SMITHSONIAN

CONTRIBUTIONS

to

ASTROPHYSICS

Smithsonian Institution

Astrophysical Observatory

Volume 8, Number 4

The Velocity of Faint

Meteors

by Gerald S. Hawkins,

Bertil-Anders Lindblad,

and Richard B. Southworth

Washington, D.C.

Smithsonian

Contributions to Astrophysics

VOLUME 8, NUMBER 4

THE VELOCITY OF FAINT METEORS

by GERALD S. HAWKINS, BERTIL-ANDERS LINDBLAD, and

RICHARD B. SOUTHWORTH

SMITHSONIAN INSTITUTION

Washington, D.C.

1964
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 Held 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.
The Velocity of Faint Meteors

by

Gerald S. Hawkins,1 Bertil-Anders Lindblad,2 and Richard B. Southworth

The meteor population is size dependent.

McKinley (1961) has summarized the photographic and the radar data, showing that there

is a tendency to find short-period orbits among

the smaller and fainter meteors. This necessarily implies that the average velocity of a

group of meteors depends on the average magnitude, and that small meteoroids tend to move

more slowly in space. The comparison of the

various orbital distributions is, however, fraught

with the effects of observational selection, and

it is difficult to establish a quantitative measure

for the difference among the various meteor

populations.

This paper describes a controlled experiment

in which the velocity distribution of meteors

was measured at several different limiting magnitudes, with the minimization of the various

selection effects.

Observational data

The multi-station radar system, described by

Hawkins (1963), is situated at Havana, 111. A

single-trough antenna was used at the transmitting site, and single yagi antennas were used

at the five remote sites. The transmitter frequency was 40.92 mcs, and the peak power was

varied from 25 kw to 2 Mw. An integration

of the ionization curve yields the total number

of electrons in the trail. From this the mass

and magnitude of the meteoroid can be computed by means of the values of ionizing efficiency of Lazarus and Hawkins (1963). At

low power the average magnitude was +6.6 on

the visual scale, and at high power the average

magnitude was +9.0.

1

 Boston University, Boston, Mass.; Smithsonian Astrophysical Observatory and Harvard College Observatory,

Cambridge, Mass.

»Lund University, Sweden, and Harvard College

Observatory.

• Smithsonian Astrophyslcal Observatory and Harvard

College Observatory.

728-630—64

It was not practical to operate the radar system continuously, because the number of meteor

echoes recorded would have been astronomical.

Therefore an operational schedule based on the

days of the week was set up, as follows:

Day

Monday

Tuesday

Wednesday

Thursday

Friday

Hour*

0000 to 0800 C.S.T

0000 to 1200 C.S.T

0800 to 1600 C.S.T

1200 to 2400 C.S.T

1600 to 2400 C.S.T

This schedule was used on alternate weeks, with

no observations being made on the other weeks.

The observing time was cut further by limiting

it to the first 30 minutes of any hour during a

run. This schedule gives a uniform diurnal

coverage when averaged over a period of one

week.

At times it was not possible to adhere strictly

to the operating schedule, and observations are

not available for the full cycle of 12 months.

Thus diurnal and seasonal effects must be taken

into account when considering the data. The

analysis covers all data available at the present

time. The observing periods and power levels

are given in table 1. In summer and fall of

1961 the radar system was not fully developed,

and observations were made at only three stations. A total of 681 meteors was recorded by

the 3-station network. It will be shown that

there is no systematic difference dependent upon

the number of stations used. A total of 2398

meteors was available in the initial analysis,

but of this number 216 Geminids and 17 Quadrantids were excluded from the final analysis.

The velocity was derived from measurements

at all stations, by use of a program on IBM7090 digital computer (Southworth, unpublished). The velocity, va, has been corrected

for atmospheric deceleration.

133
134

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Velocity at Various Power Levels

Observational Periods

15 April-31 August 1961

27-28 November 1961

Mean

4 December 1961

15 January-2 February 1962

2-5 January 1962

19 June-8 August 1961

December 1961

Mean

26 February-16 March 1962

26-30 March 1962

12-16 February 1962

9-27 April 1962

Mean

No. of

stations

3

6

6

6

6

3

6

6

6

6

6

Power

(kw)

25

25

25

700

750

900

1000

1200

950

1750

1750

2000

2500

1900

Observed

velocity

39.8

38.2

39.9

34.9

35.5

37. 1

40.6

33.3

31.4

34.3

30.9

Corrected

velocity

3& 4

35.9

38. 1

37.5

34.9

34.7

36. 1

38. 1

36.4

33.3

31.4

34.3

30.9

32.8

No. of

meteors

378

39

49

409

93

111

451

463

212

27(5

173

Hours of

obs. C.S.T.

03-15

03-09

03-09

00-24

09-15

03-15

03-09

00.24

00.24

00.24

00.24

The diurnal effect

The period 15 January to 30 March 1962

was chosen for a study of the diurnal variation of velocity, because it was during this

time that the minimum departure from the

operating schedule (see above) occurred.

This period was also reasonably free from

meteor streams. The data were grouped in 6-

hour intervals, as shown in table 2, and the

velocity distribution was determined for each

interval. It is apparent that the velocity distribution changes during a 24-hour period.

This results, of course, from the astronomical

selection effect as the earth rotates, and is of no

interest in this paper. Rather, the velocity distributions can be used to correct the observations during any period when a complete 24-

hour coverage was not available. The correction factors for the period 03-09 hours and 09-

15 hours C.S.T. are given in table 2. It was

not possible to determine correction factors for

TABLE 2.—Diurnal Velocity Distribution

v~

V km sec~'

10. 0-14. 9

15. 0-19. 9

20. 0-24. 9

25. 0-29. 9

30. 0-34. 9

35. 0-39. 9

40. 0-44. 9

45. 0-49. 9

50. 0-54. 9

55. 0-59. 9

60. 0-64. 9

65. 0-69. 9

70. 0-74. 9

Total

Velocity distributions for

15 January-30 March

03-09

2

16

58

127

148

98

42

20

15

26

22

16

3

593

09-1E

0

15

56

129

142

109

59

27

17

12

6

5

1

578

15-21

7

20

37

26

16

1

107

period

1962

21-03

1

15

23

24

8

7

3

1

82

Correction factor

to reduce to 24

hrs of observation

03-09

5.00

4. 13

3.00

2.41

2. 12

2. 19

2.48

2.40

2. 13

1. 46

1.27

1.31

1.33

09-15

_

4.40

3.11

2.37

2.21

1.97

1.76

1.78

1.88

3. 17

4.67

4.20

4.00
VELOCITY OF FAINT METEORS—HAWKINS, LINDBLAD, AND SOUTHWORTH 135

the period 15-03 hours because of the zeros

occurring in the velocity distributions.

Results

For the analysis of the velocity distributions,

the results have been divided into the three

groups shown in table 1. These groups may be

classified as low-, medium-, and high-power

runs with nominal peak transmitter powers of

25 kw, 1 Mw, and 2 Mw. The observed velocity

distribution was corrected for diurnal effects

by use of the correction factor in table 2 for

the periods when the operating schedule was not

strictly followed. The corrected velocity distributions for the high-power and low-power

runs are shown in figure 1. The corrected

velocity distributions for the medium-power

runs are shown in figure 2. In figure 2 the

results have been divided into two groups, the

3-station measurements and the 6-station measurements. All the velocity distributions have

been normalized so that the area under the

histogram is equal to 100 units.

As an internal check, it is possible to verify

the diurnal correction factor. One would expect that proper application of the correction

factor would yield the same mean velocity for

any period of the day at a fixed power level.

In table 3 the observed mean velocity and the

corrected mean velocity are shown for the lowpower and medium-power observations. It appears that although the observed velocity differs by 1 or 2 km sec"1

 for different portions of

a 24-hour period, the corrected mean velocity

differs by less than 0.5 km sec"1.

The two histograms at a peak power of 1

Mw were drawn to ascertain whether there were

any systematic differences between the 3-station

and the 6-station observations. Figure 2 shows

that the histograms are essentially the same and

that no systematic effects exist. Furthermore,

since the 3-station results were obtained in the

summer months and the 6-station results in the

winter months, the similarity of the histograms

indicates that there are no significant seasonal

variations.

The mean velocity, given in table 1, has been

used as a measure of the meteor population at

various limiting magnitudes. In figure 3 the

velocity is plotted as a function of transmitter

power; on the same diagram the average magnitudes have been assigned, based on the relation

^=40-2. 5 log q, (1)

where q is the electron line density in units of

electrons per meter. Thus the curve in figure 3

shows a decrease of mean velocity with meteor

magnitude. The average decrease is approximately 5 km sec1

 for 3 magnitudes. This corresponds approximately to a decrease of 9 km

sec"1 if one extrapolates to an interval of 5

magnitudes.

Discussion

It is unlikely that these results are affected

to any great extent by observational selection.

The diurnal effect has been removed, and there

are no detectable seasonal effects. It is possible

to introduce a bias that is dependent upon the

mean height of meteors in the various samples.

For example, if the faint meteors were occurring

at a greater height, then these meteors might

possibly be inadequately observed because of the

effects of diffusion of the trail (McKinley,

1963). An analysis of the heights of the echoing points has been made in connection with a

study of the physical characteristics of radar

meteors (Hawkins and South worth, 1963).

This work shows that the faint meteors occurred

TABLE 3.—Verification of Diurnal Correction Factors

Observational Periods

15 April-31 August 1961

19 June-8 August 1961

Power

(kw)

J 25

1 25

f 1000

1 1000

Observed mean

velocity km sec 1

41. 1

39.0

38.7

36.8

Corrected mean

velocity km sec"1

38.6

38.2

36.4

36.0

No. of

meteors

143

236

20

91

Hours of

observation

03-09

09-15

03-09

09-15
136 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

.2 h

25

20

15

10

5

— 1 T

| 1

1

1

r-J

i

j

— I

r—'

_

_

i '

i

i

High power, 2 megwatt

Lov/ power, 25 kwatt

1

_ _ _

i

1

1

1

1

i

1

i

! 1 1 1 .

J

;

—i

;

j

i

~\

i

J

I

-

—

j

1

i

|

1

1.

tq 1

10 20 30 40 50 60 70 80

VM , velocity km sec" 1

Figure 1.—Corrected velocity distributions for high-power and low-power runs.
VELOCITY OF FAINT METEORS—HAWKINS, LINDBLAD, AND SOUTHWORTH 137

25

20

15

10

5

I

I

_

_

r

w — J

1

1

1

1

1

I —1

1

1

I

1

—1

1

 1

1

-

1000 kw (3 st) • —

1000 kw (6 st.)

-

-

—

1 1

l

1

i

-

1

1

1

1

i

•

1

10 20 30 40 50

V_ , velocity km sec" 1

60 70 80

FIGUBE 2.—Corrected velocity distributions for medium-power runs.
138

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Visual magnitude

+ 6

40.0

VPO

30.0 -

i

+ 7

>(Uncorrected)

•(Corrected)

o Radio meteor project

• Jodrell bank

i

+ 8

i

+9

10 10"'

Peak power megwatts

FIGURE 3.—Velocity as a function of transmitter power.

at a lower height in the atmosphere than did the

bright meteors. For example, in the velocity

range 25-30 km sec"1 the mean height was 94.5

km for meteors with magnitudes between +5.7

and +6.9. On the other hand, meteors with

magnitudes between +9.0 and +9.9 occurred at

a mean height of 88.4 km. This result is in

complete disagreement with the single-body

classical theory. The discrepancy probably results from the change in physical characteristics that is found as one proceeds to fainter

meteors. Whatever the cause, the height distribution is certainly not responsible for the observed difference in mean velocity.

It is interesting to compare the data obtained

by the radio meteor project with data from

other observatories. The only available data

are those of Davies and Gill (1960), who carried out a meteor survey at Jodrell Bank, England. The average magnitude of meteors in

their sample was +7, and the radar wavelength was 8 meters, which is close to the 7-meter

wavelength used in the radio meteor project.

From the published data of Davies and Gill

two values for mean velocity have been determined. The first value represents the original

observational data. The second is a corrected

value, which allows for the difficulties of observing the Fresnel pattern. No correction for

pattern visibility has been included in the data

in this paper. The Fresnel patterns as recorded

are, however, somewhat clearer than the Jodrell

Bank records. We consider that our data correspond to an intermediate value between the

corrected and the uncorrected data of Jodrell

Bank.

Between visual magnitudes of +6 and +9

the average velocity of meteors decreases by approximately 5 km sec"1

. Thus in interplanetary

space the average velocity of meteoroids will

depend to a considerable extent on the mass of

the particle. There are indications that the

change in the meteoroid population becomes

accentuated among the smaller particles. The

curve in figure 3 becomes much steeper between

magnitude +8.5 and +9. The meteor population may undergo critical changes between magnitude + 9 and +12. The hope is to investigate

this region of the magnitude scale with a further extension of the sensitivity of the radio

meteor project.
VELOCITY OF FAINT METEORS—HAWKINS, LENDBLAD, AND SOUTHWORTH 139

Acknowledgment

The research reported in this paper was supported by contract NASr-158 with the National

Aeronautics and Space Administration. The

Radio Meteor Project is a joint effort of Harvard University and Smithsonian Astrophysical Observatory.

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, p. 437.

HAWKINS, G. S.

1963. The Harvard radio meteor project Smithsonian Contr. Astrophys., vol. 7, p. 53.

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

1963. The physical characteristics of meteors.

Radio Meteor Project, Research Report

No. 2.

LAZARUS, D. M., and HAWKINS, G. S.

1963. Meteor innization and the mass of meteoroids.

Smithsonian Contr. Astrophys., vol. 7, p. 22.

MCKINLEY, D. W. R.

1961. Meteor Sciences and Engineering, McGrawHill Publishing Co., Inc., New York.

Abstract

Preliminary measurements of meteor velocity to a limiting magnitude of +10 have been obtained with a

multistation radar system. A systematic change in the average velocity of meteors, which depends on the magnitude and hence on the size, has been found. Between magnitude +6 and +9 the velocity decreases by 5 km sec"1

.

There are indications that the effect becomes more marked for meteors fainter than +9. This effect is attributed

to the difference in orbits within the various meteor populations.