs. 6.3X1010 gm). Opik adopts, however, a

crushed mass of 1015 gm, about three times the

value adopted by Shoemaker, reducing the

theoretical discrepancy to a factor of eight

times. From equation (8), if «=15 km sec"1,

and <S=9X108 dyn cm"2 and p=2.6 gm cm"3

for dry earth, Opik's value of energy per gram

of displaced rock becomes 3.0X109 erg gm"1

compared to 1X109 erg gm"1 by Glasstone and

2.3 X108 erg gm"1 by Shoemaker.

In his calculations of impact craters and

meteoritic penetration at impact velocities of

5.5, 20, and 72 km sec"1, Bjork (1961a) finds

the momentum scaling law. His calculations

have been confirmed experimentally at «~6.5

km sec"1. In his preliminary report on the

formation of the Arizona Meteor Crater, he

(1961b) also adopts the momentum scaling law.

For hemispherical craters in aluminum or

stone, his formula (1961a) is

Penetration=2.35X10"2(M»)1/3 (cgsunits). (9)

Thus, Bjork's equation for crater formation

agrees with Opik's insofar as velocity is concerned, but carries no explicit term for the

strength or ductility of the material. For

stone (p=2.64 gm cm"3) his equation for ratio

of crater mass to projectile mass is closely

M

—=7.0X10-5y (cgsunits). (10)

The corresponding energy per gram displaced

at 0=15 km sec"1 becomes 1.0X1010 ergs gm"1,

a relatively high value.

I can find little experimental evidence concerning the dependence of cratering upon the

density, strength, or nature of materials.

Birkhoff et al. (1948) Jfind that the depth of

penetration of a high-velocity jet varies as

p-1/2 Thus, the volume of material displaced

in a jet-produced crater should vary more

rapidly than p"1, perhaps as much as p~3/2, and

the mass as p° to p~1/2, in contrast to Opik's

conclusion, p+1/2.

Summers and Charters (1959), from relatively

low-velocity impact (to 3 km sec"1) of copper

and lead projectiles on both copper and lead

targets, find a relation which becomes closely

M o /v\2

—=5.93—(-) (cgs units), (11)

where pm is the density of the projectile, and c is

the velocity of sound in the target material.

Equation (11) follows the energy scaling law;

the calculated energy per unit mass displaced

for ordinary materials is high, on the order of

1010 ergs gm"1. The displaced mass varies

inversely as the target material.

Applicable to the present discussion are

photographs by Charters (1960) of the crater

formed in granite by a ^-inch-diameter nylon

sphere at »=5.34 km sec"1. By measuring the

photographs and assuming that p (nylon) =

1.14 gm cm"3 and p (granite) =2.64 gmcm"8,

I calculate that the ratio of the displaced mass

to projectile mass is M/n=220, and that the

energy of displaced material per unit mass is

6.6X108 ergs gm"1, a relatively low value.
2 4 4 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

I have compared the various theories and Let us then adopt k=4.0 in equation (8),

formulas for crater formation with the Charters since the meteoroid will probably be less dense

photographs of the crater formed in granite by a than stone (£=4.3 for stone striking iron). At

nylon ball (see table 1). The theories or formulas a relative velocity v, interplanetary material of

by Opik, Glasstone, and Shoemaker fit the mean space density p, will, upon encountering a

results from the photographs fairly well, while randomly oriented surface, contribute a mass

the predictions by Summers and Charters, vp,/4 per unit area per unit time. The linear

Whipple, and Bjork are less satisfactory, pre- erosion rate dR/dt will vary as p"1 times the

dieting too small a crater volume by one to two mass erosion rate; hence by equation (8), the

orders of magnitude. linear erosion rate becomes

TABLE 1.—Crater by nylon ball on granite at dR__ p,v*

v=5.S4kmsec-1 ~dt=e==(pS)1/2' ' '

Energy of Mass displaced

displaced mass Mass projectile _ _. . . , , . .

Source era gm-i M/ M Mean space density of dust and comparisons

Opi-(eq. )• We can now apply the observed etching rates to

Glasstone l X 1O» determine a mean space density of particles by

Shoemaker 2.3X108 means of equation (12); hence

Bjork 38

Summers and Charters e(pS)112

(eq. ll) b 7.0X10»° 2.0 P.=—~2 (13)

Photographs by Charters 6.6X108 220

• Assumed crushing strength of granite, S—1.5X10»dyn cm-'. _,, , - , . ,

* Assumed velocity of sound in granite, c-6.oxio» cm sec->. 1 he space density and tne velocity of encounter both vary in some inverse fashion with

I shall adopt Opik's solution and constants in solar distance (~r~1/2?), while the time of passage

this paper, since they appear to apply fairly well varies in a direct fashion (^r372?). Hence the

in an experimental example that simulates the mean value of p, will be somewhat weighted

actual situation in space. There can be no towards the outer parts of the meteoroid orbits,

doubt that some other quantity than compres- A more refined treatment is scarcely justified at

sive strength, perhaps some function of ductility this stage of the study.

or brittleness, must more appropriately measure The last column of table 2 gives calculated

the material displaced in crater formation by values of the mean space density based on

high-velocity impact. Also density seemingly equation (13) and the adopted values of the

should enter the equation in a different manner. erosion rates for irons, stones, and photographic

More theoretical and experimental results are meteoroids. For irons the value of crushing

sorely needed. Fortunately, the velocities of strength is probably too great, but is intended to

interest are near enough to the observed velocity include some effect of ductility or malleability,

so that the still unresolved question of mo- as compared to the value for stones, checked

mentum or energy scaling does not greatly generally by the experiment of the nylon ball

affect the calculated results. In both cases on granite. For photographic meteoroids the

the scaling is proportional to mass, and no value of £ is probably too small, representing

theory suggests much deviation from mass the most fragile 20 percent observed. The

scaling so long as the projectile contains a mean velocity is taken at 10 km sec"', as

very large number of atoms. representing a value corresponding more to the

TABLE 2.—Calculations of space density from erosion rates

Compressive Meteoric Mean

Erosion rate Density strength velocity space density

t(cm sec1) p(gm cm,-

1

) S{dyn cm,-

2

) v(km sec~

l

) p.igm cm,-')

Ir°ns 3. 8X10"15

 7.8 2X1O'<> 10 1. 5X10"21

Stones 5.4X10-" 2.6 2X10» 10 3.9X10""

Phot, met, 7. SXIO-'V1 P 2X104 10 0. 10X10-lV"I/1
METEOR SYMPOSIUM—WHIPPLE 245

distance of the earth or Mars from the sun

than to the value in the asteroid belt (~5 km

sec"1)- The value y=10 km sec"1 is small for

meteors, even after neglecting earth gravity.

The mean space density calculated from data

on photographic meteoroids is more than an

order of magnitude smaller than those based on

erosion of irons and stones, if we adopt p~ l

gin cm"3. A smaller value of p is possible and

the crushing strength is probably underestimated; hence the fit is satisfactory in view of

the uncertainties in all the critical data. A

somewhat higher value of v than 10 km sec"1

might be more applicable to cometary meteoroids than to asteroidal material, because of the

greater orbital inclinations and eccentricities.

This would increase the discrepancy. On the

other hand, the greater mean applicable solar

distance and inclination would be expected to

reduce the average space density of material

encountered by cometary meteoroids. Hence

the discrepancy is in the expected direction and

may represent reality.

Comparison with other data is difficult. For

the Zodiacal Cloud in the neighborhood of the

earth's path, van de Hulst (1947) derives

1.0 X10"21 p gm cm"3 as the density near the

earth's orbit. If we accept a fraction / of this

density as applying to the mean region of

cometary asteroids, and assume that the density

of interplanetary particles equals that of the

cometary meteoroids, we can solve for p and p,

by this relation and by table 2, leading to

N(R) =

3.5X10-*°

R

2

* ' (15)

pJ/3=0.1// (cgs units). (14)

If we arbitrarily adopt some reasonable value

for/, say 1/4, allowing for a decrease in p, with

solar distance and away from the ecliptic

plane, we solve equation (14) to derive p~0.5

gm cm"3 and p,= 1.2X10~22 gm cm"3. The

corresponding value of the mean density near

the earth's orbit is then 5X10"22 gm cm"1.

Other analyses of the Zodiacal Cloud obtain

lower values of p, than van de Hulst by factors

of 10 or more times (see, for example, the list

by Nazarova, 1961). The derived density is

very sensitive to the upper limit of the cutoff

in the distribution law applicable to the smallest

particles. Typical is van de Hulst's derived

law

638805-

where N(R)dR represents the number of

particles per cm3 in the particle-radius range

dR. In his integration he cuts off the upper

limit at R=0.035 cm; the lower limit-, does not

much affect the sum.

The mean space density derived by McCracken, Alexander, and Dubin (1961) from

measures on space vehicles near the earth is

considerably greater than van de Hulst's value.

Comparison, however, is specious since their

particle-size distribution law is

N(R): 6.0X10"28

1 (cgs units). (16)

The mass integral depends almost solely

upon the lower limit in R, which at mass ~10~10

gm leads to a mean space density near the earth

of 3.2 X10"20 gm cm"3. The space density is

doubled if the mean velocity of impact is taken

as 15 instead of 30 km sec"1, and increases

rapidly as the limiting particle radius is reduced.

But the real difficulty in comparison lies in

the area provided for diffraction of light by

small particles, diffraction being proportional

to the total area. From McCracken et al.

(1961) the particle area per unit volume is

5.7X10

-17 .-2/3 cm2

 per cm3, while van de

Hulst requires only 6 X10"20 cm2 per cm3 near

the earth, or about one thousandth as much.

The newer measures by Blackwell, as indicated

by the calculations of Ingham (1961), require

even a lower scattering area, roughly 10"21 cm2

per cm3 at the earth's distance from the sun.

The great diffracting area observed by McCracken et al. is provided by particles largely

in the dimension range from 10"4 to 10~3 cm

that are most responsible for scattering at

angles of from 1° to 10° from the sun. Hence

their deduced particle density would increase

the intensity of the Fraunhofer Corona a

thousand times its observed intensity, unless

the particles are confined to a small volume

near the earth, essentially within the moon's

distance. This evidence seems to confirm the

existence of a dust cloud about the earth

(Whipple, 1961a, 1961b; Hibbs, 1961a, 1961b;

questioned by Dubin, 1961).
246 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Consequences of erosion to the PoyntingRobertson effect

Let us again accept the postulate made above

that cometary meteoroids capable of producing

photographic meteors are eliminated by space

erosion of some kind in the order of 10* years.

The average lifetime t of any such meteoroid

will then be R/e, or by equation (7),

*=#PX4.3X104 years, (17)

where R and p, the radius and density, respectively, of the meteoroid, are measured in cgs

units.

Now the Poynting-Robertson effect (Wyatt

and Whipple, 1950) will cause a particle to

spiral from an initial orbit into the sun in a

time

t=RPKX107 years, (18)

where K depends upon the initial eccentricity

and perihelion distance of the orbit, and is of

the order of unity for short-period comet orbits.

Typical values of .EL are: 0.14 for the Geminid

meteor shower; 0.6 for the Taurids and Encke's

comet; 2.8 for the Bielids; 7.2 for the Leonids;

and 18.6 for the Lyrids. We see that the

Poynting-Robertson effect acts at a rate 10~2

to 10~4 times as fast as the estimated erosion for

typical meteor showers. Thus, if we take the

erosion rate as fixed for particles of all sizes, the

Poynting-Robertson effect can be neglected for

all cometary meteoroids, but could possibly be

effective for some of the asteroidal particles (see

table 2), such as irons in highly inclined orbits.

Even for stones, however, the effect could

probably be neglected.

At least two other factors must be considered

as we apply the above reasoning to smaller

particles: (a) erosion changes to destructive

collision when the eroding mass is the order of

10~3 times the mass of the particle eroded or

greater; and (6) the physical properties of

cometary meteoroids may depend upon their

size.

Thus, as we consider erosion of smaller

particles, the upper limit of mass for the

eroding particles must be reduced proportionally

to the mass of the particle eroded. The cross

section for destructive collision by larger

particles can be neglected. The PoyntingRobertson effect becomes operative when only

10~2 to 10~4 of the total space density remains

in particles the order of 10"2 times the mass of

the particle eroded. If, for example, van de

Hulst's law (eq. 15) is valid to Jf2=10~4 cm, 1

percent of the mass would then be contained in

the range 1 to 13X10"4 cm. Hence, cometary

particles less than approximately 60/x in radius

and initially in very short-period orbits, or in

longer orbits of high inclination to the ecliptic,

might survive long enough to spiral into the sun.

Note that high-inclination orbits are always

favored because of the observed concentration of

dust to the ecliptic (really Jupiter's orbit

plane). Note also, however, that these smaller

particles are already counted in the diffraction

theory for the origin of the Fraunhofer Corona.

As the exponent a of R in the relation

N(R)~R~a becomes greater than 4, where the

increase in mass per logarithmic step in R or n

is constant, only the smallest particles allowed

by light pressure survive long enough to spiral

into the sun. The total fraction of the mass in

these small particles, however, becomes larger

as a increases. If high-energy ions contribute

appreciably to space erosion, however, small

particles may fare no better than large ones

with regard to the Poynting-Robertson effect

(see, for example, Whipple, 1959; and Reiffel,

1960).

On the other hand, if the small cometary

meteoroids are stronger and tougher than are

the larger ones, erosion may be less serious for

them. An increase by a factor of 100 in compressive strength would increase the limiting

particle size by a factor of 10 and the limiting

mass by a factor of 1,000.

We may conclude, therefore, that the data

and assumptions of the present paper would

preclude most of the small particles from

attaining low inclination, nearly circular orbits,

unless they are much stronger physically than

the average photographic meteoroids. Higher

inclination orbits would somewhat favor Poynting-Robertson reduction in orbit dimensions

for all particles. Unfortunately, we have no

satisfactory information about the physical or

chemical nature of the small particles (below

M~10- 2

gm).
METEOR SYMPOSIUM—WHIPPLE 247

Dust as a hazard to space vehicles

Penetration rates for exposed surfaces in space

near the ecliptic between Venus and Mars well

away from the earth should probably be considerably smaller than the values given by

the author in 1957. The mean space density

near the earth was taken as 4X10"20 gm cm"3

as compared to the values derived here, in the

range from 4X10"22 to ~1XK)-20 gm cm"3

near the earth's orbit. Bjork (1961a) finds

slightly smaller penetrations for given masses

and velocities, while possible low densities of

the particles themselves may reduce their penetration powers. Lower average velocities also

will apply, especially towards Mars, again

reducing the penetrating power.

In the immediate neighborhood of the earth

we still have no reliable information on the

distribution of particles in the mass range from

10~5 to 10~3 gm. Extrapolations from McCracken et al. suggest that my 1957 estimates

may be too large. On the other hand, the

rough agreement of values of mean space

density derived from etching rates and from

the Zodiacal Cloud calculations suggests that

most of the mass (or mean density) in space is

carried by particles intermediate in size between

the finest dust and optical meteoroids; i.e., in

the range 10~7 to 10~3 gm. Hence my 1957

estimates may, in fact, be realistic values rather

than safe upper limits near the earth.

The etching rates for exposed surfaces can

be determined with some confidence from table

2 as safe limits near the ecliptic between Venus

and Mars, but not in the immediate vicinity of

the earth. McCracken et al. have produced

almost incontestable evidence that a high concentration of fine dust exists near the earth.

Thus etching rates within the moon's distance

may be a few times greater, perhaps even orders

of magnitude greater, than at much larger

distances from the earth, but still negligible

for metals as tough as aluminum.

Exposed surfaces of weak and brittle materials should be avoided in space vehicles where

an etching rate of 1 micron a year would be

undesirable. On the moon, the etching (and

possibly even penetration) may be aggravated

by material ejected from meteoritic impacts.

When not in use, transparent or delicate surfaces

should be protected on the moon, and "tough"

material should be chosen insofar as is practicable for exposed surfaces whose function could

be impaired by etching.

Note that the continued operation of Vanguard I for nearly three years does not guarantee

that the protecting windows for the solar cells

are not severely etched. Even severe etching

of a glass surface does not necessarily reduce

much of its transparency to light.

Acknowledgment

I am indebted to Dr. Edward Anders for prepublication material, and especially to Dr.

Edward L. Fireman for helpful advice and

discussion.

References

BIRKHOFF, G.; MACDOUGALL, D. P.; PUGH, E. M.:

AND TAYLOR, G.

1948. Explosives with lined cavities. Journ.

Appl. Phys., vol. 19, pp. 563-582.

BJORK, R. L.

1961a. Meteoroids vs. space vehicles. Journ.

Amer. Rocket Soc, vol. 31, pp. 803-807.

1961b. Analysis of the formation of Meteor Crater, Arizona: A preliminary report.

Journ. Geophys. Res., vol. 66, pp. 3379-

3387.

BuDDHUE, J. D.

1942. The compressive strength of meteorites.

Pop. Astron., vol. 50, pp. 390-391.

CHARTERS, A. C.

1960. High-speed impact. Sci. American, vol.

203, no. 4, pp. 128-140.

DUBIN, M.

1961. Remarks on the article by A. R. Hibbs,

"The distribution of micrometeorites

near the earth." Journ. Geophys. Res.,

vol. 66, pp. 2592-2594.

EBERHARDT, P., AND HESS, D. C.

1960. Helium in stone meteorites. Astrophys.

Journ., vol. 131, pp. 38-46.

FIREMAN, E. L.

1958. Argon-39 in the Sikhote-Alin meteorite fall.

Nature, vol. 181, pp. 1613-1614.

FIREMAN, E. L., AND DEFELICE, J.

1960. Argon-39 and tritium in meteorites. Geochim. et Cosmochim. Acta, vol. 18,

pp. 183-192.

1961. Tritium, argon 37, and argon 39 in the

Bruderheim meteorite. Journ. Geophys.

Res., vol. 66, pp. 3547-3551.

FISHER, D. E.

1961. Space erosion of the Grant meteorite.

Journ. Geophys. Res., vol. 66, pp.

1509-1511.
248 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

GLASSTONE, S., ED.

1957. The effects of nuclear weapons. U.S.

Atomic Energy Commission, Washington, D.C.

HIBBS, A. R.

1961a. The distribution of micrometeorites near

the earth. Journ. Geophys. Res., vol.

66, pp. 371-377.

1961b. Author's reply to the preceding discussion

on the article, "The distribution of

micrometeorites near the earth." Journ.

Geophys. Res., vol. 66, pp. 2595-2596.

VAN DE HULST, H. C.

1947. Zodiacal light in the solar corona. Astrophys. Journ., vol. 105, pp. 471-488.

INGBAM, 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. 157-176.

JACCHIA, L. G., AND WHIPPLE, F. L.

1961. Precision orbits of 413 photographic

meteors. Smithsonian Contr. Astrophys.,

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

MCCBACKEN, C. W.; ALEXANDER, W. M.; AND DUBIN,

M.

1961. Direct measurement of interplanetary dust

particles in the vicinity of Earth. Nature, vol. 192, pp. 441-442.

MCCBOSKT, R. E.

1955. Fragmentation of faint meteors. Astron.

Journ., vol. 60, p. 170.

NAZAKOVA, T. N.

1961. Investigation of meteoric particles on the

third Soviet artificial earth satellite.

Planetary Space Sci., vol. 8, pp. 82-85.

OPIK, E. J.

1955. The masses and structure of meteors. In

Meteors, T. R. Kaiser, ed., pp. 33-35.

Pergamon Press, New York.

1958. Meteor impact on solid surface. Irish

Astron. Journ., vol. 5, pp. 14-33.

REIFTEL, L.

1960. Erosion of meteorites in space and the

density of interplanetary gas. Nature,

vol. 185, pp. 821-823.

SHOEMAKER, E. M.

1960. Penetration mechanics of high velocity

meteorites, illustrated by Meteor Crater,

Arizona. In Report Int. Geol. Congr.,

21st Session, Norden, 1960, Part 18,

pp. 418-434.

SUMMERS, J. L., AND CHARTERS, A. C.

1959. High-speed impact of metal projectiles in

targets of various materials. In Proc.

Third Symposium on Hypervelocity Impact, F. Genevese, ed., pp. 101-110.

Armour Research Foundation, Chicago.

WHIPPLE, F. L.

1955. On the mass-luminosity relation for

meteors. Astron. Journ., vol. 60, pp.

182-183.

1957. The meteoritic risk to space vehicles. In

Proc. 8th Int. Astronautical Congr.,

Barcelona, 1957, pp. 418-428. SpringerVerlag, Vienna, 1958.

1959. Solid particles in the solar system. Journ.

Geophys. Res., vol. 64, pp. 1653-1664.

1961a. The dust cloud about the earth. Nature,

vol. 189, pp. 127-128.

1961b. Particulate contents of space. In Medical

and biological aspects of the energies of

space, P. Campbell, ed., pp. 49-70.

Columbia University Press, New York.

WHIPPLE, F. L., AND FIREMAN, E. L.

1959. Calculation of erosion in space from the

cosmic-ray exposure ages of meteorites.

Nature, vol. 183, p. 1315.

WYATT, S. P., JR., AND WHIPPLE, F. L.

1950. The Poynting-Robertson effect on meteor

orbits. Astrophys. Journ., vol. Ill, pp.

134-141.

Abstract

Photographic meteor studies and spallation products of cosmic rays in meteorites provide upper limits or evaluations of erosion rates for meteoroids in orbit. The rate increases by several orders of magnitude in the sequence:

irons, stones, and photographic meteoroids. The sequence suggests that the erosion rate depends in some inverse

fashion upon the strength or brittleness of the materials, a natural expectation if erosion is produced by crater-forming

impacts with interplanetary dust. On this assumption and by applying Opik's high-velocity impact theory, the

author derives a mean space density for the dust at roughly 10~21 gm cm~*.

Only the very smallest cometary meteoroids can spiral into the sun by the Poynting-Robertson effect if the assumptions of this paper are true. Strong evidence for a high concentration of dust in the earth's immediate vicinity

suggests that erosion rates may be greater near the earth than in deep space from Venus to Mars and even beyond.

The surface of space vehicles should be carefully chosen or protected to minimize etching by interplanetary dust,

if long exposure times are anticipated. The hazard may be greatest at the moon's surface.
The Absence of Magnetic Micropulsations of Meteor Origin

By C. Ellyett1 and G. B. Gillion'

Kalashnikov (1949) claimed to have found

an increase in the occurrence of micropulsations

of the earth's magnetic field during the dates

of certain northern hemisphere meteor showers.

Pulsations of Amy amplitude could be recorded.

The measured band of micropulsation frequencies unfortunately extended upwards beyond

2 c/s, and hence into the region of sferics of

thunderstorm origin. Campbell (1960) has

reviewed this work, and concludes that the

validity of the results is increased by the fact

that the observations were made in November,

December, and January—a period of minimum activity in the annual cycle of thunderstorm activity.

Hawkins (1958) repeated Kalashnikov's investigations using apparatus of about the same

sensitivity, and found no significant increase.

His equipment, however, covered the band 0.5

to 10.0 c/s, and hence could also have recorded

sferics.

Further work was done by Campbell (1960),

who carried out a 7-month series of micropulsation measurements in California in 1958, with

a limiting sensitivity of 20mY. The periods

recorded lay between 0.04 and 0.4 c/s. An

average amplitude was obtained for each hour.

Normalizing factors ranging from 1.02 to 33.3

for various hours of the day, compared with the

rate at 10 a.m. L.T. as reference, were applied to

determine an average daily value. Departures

in micropulsation amplitude from this daily

average were then compared with the occurrence of the meteor showers. This procedure

would appear to be doubtful in two respects.

First, undue weight in scaling within the day

appears to be given to the 10 a.m. micropulsation amplitudes. Meteor shower occurrence

normally peaks well before 6 a.m. L.T., and it is

1

 Physics Department, University of Canterbury, Christchureh,

New Zealand.

only in very limited parts of the year that a

second peak of shower activity occurs around

8 to 10 a.m. Second, the association of the two

phenomena, which was claimed to exist, was

based on low-rate meteor observations (Whipple

and Hawkins, 1958). If the percentage occurrence of micropulsation activity is to increase

appreciably, an accompanying large increase

of subvisual meteors is implied. Observations

at high radar-meteor rates, however, have now

shown that major showers comprise a relatively

small proportion of the total count (Whipple

and Hawkins, 1958; Ellyett and Keay, 1956).

Finally, Jenkins, Phillips, and Maple (1960)

observed micropulsations at 1.5 c/s, with an

improved sensitivity of 0.3m7. They claim

an occasional big increase in the occurrence

of these micropulsations on some nights,

correlating with meteor showers. The graphical

correlation does not look convincing, and in

any case the meteor data used are the Harvard

visual meteor observations taken during the

first half of the century. These are again

low-rate observations.

On general grounds, there is little in the

diurnal distribution of micropulsations that

fits the picture of meteor occurrence. Continuous micropulsations (Pc), trains (Pt), giant

pulsations (Pg), and long-period fluctuations

(LPc) all increase in amplitude toward the

auroral regions. Observations of Pc show a

27-day solar period, and both Pt and Pg are

essentially nighttime phenomena. The possible

exception is "pearls" at about 1 c/s, but these

on occasion last fairly regularly for many hours.

If a single meteor produces a magnetic

pulse or train of pulses—as it must if the

suggestion of meteor origin is correct—then

it is obviously desirable that both sets of

phenomena be observed at the same site.

This has not previously been done.

249
250 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Meteor equipment

A radar transmitter maintained a signal of

81 kw peak power and 26 M pulse width at

69.5 Mc/s, with a pulse recurrence frequency

of 150 c/s. Single crossed folded dipoles

above wire-mesh artificial earth screens were

used for transmitting and receiving, and

resulted in all-sky viewing. The receiver,

followed by normal oscillograph and camera

recording, contained design features that eliminated false meteor rate variations due to both

slow variations of the background noise

(MacLauchlan, 1960) and pulse-type interference. Meteors were recorded down to a

magnitude of +9.1.

Micropulsation equipment

Magnetic flux variations were detected by a

two-turn buried loop, with an effective area

of 1.6X10* square meters, leading to a galvanometer. Light from the undisturbed galvanometer mirror fell centrally on two photocells

placed side by side. Deflection of the mirror

by an incoming signal altered the photocell

current, which was then amplified by a triode

that formed one arm of a bridge. A twin-T

rejection filter, tuned to 1.5 c/s, supplied

negative feedback. The overall gain of the

detection circuit, including an amplifier in

the pen-recording unit, was 4X108, giving a

3OO .

25O _

aoo .

ISO .

I I I I I I I I I

00

I I I I

. DO

_ 80

FIGURE 1.—Number of meteors/hr compared with the number

of %-mins/hr containing 1.5 c/s micropulsations. Observations commenced at 6 p.m., local time, on 29 July 1961.

Heavy line, meteors; dotted line, micropulsations.

minimum readable input level of 0.04 /*V,

corresponding to a magnetic field charge of

0.3mY (=0.3X10"8 gauss). The sensitivity,

and the frequency filtering at 1.5 c/s, was thus

purposely made the same as that of Jenkins,

Phillips, and Maple (1960). (There is no

reason why the particular micropulsation frequency of 1.5 c/s should be associated with

meteors. Two advantages of this frequency

are that it is below sferics interference, and is

in a region of high loop sensitivity.) The

recording paper passed through the pen recorder

at a rate of 3 inches per minute, which just

allowed 1.5 c/s to be resolved.

Results

A period of 24 hours of continuous observing

commenced at 6 p.m. L.T. on 29 July 1961.

Both equipments were looking at approximately

the same sky area.

During this period the 5-Aquarid shower

(a=340°, 8= —19°), which is the strongest

known meteor shower to occur in either hemisphere (Ellyett, Keay, Roth, and Bennett,

1961; Keay and Ellyett, 1961), exerted its

peak effect at about 3 a.m. L.T. and was above

the horizon for several hours centered on this

time.

The time of occurrence of each individual

meteor was read to an accuracy of ±2 seconds.

The micropulsation and the meteor time scales

were locked together, and a correlation was

considered positive if the two phenomena

commenced within 4 seconds of each other.

A total of 2,750 meteors was recorded during

the 24 hours.

First, large-amplitude low-range meteors,

with durations in many cases of up to 30

seconds, were individually compared with the

micropulsation trace. There was an obvious

absence of any correlation.

The number of half-minutes in each hour

when micropulsations at 1.5 c/s were present

was then plotted against the total hourly

meteor count. The micropulsation distribution

was as expected, with a noon dip. As shown

in figure 1, there is no correlation between the

two rates of occurrence.

It would thus appear fairly conclusive that

no correlation exists within the present limits

of sensitivity. Further work is proceeding.
METEOR SYMPOSIUM—ELLYETT AND GH.LION 251

Acknowledgments

This work has received contract assistance

from the Electronics Research Directorate of

the Air Research and Development Command,

U.S. Air Force, under contract AF64(500)-6

(Meteors); and from the Office of Naval Research, U.S. Navy, under contract Nonr(G)-

00027-62 (Micropulsations).

References

CAMPBELL, W. H.

1960. Magnetic micropulsations accompanying

meteor activity. Joum. Geophys. Res.,

vol. 65, pp. 2241-2245.

ELLTETT, C. D., AND KEAT, C. S. L.

1956. Radio echo observations of meteor activity

in the southern hemisphere. Australian

Journ. Phys., vol. 9, pp. 471-480.

ELLYETT, C. D; KEAT, C. S. L.; ROTH, K. W.; AND

BENNETT, R. G. T.

1961. The identification of meteor showers with

application to southern hemisphere results. Monthly Notices Roy. Astron.

Soc, vol. 123, pp. 37-50.

HAWKINS, G. S.

1958. A search for magnetic effects from meteors.

Journ. Geophys. Res., vol. 63, pp.

467-475.

JENKINS, A. W.; PHILLIPS, C. A.; AND MAPLE, E.

1960. Observed magnetic effects from meteors.

Journ. Geophys. Res., vol. 65, pp.

1617-1619.

KALASHNIKOV, A. G.

1949. On observations of the magnetic effect of

meteors by the inductive method. Dokl.

Acad. Sci. U.S.S.R., vol. 66, pp. 373-376.

(Translated by E. R. Hope, Canadian

Def. Res. Board, T-130-R, 1954.)

KEAY, C. S. L., AND ELLYETT, C. D.

1961. The latitude dependence of radar meteor

shower observations. Journ. Geophys.

Res., vol. 66, pp. 2337-2343.

MACLAUCHLAN, E. C.

1960. Noise suppression in pulse receivers.

Australian Journ. Phys., vol. 13, pp.

750-752.

WHIPPLE, F. L., AND HAWKINS, G. S.

1958. Meteors. In Handbuch der Physik, S.

Flugge, ed., vol. 52, pp. 519-564.

Springer-Verlag, Berlin.

Abstract

Simultaneous observations of micropulsations greater than 0.3m-y at 1.5 c/s, and of meteors greater than magnitude + 9.1, at the same site during the peak of occurrence of the 5-Aquarid meteor shower, failed to show any correlation, either with individual meteors, or on an hourly rate basis.

The Density Distribution of Telescopic Meteors

Around the Earth's Orbit

By L. Kresak and M. Kresakova *

Recent studies have provided substantial

evidence that the rate of meteoric particles encountered by the earth varies considerably,

owing both to the occurrence of recognized

meteor showers and to the nonuniform density

distribution of the sporadic background. These

irregularities, appearing periodically in the form

of annual variation of meteor rates, are of particular interest in connection with the constitution of minor meteor streams at advanced

stages of dispersion, and with the meteoric risk

to space vehicles, especially those moving in

satellite orbits around the earth or launched to

the moon. The evaluation of the annual variation is made difficult by the variability of the

geometrical conditions depending on geographic

latitude and by the additional effect of diurnal

variation produced by the rotation of the earth.

Another difficulty in the interpretation of

observed rates lies in the variability of the

velocity distribution; the different sensitivities

of individual observing techniques to meteors

of different velocities complicate this problem.

The main purpose of this paper is to analyze

the distribution of meteor orbits around that of

the earth, on the basis of telescopic observations

made at the Skalnate" Pleso Observatory for the

period 1946-1959. These include faint telescopic meteors down to the 10th apparent

magnitude; more than half of the data are concerned with meteors of 8th and 9th magnitude.

These faint meteors are of particular significance for two reasons: (1) In the constitution of

meteor streams they may reveal evolutionary

changes caused by the effects of solar radiation,

which are substantially greater on smaller particles; (2) the likelihood of a collision with a space

1

 Astronomical Institute of the Slovak Academy of Sciences, Bratislava,

Czechoslovakia.

vehicle is greater for smaller meteors, approximately by a factor of ten for each two magnitudes. For the telescopic meteors recorded

during the Skalnate Pleso program, the average

probability of collision is estimated at about

10~8 m~2 day"1; this is not a negligible figure even

for the space vehicles and durations of flight

expected in the near future.

Supplementing the results of earlier studies

(Kresakova and Kresak, 1955), we report here

on a total of 4,573 meteors recorded during

1,364 hours of observation more or less uniformly distributed over the various dates and

hours of the night. All observations were made

with the same type of instrument, 4-inch binoculars with a magnification of 25.

The net annual variation produced by the

changes of meteor density around the orbit of

the earth may be established only after eliminating the effect of nonuniform radiant distribution on the visible and invisible hemisphere.

This may be done by separating the annual

and diurnal variation with the use of a reference

model of apparent radiant distribution. In the

present work we used three such models:

Model A, the uniform apparent radiant distribution, giving constant hourly rates; Model

B, an isotropic distribution with respect to the

apex, with a continuous decline of radiant density towards the antapex (Hoffmeister, 1931)

(the "equivalent velocity" constant (c=3.9)

was computed directly from our observations);

and Model C, the standard distribution derived

by Hawkins (1956) from the radio-echo data.

This distribution is characterized by a pronounced ecliptical concentration, two main

maxima near the sun and antihelion point, and

a secondary maximum at the apex.

253
254 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

For each of the models the expected hourly

rates for any instant may be predicted and

compared with the observation. An overall

comparison is shown in figure 1, where the

abscissae indicate the solar longitudes and the

ordinates the time in M.E.T. In this network

of coordinates we plotted curves of constant

reduced hourly rates obtained by combining

the observations into normal places, interpolating, and smoothing the results. For a perfect representation of the diurnal variation, the

curves should change into vertical straight lines;

for a perfect representation of the annual variation, they should change into horizontal straight

lines; and for an entire agreement between

theory and observation they should vanish.

Obviously, sj7stematic departures may be anticipated in the annual rather than in the diurnal variation, and the vanishing of the diurnal

variation alone would offer convincing proof of

a nonuniform distribution of meteors around

the orbit of the earth.

Figure 1 indicates that model A is distinctly

inferior to models B and C. A systematic increase of meteor rates from the evening to the

morning hours and a sharp maximum in the

autumn reveal the main features of diurnal and

annual variations, established long ago in the

naked-eye range. In model B the total amplitude is essentially reduced, and the curves, as

expected, run mainly in the vertical direction.

Model C, which represents satisfactorily the

radio observations (Hawkins, 1956) and the

naked-eye observations (Hawkins and Prentice, 1957), is, surprisingly, less consistent with

the telescopic observations than is model B.

It appears as if there were an overcorrection

of the observed variation (a mirror-like image

of model A); the radiant distribution suggested

by Hawkins would fit better with a diminished

density gradient. This may be attributed either

to the selective effect of angular velocities

applying to telescopic observations, or to an

increasing preponderance of direct orbits with

decreasing size of particles. It may be noted

that for model B this effect was already indirectly taken into account by determining the

basic constant ("equivalent velocity") from the

telescopic data; a lower degree of apical concentration than indicated by the naked-eye

observations was also found.

It is clear that none of the models of radiant

distribution can account for the annual variation in terms of the earth's rotation combined

with the obliquity of the ecliptic. Evidently,

such features as a rapid increase of meteor

rates in June and July, or a decrease in December and January cannot be explained by any

other acceptable model of radiant distribution.

Although the trend of diurnal variation in

model A is entirely reversed in model C, nevertheless the annual variation preserves its main

features unchanged. Hence the actual variations of meteor density around the earth's orbit

are established beyond doubt.

The course of the net annual variation, freed

from the effects of the earth's orientation according to the three models, is shown in figure

0.60/

180 270 360

\(X60

360 90 180

FIGURE 1.—The combined pattern of annual and diurnal variation referred to models A, B, C. The first solid line corresponds

to the median hourly rate, the next solid lines to 1.20, 1.40, etc., and the broken lines to 0.80, 0.60 of the median value.

Abscissae, solar longitudes; ordinates, time M.E.T.
METEOR SYMPOSIUM—KRESAK AND KRESAKOVA 255

2. Here the amplitudes of the annual variation

for models B and C are 1:1.8 and 1:2.2, respectively. Despite considerable differences between these two models, the curves are similar

enough, indicating in each case a lower level of

activity in the first half of the year (©=280°

to 100°) and a higher level in the second half

(0 = 100° to 280°). Even the three maxima

near © = 130°, 190°, and 250° are consistently

reproduced in both types of representation.

FIGURE 2.—The net annual variation referred to models A,

B, C, compared with the distribution of comet approaches

Dl (P<500years) and D2 (P>500years). Abscissaesolar longitudes.

We have attempted to test the source of the

irregularities of the annual variation by means

of cometary statistics. For the reasons pointed

out by Levin (1961), Hoffmeister's (1948, p.

100) cometary indices are not suitable for this

purpose, i.e., for taking the periodic comets

together with the non-periodic comets that

appeared in a relatively short time-interval.

Instead, we used as a reference catalogue

Kramer's (1953) extensive list of cometary

orbits approaching the earth within 0.3 A.U.

The comets of this list were divided into two

groups according as their periods were less

than or greater than 500 years. With regard

to the periods of recognized meteor showers, a

correlation appears possible for the former

group but highly improbable for the latter.

The stream associated with each of the comets

was considered as possibly active within 30°

of solar longitude before and after the closest

approach for the former group of comets

(regularly of low inclination), and within 15°

for the latter group. The results are shown in

the lower part of figure 2, where we see that the

density distribution Dl of short-periodic cometary orbits agrees well with the density

distribution of telescopic meteors. As expected,

the comets moving in very prolonged orbits

(D2) exhibit no correlation at all, and this

excludes any alternative explanation of the

agreement in terms of seasonal selective effects

of the discoveries of comets on the distribution

of their nodes. Consequently, there is strong

evidence that at least some of the irregularities

of the annual variation are due to minor meteor

streams of cometary origin, with the parent

comets known, but too dispersed to be distinguished separately.

Analyses of the annual variation determined

by radio techniques have been published by

Hawkins (1956) for Jodrell Bank, and by

Weiss (1957) for Adelaide. The net variation

determined by Hawkins is based on model C,

and is directly comparable with our results.

The model chosen by Weiss is different. It

assumes a line source round the ecliptic with

an apparent strength up to the distance of 90°

from the apex four times higher than in the

remaining part of the ecliptic. Experience

with different models, however, including those

used by Weiss, indicates that the result will

not differ greatly from those based on model C.

A comparison of the annual variation determined at Adelaide, Jodrell Bank, and Skalnate"

Pleso is shown in figure 3. A previous study

(Kresakova and Kresak, 1955) demonstrated

that the annual variation of the telescopic

meteors obtained at Skalnate" Pleso agrees well

with the results of Hoffmeister (1937), derived

from the naked-eye observations of Schmidt,

Heybrock, and himself. Hence it may be

concluded that the difference in the magnitude

range covered by the different methods of
256 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

FIGURE 3.—The comparison of the net annual variation

obtained at Adelaide (dotted line), Jodrell Bank (broken

line) and Skalnate Pleso (solid line). Abscissae—solar

longitudes.

observation cannot represent the essential

source of the discrepancies. These discrepancies

may result either from the difference in geographic latitudes or from the difference in the

type of technique used for the determination of

meteor rates.

It is surprising that our telescopic observations agree much more closely with the observations at Adelaide, in the southern hemisphere,

than with those at Jodrell Bank, located in

approximately the same geographic latitude as

Skalnate Pleso. From this fact it follows that

the main discrepancies are not due to the actual

distribution of the radiants in declination.

The difference between the annual variation

of radio-echo and that of photographic rates

was pointed out by Hawkins and Prentice

(1957), who attribute it to the fact that the

sensitivities of the two methods of observation

vary with the geocentric velocities of the

meteors. This interpretation requires a concentration of high-velocity meteors in the

sector of the earth's orbit traversed in the

summer months. However, direct measurements of meteor velocities, e.g., those by

McKinley (1951), show, on the contrary, that

there is only an average number of highvelocity meteors in June and July, and a

maximum in September and October, consistent

with the extreme declination of the apex.

Figure 4 shows the annual variation of the

ratios of the hourly rates at Jodrell Bank and

at Adelaide to those at Skalnate Pleso. A

striking feature of the first of these curves is

its symmetry with respect to the summer solstice. This feature suggests some seasonal

effect producing a correlation between the duration of the daily illumination by the sun and

the ratio of ionizing to luminous efficiency of

meteors. Such an explanation would require

an inverse trend of the annual variation in the

southern hemisphere, where the seasonal shift

is in six-month periods. Some indications of

such inversion actually appear in the figure,

but they are not sufficiently conclusive. If,

however, we take into account the annual

variation of naked-eye meteors, determined for

the southern latitudes by Mclntosh (1934) and

by Hoffmeister (1937, p. 60), with a deep

minimum in January and February, the inversion of the curve becomes more distinct. There

is a considerable difference between the amplitudes of the two curves in figure 4. In fact,

the explanation suggested requires a difference

of this kind, since the conditions of illumination

are much more variable during the year at

Jodrell Bank (<£=+53°.4) than at Adelaide

(0= —34°.9). At Jodrell Bank the atmospheric levels in which meteors appear are almost

continuously illuminated at the time of the

summer solstice. If this explanation is valid,

it would partially account for the abundance

of the summer daytime meteor showers detected

only by radio techniques. Since all these

streams encounter the earth at about the time

of the summer solstice, they should be relatively

-2.0

-1.5

FIGURE 4.—The annual variation of the ratio of reduced

hourly rates Adelaide: Skalnate Pleso (broken line), and

Jodrell Bank: Skalnate Pleso (solid line). Abscissae—

solar longitudes.
METEOR SYMPOSIUM—KRESAK AND KRESAKOVA 257

much weaker if they could be observed optically.

It is important to emphasize that the basic

data of Hawkins and Weiss were obtained at

substantially different wavelengths (4.2 and

11.2 m, respectively), but the effect of this

difference is difficult to determine.

From the similarity of the curves of annual

variation at Adelaide and Skalnate Pleso,

despite their difference of 84° in geographic

latitude, we deduce that the mam contribution

of the annual variation is due to meteor radiants

of low declination. This conclusion offers an

additional proof of the ecliptical concentration

of radiants produced by a significant prevalence

of direct meteor orbits of low inclination and

short period. An earlier discussion of the

telescopic meteor directions (Kresak, 1955)

led to the same conclusion. The correlation

between the annual variation and the distribution of the points of approach of short-periodic

cometary orbits (fig.2) requires an ecliptical

concentration as well. Thus three entirely

independent types of evidence suggest that in

the range of faint telescopic meteors the orbits

are distinctly concentrated toward the plane

of the ecliptic.

We shall now comment on the occurrence of

shower meteors in the telescopic observations.

The permanent showers, which at their maxima

contribute a majority of the meteors observed,

are hardly detectable in the range of telescopic meteors of 7th to 9th magnitudes. In

the total for the whole year they were at least

seven times less frequent with respect to the

sporadic background than in the naked-eye

observations. This lack of faint showermeteors is consistent with the recent results

obtained by Kresakova (unpublished), who,

from naked-eye observations at SkalnatS Pleso,

found a systematic difference between the

magnitude functions of shower meteors and of

sporadic meteors, with the constant K=2. 6

and 3.5, respectively. An extrapolation would

require the ratio of shower to sporadic meteors

to be four times lower in the present telescopic

observations than in those made by the naked

eye. The actual relative decrease in the number of shower meteors appears even sharper,

presumably because of the effect of corpuscular

radiation on the evolution of meteor streams

(Kresak, 1960).

In addition to the showers known from other

techniques of observation, eight showers of

telescopic meteors have been established with

a sufficient degree of probability. They appeared at solar longitudes 25°, 131°, 158°,

184°, 194°, 248°, and 316°, most of them with

out any indication of periodicity. Only rarely

did their hourly rates exceed those of the sporadic background by a factor of two; striking

phenomena, comparable to the Perseids or

Geminids in the naked-eye range, are absent at

7th to 9th magnitudes. In general, it may be

concluded that the phenomenon of meteor

streaming becomes gradually less prominent

as we pass from photographic through nakedeye to telescopic meteors. This phenomenon

probably reappears again, to a much greater

extent, in the range of much smaller particles

for which rapid variations in frequency have

been established by the impact measurements

on high-altitude rockets and artificial satellites.

Among faint telescopic meteors there is rather a

system of minor, considerably dispersed streams

that do not produce abrupt changes in meteor

rates over a period of a few days, but that do

influence the total annual variation.

As for the meteoric risk to space vehicles

moving in the vicinity of the earth's orbit, we

conclude primarily that:

(1) At the level of the probability of encounter 10~6

 m~2 day"1, the risk from the

sporadic background varies with a maximum

seasonal amplitude of about 1:2, the safest

period of permanently low activity lasting from

January till May. The periods of highest

activity occur in August, September, the first

half of October, and in December.

(2) The particles producing this activity are

very likely of cometary origin and constitution,

as indicated by the relation of meteor rates to

the distribution of nodes of short periodic

coraetary orbits.

(3) The permanent meteor showers represent

a risk that is negligible in most cases, and is

generally much lower than might be anticipated

from photographic and naked-eye observations

of larger bodies, or from impact measurements

of smaller bodies.
258 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

(4) Showers rich in telescopic meteors are

scarce and without distinct periodicity. Only

quite exceptionally do they increase the risk

by a factor of two or three. It must be

remembered, however, that this result is derived from night-time observations, in which

meteor showers with apparent radiants near

the sun could not be detected.

Acknowledgments

The authors are greatly indebted to all members of the staff of the Skalnate Pleso Observatory who took part in the observations analyzed

here, especially to the most active observers:

Dr. L. Padjusakova, Mr. A. Mrkos, Dr. A.

Becvaf, Mr. M. Dzubak, and Mrs. A. Antalova.

Our thanks are due to Mrs. L. Durkovidova

and Mr. A. Aldor for their aid in numerical

computations.

References

HAWKINS, G. S.

1956. Variations 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.

HOFFMEISTER, C.

1931. Zur Theorie der Variation der Sternschnuppenhaufigkeit. Veroff. Univ. BerlinBabclsberg, vol. 9, no. 1, p. 17.

1937. Die Meteore. Akademische Verlagsgesellschaft, Leipzig.

1948. Meteorstrome. J. Barth Verlag, Leipzig.

KRAMER, E. N.

1953. Cometary radiants and the association of

meteor streams with comets. Izv.

Astron. Obs. Odessa, pp. 163-247.

KRESAK, L.

1955. The direction distribution of telescopic

meteors. Contr. Astron. Obs. Skalnat6

Pleso, vol. 1, pp. 9-35.

1960. The effect of solar corpuscular emission on

the magnitude distribution of meteors.

Bull. Astron. Inst. Czechoslovakia, vol.

11, pp. 1-9.

KRESAKOVI, M., and KRESAK, L.

1955. On the activity of telescopic meteors and

some related problems. Contr. Astron.

Obs. Skalnate' Pleso, vol. 1, pp. 40-77.

LEVIN, B. J.

1961. The distribution of true radiants of meteor

bodies down to a definite limit of mass.

Symposia at the 5th meeting of CSAGI,

Moscow, 1958. In Annals of the International Geophysical Year, vol. 11,

pp. 187-193. Published by Pergamon

Press.

MCINTOSH, R. A.

1934. Report of the section for the observation

of meteors, 1929-1931. New Zealand

Astron. Soc. Bull., no. 21.

MCKINLET, D. W. R.

1951. Meteor velocities determined by radio observations. Astrophys. Journ., vol. 113,

pp.225-267.

WEISS, A. A.

1957. The distribution of the orbits of sporadic

meteors. Australian Journ. Phys., vol.

10, pp. 77-102.
Atmospheric Trajectories of Telescopic Meteors

Lubos Kohoutek* and Jiri Grygar*

Double-station observations of telescopic

meteors were organized at the amateur meteor

expedition to Mount Bezovec (\=17O58' E.

Gr., <p=+48°40', height=500 meters above

sea level). Two teams of four members each

gathered data on 123 pairs during the period of

8 nights (July 10 to 25,1958). That represented

62 percent of all meteors recorded. The telescopes Somet 25X100 (rf=3?3) and binoculars

10X80 (d=7°3) were used, with the base 2.5 km.

We treated the observations by means of

graphic-numerical analysis. All the distortions

that might influence the determination of the

mean heights were taken into account. The

mean errors of some principal characteristics of

meteors were also computed. The mean error

of the estimates of the magnitude of one meteor

was ±0^24; the error of angular length did not

exceed 2/10 of the diameter of the field of view,

and the error of plotted direction of meteor

flight was about ±5° . The errors in the determinations of the mean heights of the beginning,

the center, and the end of meteor trajectories

were smaller than 4 percent. The apparent

frequency distribution of heights could not be

represented by the Gaussian distribution, and

therefore we considered the modal heights as

more probable mean values. The following

values were obtained for the height of the beginning, the center, and the end of meteor paths,

respectively: H6=98±4 km, fiTc=93±4 km,

He=88±3 km (the average corrected absolute

magnitude m=6.0). It was established that

the observed beginnings of meteor trajectories

agree well with the theoretical points of the beginning of rapid evaporation, and that the

observed centers of paths approximately correspond to the point of maximum light of me1

 Astronomical Institute of the Czechoslovak Academy of Sciences,

Praha and Ondfejov, Czechoslovakia.

teors. Next it was found that increase of the

mean height with magnitude, if it exists at all,

is very slight in the magnitude interval from

0^0 to 7^0. This conclusion was confirmed by

recent radar observations.

No meteor with the real height below 60 km

was recorded, thus the existence of isolated

groups of the "low" telescopic meteors, as was

suggested by Astapovich,2 is hardly possible.

The mean geocentric velocity, vg=3& ± 5 km/sec,

was estimated and the average original radius

of meteoroids was ro=0.4 to 0.5 mm, using some

assumptions of the physical theory of meteors.

According to Levin's3 formula, the energynecessary for the evaporation of 1 gm of meteor

material was estimated to be from 1.6 to 3.5

X1010 erg/gm. It follows from this that the

free molecule flow occurs during the flight of

telescopic meteoroids through the atmosphere.

The course of diurnal variation of heights and

geocentric velocities is in agreement with the

assumption of nearly circular orbits of telescopic

meteors, which is also confirmed by the distribution of apparent radiants. During the expedition the activity of the unusual meteor shower

a Lyrids, announced first by V. V. Martynenko

(Simferopol, U.S.S.R.), was detected.* Unfortunately, the great angular elongation between our field of vision (North Pole) and the

point of radiant made it impossible to determine

accurately the radiant of telescopic meteors

belonging to this shower. (For details, see also

Bull. Astron. Inst. Czechoslavakia, vol. 13,

pp. 9-26, 1962.)

* I. S. Astapovich, Meteor phenomena in the earth'/ atmosphere, chap. 33.

Moscow, 1958. (In Russian.)

» B. J. Levin, Physical theory of meteor* and meteor matter in the tolar

system, pp. 29, 97. Moscow, 1956. (In Russian.)

* J. Grygar, L. Kohoutek, Z. Kvfz, and J. Mikusek: "Observation of

the o-Lyrid meteor stream. Results of the Mount Bezovec meteor expedition." Bull. Astron. Inst. Czechoslovakia, vol. 11, pp. 84-86, 1960.

259

Statistics of Meteor Streams

By R. B. Southworth

 1 and G. S. Hawkins

In the period 1954 to 1957 a random sample

comprising 360 of the meteors photographed

from two stations by the Baker Super-Schmidt

meteor cameras were reduced under the "Short

Trail" program (Hawkins and Southworth,

1958). The radiants and velocities of 359

meteors were sufficiently accurate to permit

computation of dependable orbits (Hawkins

and Southworth, 1961). Since this is the only

random sample of photographic meteors with

individually reliable orbits, it provides valuable

material for a study of meteor distribution in

space. The degree to which the meteors are

grouped into streams is a basic feature of this

distribution.

The major meteor streams are conspicuous in

any random sample of photographic meteors

and virtually all of their members are readily

identifiable. Since in the sample there are

many meteors that belong to each such stream,

the characteristics of the stream are well defined, as is the range of each characteristic

within the stream. Furthermore, these streams

are well-known from other studies.

Members of a stream not previously known,

or not well represented in the sample under

study, are not as easy to identify. Early in

the Short Trail program it became apparent

that some of the meteors were associated into

other groups or streams, apart from the previously known major streams. Numerous

other meteors were doubtfully associated with

streams. Several attempts, based upon a

variety of principles, were made to classify

the meteors into streams and a "sporadic"

remainder. None of the classifications based

on geocentric quantities—radiants, velocities,

1

 Smithsonian Astrophysical Observatory, and Harvard College

Observatory, Cambridge, Mass.

'Harvard College Observatory, Cambridge, Mass., and Boston

University, Boston, Mass.

and dates of occurrence—was satisfactory.

It became clear that a comprehensive quantitative criterion was required that would embrace

all the elements of the orbit.

A criterion for stream membership

We may regard a meteor stream as composed

of those meteors originating from a single

comet during a single ejection or over an

interval of time. As yet, we cannot reliably

identify stream membership by physical or

chemical characteristics, although some physical differences have been observed between

different streams (Jacchia, 1960). Meteors

arising from a comet will move in orbits similar

to the comet's orbit, at least for a while. If

planetary perturbations or other forces disperse the meteors so that the similarity of

their orbits can no longer be seen, the stream

is effectively destroyed. Thus, in practice, a

meteor stream is recognized and defined as a

group of meteors in similar orbits.

Occasionally meteors from two or more

comets may have similar orbits. If the different origins cannot be recognized from the

orbits, then the meteors form a single stream

in practice, although arising from more than

one comet.

A quantitative criterion for stream membership therefore requires a quantitative measure

of orbit similarity (or difference). We shall

consider the difference between orbits to be the

difference between meteors. Let D(A, B) be

such a quantitative measure of the difference

between meteors A and B. Similarly, let

D(M,N) be of the same mathematical form, but

let it measure the difference between a mean

orbit M of a stream and an individual meteor N.

The two measures D(A, B) and D(M, N) correspond to two possible ways of defining a stream.

(1) A stream may be defined, for example, as

261
262 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

all meteors N such that D(M, N) does not

exceed a given value DM.

(2) We may define a stream by serial association

between members. We may state that two meteors A and B are associated if D(A, B) does not

exceed a standard value Ds. A stream may

then be defined as a group of meteors in which

every member is associated with one or more

other members, and all members are associated

together directly or indirectly.

As a third possibility we may define a phase

space in which each meteor is represented by a

point and the distance between points is the

difference between meteors. Then a stream can

be defined as the meteors in a region of high

density in the phase space. This form has

theoretical advantages but requires far more

data than we possess. We shall therefore use

the first two alternatives.

No particular measure of orbit difference is

specified a priori. Indeed, we have found no

way of determining a "best" or "optimum"

measure. The magnitude of the cause of orbit

difference, when known, is often the best measure of the difference. We do not know the

causes of the dispersion within meteor streams

in any quantitative manner, however, and it

would be quite wrong to assume the causes.

Consequently, we have looked for a measure

that is as simple as possible and is expressed in

terms of orbital elements as far as possible,

since these are the most familiar indices of orbit

differences. Because differences within streams

are small, our measure need not be accurate for

large differences in order to be useful.

One orbit may differ from another in any of

six independent ways. One of these, the position of the meteor in the orbit at a given time,

is not significant for our purpose because the

meteors of a stream rapidly spread out all along

the orbit. Apart from the instantaneous position of the meteor, the orbit may be specified by

five elements. These may be the usual elements:

a, e, w, Q,, i; or they may be any set, out of an

infinite number of possible sets, of five independent functions of the usual elements: Cu

where; = 1,2,3,4,5. Each of the five differences

between two orbits A, B may be expressed as

the difference between the values of an element:

The fact that all the observed meteors pass

close to the orbit of the earth imposes one

constraint on the observed five elements, and

thus reduces the number of independent elements to four. The earth is not important in

the evolution of meteor streams, however, so

that this constraint is not relevant to the differences within streams. Accordingly, we

disregard it in formulating D.

In order to construct a single measure comprising five independent differences, we draw an

analogy with a five-dimensional orthogonal

coordinate system and consider each element as

a coordinate. Any orbit then corresponds to a

point in this conceptual space, and the distance

between two points is a natural measure of the

difference between the two corresponding orbits.

Although orthogonal, the coordinates need not

be rectangular; usually these will be curvilinear

coordinates. We may approximate them by

rectangular coordinates in any sufficiently small

region, however, and this approximation will

prove to be adequate for our purpose. The

difference between meteors A, B is then of the

form

D(A, B)= (1)

where Cj are functions of the elements which are

at our disposal and which determine the geometry of the space.

The value of D as a measure of difference

depends on how well the Cj are chosen or can be

chosen. The c}, for our purpose, are scale factors

determining the relative importance of the different Cj in D. Each c}

 should be inversely

proportional to the expected standard deviation of the corresponding element Cj in a stream.

An attempt to base the scale factors only

on the streams would be an attempt to lift

ourselves by our own bootstraps, because we

are still trying to determine which meteors

are stream members and which are not. We

have checked the reasonability of the scale

factors that were ultimately chosen by computing the mean standard deviation of each

element on the assumption of an idealized

dispersing mechanism. This is discussed below.

In accordance with all the foregoing, we

have selected the elements and scale factors
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 263

described below. Angles, and thus the differences of angular elements, are measured by

their chords, i.e., by twice the sine of half the

angle. This is convenient; for small angles

it is a close approximation to radian measure,

and for all angles from 0 to 2* it is a smooth

continuous measure of the absolute value,

without difficulties of sign or definition. We

measure a difference in orbital plane by the

angle IAB between the orbital planes. IAB

comprises two elements and their scale factors;

this appears explicitly in the identity

[D(A,B)]2=[eB-eA}>

+sin iA sin iB (2 sin (2)

Three elements describe an orbit within the

orbital plane. We measure a difference of

shape by the difference in eccentricity e, and

of size by the difference in perihelion distance q.

In contrast to the major semi-axis a, q is well

determined by observation and has a small

range of values. A difference in orientation

of the orbit within the plane is measured by

the angle TLAB between the major axes,

weighted by the scale factor e. Thus UAB

is the difference between the longitudes of

perihelion. When the orbits are in different

planes, HAB is the difference between the

longitudes of perihelion measured from the

intersection of the orbits. In terms of familiar

elements,

arc sin

^ ] , (3a)

or, to a sufficient approximation when iA and

is axe small,

(3b)

By combining equations (1), (2), and (3a), we

find

+sin iA sin iB [2 sin

at low inclination, or, after substituting equation (3a) for (3b) in the last term, at any inclination. This expression is readily computed

with a desk calculator and a special table of

chords.

A model of stream dispersion

The scale factors c} of the various elements in

D, as shown in equation (4), were selected on a

variety of grounds of simplicity, reasonability,

and previous experience. By qualitative arguments we expected that, after scaling, the elements would make roughly equal contributions

to D. The utility of D is empirically established

below on known streams; nevertheless, a

theoretical basis for D is clearly desirable if it

can be found. Although we made this theoretical study after D had already been applied

to the meteors, the validity of D is confirmed

in the main.

An excellent measure of the difference between orbits, if it can be found, is the amount

of perturbation that will transform one of the

orbits into the other. A perturbation of an

orbit arises from an accelerating force applied

for a period of time; hence the velocity change

so arising is the natural measure of the perturbation. In general, no single perturbation

can suffice because the two orbits will not

intersect; we may expect that an appreciable

difference between a pair of orbits that were

once the same will normally be the result of

many perturbations. Since D comprehends

all orbital elements, it appears possible that D

is indeed a measure of total perturbation; we
264 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

must determine, however, whether the different

elements may be so combined.

We consider an idealized model for orbit

change, postulating random vectorial increments 5V to the vectorial orbital velocity yH

of a meteor. The natural unit of orbital speed

at any particular distance r from the sun is the

speed XJ of a body in a circular orbit of that

radius; U varies as r~

1/2

. We take 8V to be

proportional to U because, broadly speaking,

we would expect most kinds of perturbation to

be more intense nearer the sun. The test applied to D consisted in finding the sensitivities

of the different elements to perturbations 5V;

these sensitivities should be comparable. To

measure the sensitivities, we computed the

time averages, denoted "Grad," of the magnitudes of the gradients of the various elements

in D with respect to perturbations 5V. They

are shown in figure 1, plotted as functions of

eccentricity. The computation of these gradients is described in the appendix; they are

approximate, except for Grad IAB which is

exact. The value of Grad UAB on the graph

has already been multiplied by the scale factor

e. To obtain Grad q, the value in the figure

must be multiplied by a. Broken lines in the

figure indicate the extreme values of Grad q

possible for a meteor observed on earth.

Grad e, e Grad HAB, and Grad IAB are quite

satisfactorily similar for values of e<0.85.

Grad q is a function of both a and e, but is comparable to the others for most observed values

of a when e<0.85. For eccentricities near

unity the model implies that the different

elements in D have very different sensitivities

to perturbations of the kind postulated. At

these high eccentricities, the time averages

primarily reflect the conditions near aphelion;

the effect of this is not clear. Possibly the

apparent practical success of D for high eccentricity depends upon averaging overweighted

elements with underweighted elements.

If this computation had been available

earlier in the analysis, we could no doubt have

modified the form of D at the cost of simplicity.

Except when the eccentricity is nearly one,

however, we may conclude that D in its present

form is approximately proportional to the

average velocity increment, in units of the circular speed, which will perturb one of the

FIGURE 1.—Time average gradients of elements with respect

to velocity perturbations which are proportional to the

circular speed.

orbits into the other. Estimating the factor

of proportionality from figure 1, we find that

D is about 3/2 of the mean velocity increment.

Application to known streams

We applied D first to the known streams that

were sufficiently represented in the sample,

using both forms of the stream criterion discussed above. A list of the members of each

stream had already been prepared by use of

conventional criteria. The difference D(M,N)

between the mean orbit M of the stream and

the orbit of each member N was found, as were

the differences D(A, B) between pairs of meteors

in each stream. The values of D(A,B) were

examined to find the minimum value Ds mto of

Ds such that all the members were associated.

Table 1 summarizes the values of D(M, N) and

also includes D3 mln. There is obviously a close

correlation between Ds miD and the mean value

of D{M,N).

Both Ds mia and the mean value of D{M, N)

are also correlated with the average spread of a

stream radiant, as found by Wright, Jacchia,

and Whipple (see Whipple, 1947; Wright and
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 265

TABLE 1.—Distribution of values of D(M,N) for previously identified members of known streams, and values of

As mia and O—C

Streams

Quadrantids

Orionids

Pereeids*

Geminids

S. t Aquarids t

S. S Aquarids

N. 5 Aquarids

a Capricornid

S. Taurid-Arietid

N. Taurids

Andromedids

Total

.00

to

.04

3

4

1

14

2

24

.05

to

.08

2

3

3

2

1

1

2

1

1

2

18

Range of D(Af,i\T

.09

to

. 12

3

1

2

1

2

2

11

. 13

to

. 16

1

3

1

2

3

10

. 17

to

.20

1

1

1

3

.21

to

.24

1

1

2

.25

to

. 2 8

2

2

.29

to

.32

1

1

Total

5

12

9

16

2

3

3

2

10

7

2

71

Mean

0.04

.08

* 11

.02

. 10

.03

.10

.08

. 18

. 13

.08

.09

DSmia

0.05

. 15

* 12

.04

.20

.07

. 15

. 16

. 19

. 19

. 16

O—C

0.38

.68

.22

1.8

.80

1.2

2. 1

.83

1.02

'Incomplete observations; shower peak missed.

tOne meteor, characterized as a "very doubtful member" by Wright, Jacchla, and Whipple (1957), has been omitted.

Whipple, 1948, 1950, 1953; Wright, Jacchia,

and Whipple, 1954, 1956, 1957). Their value

of the average deviation 10— C\ of an extended

trail from the least-squares moving radiant

appears in table 1 for nine streams. They

have not determined a value of \0—C\ for

Quadrantids or Andromedids. Figure 2 shows

the correlations with Ds mla and the average

D(M,N). There is a well-known correlation

- 0.30

- 0.20 „

0.05 -

FIGURE 2.—Correlations of mean D(MJf) (solid dots) and

of Da mi n (open circles) with Wright, Jacchia, and Whipple's

average radiant deviations |O—Cl, for nine streams.

between radiant spread and shower duration

(Wright, Jacchia, and Whipple, 1957), and a

correlation of either D3mln or mean D{M,N)

with shower duration is easily shown. Thus all

these measures of meteor orbit difference within

a stream are intercorrelated.

It will be seen in table 1 that D(M, N) exceeds 0.20 for only four meteors, one Northern

Taurid and three Southern Taurid-Arietids.

Thus we may use the condition D(M,N)<DM,

where DM=0.20, as an empirical test for membership in these known streams. Similarly, no

value of Ds mtn exceeds 0.20, and we may use

Ds=0.20 as an empirical test. For all but four

streams in table 1, either test gives the same

results as conventional criteria, including all

meteors previously selected as members and

excluding all others. The Southern i-Aquarid

stream has presented difficulties to conventional

classification (Wright, Jacchia, and Whipple,

1957); the Ds test includes two additional

meteors, one of which had been considered a

member but was subsequently rejected.

The Andromedid stream has recently been

shown to be much more extensive than was

believed when the members were identified

for table 1 (Hawkins, South worth, and Stienon,

1959) and both tests add several additional
266 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

members. The Ds test adds one new Northern

Taurid and one new Southern Taurid-Arietid,

and excludes no previous members. The DM

test includes these two additional meteors and

excludes one Northern Taurid and three

Southern Taurid-Arietids. Almost all of the

additional and rejected meteors are close to the

dividing lines of the tests.

We conclude that D provides valid tests for

membership in a stream known to exist. The

essential value of these tests is that they have

the same formulation for every stream and do

not depend on prior study of it. Thus they

may be used to look for new streams.

The numerical values DM=Ds=0.20, which

were empirically determined from this sample

of meteors, will require re-evaluation if applied

to a different sample, particularly to a much

larger sample. Certainly Ds should be decreased in a larger sample. If, as above, we

use a four-dimensional point distribution as a

model of the distribution of meteor orbits,

Ds should vary inversely as the fourth root of

the sample size in random samples.

Search for new streams

We next applied the Ds test to our entire sample by computing every value of D(A,B)< 0.20

for any pair of meteors in the sample, as follows.

There already existed a card for each meteor,

on which its orbital elements had been written.

These cards were sorted and then compared

in pairs. D(A,B) was computed for every

pair unless it could be seen by inspection that

D exceeded 0.20. Because members of some

known streams had already been treated they

were not included in this process, but special

pains were taken to see that any association

existing between these stream members and

other meteors was not overlooked.

The Ds test found 25 groups of meteors,

which we may therefore consider as possible

streams.

As will be discussed below, we define the

"major" streams as those whose mean photographic rates exceed three per hour. Table 2

includes all others, termed "minor" streams,

including the 25 newly-found possible streams.

For the minor streams previously known it

includes all members as defined by the Ds test.

Three known streams, each having one member

in our sample, are included for completeness;

they are not considered further in this study.

One of the 25 possible streams has been

called the "Cyclids" because of its nearly

circular orbit. (This stream includes two

meteors that were assigned the earth's orbit

because their observed velocity falls short of

the velocity of escape.) Each of the other

streams is identified for convenience by a name

formed in the traditional manner from a star

near the radiant. Mean values of the orbital

elements, the corrected radiant (equinox 1950.0),

and the extra-atmospheric velocity are tabulated for each stream. Several of the streams

near the ecliptic have members whose node

differs by 180° from the rest. To form mean

elements of streams, we have added 180° to

the node of such meteors, and interpreted them

as having negative inclinations. Individual

values of the same quantities as for the streams,

of the date of occurrence, and of D(M,N) are

tabulated for each member. One readily sees

that the DM test (i.e., D <0.20) is also fulfilled for the great majority of the meteors in

table 2.

Several of the possible streams in table 2 are

discussed below, after a general discussion of

the statistical significance of these streams.

Probability of chance association

To evaluate the importance of the "possible"

streams listed in table 2, we clearly must

know the probability that such groups would

occur by chance. It is not proper to compare

the observed groups with the groups that

would be found in a random sample of orbits

because, quite apart from any grouping, the

observed distribution is far from random.

Furthermore, we know the distribution of

meteor orbits very imperfectly, with or without

selection effects. In order to estimate the

degree of chance grouping, therefore, we have

taken the observed distribution and smoothed

out its grouping as far as possible, and then

looked for chance groups.

Each meteor is described by the elements

g, e, w, i, and Q,. The smoothing process

consisted in removing the values of Q, from all

the meteors not originally classified in known

streams, mixing them up, and reassigning

them at random; and in doing the same with
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 267

the values of i. This substantially effaces the

grouping. To offset any residual grouping,

this process also eliminated the weak correlations between Q> or i and other elements.

Any further randomizing is hardly feasible

since there is an almost exact relation among

q, e, and w. The resulting artificial orbits in

the range 0°<&<100° were then treated

in the same way as the observed orbits. In

this way, although the sample size was reduced,

we would expect the same percentage of

"stream" meteors if table 2 were a result of

chance. Table 3 shows the groups found.

The artificial sample may be compared with

the observed meteors not originally classified

in known streams, as follows:

Observed Artificial

sample sample

Meteors 290 103

New groups found 24 8

Known streams enlarged 4

Meteors classified into groups:

Number 119 22

Percent of sample 41 21

Since the random sample has produced 21

percent of "stream meteors," we conclude that

approximately one half of the groups found

by the Ds test are chance associations. Approximately 14 groups or 62 meteors in table 2

then are included by chance; the remaining

streams and meteors are genuinely associated.

We do not know which groups in table 2 are

spurious, but it is possible to develop criteria

for the probability that a group is a genuine

meteor stream.

It is clear that the chance associations in

table 2 are principally the result of the nonrandom overall distribution of orbits. The

chance associations occur almost entirely in

the regions of the phase space most densely

populated with orbits. We have stated earlier

that the value of Ds should be adjusted to the

total number in a sample. A more refined

test should take account of crowding in part of

a sample, but the present data are insufficient

to warrant refinements. One result of the

non-random distribution is obvious; the "Cyclid" stream, in all probability, does not exist as

a physical entity but only represents the peak

of the distribution of probability of meeting

the earth. Another result of crowding will be

the association into larger groups of streams

which are genuinely distinct. The "<r Leonids"

are certainly composite; possibly an improved

test can separate this group into independent

parts.

Hourly rates of streams; major and minor

streams

For each stream, we have computed the average

number of photographic meteors per hour that

are members of that stream, as follows. The

number of meteors photographed is taken as

ten times the number in the sample, because

the sample originally consisted of every tenth

meteor photographed (Hawkins and Southworth, 1958). If there were two meteors from

one stream on a single plate because additional

meteors on the same plates as "tenth" meteors

had been reduced, the additional meteor was

not counted for this purpose. We define the

period of visibility of each stream by the earliest

and latest observed dates in the sample, and

by the rising and setting of the mean radiant.

The total number of hours of double-station

observing time within these limits, and within

the overall limits of the sample (26 February,

1952, to 3 July, 1954) was found from the

records. The hourly rate is then the number

of meteors photographed divided by the number of hours observed. Table 4 lists these

hourly rates, and also the average D(M,N)

within each stream. A meaningful hourly rate

for the "Cyclid" stream cannot be computed.

The other columns of table 4 are discussed

further on. Figure 3 is a plot of mean hourly

rate versus mean D(M,N).

Three streams—the Geminids, Orionids, and

Quadrantids—are well separated from all others

in figure 3 by their high hourly rate. Their

internal dispersions are smaller than those of

almost all the other streams. We shall call

these the major streams, and treat them as a

class apart.

The position of the Perseids in figure 3 is

anomalous in view of the known importance of

this shower. On closer examination, we find

that the shower maximum in fact is hardly

represented in our sample, observations having

been prevented in 1952 by moonlight and

almost entirely prevented in 1953 by clouds.
268 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Minor streams

(Asterisk represents newly found members of known streams)

Stream Greenwich date

a

(a.u.)

e i

(deg)

Q>

(deg)

IT

(deg)

Corr.

R.A.

(deg)

Rad.

dec.

(deg)

Foo

(km/

sec)

D(M,N)

KNOWN STREAMS

South

i Aquarids

South

5 Aquarids

North

8 Aquarids

a Capricornids

S. TauridArietids

North

Taurids

52 June 29.43208

53 July 21.35918

*53 Aug 6.17192

53 Aug 8.19278

Mean values

52 July 25.44425

52 July 28.31172

52 July 29.40913

Mean values

52 Aug 25.35970

53 Aug 10.43442

53 Aug 13.19186

Mean values

52 Aug 22.20417

53 Aug 8.36042

Mean values

52 Sept 17.31692

52 Sept 19.37056

52 Sept 20.28367

52 Sept 25.36076

52 Oct 13.28086

52 Oct 14.35000

52 Oct 19.26487

52 Oct 22.47095

52 Oct 27.35625

*53 Oct 9.24410

53 Oct 9.24725

Mean values

52 Oct 16.33975

52 Oct 19.38343

52 Oct 27.35799

52 Nov 12.19596

52 Nov 12.37045

52 Nov 12.37333

*53 Oct 10.21343

53 Nov 3.29681

Mean values

1.50

1.37

1. 71

3.32

1.98

2.85

2. 36

2.40

2.54

2.38

2.41

2.50

2.43

3. 19

2.65

2.92

2.47

1. 17

1.37

1.52

1.85

1.47

1.95

2. 76

1.79

1. 73

1.45

1. 78

2.26

1.44

2.40

2.25

2.35

1.98

2. 18

1.97

2. 10

0.852

0.921

0.827

0.927

0.882

0.978

0.973

0. 970

0.974

0.947

0.960

0.949

0.952

0.793

0.753

0. 773

0.894

0.736

0.741

0.846

0.840

0.844

0.806

0.829

0.869

0.791

0.813

0.819

0.912

0.782

0.856

0.839

0.836

0.855

0.929

0.800

0.851

7.4

2.9

1.9

7.5

1.2

27.3

30.0

29.4

28.9

17.0

22.5

24. 1

21.2

8.3

7.7

8.0

4.5

6. 1

3.0

7.9

5.9

6.2

4.3

5.3

9.9

5.4

7.5

5.0

3.4

5.0

3.0

3. 1

2.3

5.3

4.7

3.6

3.8

97.6

298.2

313.4

315.3

301. 1

302.4

305. 1

306.2

304-6

152.0

137.4

140. 1

143.2

149.0

135.4

142.2

354.3

356.3

357.2

2.2

19.8

20.9

25.8

29.0

33.8

195.6

15.6

13. 7

202.9

205.9

213.8

229.7

229.9

229.9

196.6

220.5

216. 1

51.8

87.9

77.8

80.8

74.6

96.2

99.3

98.8

98.1

114.9

105.2

102.8

107.6

46.6

35.5

41.0

118. 7

125.7

118.4

134.5

142.6

154. 1

138.6

128. 1

163.8

131.9

144. 1

136.4

155.6

149.9

148.4

162.8

159.7

172.5

155.5

151.4

157.0

299.3

32a 7

331.9

335. 1

323.8

335.9

339.6

340.2

338.6

354.3

342.8

343.0

346. 7

321.2

309.8

315.6

10.6

16.8

12.5

22.8

34.8

40.6

36.0

33.6

52.5

24.7

34. 1

29.0

39.7

38.8

42.6

58.4

57.1

53.0

36.0

47.6

47.9

-16. 1

-13. 9

-13. 1

-15 . 1

-14.6

-17. 1

-16. 5

-16.6

-16.7

+ 4.7

+0.5

+ 2.5

+2.6

-2. 2

-6. 3

-4.2

+ 1.4

+ 1.2

+ 2.2

+ 4.0

+ 9.2

+ 11.5

+ 10. 1

+ 7.4

+ 12.5

+ 15.6

+ 7.7

+ 7.5

+ 17.4

+ 19.6

+ 18.9

+ 23.0

+22. 1

+25. 1

+ 16.6

+ 21.3

+ 20.5

32. 1

35.9

30.9

36. 1

S3. 8

43.0

43.7

42.2

42.6

39.0

40.5

40.0

39.8

24. 3

23.5

23. 9

33.8

26. 5

29. 9

31.8

31.4

31.8

29. 2

27.9

33.3

28. 8

30.4

so. 4

35.7

28. 6

31. 1

30.7

29.8

32.0

37.4

2a 8

31.9

0.38

0.24

0. 11

0. 16

0.22

0.05

0.03

0.02

0.03

0. 15

0.06

0.09

0.10

0.08

0.08

0.08

0.28

0.17

0.26

0. 10

0. 10

0.27

0.08

0.12

0.42

0.20

0. 12

0.19

0. 12

0. 12

0. 13

0. 10

0.10

0.23

0. 17

0. 13

0.14
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS

TABLE 2.—Minor streams—Continued

269

Stream Greenwich date

a

(a.u.)

e i

(deg)

a

(deg) (deg)

Corr.

R.A.

(deg)

Rad.

dec.

(deg)

F c

(km/

sec)

D(M,N)

KNOWN STREAMS—Continued

Andromedids

(Bielids)

North

i Aquarids

Draconids

(Giacobinids)

Monocerotids

*52 Sept 20.28438

*52 Sept 25.36001

*52 Oct 9.19792

*52 Oct 13.27778

*52 Oct 21.32940

*52 Oct 24.35000

52 Nov 7.10870

*52 Dec 9.26872

*53 Oct 2.31090

*53 Oct 6.28447

*53 Oct 7.39307

*53 Oct 10.31215

53 Nov 7.46139

*53 Nov 13.24583

Mean values

2.80

2.80

2.50

2.38

1.75

2.48

2.59

2.68

2.54

1.81

1.92

2.39

2.29

2.02

2.85

0.764

0.775

0.773

0.787

0.558

0.707

0.708

0.666

0.773

0.703

0.649

0.700

0.679

0.577

0.701

KNOWN STREAMS HAVING

52 July 27.22705

53 Oct 9.19222

53 Dec 10.51604

3.48

3.37

20.16

0.947

0.704

0.992

0.8

4.7

2. 1

8. 1

8.0

4. 1

8.4

3.5

3.7

3.6

1.9

7.5

0.0

3.8

0.4

357.2

182.2

195. 8

199.8

27.8

30.8

224.6

77.1

188.8

12.7

13.8

16. 6

224.7

50.5

25.9

ONE MEMBER IN

15.0

24.6

39.8

124. 1

195.5

78. 1

75.0

83.6

105.2

116. 6

95.4

100.4

10&9

116.8

97.0

109.6

93.9

88.3

113.5

102.0

100.4

351.8

355.2

13.3

18.5

22.6

21.4

22.9

44.8

5.4

16.9

9.3

12.3

31.1

29.5

18.6

OUR SAMPLE

76.9

12.5

209.4

323.8

270.9

101.6

-4. 9

+5.5

+8.7

+ 18. 1

— 10.4

+0.6

+27.6

+6.0

+7.7

+2.0

+0.3

-9.6

+ 12.7

+0.6

+ 4-6

-6.8

+47.2

+7.7

23.0

23.8

25.2

26.8

18. 1

20.7

20.9

16.5

24.8

24. 1

20.6

21.2

19.8

16.6

21.6

38.5

20.2

43.9

0.33

0.25

0. 16

0.32

0.22

0.07

0.20

0.29

0. 16

0.20

0.07

0. 16

0. 17

0.25

0.20

_

—

NEWLY FOUND POSSIBLE STREAMS

X Geminids

p Geminids

53 Jan 13. 29493

53 Jan 13. 45089

53 Jan 13.45411

53 Jan 23. 38956

Mean values

53 Jan 15.40959

53 Jan 19.19278

53 Jan 21.37852

54 Jan 28.17159

Mean values

2.01

2.58

2.52

2.41

2.88.

2.41

2.55

2.81

3.34

2.78

0.739

0. 779

0.798

0.725

0. 760

0.716

0.694

0.723

0.762

0. 724

1.0

17.2

11.3

4.2

6.8

7.4

4.4

1. 1

7.9

5.2

292.8

292.9

292.9

123. 1

295.4

294.9

298.8

301.0

307.6

300.6

208.3

200.6

208. 1

200.0

204-2

189.0

179.5

180.6

184. 1

183.3

118.4

123.0

122.4

117.9

120.4

111.6

105.5

105.9

114. 6

109.4

+ 22. 1

+ 41.8

+ 33.2

+ 14.0

+ 27.8

+ 34.6

+ 31.9

+24.9

+ 37.8

+32.3

25.6

27.0

27.6

22.7

25. 7

22.3

20. 1

20.0

21.0

20.8

0. 11

0. 19

0. 13

0.20

0. 16

0. 11

0.06

0.08

0.07

0.08

638805—63 22
270 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Minor streams—Continued

Stream

<r Leonids

£ Orionids

*Ursa

Majorids

a Bootids

y Bootids

£ Librids

Greenwich date

52 Feb 26.40208

52 Apr 26.28750

52 May 22.28093

53 Feb 5.14883

53 Feb 17.20441

53 Feb 17.20626

53 Feb 18.35000

53 Mar 12.17613

53 Mar 12.27841

53 Mar 13.29792

53 Mar 14.34103

53 Mar 18.33892

53 Mar 19.31853

53 Mar 19.39518

53 Mar 20.42303

53 Mar 21.40331

53 Apr 9.29081

53 Apr 11.22535

53 Apr 11.34984

53 Apr 14.28612

53 Apr 15.24583

53 May 6.28495

53 May 7.22324

54 Feb 6.38914

54 Feb 6.42292

54 Feb 26.30579

54 Mar 1.36968

Mean values

53 Mar 14.16204

54 Feb 11.42659

54 Mar 5.29565

Mean values

53 Mar 18.33889

53 Apr 10.24583

Mean values

53 Apr 9.35927

53 Apr 16.28881

Mean values

53 Apr 13.25625

53 Apr 21.36280

Mean values

53 Apr 13.25916

53 May 5.28417

Mean values

a

(a.u.)

NEWLY 1

1.65

1.98

2.04

2.71

2.49

1.89

1.95

1.53

2.53

1.55

1.68

1.35

2.91

8.49

2. 14

2.71

2.77

2.58

2.30

2.01

2.92

2. 15

2.37

2.63

2.45

1.91

2.01

2. 43

1.94

1.80

1.84

1.86

1.80

1.63

1. 72

1.90

2. 13

2.02

3.76

3.34

3.55

1.71

2.95

2. S3

e i

(deg)

Q,

(deg) (deg)

^OTJND POSSIBLE STEEAMS—Continued

0.621

0.592

0.581

0.858

0.758

0.720

0. 701

0.456

0.671

0.414

0.596

0.492

0.731

0.913

0.625

0.710

0.688

0.682

0.694

0.605

0.708

0.671

0.674

0.810

0.807

0.660

0.639

0.670

0.488

0.479

0.472

0.480

0.497

0.398

0.448

0.599

0.674

0.636

0.786

0.733

0. 760

0.914

0.925

0.920

8.9

4.6

2.2

0.8

2.4

14.5

4.8

9.6

0.5

5.6

4.4

2.3

11.5

9.5

7.5

4.3

8.9

4.9

4.2

2.6

2.4

0.5

1.0

16.6

2.6

4,6

7.3

2.2

4.2

3.4

1.0

0.9

6.9

12.0

9.4

21.0

16.0

18.5

26.6

29. 1

27.8

2.8

3.2

0.2

336.7

216. 0

61. 1

136.0

148.2

328.2

329.4

171.3

351.4

172.4

173.4

177.4

358.4

358.4

179.5

0.4

19. 1

21.0

21.1

24.0

204.9

225.4

46.3

317.0

317.0

157. 1

340.2

359.0

173.2

322. 1

164. 1

159.8

357.4

20.0

8. 7

19.2

26.0

22. 6

23.0

30.9

27. 0

23.0

224.4

213. 7

244.6

278.2

295.9

244.8

232.5

244.6

239.3

232.3

225.2

217.9

255. 1

264.3

238.8

241.5

239.8

240.8

247.6

257.4

275.4

267.3

255.3

300.6

291.7

233.0

236.4

239.5

231.9

250.8

169. 1

173.9

185.6

176.2

220.9

222.5

221. 7

26a 3

282.3

275. S

259.5

253.3

256.4

344.9

353.3

349.0

Corr.

R.A.

(deg)

164.6

195.3

219.6

147.2

147.0

162.9

154.6

150.4

153.2

143.0

167.6

174.7

174.8

172.2

159.8

169.6

184.8

186.3

194.9

191.0

178.9

214.7

211.0

152.0

145.4

153.2

159.3

171.4

80.6

106.4

113.6

100.2

161.8

185.4

173.6

209.8

210.4

210. 1

213.0

222.3

217.6

224.4

239. 1

231.8

Rad.

dec.

(deg)

+21.8

-17.6

-9. 7

+ 12.4

+ 9.7

+26.2

+ 17.7

-15.2

+ 12.2

-6. 6

- 3. 1

-2. 8

+26.3

+20.0

- 9.0

+ 14.2

+ 20.9

+ 9.0

+ 1.4

+ 1.4

-5. 7

-14. 8

-10.6

+ 30.5

+ 16.8

+ 3.2

+ 23.5

6.4

+ 0.2

+ 36.5

+ 12.6

+ 16.4

+ 31.8

+ 53.7

+ 42.8

+27.6

+ 14.8

+ 21.2

+ 33.4

+42.7

+ 38.0

-15.6

-22.2

-18.9

Vao

(km/

sec)

22. 1

18. 5

17.3

31. 7

25.0

26. 6

24. 1

17. 1

18.7

14.6

20. 6

18. 6

21. 6

24.7

19. 0

20. 2

19.0

19. 6

21.9

18.8

18.8

21.4

20.4

29.0

28. 1

22.3

20.7

21.5

12. 9

13.9

13.2

IS. 3

15. 6

14.6

15. 1

22.4

23.4

22.9

25.9

24.5

25.2

37.0

36. 8

36. 9

D(M,N)

0. 17

0.35

0.51

0.39

0.28

0.30

0.20

0.37

0.32

0.47

0. 15

0.24

0.24

0.30

0.23

0. 15

0.20

0.14

0.29

0.21

0. 17

0.56

0.47

0.43

0.34

0.19

0.24

0.29

0.09

0.09

0.08

0.09

0.08

0.09

0.08

0.10

0.10

0.10

0.08

0.08

0.08

0.09

0.09

0.09
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS

TABLE 2.—Minor streams—Continued

271

Stream

p Draconids

4> Bootids

£ Cepheids

a Ursa

Majorids

Cylids

$ Ophiucids

M Draconids

r Herculids

M Ophiucids

Greenwich date

53 Apr 16.42532

53 Apr 21.36042

Mean values

53 May 7.33958

53 May 8.38998

54 June 4.24583

Mean values

53 May 9.42072

54 Apr 28.30873

Mean values

53 May 13.16348

53 June 5.17987

53 June 6.19792

Mean values

52 May 19.21518

52 Oct 19.44228

53 Apr 11.14238

53 Apr 15.24742

54 June 3.25929

Mean values

52 May 21.36274

53 June 4.20432

53 June 8.37832

53 June 16.30529

53 June 16.31098

Mean values

52 June 17.36898

53 June 8.28750

53 June 13.26806

54 June 9.37083

54 June 11.38442

54 June 23.21042

Mean values

53 June 20. 35000

54 June 25. 24461

Mean Values

53 Aug 6. 16985

53 Aug 7. 39845

53 Aug 10. 22697

Mean values

a

(a.u.)

NEWLY

4.32

15.72

10.02

1.50

1.39

1.70

1.5S

1.00

1. 15

1.08

2.04

2.48

3.55

2.69

1.03

0.95

1.00

1.00

1.08

1.01

2.62

2.34

3.42

3. 11

2.86

2.87

2.83

3.28

3.70

2.81

3.27

2.74

S.10

2.07

2.81

2.44

2.53

2.06

2.36

2.82

e i

(deg)

a

(deg)

,x

(deg)

FOUND POSSIBLE STREAMS—Continued

0.770

0.936

0.853

0.379

0.321

0.417

0.S72

0. 157

0. 172

0.164

0.512

0.596

0.725

0.611

0. 131

0.120

0.017

0.017

0.148

0.087

0.915

0.838

0.893

0.827

0.837

0.862

0.641

0.720

0.736

0.644

0.697

0.629

0.678

0.521

0.642

0.582

0.624

0.515

0.587

0.575

43.6

47.1

45.4

19.9

17.9

22.7

20.2

16.4

22. 1

19.2

2.8

9.4

13.3

8.5

0.8

2.7

0.0

0.0

6.2

1.9

4.5

3.0

3.1

4.5

4.9

£ 0

26.7

31.8

31.3

39.6

33.6

38.2

S3. 6

28.9

21.3

25.1

1.2

7.7

4.3

S.6

26. 1

30.9

28.5

46.4

47.4

73.0

55.6

48.4

37.4

42.9

52.0

74.2

75. 1

67. 1

58. 1

26.0

—

—

72. 1

52.1

240.2

253.2

257.2

264.8

264.8

256.0

86. 1

77. 1

81.9

77.9

79.8

91. 1

82.8

sa 7

93. 1

90.9

313.4

134.5

137.2

185.0

218.3

217.9

218. 1

270.3

270. 1

275.0

271.8

127.4

164.7

146.0

24a 3

240.5

230.6

289.8

148.7

144.7

101.2

101.2

179.9

185.1

9.4

5.2

8.2

357.0

5.7

5.1

269.4

296.2

286.4

273.5

280.1

270. 1

279.8

291.0

286.2

288.6

347.0

330.7

343. 1

840.8

Corr.

R.A.

(deg)

256.6

263.4

260.0

231.6

231.8

245.0

286.1

341.8

313.8

827.8

17a 0

161.0

143.5

160.8

57.5

50.2

—

—

76.9

60.5

256.3

262.4

266.3

265.0

269.7

264.0

23a 4

255.5

253. 1

267.7

255.9

267.8

256.4

25a 6

237.8

248.2

272.3

254.0

266.9

264-4

Rad.

dec.

(deg)

+ 59.8

+ 61.0

+60.4

+40.4

+41.5

+50.5

+44.1

+63.9

+ 6a3

+ 66.1

+ 15.1

+49.0

+57.9

+40.7

+27.2

-7. 4

—

—

+ 62.8

+27.6

-25. 4

-25.9

-25. 8

- 2 a 6

- 2 a 4

-26.8

+60.3

+37.9

+46.8

+56.6

+51.7

+ 66.9

+68. 4

+ 50.4

+46.4

+48.4

-27. 4

+ 11.6

-6. 6

-7.5

Foo

(km/

sec)

29.6

32.4

81.0

17.6

16.2

18.2

17.8

14.7

16.6

15.6

13.6

14.8

17.2

15.1

11.5

11.4

10.6

11.0

12.2

11.8

36.0

30.8

32.4

27.4

29.0

81.1

20.6

25.0

24.1

26.7

24 4

25.9

24-4

21.2

l a s

20.0

15.5

13.7

14.5

14.6

D(M,N)

0.09

0.09

0.09

0.06

0.08

0.13

0.09

0.10

0.10

0.10

0.16

0.03

0. 18

0.12

0.06

0. 10

0.10

0. 10

0. 14

0.10

0. 19

0.03

0.06

0.19

0.08

0.11

0. 18

0.24

0. 12

0. 13

0.04

0. 18

0.15

0.10

0. 10

0.10

0. 12

0. 13

0. 10

0. 10
272 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Minor streams—Continued

Stream Greenwich date

a

(a.u.)

e i

(deg)

a

(deg)

X

(deg)

Corr.

R.A.

(deg)

Rad

dec.

(deg)

(km/

sec)

D(M,N)

NEWLY FOUND POSSIBLE STBEAMS—Continued

t» Herculids

0 Cetids

Capricornids

a Pegasids

X Draconids

c Geminids

I Taurids

53 Aug 9. 23255

53 Aug 13. 42525

53 Aug 15. 42275

Mean values

52 Sept 14.37389

52 Sept 20.29047

Mean values

52 Sept 16. 33958

52 Oct 9. 19742

53 Aug 13.35836

Mean values

52 Sept 19. 23462

52 Sept 27.30972

52 Oct 16. 21458

52 Nov 12. 19033

52 Nov 12. 19349

52 Nov 12. 26391

53 Oct 3. 25367

53 Oct 3. 29383

53 Nov 6. 33041

Mean values

52 Oct 12. 33141

52 Oct 19. 44602

Mean values

52 Oct 17. 40034

52 Oct 22. 26372

53 Oct 16. 42579

Mean values

52 Dec 9. 26560

53 Jan 15. 21244

Mean values

2.59

2.50

2.06

2.38

1.93

1.40

1. 66

1.57

1.46

1.37

1. 47

2.70

1.79

2.61

3.41

2.46

3.42

1.46

1.73

3.06

2.52

5.49

3. 14

4.82

10.37

26.77

22. 87

20. 00

2.60

3.98

3.29

0.611

0.617

0.518

0.582

0.720

0.592

0.656

0.422

0.314

0.348

0.361

0.713

0.599

0.670

0.717

0.605

0.719

0.432

0.501

0.704

0.629

0.818

0.683

0.750

0.919

0.971

0.965

0.952

0.682

0.763

0.722

i a 6

17.3

18.7

i8.se

12.0

15.5

13.8

1.0

&9

0.9

3.0

0.7

10.9

2.6

7.6

6.9

7.4

11.5

5.4

7.0

4-5

72. 1

77.4

74.8

173.8

173.0

173.3

173. 4

2. 1

0.7

0.7

136.3

140.3

142.2

139.6

351.4

357.2

354.3

173.4

195.8

320.2

169.8

176.2

184 1

22.8

229.7

229.7

229.8

189.7

189.7

43.6

206.1

198.9

206. 0

202. 4

203.9

208.8

202.7

205.1

257. 1

114.7

275.9

327.5

352. 1

341.2

840.3

87.4

96.7

92.0

41.6

17.6

17.1

25.4

59.4

79.8

71.3

70. 1

68.7

70.6

74.5

64.0

81.2

71.1

1&4

24.3

21.4

71.4

85.6

76.3

77.8

130.3

140.7

185.5

257. 1

280.1

270.2

269.1

2.5

14.0

8.2

327.2

278.6

302.4

302.7

341.4

349.8

359.5

342.2

339.8

343.0

345.0

343.1

15.8

848.8

181.9

167.3

174.6

102.4

104 2

9a 6

101. 7

51.0

65.3

58.2

+ 38.8

+ 26.6

+ 38.8

+84-7

-15.7

-18.8

-17.2

-9.0

+ 30.2

-23.7

-0.8

-6.3

+ia5

-7.7

+22.1

+ 22.4

+21.9

+2a5

+ 10.4

-15.5

+ 10.5

+ 81.4

+ 76.0

+ 78.7

+ 26.3

+ 26.5

+26.8

+ 26.5

+ 24.0

+ 19.3

+21.6

17.4

17.7

16. 9

17.2

25.0

22.5

23.8

13.9

12.7

13. 6

13.5

20.0

20.0

17.5

15. 6

14 4

15.5

16.5

15. 7

16.8

16.9

43. 5

45.0

44.2

70.6

70. 6

70.5

70. 6

18.3

16. 0

17.2

0.04

0.13

0.06

0.08

0.09

0.09

0.09

0.13

0.10

0. 14

0.12

0.20

0.22

0. 13

0.14

0. 12

0.14

0.24

0.15

0.25

0.18

0. 10

0. 10

0. 10

0. 11

0. 14

0.03

0.09

0. 10

0. 10

0. 10
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS

TABLE 3.—Spurious streams found in the artificial sample

273

Stream

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(H)

Greenwich Date

52 Mar 21. 36111

52 Sept 25. 17361

53 Aug 13. 42525

53 Aug 15. 42275

Mean values

52 Apr 2. 38125

53 May 13. 16348

54 June 25.24461

Mean values

52 June 24. 20301

52 Sept 16. 33958

52 Sept 19. 23462

53 Oct 3. 29383

54 Mar 1. 36968

Mean values

52 Sept 16. 33723

53 Apr 13. 25916

Mean values

52 Sept 25. 17579

53 Nov 2. 35675

Mean values

52 Aug i a 25543

53 Oct 9. 31647

Mean values

53 Jan 13. 45411

54 Feb 6. 38914

Mean values

53 Apr 7. 28372

54 Feb 10. 40343

Mean values

a (a.u.)

3.23

1.79

2. 50

2.06

2.40

2.80

2.04

2.81

2.55

2. 79

1.57

2. 70

1.73

2. 01

2. 16

3. 22

1. 71

2.96

15.94

6.87

11.41

20.92

19.45

20. 18

2.52

2.63

2.58

1.98

3.69

2. 84

e

0.713

0.510

0.617

0.518

0.590

0.644

0.512

0.642

0.599

0.720

0.422

0.713

0.501

0.639

0.699

0.937

0.914

0.926

0.947

0.872

0.910

0.952

0.949

0.950

0.798

0.810

0.804

0.809

0.871

0.840

i (deg)

4.3

11.5

4.8

4.6

6.S

1.9

4.9

1.2

2.7

8.6

4.4

7.6

4.2

4.8

5.9

8.9

3.9

6.4

7.0

13.3

10.2

0.2

9.7

5.0

1.9

2.4

2.2

4.2

0.9

2.6

G (deg)

43.6

25. 1

46.4

47.4

40.6

21. 1

0.6

16.6

12.8

39.6

48.4

30.0

46.3

25. 1

37. 9

63. 1

46.5

64.8

48.4

51.2

49.8

24.0

30.9

27.4

23.2

32. 1

27.6

53. 0

77.9

65.4

x (deg)

257.2

256.4

25& 2

246.4

254-6

210.4

196.8

209.7

205.6

283.2

276.7

273.2

280.5

276.8

278.1

13.6

8.4

11.0

275.9

271.7

273.8

207.4

207.9

207. 6

298. 4

30a i

SOS. 2

346. 0

354.2

350. 1

Original Classification

Sporadic

Sporadic

# Herculid

Sporadic

Sporadic

o) Ursa Majorid

T Herculid

Sporadic

£ Capricornid

a Pegasid

a Pegasid

<r Leonid

Sporadic

f Librid

Sporadic

Sporadic

Sporadic

Sporadic

x Geminid

a Leonid

Sporadic

Sporadic

D(M,N)

0. 13

0. 14

0.06

0. 12

0.07

0. 13

0.07

0. 15

0.20

0. 14

0. 12

0.10

0.07

0.07

0.08

0.07

0.08

0.08

0.06

0.07

0.09

0.09
274 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 4.—Further data on streams

Stream Hourly

rate

Number of

members

Inclination

Mean

D(M,N)

Radiant

X—X©

MAJOR STREAMS

Quadrantids

Orionids

Perseids*

Geminids

4.30

3.69

*1. 67

5.92

5

12

9

16

71?6

164.9

113.8

23.3

0.04

.08

*. 11

.02

278°

247

283

208

64°

- 7

37

10

KNOWN MINOR STBEAMS

S. t Aquarids

S. & Aquarids

N. 5 Aquarids

a Capricornids

S. Taurid-Arietids

N. Taurids

Andromedids

0.46

1.80

0.37

0.29

0.71

0.54

0.67

4

3

3

2

11

8

14

1?2

28.9

21.2

8.0

5.0

3 . 8

0.4

0.22

.03

.10

.08

. 19

. 14

.20

201°

210

207

175

197

195

172

- 1 °

- 7

7

12

- 5

2

— 1

KNOWN MINOR STREAMS HAVING ONE MEMBER m OUR SAMPLE

N. Aquarids

Draconids

Monocerotids

_

—

—

1

1

1

15?0

24.6

39.8

—

—

202°

78

205

7°

70

- 1 4

NEWLY FOUND POSSIBLE MINOB STREAMS

X Geminids

p Geminids

a Leonids

£ Orionids

$ Ursae Majorids

a Bootids

7 Bootids

8 Librids

v Draconids

<p Bootids**

£ Cepheids

w Ursae Majorids

Cyclids

0 Ophiucids

fi Draconids**

T Herculids

M Ophiucids

f> Herculids**

0 Cetids

( Capricornids

o Pegasids

X Draconids

« Geminids**

7 Taurids

0.63

0.89

0.74

0.43

0.20

0.44

0.67

0.24

1.24

0.29

0.32

0.38

—

0.37

1.31

0.84

1.76

0.92

0.71

0.24

0.56

0.57

1.09

0. 15

4

4

27

3

2

2

2

2

2

3

2

3

5

5

6

2

3

3

2

3

9

2

3

2

6! 3

5.2

2.2

0 .9

9.4

18?5

27.8

0.2

45.4

20.2

19?2

8 .5

1.9

4 . 0

33.5

25! 1

3.6

18.2

13.8

3.0

4?5

74.8

173.4

0 . 7

0. 16

.08

.29

.09

.08

. 10

.08

.09

.09

.09

.10

.12

.10

. 11

.15

.10

.12

.08

.09

. 12

.18

.10

.09

.10

182°

166

171

119

144

176°

171

201

204

159

344°

79

189

148

140°

128

129

186

134

148°

273

256

145

8°

10

2

- 2

36

31°

49

0

82

60

68°

31

—4

74

68°

15

58

- 2 0

18

15°

68

3

2
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS

TABLE 4.—Further data on streams—Continued

275

Stream

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(H)

Hourly

rate

Number of

members

SPURIOUS STREAM

_

—

—

—

—

—

—

4

3

5

2

2

2

2

2

Inclination

6?3

2.7

5.9

6.4

10.2

5.0

2.2

2.6

Mean

D(M,N)

0. 11

.09

. 14

.07

.08

.08

.06

.09

Radiant

X—\Q /3

136°

98

161

202

152

90

183

192

22°

13

14

6

22

16

2

2

'Incomplete observations; shower peak missed.

••The most probable streams.

**- Geminids

Known streams.

• Newly found

possible streams.!

k— Quadrantids

S. < Aquarids

Perseids

» Leonids . _

S. Taurids-A

Andromedids

nids .

rietids \

dids

N. I Aquarids

• Capricornid:

<J» ~^Al « • v N- Taurids

6. > Aquarids

0.10 0.20 0.30

MeanD(M.N)

FIGURE 3.—Relation between hourly rate and internal

dispersion of streams.

Thus neither our value of the rate nor of the

mean dispersion within the stream is representative of the stream. Accordingly, no further

use is made of values of D from the Perseid

stream.

Streams with a photographic rate less than

three per hour we shall call the minor streams.

The Southern 5 Aquarids are the only minor

stream in our sample with a mean D(M,N) less

than 0.08. Because the duration of a shower

is correlated with its mean D(M,N), the total

number of meteors in the sample is correlated

with the product of ordinate and abscissa in

figure 3; thus a stream in the lower left corner

is comparatively unlikely to be detected.

Nevertheless, the sharp boundary of the points

at Z?=0.08 seems meaningful as an approximate

lower bound to the mean dispersion within the

majority of minor streams.

On the right edge of figure 3, the "<r Leonids"

are doubtless a composite of two or more

streams. The Southern Taurid-Arietid stream

is known to be composite, as its name indicates.

Either of these composite streams, if it could

be divided into its originally independent parts,

would be represented by two or more points

nearer to the majority of streams in the

diagram.

Nature of the newly found minor streams

Figure 4 shows histograms of the normalized

distribution of values of D(M,N) in each of

four classes of streams. The data for major

streams and previously known minor streams

are drawn from table 1, Perseids being omitted;

for newly found minor streams from table 2;

and for spurious streams from table 3. For

each class of stream the ordinate is the percent
276 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

60%

50%

40%

30%

20%

10%

\

j

1

1 1 1 1 1

- Major streams

1

" ^ Spurious streams

\

K \

/ \ *^\^ ^ Newly found minor streams

\ V \

\ V /C~~\^ — Previously known minor streams

0.1 0. \-V\2 x 0.3 0. . 4 0.5 0.6

D(M.N)

FIGURE 4.—Normalized distribution of D(M,N) in different

classes of streams.

of values of D within an interval 0.04 unit

wide.

All these curves indicate high central condensation in the streams. D may be interpreted as distance in a four-dimensional phase

4 5 -

40

35

2 0 -

- Previously known

minor streams

Spurious

streams

0.0

FIGURE 5—Distribution of D(A,B) in different classes of

streams.

Previously known streams

7 8 9 10 11 12 13 14 15 16

2345678 9

Spurious streams

2 3 4 5

Number of meteors

FIGURE 6.—Distribution of number of meteors in a stream.

Major streams are unshaded.

space from the mean elements of the stream.

A stream with members uniformly distributed

through a volume in this phase space would

have a histogram in which the ordinate varied

as the cube of the abscissa. Thus, the histogram for newly found minor streams indicates,

so far as the numbers are significant, that the

density of points at D(M,N)=0.1 has actually

decreased from the density at lower values of D.

Figure 5 shows the distribution of values of

D(A,B) within streams. It is clear in both

figures 4 and 5 that the newly found streams are

less compact than the previously known minor

streams. Figure 6 shows the distribution of

the number of meteors in a stream. The

comparatively low values of D(M,N) for

spurious streams occur because such a large

proportion of the spurious streams have two

members only. We may also conclude from

figure 6 that it is the newly found minor streams

with two or few members that are more likely

to be chance groupings.

Figure 7 shows the distribution of the inclinations of the mean orbits of streams. From the

concentration of all the spurious stream inclinations to low values we conclude that the newly

found minor streams with low inclinations, like

those with few members, are less likely to be

genuine streams.

The distribution of radiants of meteors and

streams in our sample is shown in figures 8 and 9,

referred to a system of coordinates defined by

the ecliptic plane and the direction to the sun.
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 277

Previously known streams

n n n

Newly found minor streams

Spurious streams

FIGURE 7.—Distribution of inclinations,

streams are unshaded.

Major

These radiants have been corrected for zenith

attraction and diurnal aberration. We found

the ecliptic latitude /3 of each radiant and also

the ecliptic longitude X—Xo measured from the

sun's direction as origin. The radiants of

major streams and of all other meteors in the

sample are so plotted in figure 8. The apex

of the earth's motion is in the center of the

diagram, the antapex at the right and left ends.

The large cluster of points at the right is nearly

centered on the anti-sun at X—Xo = 180°,

/S=0°; while the direction to the sun at left

center is X—Xo=/3=0°.

The last two columns of table 4 list the mean

values of X—Xo and (J for each stream radiant.

Figure 9 repeats figure 8, substituting mean

radiants of minor streams for the individual

radiants of their members. The "Cyclid"

radiant spread is too large to permit plotting.

In figure 9, the minor streams are seen to

cluster principally around the ecliptic in

longitude 120° to 210° with respect to the sun.

Table 4 also lists the mean radiants of the

spurious streams, computed from their orbital

elements neglecting the eccentricity of the

earth's orbit. These spurious stream radiants

are all in or close to this cluster of stream

radiants. All the streams with low inclination

are in this cluster, and no stream with high

inclination; thus we again conclude that the

newly found streams with high inclination are

much more probably genuine.

All the information that we have found

useful in estimating the probability of a stream

has been assembled in table 4, although some

of it appears also in the other tables. By

means of the criteria described above, we have

selected four of the provisional streams as the

most probable, the ^Bootids, yuDraconids,

0Herculids, and eGeminids. We have indicated

above that the Cyclids are quite probably not

a stream, and that the a Leonids are certainly

not a single stream. More definite conclusions

can hardly be drawn from our sample.

Comparison with other results

McCrosky and Posen (1959) have examined

2538 meteors photographed by the SuperSchmidt cameras, and by comparing radiants,

velocities, and dates, have found seven new

streams. Substantially all of our meteor sample

is included in theirs. Four of the streams in

each list are associated. The e-Geminid stream

bears the same name in both lists. Their h

Arietids are the same as our ijTaurids, and

their ^Pegasids are included in our TPiscids.

Finally, their aVirginids are included within

our overgrown <r-Leonid association. This

result emphasizes the difficulty of deciding the

validity of a possible stream in our sample for,

while the cGeminids had already been selected

as one of the most probable, there was hardly a

less promising stream than the ^Taurids.

Associations with comets

We have compared the mean orbits of the

possible streams with the orbits of comets

observed since 1700, seeking similarities. The

nearest associations found appear in table 5.

The comets listed have been seen on only one

revolution, except Comet De Vico-Swift, for

which we list all three observed perihelion

passages. The difference D between each

stream and its provisionally associated comet is

tabulated.
70'

\-\ \\\ x

/ / / /7TT7

:\ \ \A \ v\\

#

• . . .\ V.\ \ V.\A..\

--\\\'x:\ \ 

u

\\\\\\\ \ \ \ \ J'- h i

L/XZV//7 \\\ \ \ \ \.\

x\\\\\

-70'

-80°

-90'

-80°

-70°

• RESIDUAL METEOR

0 MAJOR STREAM

FIGURE 8.—Distribution of radiants of major streams and residual meteors.
30°X//

rtl—LLL 1

/3o°

'

l<fVW\T

-2>rWv

-40 ^

/

\

60°

50°^^%^

uYZL

LJTT

\xx\

§§§^

-60° ^

/ ,

/

/

/

i

\

\

**—

. — •

x:

y

y

*c

/

/

I

—

\

\

\.><

-^-—.

70" m

//

/ /'

/

1

\

\ \

\

—v—*c

^ ^ :

-70 °

y

/

/

/

i

\

3

\

\

\

• — .

>

_—• —

/ .

/

/

/

\

\

\

X

X

s

S>

>^•~~-— .

— —

. — —

/

/

/

/

\

\

\

v

X

.

80°

y//

i r

i

i

•

\

\

90°

V

y

 /

7/

'/•

./.

/ p a

r

t

\

\

\ \ \ \

^ >

-80 °

A

1

^

^\

I.

I -—

•

•

\

\

A

\

>\

- q

. \v _

80°

rt\v\\

•

—•—

•

—r

•

•

\

\-

1 •

•

1

\ 1

\ ' \

• \ >

. \ -

•

OR!

a

•

/

/ /

/ /

-\44-LL

1th

/,

^ ^

-80°

—-—-* P

^ ^

i

7

\ • \

1

1

f

l

/•• /

•/ / /

-J-Z2

Y77Z

///^

— ^70

>

°

<\

X"

\

1

•

• •

. /

* ~

/

y

^^

IIS

\ \

.\

1 1

/.-

/ /

y ^

<<&

60'

?=>-

.\.

/

/: /

^60° '

^^

N

\

' \

c

(J

/

/

"o?

><

*y

^ -

\°

.\

\

1 /

/ •

/ ,

50°

\ \

1 1

/

> /

^50 °

t

O

n

\

\

•

\

\

/

/

/

7

/

'A

SPORADIC

MINOR

MAJOR

\X

X

\ 

l_ 

I

'/

/X

5^

M

STR

STR

FIGURE 9.—Distribution of radiants of major streams, minor streams, and sporadic meteors.
2 8 0 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 5.—The closest correspondences between newly found possible streams and known comets

Stream

£ Orionids

Comet 1928 III

T Herculids

Comet 1930 VI

n Ophiucids

Comet 1 1678

De Vico-f 1844 I

Swift J 1894 IV

a Pegasids

Comet 1819 IV

17 Taurids

Comet 1894 I

a

1.86

3.43

2.44

3.09

2.32

3.07

3. 10

3.25

2.52

2.96

3.29

3.80

e

.480

.71

.582

.672

.575

.627

.617

.572

.629

.699

. 722

.698

q

.947

.995

.998

1.011

.975

1. 145

1. 186

1.392

.872

.892

.885

1. 147

i

0?9

1.4

25! 1

17.4

3?6

2.9

2.9

3.0

4?5

9.1

0?7

5.5

SI

159?8

196.8

90?9

76.8

135?0

163.3

63.8

48.8

206? 1

77.4

275?9

84.4

CO

16?4

345.2

197?7

192.3

205?3

159.5

278.7

296.6

225? 0

350.1

219?6

46.2

176?2

182.0

288?6

269.1

340?3

322.8

342.5

345.4

71?1

67.5

135?5

130.6

Equinox

1950

1928

1950

1930

1950

1678

1844

1900

1950

1820

1950

1894

D

.24

.28

.26

.23

.43

.23

.29

Only the connection between the a Pegasids

and Comet 1819 IV, which was previously

found by McCrosky and Posen (1959), is fully

convincing. We should expect a parent comet

to differ from the mean of an observed stream

by more than the average observed meteor

because the observed meteors, all of which

strike the earth, are a restricted sample of the

stream. Since all these comets except 1819 IV

differ from the streams by more than 0.2,

however, and since some of the streams themselves may not exist, anything more than the

possibility of association between these remaining streams and comets remains to be shown.

Space density of minor streams

In this discussion we shall use the symbols

defined as follows:

Va: Heliocentric velocity of meteors.

Va: Geocentric velocity of the meteors, neglecting the

earth's attraction.

Vt: Accelerated geocentric velocity of the meteors, at

the top of the atmosphere.

Vm: Velocity of the meteors with respect to the earth's

surface, at the top of the atmosphere.

L: Angular elongation of the corrected radiant from

the apex of the earth's way.

y: Angle between Vo and Vg.

ID: Width of meteor stream in the plane of the figure.

p: Density of meteors in the stream.

X: Earth's collisional cross-section for meteors.

R: Earth's radius including the atmosphere.

VM: Earth's orbital velocity.

The number of meteors swept up by the

earth in one pass through the stream is iV"i=

Xpw cosec 7. The number of meteors in the

stream passing within any given small distance

h from the earth's orbit per unit time is

N2=2hwpVB. It is well known (see, for

example, Schiaparelli, 1871, p. 116) that

X=T&VllVl. From figure 10 we see that

VB cosec 7 = Va cosec L. Thus the ratio of the

number of meteors striking the earth to those

crossing its orbit,

iV, TR2 VI

N2~2hVB VI sin L

is independent of w and p. Following Whipple

(1954), we approximate by Vt the velocity

dependence of the ratio of the number of

meteors brighter than a given magnitude on

photographs to the number above a given

mass, but omit his special factor for velocities

FIGURE 10.—Geometry of the intersection of the earth with

a meteor stream.
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 281

below 19 km/sec. The qualitative result is

not sensitive to a fractional change in the

power of Va* We approximate Vm by the

closely similar Ve. Thus (neglecting constants)

we find that the ratio of the number of meteors

passing near the earth's orbit to those photographed is given by

w V% sin L

W =

 T/ Vi5 > (5)

which may be interpreted as a weight of a

photographic meteor in determining the present

strength of its stream at the earth's orbit.

Figure 11 shows ifa s a function of L for

various values of the stream major semi-axis a.

For all except nearly circular orbits, W has a

strong maximum between Z=90° and L=130°.

Figure 9 contains, in addition to the cluster

of stream radiants already discussed, a smaller

group in high latitudes which includes three of

the most probable streams. All of this group,

and most of the larger group fall within the

range of high W, 90°<Z<130°. The minor

streams, therefore, are perhaps twice as important numerically in the earth's neighborhood

with respect to sporadic meteors, as the

observed numbers indicate.

Origin of the newly found minor streams

As shown above, the newly found streams are

broader and more diffuse than the major

streams, or than most of the previously known

minor streams. By this characteristic, we

readily recognize that in the dynamical sense

they are old streams, which have been more

disturbed and perturbed than previously known

streams. The absence of closely associated

comets corroborates their relatively great age.

There are some interesting relationships

among certain of these streams. The n Ophiucids and # Herculids form a pair of very similar

streams differing only in inclination. In contrast to known pairs of streams on either side

of the ecliptic, the juOphiucids are nearly in

the ecliptic while the t? Herculids have an

inclination of 18°. The eGeminids bear a

somewhat similar relation to the Orionids, but

in this case the longitudes of perihelion also

differ.

In figure 12 the orbits of all the newly found

minor streams with inclinations less than 15°

are projected onto the plane of the ecliptic.

Although the majority of the streams plotted

here doubtless are chance associations, some

conclusions can be drawn. The tendency of

these orbits to be approximately tangent to the

earth's orbit is clearly a selection effect. The

tendency to have aphelia at or near Jupiter's

orbit appears to be significant. Jupiter will

strongly affect these streams, and they will

age rapidly.

Conclusions

The differences D between meteors may be

used as a means of determining membership in

known streams, or of finding new streams. As

we have applied D to the search for streams, the

result is certainly complete in the sense that all

streams with two or more members in the

sample doubtless were found. Unfortunately,

the method as applied was not very discriminating, since many streams were "found"

FIGURE 11.—Weight W of a photographic meteor

in determining the present strength of its stream

at the earth's orbit, as a function of the angular

elongation L of the radiant from the apex, and

the major semi-axis a.
/3 CETIDS

17 TAURIDS

PEGASIDS

L

CYC LIDS

p GEMINIOS

X GEMINIOS

URSA MAJORIDS \O"LE0NIDS

FIGURE 12.—Orbits of all the newly found minor streams with inclinations less than 15° are projected onto the plane of the ecliptic
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 283

which no doubt do not exist, but the number

of spurious streams may be estimated. Streams

too small to have at least two meteors in our

sample, streams with brief showers during a

gap in the observing, variable and temporary

streams: all may or will be missed.

Of the 359 meteors in the sample, 42 or

12 percent belong to major streams, i.e., those

with mean photographic hourly rates exceeding

three; 48 or 13 percent belong to previously

known minor streams, and approximately 39

or 11 percent to newly found streams. About

64 percent of the sample is sporadic. In the

immediate neighborhood of the earth's orbit,

the minor streams, compared to other meteors,

are roughly twice as numerous as in the photographic sample.

The newly found streams are in fact old

streams; they have been much perturbed, and

some show obvious relationships with Jupiter.

In overall orbital distribution, the minor

streams do not differ, in any way that has been

conspicuous to us without special scrutiny,

from the sporadic meteors with which they are

intermingled.

Appendix

To compute the average gradients of orbital

elements with respect to perturbations, let

the units be the astronomical unit, the solar

mass, and s~ year. Consider perturbations at

a point P in a meteor orbit, at a distance r from

the sun. Resolve the meteor's heliocentric

velocity VH into components as in figure 13:

VR directed away from the sun, and Vs directed

forward in the orbit plane normal to VR. Resolve the perturbations in velocity into components: bVR and 8VS along VR and Vs

, respectively, and dVT normal to the orbit plane

forming a right-handed set with SVR and SVS.

Let G denote any orbital element, and \VG\

the magnitude of the gradient of G with respect

to perturbations in velocity. Then

1/2

(Al)

It is evident that differentiation with respect

to dVR and 8VS may be replaced by differentiation with respect to VR and Vs

, respectively.

svR

FIGURE 13.—Components of velocity and of perturbations

in velocity.

Let the perturbations be expressed in units of

the circular speed U=r~l/2; the magnitude of the

gradient of G with respect to such perturbations

is

(A2)

Let Grad Q denote the average of \VG\e over

the orbit with respect to time. Let t be the

time of the meteor's arrival at P, counted from

perihelion passage. Then, since the period of

revolution is 2jra3/2,

Grad G= (A3)

This is the desired measure of the importance of

GinD.

Of the components of D, differences within

the orbital plane are measured by 8e, Sq, UAB.

Obviously, Grad 8g=Grad e, and Grad Sq—
284 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Grad q. Let v be the true anomaly at P. Any

perturbation hv in true anomaly implies a perturbation — 8v in the direction of perihelion;

thus

Grad nA B=Grad v. (A5)

By standard formulae, if p=a(l—e2) is the

parameter of the orbit, then

r=p/(l-\-ecosv),

Vs=(\+e cos v)lp112,

dv/dt=Vslr.

(A6)

If r, VB, Vs are given at any point, then by

equally standard formulae:

e sin v=rVRVs,

e cos v—rV*s— 1, (A7)

Straightforward analysis yields:

bv/bVs=rVs(rVs

2

-l)/e2,

= -rVB(rVs

2

(A8)

Since e, v, q are functions of r, VB, Vs only,

=O. (A9)

Expressions for Grad e, Grad v, Grad g

may now be found by substitution of equations

(A6), (A8), (A9) into equation (A4). We

have not found it possible to evaluate those

expressions in closed form. Since an approximate result is sufficient for the purpose, we

take advantage of the following lemma.

Lemma: If y and z are functions of x which

are finite throughout a<x<b, and if

y>o,

2>0,

rb Y=Ja

ydx>

Z= 1 zdx,

(A10)

(All)

(A12)

(A13)

then

(Y2+Z2y<2<R<Y+Z.

(A14)

(A15)

If y bears a constant proportion to z for all x in

a <x<b, then R=(Y2-\-Z2)

1/2

. Any deviation

from constant proportionality between y and z

increases R; for example, if y(x{) is increased

by Ay over a range dx about xif and then

y (x2) is decreased by Ay over a range dx about

x2 in order to satisfy equation (A12), some

algebra will show that R increases. If y=0

for all x such that 2>0 and vice versa, then

R=Y-{-Z; if there is any range in x in which

both y>0 and 2>0, then R<CY-\-Z because

By substituting equation (A9) into (A4),

and taking the mean of the limits in equation

(A15), we find that an approximation to equation (A4) when 0 is he, I1AB, or dq is

where

and \jTr~) is similarly defined.

With the aid of a particular set of elliptic

integrals,

= r[lJo

) = C*[iJo

(A18)

-

1

 sin2 u\l'

2

du, (A19)

we may now evaluate Grad G. By substituting equations (A6) and (A8) into (Al7),

and performing the necessary algebra, we find:

(A20)

<d«/d FS>=8(1 - e

2

) {(1 -e)l'

2

[2Ff (A)-Ff (x/2) ]

- (1 -e)-l'

2

[2E' {A) -E' (w/2) ]+[2

- 2 (l-e2y<2Y<2{2(l-e2)-1/2+l/2]}/3ire, (A21)
METEOR SYMPOSIUM—SOUTHWORTH AND HAWKINS 285

where

-4=2 arc cos{[— (A22)

Also,

2

, (A23)

2

, (A24)

(A25)

(dqJbVs)=4a(l-e)1/2[2(l+e)E'(Tr/2)

-(2-e)(l-e)F'M2)}/3ire. (A26)

The values of Grad e, e Grad UAB, and of I/a

Grad q in figure 1 were computed from equations (A5) and (A16) through (A26). The

largest possible error, computed by equation

(A15), is 15 percent.

Grad IAB remains to be discussed. Since

IAB measures the change of orbital plane, it

is independent of velocity changes within the

plane; hence

0. (A27)

From figure 13 we see that

(A28)

Thus Grad IAB may be found exactly from

equations (A4), (A6), (A18), (A19), (A27),

(A28), as

Grad IAB=2(l-e)-1/2

-(1-e) F'(X/2))/ZT, (A29)

and the values in figure 1 were so computed.

References

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.; SOUTHWORTH, R. B.; AND STIENON, F.

1959. Recovery of the Andromedids. Astron.

Journ., vol. 64, pp. 183-188.

JACCHIA, L. G.

1960. Individual characteristics of meteor families

(abstract). Astron. Journ., vol. 60, pp.

53-54.

MCCROSKY, R. E., AND POSEN, A.

1959. New photographic meteor showers.

Astron. Journ., vol. 64, pp. 25-27.

SCHIAPARELLI, G. V.

1871. Entwurf einer Astronomischen Theorie der

Sternschnuppen. G. von Boguslawski,

transl. Stettin.

WHIPPLE, F. L.

1947. Photographic meteor studies. IV. The

Geminid shower. Proc. Amer. Phil.

Soc, vol. 91, pp. 189-200.

1954. Photographic meteor orbits and their

distribution in space. Astron. Journ.,

vol. 59, pp. 201-217.

WRIGHT, F. W.; JACCHIA, L. G.; AND WHIPPLE, F. L.

1954. Photographic 5-Aquarid meteors. Astron.

Journ., vol. 59, pp. 400-406.

1956. Photographic a-Capricornid meteors.

Astron. Journ., vol. 61, pp. 61-69.

1957. Photographic i-Aquarid meteors and evidence

for the northern 5 Aquarids. Astron.

Journ., vol. 62, pp. 225-233.

WRIGHT, F. W., AND WHIPPLE, F. L.

1948. Photographic meteor results for the month

of October (abstract). Astron. Journ.,

vol. 54, p. 54.

1950. The photographic Taurid meteors. Harvard Coll. Obs. Reprints, ser. 2, no. 35.

1953. The photographic Perseid meteors. Harvard Coll. Obs. Reprints, ser. 2, no. 47.

Orbital Elements of Photographic Meteors

By P. Babadjanov1

During the period June 1957 to December

1959, 592 meteors were photographed at two

stations of the Institute of Astrophysics of the

Academy of Sciences of Tadjikistan, 359 of

them from both stations; 185 doubly photographed meteors were selected for accurate

reduction on the basis of trial length and

quality of image. The photographs were

taken with cameras NAFA 3C/25 (D=100 mm,

F=250 mm); a panchromatic emulsion with

sensitivity 1,100-1,300 units of GOST 0.85

(approx.=350-400 ASA) was used.

The details of the cameras and the methods

of reduction have been described elsewhere

(Babadjanov and Sosnova, 1960). The velocity of the meteor outside the atmosphere was

computed on the basis of the formula:

The parameter k was determined by a graphoanalytical method, and va and c were evaluated

by the method of least squares. The instants

of the meteors were determined by using a

shutter with a gradually changing width. The

error of a time observation did not exceed 1

minute.

Table 1 presents orbital data for 132 meteors

that have been reduced up to the present.

Following are definitions of the column heads

of the table:

No: Meteor number, of the year of observation minus 1900 (the first two digits);

number of the exposure in the current year

(the next three digits); number of the

camera (the last digit). If two or more

' Astrophysics! Institute of the Academy of Sciences of Tadjikistan,

U.S.S.R.

meteors were photographed simultaneously on one camera, they are distinguished

by an added Roman letter.

Date: Day and month.

U.T.: Hour and minute in Universal Time.

Shower: Name of the shower.

Corr. rad.: Radiant (right ascension a and

declination S) after correction for the

earth's attraction and diurnal aberration,

in degrees. Equinox 1950.0.

Sin Q: Q is the angle between the great circles

traced by the meteor, as seen from two

stations.

e: Elongation of the corrected radiant from

the apex of the earth's motion, in degrees.

va: Pre-atmospheric velocity, km/sec.

Vg' Geocentric velocity, km/sec.

vB: Heliocentric velocity, km/sec.

a: Semimajor axis, in a.u.

e: Eccentricity.

q: Perihelion distance, in a.u.

q': Aphelion distance, in a.u.

&: Longitude of the ascending node, in degrees.

Equinox 1950.0.

&>: Argument of perhelion, in degrees. Equinox

1950.0.

i: Inclination of the orbit plane to the ecliptic,

in degrees. Equinox 1950.0.

r: Longitude of perihelion, in degrees.

k: Whipple's comet-asteroid criterion.

aCAP: a Capricornids.

IAQU : i Aquarids.

5AQU: S Aquarids.

PER: Perseids.

S.T.: Southern Taurids.

LMIN: Leo Minorids.

N.T.: Northern Taurids.

GEM: Geminids.

287
288 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 1 contains many meteors belonging

to well-known showers: 30 Perseids, 4 Genrinids, 3 6 Aquarids, 3 Northern and Southern

Taurids, and 6 a Capricornids. The sporadic

meteors also form some groups with analogous

radiants, velocities, and orbital elements. One

group, designated as "I," is formed by the

meteors Nos. 570673, 570706, 570774, and

582565b, and posesses the following mean

characteristics:

a=278?5

8= 48?8

o.= 27.0

e=0.86

fi=127?6

a>=202?2

i = 36?2

The mean coordinates of the radiant are close

to that of Maltsev's (1930) radiant No. 76

near c Draconis (a=279°, 5=55°); moreover,

the Harvard meteor No. 8089 has almost the

same characteristics.

The second group, designated as "II,"

consists of three meteors, Nos. 572181, 572182,

and 572384, and has the following mean

characteristics:

a= 0?9 a-'=0.33 G= 2?7

5 = _ 8?9 e=0.77 co=79?3

va= 23.7 9=0.65 i= 5?6

No known visual radiant corresponds to the

mean coordinates of the radiant of this group.

Some meteors can be related to the meteor

associations discovered recently by Jacchia

and Whipple (1961). Such meteors are Nos.

591444 and 570214, related to the association

63; No. 570233 (association 61 or 62); Nos.

591774, 570556, and 570582 (association 72 or

73); No. 570354 (association 69); and No.

573162 (association 88).

Thus, we see that an increase in the observational material results in a decrease in the

number of the so-called sporadic meteors.

Evidently the majority of sporadic meteors

belong to various not-yet-known showers.

Application of Whipplo's K criterion to the

elliptic orbits of sporadic meteors shows that

73 percent aro connected with comets (K>0),

the rest being of anteroidal origin (K<0).

Tablo 1 contains 26 hyperbolic orbits, but

almost all of them am perhaps due to observational errors. Only one hyperbolic orbit, that

of meteor No. 570707, is probably real. This

indicates that the actually hyperbolic orbits

constitute less than 1 percent of the whole

material.

References

BABADJANOV, P. B., AND SOSNOVA, A. K.

1960. Photographic observation* of meteore in

1957. Bull. Astrophys. Inst. Acad. Sci.

Tadjikistan, U.S.S.R., no. 29, pp. 3-15.

JACCHIA, L. G., AND WHIPPLE, F. L.

1961. Precision orbits of 413 photographic meteors. Smithsonian Contr. Astrophys.,

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

MALTSEV, V. A.

1930. Radiants of the most important meteor

streams. Russian Astron. Calendar, ed.

4-e (permanent section), pp. 448-453.
METEOR SYMPOSIUM—BABADJAXOV 289

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On the Structure of the 5-Aquarid Meteor Stream

By A. K. Terentjevax

The 5-Aquarid meteor stream has some

exclusive and peculiar properties:

(1) The perihelion distance 2=0.06 a.u. is

shorter than that of all other streams (having

g>0.1 a.u.). The theoretical temperature Tof

the meteor bodies near the perihelion should be

T~1100o K (melting point of silicates). It is

possible that this high temperature accounts for

the peculiar general appearance of the shower

meteors which are sharp, show no wakes, and

give off no sparks. The 5 Aquarids are also

observed at the ascending nodes of their orbits

as a daytime meteor shower, the Arietids.

(2) The radiants of this shower cover a large

area, and many other radiants of some minor

ecliptical streams occur in the same region.

(3) The 5 Aquarids are the richest shower of

the southern hemisphere, but the number of

good photographic and visual observations is

insufficient. There have been some attempts

(Wright, Jacchia, and Whipple, 1956; 1957) to

obtain the structure of S Aquarids and neighboring streams (i Aquarids, aCapricornids), based

upon an insufficient number of double-station

photographs; only some of the single-station

meteors are genuine S Aquarids.

Much reliable data concerning a great number

of the 5-Aquarids' visual radiants have been

compiled in the U.S.S.R., some with a determination of geocentric velocities. These data

were published in Russian, and have remained

insufficiently known abroad. A new paper

(Terentjeva, to appear) tabulates all doublestation photographs, visual radiants, and radar

observations of the 5Aquarids since their

discovery in 1871. The total number of radiants

is about 600, and they include radiants of the

neighboring showers (i Aquarids, aCapricornids, etc).

'Kiev Astronomical Observatory, V S.8.R.

The general study of the radiants shows the

complexity of the S Aquarids and their large

area with some "centers" (Pokrovsky, 1922;

Astapovich, 1950). A study of the improved

geocentric radiants and all the orbital data

gives the following results:

(1) The S Aquarids show two groups of

radiants: one north and one south (main group)

of the ecliptic; the symmetry line is parallel to

the ecliptic and lies 1?3 to the south. The north

and south branches are symmetrical relative to

the plane of Jupiter's orbit. This may be the

effect of perturbations. The visually determined third "ecliptic branch" of the 5 Aquarids

is, apparently, a group of different radiants of

many minor streams and of sporadic meteors.

Simultaneous visual and photographic observations of this group are needed. The new

ephemeris (daily motion) of the improved

geocentric radiants is given in table 1. McIntosh's (1935) ephemeris is in good agreement

with these data for the southern 5 Aquarids.

Derbeneva (Stalinabad) in 1960 obtained the

following ephemeris for the radiant from

telescopic meteors (Equinox 1950.0):

a«=338?8+0°89 (Long, of o-122?4),

5«=-15?4-|-0o39 (Long, of O-122?4).

(2) The period of visibility is apparently from

long, of o = 120° (July 23) to long, of © = 148°

(August 22), with maximum at long, of

O = 125°-126° (maximum of southern 8 Aquarids only, about July 29), Equinox 1950.0.

The 600 fireballs observed in China (10th to

12th centuries) give for the 5 Aquarids a shift

of 4 to 5 days in the maximum date over 1000

years; the radiant area then was also very large.

Undoubtedly, Jupiter disturbed this stream.

During a period of 28 days the earth passes

through the stream, which passes very close to

293
294

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

the sun; therefore a very small variation in

radiant position gives a great difference in

inclination, perihelion distance, and other

elements. The perturbations alone are insufficient to explain all the peculiarities of the

observed orbit which may be affected by physical agents as well.

The velocities of the photographic 5-Aquarid

meteors show a systematic difference AVg of

about +4 km/sec relative to the velocities

obtained by radar (Almond, Bullough, and

Hawkins, 1952; Almond, 1952). The semimajor

axes of photographic orbits are thus enlarged

by a factor of 2. The mass distribution and the

space density in the stream were studied in

detail (Terentjeva, 1961); the mass distribution

j {M)~Mr%0, the mean space density D(M) =

12X10"9 km"3, in accord with the later

determination by Moscow Section of VAGO,

Crimea Expedition of 1960.

A fine shower of i Aquarids and more than

three other showers are acting simultaneously

in the same region; to separate them we need

double-station photographic and exact visual

observations. The data obtained by Wright,

Jacchia, and Whipple (1957) concerning i

Aquarids are doubtful: of nine double-station

meteors, some are not i Aquarids. The radiants

of the i Aquarids are also near the ecliptic, in a

very confusing region. There are many

radiants of meteor streams near the ecliptic,

acting successively; they correspond to the

orbits of short period (Astapovich, 1950).

The study of these streams (i Aquarids, a

Capricornids, 8Aquarids) therefore demands

great care.

The neighboring shower of the a Capricornids

has two groups of radiants: the proper a

Capricormds (an old meteor stream observed in

the 19th century), and a possibly new group of

ecliptical a Capricornids. Their correlation

cannot be explored because of the absence of

exact observations of the later shower. It is

possible that the structure of the Capricornids

is identical with that of the 8Aquarids:

Mclntosh's (1935) radiant No. 250 being the

southern branch, the a Capricornids the

northern one. Mclntosh's radiants Nos 240

and 264 apparently fit the ecliptical branch

of the Capricornids, but not that of the "southern lAquarids," as suggested by Wright,

Jacchia, and Whipple (1957). The ecliptical

group of "August a Capricornids" (Wright,

Jacchia, and Whipple, 1956) is doubtful. If

the "August a Capricornids" were real, the

photographic error of the radiant would be 6°

to 8°. The preliminary ephemeris of the a

Capricornids (Equinox 1950.0) is:

ttB=303? 14-0.63 (Long, of o-124?0)

5B=_10?4+0.17 (Long. ofo-124?0)

(photographic obs.)

The association between the a Capricornids

and Comet Lexell 1770 I is more probable than

that with Comet 1948n (=1948 XII) as suggested by Wright, Jacchia, and Whipple (1956).

Comet 1770 I is also connected with some

ecliptical streams and may be related to Comet

1948 XII (Tisserrand's criterion). The application of Tisserrand's criterion to the study

of the connection between comets and streams

gives a considerable dispersion of the Cconstant (for a single meteor orbit). Apparently the meteor bodies not only suffer

gravitational perturbations, but are possibly

influenced by other physical agents. In these

cases Tisserand's criterion cannot be applied.

A lengthy paper on this subject with a

bibliography of sources (over 100 references)

will be published in Russian.

TABLE 1.—New ephemeria of geocentric S-Aquarid radiants (Equinox 1950.0)

Stream

Northern 5 Aquarids

Southern 5 Aquarids

Radiants

as = 334!5

«s=-5?4

as=338?5

«s=-16?9

Daily motion

+ 0?85

+ 0?35

+ 0?88

+0?36

Long, of©

125!0

125T0

125T0

125T0

Type of observation

All photographic

and visual

All photographic
METEOR SYMPOSIUM—TERENTJEVA 295

References

ALMOND, M.

1952. The orbit of the 8 Aquarid meteor stream.

Jodrell Bank Ann., vol. 1, pp. 22-28.

ALMOND, M.; BTXLLOUGH, K.; AND HAWKINS, G. S.

1952. Radio echo observations of the daytime

meteor streams in 1952. Jodrell Bank

Ann., vol. 1, pp. 13-21.

ASTAPOVICH, I. S.

1950. The ecliptic orbits of meteor bodies in the

solar system. Izv. Turkmen Sec. Acad.

Sci. U.S.S.R., no. 4, pp. 95-96.

MCINTOSH, R. A.

1935. An index to southern meteor showers.

Monthly Notices Roy. Astron. Soc, vol.

95, pp. 709-718.

POKROVSKY, K. D .

1922. Meteor showers of the southern hemisphere.

In Trans. 1st Meeting of the Russian

Society of Amateur Astronomers (Mirove'de'nie'), pp. 172-173. Petrograd.

TEBENTJEVA, A. K.

1961. Results of the 5-Aquarid and Perseid

meteor showers observations in 1959.

Bull. Comiss. Comets and Meteors,

Acad. Sci. U.S.S.R., no. 5, pp. 29-35.

WEIGHT, F. W.; JACCHIA, L. G.; AND WHIPPLE, F. L.

1956. Photographic a-Capricornid meteors.

Astron. Journ., vol. 61, pp. 61-69.

1957. Photographic i-Aquarid meteors and evidence for the northern S Aquarids.

Astron. Journ., vol. 62, pp. 225-233.

Masses of Comet Giacobini-Zinner and the

Draconid Meteor Stream

By Y. V. Yevdokimov1

Comet Giacobini-Zinner is of great interest

because of the many valuable observations

made of the related Draconid meteor showers.

A precise study of the comet's motions leads

to some striking conclusions about the manner

in which meteor particles are ejected from the

comet's nucleus.

An earlier paper (Yevdokimov, 1955) on the

relation between the comet and the Draconid

meteor stream gave the exact value of the

longitude of the ascending node of the meteor

stream in 1946 at its maximum as

J2max=196°14'3ir6±3!2 (1946.0).

This paper also established the displacement of

the plane of the central part of the stream's

orbit. The longitude of the ascending node of

the stream was greater than that of the comet.

In 1898 the comet approached Jupiter and

markedly changed its orbit. Table 1 shows

the changes in the perihelion distances since

1897.

In view of these data we may conclude that

the earth could encounter only the meteoritic

bodies of the stream ejected since 1900. Hence,

the tangential component of velocity could not

be less than 14.5 meters/second.

The minor distance along the orbit between

the comet and the meteors that encountered

the earth in 1946 (15.4 days) indicates that

the tangential component of velocity must not

be greater than 13.7 meters/second.

If we suppose that the meteors were ejected

earlier (in 1913, 1926, or 1933), the ejection

velocities would be lower than those of the

meteors observed in 1933. Thus we conclude

that the main mass of meteors observed in

1946 at maximum was ejected by the comet

i Kazan University, U.S.S.B.

in 1940, with a tangential component of velocity

not greater than 13.7 meters/second.

We have recently worked at combining observations of the comet in 1933, 1939, and 1946.

The perturbations from five planets, in the

period from 1933 to 1946, have been computed,

and we have obtained two systems of elements:

(1) For observations in 1933 and 1939,

osculation 1939, Oct. 14.0:

M0=341o06'57!45±0r22

a=3.5138522±16

e=0.7166606±7

co=171°47/27?62±0!93

z=30o44'28T67±0?62

G=196°14'59T75±ir64

(1950.0)

(2) For observations in 1939 and 1946,

osculation 1939, Oct. 14.0:

M0=341o06'55!46±3?71

a=3.5139365±63

e=0.7166601±9

w=171o47'3l!49±0!93

(1950.0)

G=196o14'56T71±l!73

A comparison of these elements shows the

changes from one revolution (1933-1939) to

another (1939-1946), as follows:

AM0=-l/r99

Aa =+0.0000843

Ae =-0.0000005

Aco =+3?8 7

M =—0715

A£2 =—3*04

297
298 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Changes in perihelion distance

Year

1897

1900

1913

1926

1933

1940

1946

1959

Penhelion

distance (a.u.)

1.20

. 9 3

. 9 8

.99

1.00

1.00

1.00

.94

In contrast to the change in the longitude of

the ascending node of the meteor stream

(+16? 8), that of the comet diminished

(— 3? 04) and became equal to

196°14'll!82±l!73 (1946.0).

It is well known that a change in the longitude of the ascending node depends only on the

force perpendicular to the plane of an orbit.

Hence we may conclude that the changes in the

longitude of the ascending node of both comet

and meteor stream resulted from the same force

at the time of ejection in 1940, and that some

component of that force was perpendicular to

the plane of the orbit. This may be expressed

as follows:

AflCom.=r sin (»+«) cosec i „- *

Ai2met.=7" sin (»+«) cosec i „ *

Afin

3.04

:

16.8

Hence we conclude that during the period of

one revolution, from 1939 to 1946, Comet

Giacobini-Zinner ejected 17.5 percent of its

mass.

This result is consistent with that obtained

by Dubyago (1948), who concluded that the

velocity of the ejected meteor particles multiplied by the ratio of their mass to the mass of

/" e t the comet (vt' in cm/sec) has the following values: for Comet Encke, 19; for Comet

Biela, 14; for Comet Brooks, 17.

If we assume the velocity of ejected particles

to be 10 meters/second, we obtain for Comet

Encke 2 percent, and for Comets Biela and

Brooks 1.5 percent of mass lost. Thus, our

conclusions that a considerable loss of mass

occurs during each cometary revolution are

proved in various ways.

References

DUBYAGO, A. D.

1948. On secular acceleration in the motion

of periodic comets. Astron. Journ.,

U.S.S.R., vol. 25, pp. 361-368.

YEVDOKIMOV, Y. V.

1955. Concerning the association of the Giacobini-Zinner comet with the Draconid

stream. Astron. Circular, Acad. Sci.,

U.S.S.R., no. 159, pp. 21-24.
Dynamical Evolution of the Perseids and Orionids

By Richard B. Southworth

 x

This report sketches the methods and the

conclusions to date in a study of the effects

of planetary perturbations on meteor streams.

The research is continuing, and the material

will be published in greater detail in another

volume of these Contributions.

Method

Chiefly to be considered here are the differences among the orbits of different meteors in

a stream, or equivalently the distribution of

meteors in a stream. Since these differences

can be directly observed in photographs, the

principal task here is to predict them. Neither

the observation nor the prediction would have

been possible a few years ago; now, however,

the Harvard Meteor Program has made

sufficiently accurate observations, and the

IBM 704 and 7090 computing machines at

the Smithsonian Observatory have been able

to perform the computing.

The only streams treated thus far in the

study are the Perseids and Orionids. Sufficiently accurate observations have been published for 30 Perseids and 19 Orionids (Wright

and Whipple, 1953; Whipple, 1954; Jacchia

and Whipple, 1961; Hawkins and Southworth,

1961). Every meteor within about 10 km/sec

in speed, 10 degrees in radiant, and 10 days in

date from the shower mean has been included.

The observational errors are all probably less

than 0.2 km/sec or 0°.2.

For each stream a reference orbit was computed for a hypothetical meteor coming from

the observed mean radiant at the observed

mean speed on the observed mean date. The

analysis deals primarily with differences from

this reference orbit, but neglects squares and

i Harvard College Observatory, and Smithsonian Astropby steal

Observatory, Cambridge, Mass.

products of the differences; in that sense, it

is a first-order computation.

The secular perturbations of an orbit by a

planet are the average of the total perturbations by that planet, where the average is

taken over all positions of the planet in its

own orbit. The effect of secular perturbations

on a meteor stream is a gradual shift of the

whole stream; differential secular perturbations between different parts of the stream may

gradually further distort the stream. The

secular perturbations of the Perseids and

Orionids were computed by Smart's (1953,

pp. 218-231) formulation of Gauss's method.

The results, especially the differential secular

perturbations, were found to be negligible

compared to the other perturbations to be

discussed next.

The average perturbation of a planet over

a few revolutions does not differ much from

the secular perturbation. This is not true,

however, for meteor streams. In particular,

when as in the case of the Perseids and Orionids

the stream passes close to the orbit of Jupiter

or Saturn and has a long period, the meteors

undergo large perturbations at irregular intervals. The effects of these perturbations on

the stream are treated here by a numerical

method, partly due to Hamid (1950). This

method, which involves a good deal of computing, is described as follows.

First, tables are prepared of the perturbation

of a single meteor during one complete revolution from aphelion to aphelion. The values

are found by numerical integration along the

orbit. A table is prepared for every perturbing

planet that may be considered, and a set of

initial positions of the planet is chosen, uniformly spaced around its orbit. The different

values in each table are the perturbations

that would occur if the planet were at these

299
300

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

different initial positions when the meteor

was at aphelion. The chief approximation

in this entire study is that these perturbations

are computed only for meteors moving in the

reference orbit. From another point of view,

this is the limitation of the first-order formulation. This approximation should be adequate

for the Perseids and Orionids, but will be

discontinued in future studies of other streams.

The second part of the perturbation computation is a Monte Carlo computation. This

consists in tracing out the individual perturbations of a set of meteors chosen at random

from an initial Gaussian distribution. Each

chosen meteor is treated one revolution at a

time. The initial elements and the initial

positions of the perturbing planets are given.

The meteor's perturbations in its first revolution are found by interpolation in the tables

previously computed from the initial planet

positions. Thus the elements at the end of

the first revolution are found, and then, from

the new value of the period, the positions of

the planets at the end of the revolution. It is

then possible to compute the perturbations in

the second revolution, and so on. This process

is performed about a hundred times on about

a hundred meteors.

One can theoretically predict the general

behavior of the perturbed meteors, but it will

be sufficient here to examine the computed

results, which agree with the theory. The first

feature is the well-known rapid speed of the

meteors along the orbit of the stream. Of

course, the time required to spread out depends

on initial circumstances, but, for example, a

set of Perseids leaving their comet in the

vicinity of the earth with root-mean-square

relative velocities of 30 meteors per second

were spread all along the orbit four revolutions

later. Consequently, it has not been necessary

to take account of the distribution in the

stream along its orbit.

Once the meteors are well separated, they

undergo independent perturbations which are

(effectively) a random walk in the elements.

It is not a true random walk because, if only

one perturbing planet is considered, the perturbations have a complicated periodic character. Saturn's perturbations upset the periodicity of Jupiter's, however, at least for the

Perseids and Orionids. It is convenient to

express the average difference between meteors

in the stream by the variances and covariances

of the elements. The computed variances

increase approximately linearly with the time,

as they would in the case of a true random

walk.

The last part of the perturbation computation is the calculation of the effects of the

perturbations on the observable part of the

stream. The observable meteors—those whose

orbits intersect the earth's orbit—form only a

four-dimensional cross section of the fivedimensional distribution of meteors in the

stream. It is convenient to define a set of

descriptive parameters called "local quantities"; these comprise the (unobservable) minimum distance between a meteor's orbit and

the earth's orbit, and four observable quantities: the right ascension and declination of the

true radiant, the geocentric speed, and the

date of observation. To the first order, there

is a linear matrix transformation between

orbital elements and local quantities, and the

two modes of description are equivalent. This

transformation is applied, in fact, to the tables

of perturbations per revolution, and the Monte

Carlo computations are actually performed in

terms of local quantities. Thus the time rates

of increase of the variances of the local quantities are computed directly, and the rates of

increase of the variances in the observable

sample can be found by subtracting the parts

of the overall variances that depend on correlation with the distance from the earth's orbit.

For the Perseids and Orionids, it is found that

the observable quantities are highly correlated

with the distance from the earth's orbit; thus

the variance in the observable sample is much

smaller than in the stream. From another

point of view, this means that perturbations

tend to disperse meteors of both streams

mostly within the orbit planes.

Perseids

The Perseid reference orbit is very similar to

the orbit of the parent Comet 1862 III, except
METEOR SYMPOSIUM—SOUTH WORTH

TABLE 1.—Differences within the Perseid stream

301

Observed standard deviation

as

Observed variances S B

Va

Date

Computed increase in as

variances per revolu- SR

tion (per 100 years) Va

Date

Deduced age (years)

4?7

21.9

. 0 8

27,000

1!7

1.2

2.8

.08

. 11

2,600

Va

1.0 km/sec

0.5

-1. 3

1.0

-.0 4

-.0 4

.02

5,300

Date

3.4 days

15.0

1.1

0.5

11.6

.08

.09

-.0 4

.09

13, 200

for a shorter period. The reference orbit passes

1.3 a.u. from Jupiter's orbit, and only 0.3 a.u.

from Saturn's.

OBBITAL ELEMENTS (1950.0)

a

e

q

P

i

w

D,

Reference

21.56

.956

.946

100. 1

113?2

149?8

137?9

1862 III

24.28

.960

.963

119.6

113!6

152?8

138?7

The first line of table 1 shows the standard

deviation of Perseids from the mean. aR and

8R are the right ascension and declination of

the radiant, and Va is the geocentric speed.

The radiant deviations are from a fixed mean;

standard deviations from a moving mean

radiant are 1?6 in both coordinates. The

next four lines show observed values of the

four variances and six covariances in the same

units as the standard deviations.

The computed increase of the variances per

revolution (i.e., per century) is shown in lines

6 through 9 of table 1. On the simplest model

for the stream history—all the meteors leaving

the comet at one time—the age of the stream

would be found by dividing the present variances by their rates of increase. line 10 shows

these ages; they are quite discordant. If one

considers models in which the meteors leave

the comet at different times, the average age

of the meteors would be somewhat less than

these ages, but the results agree no better.

It follows from table 1 that planetary perturbations alone cannot explain the present

Perseid distribution. Since other processes

can scatter the meteors, but can hardly bring

them back together, the ages in line 10 are

upper limits. If we take the smallest of those,

and allow an additional 400 years for the initial

spread along the orbit, the conclusion is that

the average age of the Perseids does not exceed

3,000 years, and that the overall age is not

likely to exceed 6,000 years.

To explain the remaining variances, there

must be another force that must be nongravitational and must have large components perpendicular to the orbit plane. It is impossible

to determine the nature of this force definitely

because only a sample of the stream is observed;

nonetheless it is possible to guess. Guigay

(1947, 1948) pointed out that the observed

Perseid orbits tend to diverge from a point on

the comet orbit before perihelion. Accordingly,

the hypothesis was made that an explosion

took place there in the past, and several Monte

Carlo computations were performed to study

the subsequent perturbations. By adjusting

the date and place of the explosion, and the

relative speed, the best fit to the observed

variances was found to be with an explosion

1.5 a.u. from the sun, 1.3 a.u. north of the

ecliptic plane, roughly a thousand years ago.

638S05—63 -24
302

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Table 2 shows the computed variances, which

are a passable fit. The root-mean-square

relative velocity found is 2.6 km/sec, which is

very high, but is actually observed in dust

outbursts from comets (Whitney, 1955). These

outbursts are not well understood, but it is

clear that a large quantity of material is ejected

at high velocity; hence some connection with

meteors seems likely.

Orionids

There has long been a doubtful association

between the Orionids and Comet Halley.

Although the reference orbit is quite similar

in size and shape to the comet orbit, the

mutual inclination is eight degrees. All the

observed Orionid orbits lie in nearly the same

plane and are scattered in that plane. The

comet orbit is well outside the apparent

distribution of meteor orbits.

ORBITAL ELEMENTS (1950.0)

a

e

q

P

i

H

Reference

17.80

.968

.569

75. 1

164T7

82?6

29?1

Halley

17.95

.967

.587

76.0

162?2

111?7

56?7

TABLE 2.—Computed Perseid variances on the explosion

hypothesis

<*B

SB

Va

Date

23. 1

SR

4.

2.

1

0

V

2.

- 0 .

1.

o

5

1

1

Date

11.6

2.4

0.4

10.5

Table 3 shows the observed and computed

differences within the Orionid stream. As in

the case of the Perseids, line 10 contains upper

limits to the average time since the meteors

were spread along the orbit. The observed

dispersions in the declination of the radiant

and in the speed are both so small that they

are certainly affected by observational errors,

and should in fact be even smaller. Furthermore, it is not difficult to produce small dispersions—for example, by collision with dust

particles (see Whipple, this symposium, p. 239).

Thus one can accept the results from the right

ascensions and dates without being troubled

by the declinations and speeds. The conclusion

is that the Orionids have been spread along

the orbit for only 400 or 500 years, and are

perhaps 700 years old in all.

Conclusions

The perturbations of individual meteors in a

stream can be much more important than the

secular perturbations of the stream as a whole.

The dust outbursts from comets deserve more

attention as a possible source of meteor streams.

TABLE 3.—Differences within the Orionid stream

Observed standard deviation

a«

Observed variances 8&

Vo

Date

«B

Computed increase in 8S

variances per revolu- Va

tion (per 75 years) Date

Deduced age (years)

«B

l?03

1.06

.170

470

0?48

-.0 3

.23

.006

.0004

44, 000

Vo

. 87 km/sec

.57

.02

.75

-.01 9

-.00 1

.002

26, 000

Date

1.23 days

.72

.25

.51

1.52

.228

.008

-.02 5

.304

380
METEOR SYMPOSIUM—SOUTHWORTH 303

References

GUIGAT, M. G.

1947. Recherches sur la constitution du courant

d'etoiles filantes des Perseides. Journ.

Observateurs, vol. 30, pp. 33-48, 69-87.

1948. Recherches sur la constitution du courant

d'etoiles filantes des Perseides (suite).

Journ. Observateurs, vol. 31, pp. 1-32,

49-64, 77-94.

HAMID, S. E.

1950. The formation and evolution of the Perseid

meteor stream. Doctoral thesis, Harvard University.

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

1961. Orbital elements of meteors. Smithsonian

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

85-95.

JACCHIA, L. G., AND WHIPPLE, F. L.

1961. Precision orbits of 413 photographic meteors. Smithsonian Contr. Astrophys.,

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

SMART, W. M.

1953. Celestial mechanics. Longmans, Green

and Co., New York.

WHIPPLE, F. L.

1954. Photographic meteor orbits and their

distribution in space. Astron. Journ.,

vol. 59, pp. 201-217.

WHITNEY, C. A.

1955. Comet outbursts. Astrophys. Journ., vol.

122, 190-195.

WRIGHT, F. W., AND WHIPPLE, F. L.

1953. The photographic Perseid meteors. Harvard Coll. Obs. Reprints, ser. 2, no. 47.

A Note on the Cometary Nature of the

Tungus Meteorites

By V. Fessenkov1

The Tungus meteorite appeared in the early

morning of June 30, 1908, at 0b17m UT near

Vanovara, Central Siberia (X=6h47m2

8

, <p=

60°9). Its trajectory was oriented nearly

along the meridian from south to north, inclined toward the horizon at 10° to 15°. The

meteorite moved toward the earth with an

apparent relative velocity of about 40 to 50

km/sec. According to all evidence, this body

possessed a retrograde motion in the solar system and consequently could not be any fragment of an asteroid; i.e., an ordinary meteorite.

It is known that all meteorites so far studied

in our laboratories are the ancient constituent

parts of asteroids separated apparently by their

mutual collisions with a small kinetic energy,

leaving their internal structure unaltered. In

the solar system only comets may possess retrograde motion. For this reason the Tungus

meteorite must be considered as a small comet

encountering the earth. Several other data

strongly support this conclusion.

This meteorite produced an exceptionally

strong aerial explosion wave that spread over

the world and was registered at many stations.

Especially significant was the barogram obtained at Potsdam, Germany; it contained the

direct as well as the inverse wave propagation

and, consequently, the corresponding height

above sea level, which was found to be only

5 to 6 km.

The meteoritic matter dispersed by the explosion was spread as far as California during

the following two weeks and produced a marked

increase in the atmospheric extinction not

strongly dependent on wavelength.

If we suppose that the absorbing matter was

uniformly distributed over the whole of the

> Director, Astrophysical Institute, Alma Ata, U.9.S.R.

Northern Hemisphere, its total amount could

be roughly estimated to be 106 tons. Nevertheless, no meteoritic fragments were discovered

either at the place where the explosion occurred

or in the neighborhood, although very careful

search was made by numerous parties during

1958, 1959, and 1960. Boring in the marshes

and in the lakes situated in the central area of

the fall likewise produced no results.

There were no traces of direct blow or explosion at the surface, no craters or even

cavities. The only remnants of the material

substance of the meteorite were the microscopic spherules, about 0.01 to 0.1 mm in

diameter, which were very irregularly distributed over the central area where the forest

was greatly damaged. These spherules could

perhaps have originated by the condensation

of melting products of the explosion of the

meteorite. On the other hand, the explosion

energy was enormous, as was evident from the

crushing of the trees in an area of several

hundred square kilometers. At a certain distance, the fallen trees clearly assumed a radial

character. The corresponding energy manifested by this effect in the central area was

evaluated to be 1023 ergs. This is only about

1 percent of the initial kinetic energy of the

Tungus meteorite if its mass is taken to be 106

tons and the relative velocity as 50 km.

The first night following the fall of the

meteorite appeared unusually bright in the

areas westward from the spot of the fall.

This unusual illumination was due not to the

intensifying of emission lines in the spectrum

of the night sky but uniquely to the continuous

part of the spectrum and, therefore, was

produced by the scattering of the solar light

by dust particles.

305
306 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

The numerous reports obtained by the

Committee of Meteorites of the U.S.S.R.

from all over the world established the region

at the earth's surface where bright nights

occurred. The western boundary was apparently limited by Ireland. At least there is no

knowledge of a similar anomaly in the Atlantic,

and it is certain that nothing unusual occurred

in the United States. The southern boundary

was placed at $>=45° to 46° in Western Europe

and apparently descended to 42° in Central

Asia. In Tashkent the nocturnal sky was of

such a brightness that photographic exposures

with a normal astrograph were not possible at

all. The next night the brightness of the night

sky became much fainter and then completely

disappeared.

All these striking phenomena can be easily

understood if we imagine that simultaneously

with the meteorite a dust cometary tail penetrated into the atmosphere and was detained

in its upper strata. It is evident that the dust

particles composing the tail must have invaded

the atmosphere in the Northern Hemisphere and

were restricted only to an area determined by

longitude 180° relative to the sun. The western borders of Ireland are just within this area.

On the other hand, the southern boundary of

the nocturnal illumination was determined

evidently by the height of the atmospheric

layers still illuminated by the direct solar rays

at midnight near solstice. For Europe this

corresponds to nearly 350 km, but for Central

Asia to 700 km. In order to be detained at

these altitudes, dust particles must be exceedingly small. In fact, their dimensions must be

of the order of some tenths of a micron. The

abundance of such matter in the atmosphere

corresponds to an optical thickness of the order

of 10~8. Evidently this insignificant amount

cannot be found in some optical anomaly in

daylight conditions. It is in striking contrast

to the matter provided from the explosion of

the head of the meteorite; it had gradually

dispersed over the whole of the atmosphere

and resulted, as mentioned above, in an increase in atmospheric extinction but not in

any discernible change in nocturnal brightness.

It is highly probable that all these data show

that the Tungus meteorite was in fact a small

comet with a dust tail oriented in the direction opposite to the sun. The central area of

the meteorite explosion was characterized by

the fall of trees generally oriented radially.

The direction of the fallen trunks marked the

initial propagation of the explosion waves.

This orientation can still be seen at the spot

where the explosion occurred and also on the

photographs made by an aerial survey of this

area in 1939 (scale 1:5000), which clearly show

the separate trunks of the fallen trees. The

whole picture is nevertheless a very complex

one. In the very center of the area of devastation there are many trees standing with torn

branches and looking like telegraph poles.

The orientation of the fallen trees cannot be

accounted for by one single center of explosion.

Clearly, aerial waves issued from the flying

body with at least three major outbursts lying

apparently not exactly on the same straight

trajectory. It is possible to localize approximately the places of projection on the ground of

these outbursts occurring at a height of several

kilometers.

The first outburst corresponds to the so-called

South Marsh and was found to be at a distance

of 1.4 km in a southerly direction from the

Kulik camp; the second outburst, apparently

much stronger, occurred at a distance of about

0.8 km in a northeasterly direction from this

camp; and the third one at a distance of 2.2 km

to the north-northwest. The consecutive and

nearly simultaneous explosion waves interfered

with each other and produced a complex picture that cannot easily be interpreted with any

exactitude. Only at a certain distance from

the central area does the direction of the fallen

trees become more homogenous and nearly uniformly radial. The mountains, some hundred

meters in height, and other elevations in the

close neighborhood of the area appear to have

had no influence on wave propagation.

Finally, one may ask how it is possible that a

comet, representing even in its nucleus a dispersed state of matter similar to a very dense

cluster of particles, can penetrate into the lower

layers of the atmosphere.

A single body of a mass of 10" tons must fall

on the ground with a considerable remnant

of its initial mass and cosmic velocity. As a

result, a crater or even a field of craters can be
METEOR SYMPOSIUM—FESSENKOV 307

expected, and actually has occurred in many These are the preliminary results of the

similar cases. Nevertheless, the dimensions examination of different data concerning this

of the nucleus of the Tungus comet could not exceptional phenomenon. A further study

have been very large, perhaps only about 0.5 being undertaken by the Academy of Sciences

km in diameter with a mean density of several of the U.S.S.R. (Committee of Meteorites)

hundredths gm/cm3. The mutual separation in and other institutions will help to elucidate

the nucleus between the particles appears to be many questions about the Tungus fall and its

several times greater than their linear dimen- cometary nature, and may well have some bearsions. ing on other comets.

A Short Note on the Origin and Age of the Quadrantids

By S. E. Hamid * and Mary N. Youssefl

The Quadrantid shower is distinguished

among the periodic meteor streams by its very

short duration (<O° in longitude of node),

very high inclination (~70°), short period (~5

years), and high eccentricity (~0.70).

The stream, meeting the earth at descending

node, approaches the orbit of Jupiter (its radius

vector at ascending node is ~4.8 a.u.). The

stream's orbit, except for its high inclination,

is similar to that of Jupiter's short period cometary group.

The present study is based on six doubly

photographed meteors whose orbital elements

are given in table 1.

By integrating numerically the secular perturbation of Jupiter on these orbital elements

and carrying the integration back 5000 years,

we find that:

(1) The inclination of the stream decreases

from its present high value to a minimum

value (~13°) around 1500 years ago, and then

increases again to a maximum value (~76°)

around 4000 years ago.

(2) The perihelion distance of the stream

decreases from its present value (~1 a.u.) to

i National Planning Institute, Cairo, Egypt.

a minimum value «0. 1 a.u.) around 1500

years ago (time of minimum inclination), and

then increases again to maximum (~1.0 a.u.)

around 4000 years ago (time of maximum

inclination).

(3) As we go back in time, the stream recedes

from Jupiter's orbit, arrives at its maximum

distance about 1500 years ago, and then approaches Jupiter's orbit again to within 0.2 a.u.

about 4000 years ago.

(4) The longitude of the perihelion of the

stream undergoes periodic variation, with its

minimum value ~86° around 500 years and its

maximum value ~111° around 2800 years.

Figures 1 to 5 show typical changes of the

orbital elements of a Quadrantid meteor (No.

9983). Comparing the orbital elements of the

six meteors in the past, it is found that they

agree around 3000 years ago (see table 2).

We are suggesting that sometime around

4000 years ago (see fig. 1) a comet was captured

by Jupiter. After the capture the comet developed meteors along its path. Because an

appreciable number of these meteors, which

now form the Quadrantids, did not suffer another close approach to Jupiter, the shower is

observed to be compact.

TABLE 1.—Orbital elements of Quadrantid meteors

Trail no.

9945

9985

9953

9983

9974

9907

o (a.u.)

3.046

3.074

2.906

3.002

2.999

2.880

e

0.682

0. 683

0.664

0.675

0.674

0.659

i (degrees)

6& 6

70.8

72. 7

72.4

72.5

72. 1

to (degrees)

165.2

16a 3

170.3

169.6

170.4

177.2

Q> (degrees)

282.5

282.5

282.5

282.5

282.5

281.4

x (degrees)

87.7

90.8

92.8

92. 1

92.9

9a 6

Reference

(1)

(1)

(1)

(1)

(1)

(2)

(1) L. O. Jacchia, and F. L. Whipple, "Precision Orbits of 413 Photographic Meteors," Smithsonian Contribution to Astrophysics, vol. 4, no. 4,

pp. 97-129,1961.

(2) O. 8. Hawkins, and R. B. Southworth, "Orbital Elements of Meteors," Smithsonian Contribution to Astrophysics, vol. 4, no. 3, pp. 85-95,1961.

309
310 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Angular orbital elements (in degrees) of the Quadrantids in the past

Time

(years)

0

-400

-800

-1200

-1600

-2000

-2400

-2800

-3200

-3600

-4000

-4400

-4800

Trail no.

i

69

65

58

42

15

37

57

66

71

73

73

72

70

9945

CO

165

162

160

157

107

24

18

17

14

8

- 2

-11

-17

282

284

288

295

351

440

450

454

456

457

459

460

462

i

71

68

60

40

14

47

63

71

74

75

74

71

65

9985

CO

168

164

163

159

66

18

16

14

9

— 1

-10

-16

-17

a

282

284

287

295

394

449

455

457

458

459

461

463

465

i

73

71

67

58

36

22

53

67

73

75

76

76

75

9953

CM

170

165

162

161

153

42

19

17

15

11

3

-6

-13

282

284

286

289

302

420

449

454

456

458

459

460

461

i

72

70

64

50

17

41

62

71

74

76

76

75

71

9983

eo

170

164

163

161

128

21

16

15

12

4

-6

-13

-17

a

282

284

286

292

331

445

454

456

458

459

460

461

463

»

73

70

65

51

17

41

62

71

75

76

76

74

70

9974

(0

170

165

163

161

128

20

16

15

11

3

-7

-14

-17

a

282

284

286

291

331

445

454

457

458

459

460

462

463

i

72

71

68

62

46

14

46

64

71

74

75

75

73

9907

a

177

169

164

162

158

94

20

16

14

9

1

-8

-14

281

283

284

287

294

365

446

452

456

457

458

459

461

rA Radius

r_ Radius

— r.

\

\

\

\

\

\

I |

1 /

I /

1 /

1 /

1 /

* /

_ 1 /

>v 1 1

\ . 1

vector at ascending node

vector at decending node

rD -

/

 N

/

—

^ — — ^

• N,

• N

^' >^

1 1

(au.)

5.0

4.0 -

3.0 -

2.0 -

1.0

0 -1000 -2000 -3000 -4000 -5000

T (years)

FIGURE 1.—Quadrantid meteor no. 9983. Radius vectors

at the nodes plotted against time in the past.

-1000 -2000 -3000 -4000 -5000

T(years)

FIGURE 2.—Quadrantid meteor no. 9983. Orbital inclination t plotted against time in the past.
METEOR SYMPOSIUM—HAMID AND YOUSSEF 311

O -1000 -2000 -3000 -4000 -5000

T (years)

FIGURE 3.—Quadrantid meteor no. 9983. Longitude of

perihelion x plotted against time in the past.

-1000 -2000 -3000 -4000 -5000

T (years)

FIGURE 4.—Quadrantid meteor no. 9983. Perihelion distance q plotted against time in the past.

180

160 -

- 2 0

0 -1000 -2000 -3000 -4000 -5000

T (years)

FIGURE 5.—Argument of perihelion w plotted against time

in the past.

Abstracts of Other Papers

Southern Hemisphere Vela-Puppid Meteor

Activity: C. Ellyett and K. W. Roth

 1.—It has

gradually become established from radar surveys

at Christchurch, New Zealand, in 1953, 1956,

and 1960, that intense meteor shower activity

occurs annually in early December, with radiants in both the Velid and the Puppid constellations. The Velid group has a mean right

ascension of about 133°, and the Puppid group

is somewhat widely spread around 110°. The

declination of both showers is about —45°.

The Absence oj Detectable Infrared Radiation

from Meteor Trails: B. A. Tinsley, J. J. Tait,

and C. Ellyett1.—A lead sulphide cell immersed

in dry ice was used in conjunction with an

arsenic trisulphide lens to look from ground

level for transient infrared bursts radiated from

the trails produced by large incoming meteors

in the upper atmosphere. No bursts were

detected. A theoretical analysis was then

made of the probability of detection. The

mechanism of infrared radiation from meteor

trails is largely unknown, so assumptions must

be made in order to give a figure for radiated

power. It is then possible to calculate the infrared flux at the ground. The conclusion

reached was that, with the equipment available,

an average of 200 hours of clear night-time

observing would be required to detect a single

meteor.

The Latiivde Dependence oj Radar Meteor

Shower Observations:2 C. S. L. Keay and C.

Ellyett.1—A simplified method of assessing the

relative significance of meteor showers is discussed. Most of the tables of meteor showers

quoted in the literature give a false impression

of the actual influx of meteoric shower particles

into the earth's atmosphere, particularly when

rate measurements are quoted. The bias inherent in single-station rate measurements is

largely eliminated by the present method, and

i The authors are associated with the University of Canterbury, Christchurch, New Zealand.

> Published in Journ. Oeopbys. Res., vol. 66, pp. 2337-2343,1961.

the importance of short-range echoes is emphasized. Comparison of results obtained from

both hemispheres reveals a considerable measure of agreement between various surveys.

The Seasonal Variation oj the Twilight Sodium

Air glow in the Southern Hemisphere:3 B. A.

Tinsley4 and A. Vallance Jones.8—The plateau

brightness of the sodium twilight airglow has

been measured near Christchurch, New Zealand, by photographic spectroscopy between

July 1960 and September 1961. A seasonal

variation with a maximum in mid-winter and

a minimum in mid-summer was observed.

This is similar to the seasonal variation in the

northern hemisphere, indicating a six-month

phase difference between the two hemispheres.

The annual distribution of meteors at high

rates has just been determined at Christchurch,

New Zealand, for a complete year. The southern hemisphere meteor distribution is out of

phase with the northern hemisphere, and both

are out of phase with their own sodium distributions. Thus, unless the concept of long-term

storage of sodium in the upper atmosphere is

introduced, it is unlikely that upper atmospheric

sodium is of meteor origin, at least from meteors

of a size detectable by radar methods.

All-Sky Meteor Rates in the Southern Hemisphere:6

 C. Ellyett and C. S. L. Keay.1—An

extensive experiment has been carried out

at Christchurch, New Zealand (43°37'S,

172°24'E), to determine meteor rates over the

visible sky, using radar equipment with all

parameters maintained constant throughout a

complete year. The effect of varying background noise was eliminated.

From a total of 724,681 meteors, a seasonal

variation has been established, with a peak

rate in local summer. The meteor rate at

69.5 Mc/s was found to be unaffected by iono-

» Published hi Journ. Atmosph. Terr. Phys. vol. 24, pp. 345-351, 1962.

• University of Canterbury, Christchurch, New Zealand.

• University of Saskatchewan, Canada.

• Published in Journ. Geophys. Res., vol. 66, pp. 2590-2591,1961.

313
314 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

spheric behavior, such as increased absorption,

magnetic storms, or aurorae.

The Identification of Meteor Showers with

Application to Southern Hemisphere Results:7

C. Ellyett, C. S. L. Keay, K. W. Roth, and

K. G. T. Bennett.8—Further meteor shower

results observed by radar at Christchurch, New

Zealand, are now given, including results at

high rates, and all Christchurch data are

compared with visual observations, and radar

results from Adelaide, for the declination range

from +26°.5 to about —50°. Seven meteor

showers appear in all three surveys, and can

be regarded as certain, and another 6 to 9,

which are each reported twice, are probable.

' Published In Monthly Notices, Roy. Astron. Soc., vol. 123, pp. 37-

60, 1961.

1

 The authors are associated with the University of Canterbury,

Christchurch, New Zealand.

An additional 9 to 10 radiants, however, are

found by each survey alone.

The errors inherent in the identification of

meteor showers from radar data are considered.

Different techniques have been used at Christchurch and at Adelaide. It is concluded that

no single method of analysis is fundamentally

better than any other.

The technique of shower identification

depends partly on the nature of the background rate, which may bo due either to

sporadic meteors, or to the resultant of many

minor radiants. The resolution of this uncertainty is necessary before the occurrence of

less active showers can be confirmed.

The rate-count method has been extended to

multiple range bands, resulting in a useful

additional means of sorting out the significance

of peaks in the rate curves.