Smithsonian

Contributions to Astrophysics

VOLUME 4, NUMBER 2

ORBITAL ELEMENTS

OF PHOTOGRAPHIC METEORS

by RICHARD E. MCCROSKY and ANNETTE POSEN

SMITHSONIAN INSTITUTION

Washington, D.C.

1961
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.

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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

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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.

FRED 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 40 cents
Orbital Elements

of Photographic Meteors

By RICHARD E. MCCROSKY1 and ANNETTE POSEN2

This paper presents an analysis of the trails

and the distributions of the orbital and physical

parameters for 2,529 meteors photographed

simultaneously from two camera stations in

New Mexico. The two Baker Super-Schmidt

cameras of the Harvard Meteor Project were

located at the Soledad Canyon and Dona Ana

stations, separated by a distance of 28.6

kilometers. The sample reported here comprises 70.4 percent of all meteors photographed

during 1,125 hours of exposure by two cameras,

operating simultaneously, during the period

February 1952 to July 1954.

The data

Of the meteors included in this analysis, 2,059

were analyzed by the method of graphical

reduction (McCrosky, 1957). A partial graphical reduction has positively identified as shower

members an additional 115 meteors comprising

108 Geminids, 5 Perseids, and 2 Taurids. We

have also included 355 meteors reduced by

Jacchia (Whipple and Jacchia, in press) that

would have been accepted for a graphical

reduction had they not already been treated by

the more accurate technique.

The orbital elements for all the fully reduced

meteors were computed by the method described

by Whipple and Jacchia (1957). We have

assigned the mean orbital elements of the

appropriate shower to the 115 meteors identified

by partial graphical reduction.

The graphical reduction method was used to

obtain geocentric velocities and radiants. All

meteors were accepted for graphical reduction

except those excluded by limitations inherent in

the method.

1

 Harvard College Observatory and Smithsonian Astrophysical

Observatory.

1

 Harvard College Observatory.

Determination of the radiant by this method

requires the superposition of the two films, and

one image must be dense enough to be visible

through the other film. Some very faint

meteor trails (10.4 percent of the total) did not

meet this requirement, and hence were not used.

The method also requires the selection of a

common point on the two meteor trails—the

same point in space as seen from the two

stations. Finding a common point precisely

enough on the two films is not always possible,

particularly if the meteor begins or ends outside

the field recorded by the camera, or if a part of

the trajectory lies on the outer 12 percent of the

field that is not occulted by the rotating shutter.

This difficulty in finding a common point led

us to reject 13.8 percent of the meteor trails.

We also excluded 0.6 percent of the meteors

because of an ambiguity of 180° in the position

of the radiant. Other meteors (4.8 percent)

could not be reduced by this method because

the photographic records had been affected by

instrumental faults, clouds, and other random

factors.

Reliability of the method

The speed of the graphical method results, in

part, from the use of a common point—which

involves human judgement in its selection—

instead of detailed measurements alone. The

consequent possibility that systematic errors or

selection effects were introduced by the human

computer, affecting the reliability of the

method, warrants investigation.

Effects of selection.—A random selection of 360

meteors reduced by the short trail method

(Hawkins and Southworth, 1958) includes 254

meteors that were reduced independently by the

graphical technique. The short trail reductions

15
16 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

are more accurate than the graphical by an

order of magnitude. Comparisons of the

results of these two sets of reductions have been

made to determine the errors and selection

effects in the graphical reduction.

The velocity distributions of the meteors

chosen for short trail and graphical reductions,

shown in figure 1, indicate that the choice of

meteors was essentially random with respect to

velocity. The larger errors inherent in the

graphical method result in a greater diffusion

into the hyperbolic velocity range, but the

percentages of high velocity meteors (V greater

than 60 km/sec) are similar in the two sets of

data. The elimination of the very faint meteors

from our data does not represent a new selection

factor but merely places a slightly lower limit

on the limiting magnitude than is already imposed by the observing technique. The distributions of maximum and minimum magnitudes are given in table 1. The influence of

selection in meteor brightness becomes effective

at magnitudes fainter than Mpt=\, for discovery of the meteor on the film is no longer a

certainty. The distributions given here therefore apply to meteors whose magnitudes have a

median value of Mpg=0.8.

TABLE 1.—Distribution of maximum and

magnitudes of 2,529 meteors

minimum

2529 meteors

Short trail meteors

VELOCITY V . KM/SEC.

Photographic magnitude

(MPf)

<-3. 0

-2.5 to -3.0

-2.0 to -2.5

-1.5 to -2.0

-1.0 to -1.5

-0.5 to -1.0

0.0 to -0.5

0.0 to +0.5

+ 0.5 to +1.0

+ 1.0 to +1.5

+ 1.5 to +2.0

+ 2.0 to +2.5

+ 2.5 to +3 0

+ 3.0 to +3.5

+ 3.5 to +4.0

+ 4.0 to +4.5

> + 4.5

Percentage of meteors with

Maximum

magnitude

within range

in Mv,

0.3

0.6

0.9

1.8

3.0

7.0

7.2

19.3

22.4

18.8

11.9

5.2

1. 1

0.5

Minimum

magnitude

within range

in Mv,

1.5

8.7

18. 1

32.3

34.4

4.9

0. 1

The rms errors in geocentric velocity and

apparent radiant, as derived from comparisons

of the short trail and graphical reductions, are

3 percent and 3°, respectively. These and the

mean and median deviations determined for

inclination (i), eccentricity (e), perihelion distance (g), and longitude of perihelion (TT) are

given in table 2. There is no systematic error

in the geocentric velocity or the orbital

elements.

The apparent degree of error in the elements

is misleading, since most of the error was

TABLE 2.—Errors in elements of graphically reduced

meteors

FIGURE 1.—Velocity distribution for meteors reduced by the

graphical and short-trail methods.

Element

i

e

Q

T

vm

Radiant

1/a

Absolute deviations

Mean Median

2?0 l?0

. 078 . 032

. 029 a.u. . 011 a.u.

6?0 2?0

rms

deviations

3%

3°

.14* a.u.

•See p. 17.
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 17

contributed by only 5 percent of the meteors,

whose measurements show deviations of more

than five times the mean. The median of the

deviations is less than half their mean. Most

of the extremely large errors are attributable to

poorly determined radiants. It was not

possible to discover any criteria for rejecting

these cases.

The error in I/a—the reciprocal of the semimajor axis—is a function of geocentric velocity

and elongation X, the angle between the

heliocentric velocities of the earth and the

meteor. For an error of 3 percent in geocentric

velocity, the computed rms error in I/a varies

from 0.10 to 0.18 (a.u.)"1. However, for most

of the meteors in our sample, the computed error

in I/a due to the velocity error lies between

0.13 and 0.15 (a.u.)"1. Errors in the radiant

generally contribute smaller errors to I/a except

in the extreme cases mentioned above.

The error in q', the aphelion distance, will be

similar to that in a.

Cosmic weights.—The orbital data can be

weighted to remove some of the effects of

physical and observational selection which

prejudice our view of matter in space. These

effects include (1) the dependence of mass on

velocity for meteors of a given luminosity; (2)

the law governing the increase in meteor

numbers with increasing magnitude; (3) the

velocity dependence of the photographic technique; and (4) the probability that meteors of

a given orbit will collide with the earth. When

the data are weighted for the first three factors,

the resultant distributions refer to meteors of

uniform mass. For these effects we have

adopted Whipple's (1954) weighting factor of

1/VZ, where Vm is the velocity of the meteor

outside the earth's atmosphere. The uncertainties in the velocity-mass law and in the

number-luminosity law are such that attempted

corrections for these effects will probably be in

error by at least 1 in the velocity exponent.

In Whipple's earlier work a weight of 1/3 Vi

was applied for meteors with F<19 km/sec,

to compensate for the greater length of the

trails, and for a possible decrease in the

luminous efficiency in low velocity meteors.

The low velocity meteors in our data are not

characterized by exceptional length and, consequently, the 1/Vi factor has been used for

meteors of all velocities.

Opik (1951) has investigated selection effect

"(4)", above. On the basis of his analysis we

will write the probability of collision as follows:

2—-—? (1)

where i is the inclination, a the semi-major axis,

p the parameter of the orbit, and Vo the

geocentric velocity of the meteor. When the

data are weighted by the factor 1/P the resultant

distributions of orbital elements are proportional to the number of meteoroids with such

orbits that pass perihelion per unit time. The

product of these two weighting factors, 1/PVl,

has been called the "cosmic weight" and is used

here to weight the observed numbers of meteors.

Distributions of orbital elements

Figure 2a,6 presents the distribution of the

reciprocal of the semi-major axis of the orbits

of our meteors. Figures 3 through 6 present

distributions—based on numbers of meteors

(solid lines) and on numbers weighted by the

cosmic weight (dotted lines)—for the orbital

elements i, e; for perihelion distance q, and for

aphelion distance q'. In each case the weighted

distribution has been normalized to the observed distribution. Various two-dimensional

distributions of these parameters appear in

figures 9 to 14. Shower meteors include

members of all major streams, as well as the

seven new showers revealed by these data

(McCrosky and Posen, 1959).

Inclination.—The distributions demonstrate

the existence of a large number of direct, small

meteor orbits of low inclination. The median

inclination of the observed distribution is 18°,

that of the weighted distribution 21°. The

steady decrease in weighted numbers of orbits

below i=5° is due, in part, to an obvious

inexactness in the weighting function at very

low inclinations. Opik showed, however, that

the weighting function is accurate within 10

percent for orbits with inclinations greater than

0.3°; hence the decrease must be attributed to

the fact that these orbits have been eliminated

by planetary collision and perturbations.
18

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

IB

16

14

S 12

2

I»PERCENT OF 1

6

4

2

n

< 1

-

-

_

_

r —

i

1

2529 meteors

— w.pple

I

I

i

1

I

I

i

I

i

X \

-T

-

1

°

i i •

jJ u

-

-

—i

1

 -i i

1 1 • 1 • 1 1 1 1 1 1 1 1 1 1 1 1 L = 1=1—=—1

1.6 1.8 2.0

RECIPROCAL SEMI-MAJOR AXIS i/a (a.u.r 1

-

_

-

-

-

0

1°, I

— — Sporadic of 2529 meteors

1 '

1

0

J •

O Oavies -

-

o

o

D

0

' 1 o °

1 °

• —I O

1—1—1—1—1—1—1 1—1 1 1 1 1 1 1 1 1 -1 »—I °

1.0 1.2 1.4

RECIPROCAL SEMI-MAJOR AXIS l/a la.u.r 1

FIGURE 2.—Distribution of meteor orbits in reciprocal semi-major axis: a, the 2,529 meteors compared

with Whipple's bright photographic meteors; b, the sporadic component of the 2,529 meteors compared with Davies' radar data weighted for observational selection.
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 19

FIGURE 3.—Distribution of meteor orbits in inclination, i°.

Figure 9, which gives the observed distribution of meteors in inclination and aphelion

distance, shows that the ecliptic concentration

is limited primarily to small orbits with q'<C.S

a.u.

The paucity of orbits at i^90° was also

noted in the data on brighter meteors (Whipple,

1954) and radar meteors (Davies, 1957).

Orbits of both large and small aphelion distance

exhibit this gap, although the latter group shows

it more markedly. Of our 2,529 meteors, the

number of short orbits (g'<10 a.u.) with

80°<i<100° is 12 as opposed to 41 with

70°<t<80°, 100°<i<110°. For long orbits

(g'>10 a.u.) the corresponding numbers are

39 and 61. An inspection of the weighted

numbers of meteors at various inclinations

shows that the decrease in numbers at i«90°

is primarily a result of observational selection.

In the radar meteors, which are observed at

magnitudes of about Mpt=6, and have an

average maximum brightness of somewhat

more, possibly Mpt=5, Davies observed a bimodal distribution of inclination for g'<3 a. u.

and e<0.3. The maxima occur at 60° and

140°; there are almost no meteors with »<30°.

The reverse situation occurs in our faint

photographic meteors; the smaller and less

eccentric the orbit, the more pronounced the

ecliptic concentration. Our data include 146

meteors whose aphelion and eccentricity lie

within the limits specified by Davies. Only 8

of these have inclinations greater than 30°.

The medians of the observed and weighted

distributions are respectively 11° and 14°, both

substantially lower than those found for the

sample as a whole.

Semi-major axis.—Figure 2a shows the distribution of the reciprocal semi-major axis I/a

for our sample, compared with that for the

brighter photographic meteors analyzed by

Whipple (1954). The median absolute photographic magnitude for the bright meteors is

—3.8. Shower meteors, representing over 50

percent of Whipple's data, are included in both

histograms.

The difference between the two sets of

photographic data suggests that orbital characteristics vary considerably with meteoroid

size, a conclusion supported by other evidence to

be presented. The bright meteors do not represent a completely random sample. A very

few meteor trails with closely spaced shutter

breaks were not suited for measurement, and

possibly a few slow meteors—those whose semimajor axes are statistically small—were excluded. Nevertheless, the two samples exhibit

about the same percentage of orbits with mean

distance greater than 5 a. u. The major difference lies in the distribution of short orbits;

except for the Geminids, Whipple's data contain almost no examples with a<1.3 a. u.

Davies (1957) has presented a distribution of

I/a for radar meteors, sporadic meteors weighted

for observational selection but not for the

probability of collision with the earth. Davies'

weighted distribution and our observed numbers of sporadic meteors are compared in figure

2b. The sensitivity of the photographic technique is inversely proportional to the velocity
20

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

of the meteor. However, the greater area of

sky observed at the greater heights where high

velocity meteors occur compensates to some

extent for the diminished photographic sensitivity. To place our data on a basis comparable

with the radar data, we must weight the

photographic data by a small power of the

velocity, say VH. Generally, this will give

greater weight to meteors with small values of

I/a and will accentuate the differences seen.

Figure 2a, 6 shows that the proportion of short

orbits increases gradually as one proceeds from

the bright photographic to the faint photographic to the still fainter radar meteors.

However, in the progression to radar meteors

the proportion of long orbits decreases abruptly

(table 3). Whipple (1955) has suggested that

rapid diffusion of the ion column of high altitude

(high velocity) meteors inhibits their observation by radar. Since the meteors with long

orbits enter the atmosphere at high velocity,

statistically this abrupt decrease with magnitude may result from limitations in the experimental technique rather than from radical

differences in the nature of the orbits.

The difference in orbital characteristics as a

function of magnitude is further indicated by

Whipple's (1954) empirical comet-asteroid criterion, K. He found that the parameter

is positive for 96 percent of known comet orbits,

and negative for all but 3 asteroid orbits. Of

the 144 meteors in Whipple's analysis, only 8,

TABLE 3.—Proportion of long orbits in photographic and

radar meteor data

Meteors

Bright photographic

Faint photographic

Radar

Photographic

magnitude

-3. 8

+0.8

- + 5

Percent of orbits with

l/o<0.2(a.u.)-»

Sporadic Sporadic

and meteors

shower only

meteors

33.3

27. 5 27. 4

13. 1

or 5.6 percent, had a negative K, a fact that suggested a cometary origin for most meteors.

The faint meteors also are of cometary origin,

as indicated by their fragility and the degree of

fragmentation observed, but on the basis of the

K criterion, 25.5 percent of their orbits are

indistinguishable from those of asteroids (see

fig. 15). The region of negative K embraces

the orbits of small aphelion distance, and thus

small semi-major axis. Any effect of selection

for velocity in the bright meteor data is certainly not large enough to account for the

appreciable difference in the proportion of

meteors with negative K between the bright and

faint photographic meteor samples.

Eccentricity.—The distribution of the eccentricity of meteor orbits is given in figure 4,

which shows a smooth rise to a maximum at

about 0.9. The 12.5 percent that filter into the

hyperbolic range are an indication of the errors

made in reduction. The number of sporadic

meteors increases approximately as e2. The

appreciable number of orbits with small values

of e is characteristic of these faint meteors.

Whereas only 8 percent of the sporadic orbits

discussed by Whipple had e less than 0.6, 25

percent of our orbits are within this range.

Figure 10a shows the observed distribution of

orbits as a function of the semi-major axis and

the eccentricity. The areas of the circles are

proportional to the numbers of meteors in a cell

representing a range of values of the semimajor axis and eccentricity. The distribution

is bounded by envelopes which are described

by the limits on q and q' for observability at

the earth. Figure 106 shows a similar distribution, for weighted numbers, for those orbits

within 15° of the ecliptic plane. Both direct

and indirect orbits are included. Figure 10c

shows the same distribution as in figure 106,

but for those orbits with inclination between

15° and 165°.

A large majority of small orbits has both low

inclination and low eccentricity. The tendency

of small orbits to exhibit low eccentricity is also

evident in figure 11, and is particularly striking

in view of the small area in the a-e plane

available at low eccentricity. The Geminids

are responsible for a large number of orbits at

a=1.25 and e = .775. Other showers are all

but indistinguishable in these distributions.
NO. 2

400|-

350

300

250

200

150

100

50

ORBITAL ELEMENTS OP PHOTOGRAPHIC METEORS

400

21

r

Observed number

Weighted number

n_

n

L - ,

Alt METEORS!

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 >1.0

ECCENTRICITY e

FIGURE 4.—Distribution of meteor orbits in eccentricity, e.

Perihelion.—Perihelion distance q is a particularly well-determined element and details

of the distribution (fig. 5) are worthy of scrutiny. The observed and the weighted distributions of perihelion distance are both approximately linear with q if the shower component

is neglected. This relationship holds for both

long and short orbits. There is a slight depar350

300

250

200

150

100

50

-Observed number

-Weighted number

n

f.

I ALL METEORS I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 >1.0

PERIHELION DISTANCE q a.u.

200 -

250 -

300

FIGURE 5.—-Distribution of meteor orbits in perihelion

distance, q (a.u.).

ture from linearity in the vicinity of Venus

(.72 a.u.), perhaps because there is a relatively

high probability of capture by Venus for meteors

with perihelion in the vicinity of the planet.

A comparison of the distribution of perihelion for meteors with that for comets is of

interest. Figure 7 shows the distribution of

556036 O - 61 -2
22 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

500

450

400

350

300

250

200

150

100

50

677

P

— — Observed number

Weighted number

[All METtOJSl

345678 9

APHELION DISTANCE q' a.u.

10 > 10

50 -

100 -

150 -

—1

J

ISHOWERS ONLYl

L-J

240

FIGURE 6.—Distribution of meteor orbits in aphelion distance,

q' (a.u.).

cometary perihelia for 369 comets with g<1.9

a.u. and discovered since 1800, as listed in the

Baldet and De Obaldia catalog (1952). These

are observed numbers and should be corrected

for observational selection. One expects comets

with small perihelion to appear brighter than

0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8

FIGURE 7.—Distribution of perihelia for 369 comets with

average; on the other hand, observations

may be hindered by their small elongation from

the sun. Comets of large perihelion may have

a wide range in brightness, depending on the

earth-comet distance. The observational selection factors are complicated and an empirical

approach is indicated.

R. J. Dunn has kindly supplied a previously

unpublished analysis of cometary brightness as

a function of q. Figure 8 is Dunn's compilation

of the absolute magnitudes of 83 comets derived by Bobrovnikoff (1941, 1942) and Vessviatsky (1925). When both catalogs give the

brightness, Bobrovnikoff's value is chosen. It

should be noted that this plot represents a

select list of well-observed comets, with apparent magnitudes less than the average. They

represent only a fifth of those shown in figure 7,

and are not necessarily representative of all observed comets. Had absolute brightness played

a role in observational selection, one would
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 23

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24 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

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FIGURE 9.—Distribution of meteor orbits in inclination and aphelion distance.

expect the mean magnitudes to be distributed

with q somewhat in the fashion indicated by

the schematic dotted line in figure 8. In fact,

the absolute brightness of the comets in any

given range of q is relatively constant. One

can, then, accept the observed distribution of

perihelia of comets as a true distribution out to

1 a.u., excepting at very low q where the photometric data are sparse. With the exception of

the marked and unexplained peak at 0.75 a.u.,

and the neighboring minimum at 0.85 a.u., the

distributions of the perihelia of comets and of

the meteors they have presumably produced

are essentially identical.

Aphelion.—The low accuracy in the determination of aphelia does not permit any significant conclusions. The distribution shown in

figure 6 perhaps allows us to say that the meteor

population is roughly constant with aphelion

as far out as Jupiter's orbit, at which distance

a substantial decrease in numbers occurs.

Line of apsides.—The tendency of asteroids

to align their lines of apsides with Jupiter's is

well known (see fig. 16). The asteroidal alignment is a function of aphelion distance. The

ratio of the number of asteroids aligned within

15° of Jupiter to those similarly opposed is

twice as large for asteroids with 3.5 a.u.^?'

<4.0 a.u. as for those with g'<C3 a.u., the proportions being 4.3 and 2.2. Of 29 short-period

comets with i<30° and with aphelion within

Jupiter's orbit, twice as many are aligned within

90° of Jupiter as have their perihelia in the

remaining two quadrants. It is of interest to

look for this same alignment in meteor data.

The influence of Jupiter is largest for low

inclination orbits with aphelia inside its own

orbit. Therefore, we sought the effect only for

those meteors with t<30° or t>150°, and with

g'<C5 a.u. In this range of inclination, the line

of apsides and the longitude of perihelion, T,

define essentially the same direction, and so the

following distributions are based on the values

of T for our meteor orbits. For meteors observed at the earth, w is a marked function of the

time of year, 40 to 50 percent of the meteors

recorded in any one month having a T within a

range of 50°.

The data for each month were weighted for

three effects: (1) the number of hours of

exposure in each month; (2) the proportion

of the observed meteors that were reduced in a
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 25

given month; and (3) the seasonal variation in

proportion of ecliptic orbits observed, which

results from the varying elevation of the

radiants of ecliptic orbits. This last correction

was determined empirically by noting the

proportion of orbits with small i and q' (i<^30°

or i]>150°, <z'<5 a.u.) to the total number

of meteors reduced for each month. The

reciprocal of this ratio was used as the weighting

factor for "(3)."

While the correction for "(2)" was always

small, there was a large variation in the weights

applied for "(1)" and "(3)." Table 4 gives the

weighting factors for each of these corrections,

and the median TT for each month. The weights

for July—a month of short nights, low elevation

of the ecliptic, and perpetual bad weather in

New Mexico—are, of necessity, very high.

The weighted distributions of the lines of

apsides of low inclination meteors are given in

figure 17 for meteors with 3<q'<^5 a.u., and in

figure 18 for meteors with g'<C3 a.u.

In both distributions, there is a minimum at

20°, where the asteroids exhibit a maximum.

Since much of the contribution at this longitude

comes during the month of July, the significance

of this minimum may be questioned. However, the data for July have probably been

overcorrected already. An additional multiplicative weight of 3, to reproduce the asteroidal

maximum at 20°, is certainly not reasonable.

In our data, the aphelia are relatively illdetermined and so the data of figure 17 probably

include orbits whose aphelia are, in reality,

outside Jupiter's. Thus, figure 18 is a better

representation of the alignment of our orbits

inside Jupiter.

As a check on the reality of the distributions

shown in figures 17 and 18, we have analyzed

106 meteors with t<30° and g'<5 that were

reduced by Jacchia (fig. 19). The same

weighting factors were used for seasonal effect

and for proportion of low i, low q' orbits. The

weights for the proportion of meteors reduced

to those observed were derived from Jacchia's

numbers. The correction factors are uncertain

for so small a collection of data, but these

data have the marked advantage of considerable

accuracy in the determination of q', and are

not contaminated by those orbits whose q

f

 is,

in reality, greater than 5 a.u., which would

not be expected to show the same degree of

alignment. Figure 19 shows the same general

features found for the fainter meteors reduced

by the approximate method: minima at 20°

and 190° and a significant maximum around

100°. The second maximum, centered about

315°, also shows to some extent in the faint

meteor data. In fact, we must apparently

account for a double-humped curve in the

distribution of lines of apsides of meteors,

rather than for the single-humped curve disMonth

January

February

March

April

May

June

July

August

September

October

November

December

TABLE 4.—Correction factors applied in the distribution of longitude of perihelion (T)

Weights applied to correct for variation in

Number of

hours of

exposure*

1.31

1. 46

1. 46

1.00

1. 12

1.27

2. 15

1. 19

2. 24

1. 18

1.73

1. 19

Proportion

of meteors

reduced

1. 31

1. 59

1. 51

1.35

1.37

1. 43

1.59

1. 50

1. 20

1. 44

1. 57

1. 40

Proportion of

meteors with

i<30°,

g'<5 a.u.

2. 15

1.72

1.86

1.83

1.84

2. 21

4 0 0

2.69

2.32

1. 93

2.27

2. 10

Total correction

factor

3. 69

3. 99

4 11

2.47

2. 82

4 02

13. 67

4. 80

6. 24

3. 28

6. 17

3. 50

No. meteors

(with i<30°

g'<5 a.u.)

reduced

77

71

90

142

145

95

20

62

67

110

38

66

Median T

200°

235°

250°

270°

300°

310°

0°

80°

95°

120°

145°

160°

•Normalized to April-1.00.
26 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

> 10

10

9

o

o

7

6

a

5

4

3

c

1

-

—

_

_

-

>^hi3GeeoDoot

• i i i i i • i . i

(fi

o /O

q o

O O

0 O

p o

o/O/ O

o/o o

O O o

Do O

OOO o

Jw° ° °

ytxxJOXQ 3000000 g

3 0 O O 0 Q C^QSO

, ,

L

0 y

0

0

O

0

O

O

0

0

0

O

O

0

)O

) O

O

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FiouiiB 10a.—Distribution of meteor orbits in eccentricity and semi-major axis: observed numbers,

all orbits.

played by the asteroids. There is a preferential

direction for the line of aspides of small meteor

orbits at about 90° from that of Jupiter.

We suggest that the observed distribution

of the lines of apsides of meteors is a chance

result due to contributions from a limited

number of comets. The association between

individual comets and meteor showers is well

known. Nearly half the meteor showers are

attributable to known comets. Probably, however, the reverse correlation has not been sufficiently emphasized: a stream has been found

for about half the known comets that might

produce a shower (say, those approaching

within 0.1 a.u. of the earth's orbit). Such

comets may also supply meteors that are perturbed into broad streams and hence are not
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 27

1.0

FIGURE lOi.—Distribution of meteor orbits in eccentricity and semi-major axis: cosmic-weighted

numbers^ orbits within 15° of the ecliptic plane. The areas in figures 10 b, c have been normalized

to the same total.

recognizable as a distinct shower. The most

difficult element to perturb is the line of apsides,

and the streams associated with particular

comets might maintain this partial identity

with the parent comets.

Porter (1952) lists 19 approaches of shortperiod comets within 0.1 a.u. of the earth's

orbit. Ten of these, including 1819 IV (see

McCrosky and Posen, 1959) and 1917 I

(Whipple, 1954) have produced recognized

showers. For 5 of the remaining 9, meteor

radiants have been predicted at declinations

south of —20° and generally out of the range

covered by observatories making comprehensive photographic observations of meteors. Of

the 19 close approaches, 8 are for comets with
28 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

> 10

10

9

8

7

6

a

5

4

3

2

1

-

1 1 1 1

S "N. f *\/

o OQ

i , i

(

r-J, CA cm

v X y — ^—-^

oooo o

^—s —

1 1 1 1 1 1 1

(Jin ]

JoV7

d o o

7 °

OOo

•pOO

o/oOo

£)oOo

opoo O

7 ) o oo o >—< DOO o w&I i 1 i 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

FIGURE 10C.—Distribution of meteor orbits in eccentricity and semi-major axis: cosmic-weigh ted numbers,

high inclination orbits (1>15°). The areas in figures 10 b, c have been normalized to the same

total.

t>30°, outside the ecliptic range considered in

our distribution of the line of apsides. The

values of x for the 6 approaches of comets with

*<30° and with radiants north of 8= —20° are

plotted with arrows in figure 19. The lines of

apsides of all of these comets avoid the regions

of minima around 20° and 200° observed in the

meteor data. Although the data on both

meteors and comets are limited, one must

consider the hypothesis that the distribution

of the lines of apsides of meteors varies with

time, and is related to the distribution of the

elements of particular comets that chance to

approach the earth's orbit.
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 29

> 10

10

Q

Q

o

7§

6

q'

5

4

o

o

1

p

0

o

"o

o

~o

o

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o

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c

C

o

o

1

/•—X 0

o

o

o

o

o

o

o

o

Go OG

o

o o

O

O o

° o

o o

O o

O o

OO

oo

\ A / ) 0(

o O

O o

o o

o

o °

O o

o o

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o o

o

o

o

o

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o

o

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OOO(

OOOOO

o

9

)6

o

o

o

i

O

OOOOO

OO

oo

o o

o O

oo

Oo

Oo

OO

oOOO

o o

1 1

O

o<

o

o

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o

f

I

X

o

o

o

o

o

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o

o

O(

3

0

O

0

0

p

"1

v so

\

) (

O

O

o

o

o

o

o

o

c

c

c

t

y

o

o

o

o

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o

o

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)O

)o

)O

)O

)o

)o

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X)

I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

q

FIGURE 11.—Distribution of meteor orbits in perihelion

distance and aphelion distance.

The table of data

A large number of the more important statistical relations among the orbital elements of

meteors are given in the distribution graphs

(figs. 2-6, 9-14). However, to facilitate the

work of other investigators who may wish to

analyze the data further, we present in tabular

form (table 7) all of the geometrical and physical

parameters of each meteor. Table 5 gives the

code for identifying the shower meteors, and

table 6 explains the column heads used in

table 7.

It should be stressed, however, that because

of the nature of the reduction method, these

556036 O -61 - 3

data have only statistical significance. In our

experience, when a meteor with anomalous

parameters has been investigated more carefully, the cause of the abnormality has always

been found in the approximate reduction and

not in the meteor.

Masses have been determined from the integrated intensity, /, and the equation

(3)

where T is the lifetime of the meteor, and T0 is

the luminosity coefficient. Integrated intensities have been derived from limiting and

maximum magnitudes in the manner described

by Hawkins (1957). Considerable uncertainty

remains as to the proper value of T0, and the

masses given should be considered as only

relative. The value of T0 used here is that

determined by Opik (see Whipple, 1943) and

the masses are therefore based on the same

scale as others published by the Harvard

Meteor Project. Scaling factors of as great as

220 (Cook, 1955) have been suggested.

The number given in the column for "abruptness" (A) refers to the special meteors discussed

by McCrosky (1955), which show a pronounced

discontinuity in the light curve, usually at the

beginning of the meteor's path.

There was no precise criterion for establishing shower membership for the graphically reduced meteors. The orbital elements exhibit

too much scatter to serve as a criterion. The

radiants were plotted, and compact clumps of

points with similar velocities were called showers. This particularly misrepresents extended

showers like the Taurids, and overlapping showers like the i and 5 Aquarids and a Capricornids.

Although some nonmembers of showers must

have been erroneously included, the error is

mainly one of omission.

For 31 meteors reduced by the graphical

method, photometry was not possible. For

these, the column entries Mpt and m«, have

been left blank. Blanks throughout the table

appear for those elements not obtained.

A dash appearing as an entry in the table

represents an undefined element, such as q' and

K, for those meteors whose computed orbits

are hyperbolic.
30 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

10

10

9

8

7

6

a

5

4

3

2

1

0

c

OO

o

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0

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Q

c

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o

o

o

o

o

o

o

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PD

S

o

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0

0

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u

t

o

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D

QC

)

£>

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o

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o

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o

o c

c

o c

°

o

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°

o

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o

o

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o

o

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°

J O

0

1

o

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°

°

o

°

0

o

o O

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°

o

o o

o

o O

o

o

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0

o

o

0

0

0

0

°

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c

o

c

°

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o

o

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1

o

o

°

°

°

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0 O

. o

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0

°

o

o

o

o

o

°

O

°

0 O

°

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o

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0

0 0

o

0 0 O

O o

o 0

O 0

0 O

0

0

I.I .

o

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o

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°

10 20 30 40 50 60 100 11° 120 130 140 150 160 170 180

FIGURE 12.—Distribution of meteor orbits in inclination and semi-major axis.

O o o o o O

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QQO

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SEP

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oo

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0

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o

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o o °

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1 '

110 120 130 140

FIGURE 13.—Distribution of meteor orbits in inclination and eccentricity.
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 31

1.0

1.0

.8

.6

nM

.4

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0

v—•v—j^~y

•WbP

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•rno

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i

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° O

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o

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O

o

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o

o

o

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o

o

o

o

o

o

o

o

o

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o

o

o

°

o

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o

O

o

o

o

o

o

o

o

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o

o

o

o

O

O

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o

o

o

o

O

O

o

O

o

o

o

0

0

0

o

o

o

o

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o

o

0

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FIGURE 14.—Distribution of meteor orbits in inclination and perihelion distance.

TABLE 5.—Code for identifying shower meteors

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

33

a Capricornids

Southern Taurids

t Aquarids (southern branch)

Geminids

6 Aquarids (southern branch)

Lyrids

Perseids

Orionids

Draconids

Quadrantids

Virginids

* Cygnids

Leonids

x Orionids

Ursids

c Hydride

Northern Taurids

Southern Arietids

Monocerotids

Coma Berenicieds

a Virginids

Leo Minorids

c Geminids

n Pegasids

5 Arietids

S Aquarids (northern branch)

« Serpentids

t Aquarids (northern branch)

TABLE 6.—Explanation of column heads used in table 7

Trail : Number of the photographic meteor trail;

No. an asterisk preceding the number

indicates that the meteor was reduced

by Jacchia.

Yr. : The year: 1950 plus the number given.

Mo. : Month.

Day : Day of the month and fraction of day

expressed in Universal Time.

Sh. : Meteor shower; identity given by the code

number in table 5.

i 2 :

COMET-ASTEROID CRITERION K

FIGURE IS.—Distributions of the 2529 meteors (solid line)

and the bright photographic meteors (broken line) in the

comet-asteroid criterion K. The areas under the two histograms are equal.

TABLE 6.—Explanation of column heads used in table 7

(continued)

S,a : True radiant (equinox 1950.0).

Va> : Meteor velocity (km/sec) outside the earth's

atmosphere.

Vo : Geocentric velocity (km/sec) of meteor.

VB '• Heliocentric velocity (km/sec) of meteor.

a : Semi-major axis (a.u.) of meteor orbit

(equinox 1950.0).

e : Eccentricity of meteor orbit (equinox

1950.0).

q : Perihelion distance (a.u.) for the orbit.

q' : Aphelion distance (a.u.) for the orbit.
32 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

170

160

150

140

130 -

K

m 120 -

ZJ

z

q 110 -

VOL. 4

FIGURE 16.—Distribution of longitude of perihelion for

asteroids.

40 80 120 160 200 240 280 320 360

LONGITUDE OF PERIHELION 7T

FIGURE 17.—Distribution of longitude of perihelion for meteors

with 3^j'<C5 a.u. The observed numbers of meteors have

been weighted for seasonal observational selection. They

were also weighted for the proportion rejected for graphical

reduction.

80 120 160 200 240 280

LONGITUDE OF PERIHELION *

320 360

FIGURE 18.—Distribution of longitude of perihelion for meteort

with q'<C.3 a.u. The observed numbers of meteors have

been weighted for seasonal observational selection. They

were also weighted for the random variation throughout the

year of the proportion rejected for graphical reduction.

80

70

60

X

n 50

z

o 40

LU

—

i 30

20

10

n

JM H I

-

-

-

-

-

-

-

—

—1

i—

i

-

-

-

-

-

80 120 160 200 240 280

LONGITUDE OF PERIHELION 7T

320 360

FIGURE 19.—Distribution of longitude of perihelion for

accurately reduced meteors with orbits in which ?'"O

a.u. The observed numbers of meteors have been

weighted for seasonal observational selection, and for

the random variation throughout the year of the proportion

accepted for reduction.
ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 33

TABLE 6.—Explanation of column heads used in table 7

(continued)

u : Argument of perihelion for the orbit (equinox

1950.0).

Q> : Longitude of ascending node for the orbit

(equinox 1950.0).

t : Inclination of the orbit to the ecliptic

(equinox 1950.0).

x : Longitude of perihelion (» + &).

X : Elongation: the angle between the true

radiant and the apex of the earth's

motion.

C.W. : Cosmic weight =1/PV2 (see equation 1).

K : Comet-asteroid criterion (see equation 2).

CZR : Cosine of the zenith angle of the apparent

radiant.

Mv, : Maximum photographic magnitude of the

meteor trail (apparent photographic

magnitude at a distance of 100 km).

wio, : Initial mass of the meteoroid in grams (see

text for mass scale). For example,

37-4 is to be read as .0037.

n : Number of shutter breaks visible on the

trail (of the pair) used for photometry

(1 shutter break=.O167 sec).

HB '• Height (km) above sea-level at beginning

of trail.

A : Abruptness: The number of the shutter

break at which the trail exhibited an

abrupt rise to maximum light. A

minus sign indicates that the light curve

lies somewhere between normal and

abrupt. A break number of zero

indicates that the meteor was at

maximum brightness when it just

became visible on the film.

References

BALDBT, F., AND D E OBALDIA, G.

1952. Catalogue g6ne>al des orbites de cometes

de l'an -46 6 a 1952. Paris Obs., Sect.

Astrophys. de Meudon, 59 pp.

BOBBOVNIKOFF, N. T.

1941. Investigations of the brightness of comets.

Pt. 1. Contr. Perkins Obs., vol. 2,

No. 15, pp. 49-187.

1942. Investigations of the brightness of comets.

Pt. 2. Contr. Perkins Obs., vol. 2,

No. 16, pp. 189-300.

COOK, A. F.

1955. On the constants of the physical theory of

meteors. Astron. Journ., vol. 60, p. 156

(abstract).

DAVIES, J. G.

1957. Radio observation of meteors. In, L.

Marton, ed., Advances in electronics

and electron physics, vol. 9, pp. 95-128.

HAWKINS, G. S.

1957. The method of reduction of short-trail

meteors. Smithsonian Contr. Astrophys.

vol. 1, pp. 207-214.

HAWKINS, G. S., AND SOUTHWOBTH, R. B.

1958. The statistics of meteors in the earth's

atmosphere. Smithsonian Contr. Astrophys., vol. 2, pp. 349-364.

JACCHIA, L. G., AND WHIPPLE, F. L.

In Reduction methods for photographic meteor

press trails. Pt. 2. (To appear in Smithsonian Contr. Astrophys, vol. 4.)

MCCBOSKT, R. E.

1955. Fragmentation of faint meteors. Astron.

Journ., vol. 60, p. 170 (abstract).

1957. A rapid graphical method of meteor trail

reduction. Smithsonian Contr. Astrophys., vol. 1, pp. 215-224.

MCCBOSKT, R. E., AND POSEN, A.

1959. New photographic meteor showers. Astron.

Journ., vol. 64, pp. 25-27.

OPIK, E. J.

1951. Collision probabilities with the planets and

the distribution of interplanetary matter.

Proc. Roy. Irish Acad., vol. 54, sec. A,

pp. 165-199.

POBTEB, J. G.

1952. Comets and meteor streams. 213 pp.

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1925. On the brightness of comets. Russian

Astron. Journ., vol. 2, pt. 3, pp. 68-84.

WHIPPLE, F. L.

1943. Meteors and the earth's upper atmosphere.

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59, pp. 201-217.

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meteor luminosity and ionization. Astrophys. Journ., vol. 121, pp. 241-249.

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1957. Reduction methods for photographic meteor

trails. Smithsonian Contr. Astrophys.,

vol. 1, pp. 183-206.
34 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

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ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 37

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ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 39

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50 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

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ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 53

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54 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. «

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ORBITAL ELEMENTS OF PHOTOGRAPHIC METEORS 55

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84 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 4

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