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 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. 

FRED L. WHIPPLE, Director, 

Astrophysical Observatory,

Smithsonian Institution. 

Cambridge, Mass.

Contents

Publications of the Astrophysical Observatory

The Velocity of Faint Meteors

Observational data

The diurnal effect

Results

Discussion

Acknowledgment

References

Abstract

## The Velocity of Faint Meteors

## by

Gerald S. Hawkins,1 Bertil-Anders Lindblad,2 and Richard B. Southworth 3

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, Ill. 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.

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

2 Lund University, Sweden, and Harvard College Observatory.

3 Smithsonian Astrophysical Observatory and Harvard College Observatory.

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:

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 IBM–7090 digital computer (Southworth, unpublished). The velocity, υ∞, has been corrected for atmospheric deceleration.

TABLE 1.—Velocity at Various Power Levels 

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 the period 15–03 hours because of the zeros occurring in the velocity distributions.

TABLE 2.—Diurnal Velocity Distribution 

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 low-power 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

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 sec–1 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 Southworth, 1963). This work shows that the faint meteors occurred 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. 

TABLE 3.—Verification of Diurnal Correction Factors

Figure 1.—Corrected velocity distributions for high-power and low-power runs. 

FIGURE 2.—Corrected velocity distributions for medium-power runs.

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

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.

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 SOUTHWORTH, R. B. 

1963. The physical characteristics of meteors. Radio Meteor Project, Research Report No. 2. 

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

1963. Meteor ionization and the mass of meteoroids. Smithsonian Contr. Astrophys., vol. 7, p. 22. 

MCKINLEY, D. W. R. 

1961. Meteor Sciences and Engineering, McGraw-Hill 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. 

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