Smithsonian

Contributions to Astrophysics

VOLUME 4, NUMBER 4

PRECISION ORBITS

OF 413 PHOTOGRAPHIC METEORS

by LUIGI G. JACCHIA and FRED L. WHIPPLE

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. 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.

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Contents

Publications of the Astrophysical Observatory

Precision Orbits of 413 Photographic Meteors

The observational material

Reduction techniques

Sources of error

Orbital data

Classification on the basis of quality

Frequency distributions of orbital elements

Sources of meteors

Meteor streams and associations

Acknowledgments

References

Abstract

Precision Orbits of 413 Photographic Meteors

By LUIGI G. JACCHIA [1] and FRED L. WHIPPLE [1]

The 413 doubly photographed meteors discussed here represent a selection of the longest and brightest trails from 3,500 such meteors obtained in the Harvard Meteor Program. The meteors were selected to give the greatest precision in derived velocity and deceleration, in order to establish with high certainty the immediate origin of meteors in the visual range and to provide exact data for studies of meteoric processes, meteoroid characteristics, and the properties of the upper atmosphere. The present paper considers orbital characteristics and associated problems of meteoritic origin, while physical problems will be discussed by L. G. Jacchia in other papers. A preliminary discussion of 308 of the present meteors was presented previously (Whipple and Jacchia, 1957a).

The observational material

The meteor orbits presented here are based on precise reductions of selected photographs taken simultaneously at two Harvard stations in New Mexico with the Baker Super-Schmidt meteor cameras. The first of these cameras was installed during the summer of 1951 at Soledad Canyon, but the double-station program did not get under way until March 1952, when a second camera started operations at Doña Ana. In July 1954 the cameras were moved to Sacramento Peak and Mayhill. All the meteors included in this paper were photographed prior to the move, between March 1952 and July 1954, with the exception of Nos. 4702 and 2961, which were photographed in September and October 1951 with a Super-Schmidt camera at Soledad and smaller meteor cameras at Doña Ana. The Super-Schmidt meteor cameras and the details of the program have been described elsewhere (Jacchia and Whipple, 1956).

[1] Smithsonian Astrophysical Observatory and Harvard College Observatory, Cambridge, Mass.

In all, approximately 4,500 meteors were photographed during this period, about 3,500 of them from both stations. Of these meteors, 413 were selected for accurate reduction on the basis of trail length and quality of image.

The shutters of the Super-Schmidt cameras have two 45º openings and rotate at 1,800 rpm; the meteor trail is thus interrupted 60 times a second and presents the aspect of a row of segments separated by wider breaks. In making the selection we deliberately chose only those meteors that were likely to yield excellent decelerations. On this basis we discarded nearly all meteor trails showing fewer than 20 clearly discernible segments and those whose segments were too closely spaced, as well as trails appearing against rich star fields or too faint to be measured with accuracy. The selected meteors have an average of 40 well-measured segments on the better of the two films, and 34 on the other, and for all but 17 meteors the instant of appearance was recorded visually. A secondary criterion for selection was that comparable numbers of meteors should be chosen in the low, the medium, and the high-velocity groups, and for each month of the year. For months particularly rich in meteors the standards of acceptance were set a little higher, so that the month in question should not exert an overwhelming weight in the analysis of seasonal effects on decelerations.

As a result of this selection, the orbits presented here do not represent a random sample, and this fact should be kept in mind in evaluating the analysis. Thus, while statistical correlations between the various orbital elements are justified, frequency distributions of orbital elements should be accepted with some degree of caution. In particular, it should be remembered that by excluding meteors with closely spaced segments we have, in all likelihood, eliminated more of the low-velocity than of the high-velocity meteors. The bias introduced by our selection is added, of course, to the bias already inherent in meteor photography, allowed for in the calculated quantity, cosmic weight.

Reduction techniques

A detailed description of the reduction methods for Super-Schmidt meteors has been given by the authors (Whipple and Jacchia, 1957b). For all but five meteors the radiant was determined from the intersection of the two great circles of motion of the meteor as seen from the two stations. The five exceptions were meteors for which the angle of intersection Q of the great circles was small enough to impair the accuracy of the solution by this method. For these meteors direct triangulation was used (Whipple and Jacchia, 1957b). When a good common point is available, this method can lead to quite accurate results.

The velocity V∞ of the meteor outside the atmosphere was computed as a by-product of the deceleration; an equation of the type

was fitted to the distances D on the meteor trajectory, observed in function of time t at the instants corresponding to shutter segments.

The parameter k is computed from four equidistant points on a graph, and a, b, and c are evaluated by least squares. The value of b, which represents the velocity of the meteor at t=–∞, was taken as V∞. In general, the aim was to obtain decelerations greater than their inner probable error by a factor of 20 to 40; therefore when it appeared likely that the factor would be greater if a single solution were to be computed for the whole meteor, the trajectory was divided into two, three, or more sections and separate least-squares solutions were computed for each of them. In such cases the value of b from the earliest solution was taken as V∞. In practically all cases V∞ was computed independently from each of the two trails, and a weighted mean taken.

Sources of error

The main sources of error in the individual solutions are briefly described as follows.

The assumed instant of the meteor. —Without a recording aid the error of a time observation can be estimated at ± 2 seconds. After August 1952 the New Mexico observers used a printing chronograph, accurate to A comparison of the records from the two stations shows that when the same meteor was observed simultaneously by both stations (as happened for approximately three-quarters of all meteors), the recorded instants agreed within to Very seldom did the discrepancy amount to For average geometric conditions an error of 2 seconds in time is reflected in an error of 0.01 percent in the meteor velocity. In the reduction method based on the intersection of the circles of motion, the error varies as the inverse of sin Q. The average value of sin Q for our meteors is approximately 0.3. Only 37 meteors had sin Q less than 0.1, and, as a rule, when sin Q was found to be less than 0.03, direct triangulation was used, in which the error is independent of Q.

When no visual observations were available, the instant of the meteor had to be computed from one or more points that could be identified as common on both photographic trails. Under good conditions the error of such a determination is not more than 1 minute (0.3 percent in the velocities), but it can occasionally be as large as 6 minutes (one-half of the standard exposure time) when no definite common point can be found.

The determination of the radiant.—A source of error lies in the uncertainty with which the straight line, representing the great circle of motion of the meteor, can be determined in gnomonic projection. For a good meteor the error in the direction of motion is of the order of 10″, but 20″ is probably closer to the average. Under average conditions (center of visible trails 45° from the radiant; sin Q=0.3), an error of 10″ in the direction of each of the trails is reflected in a maximum error of 1' in the radiant position and in a relative error of 0.06 percent in the velocity. This error also varies as the inverse of sin Q; it does not apply when direct triangulation is used.

The extrapolation to V∞.—The inner probable error of V∞, as computed by the least-squares method for a great number of meteors, appears to be of the order of 0.01 percent for a good, long meteor, and close to 0.03 percent for an average good meteor. In the worst cases on record (short, poor meteors), this type of error amounts to 0.3 percent. These errors refer to a single photographic trail. The fact that a weighted mean was taken between two values of V∞ should reduce the error in the final value; on the other hand, uncertainty of the parameter k of equation (1) should add a little to the error. It is quite safe to assume that, when the two effects are added together, the final error is not greater than the values given above for individual trails.

Shutter flutter.—After a number of Super-Schmidt meteors had been completely reduced, there was clear evidence that a “flutter” affected the rotation of all camera shutters. Although this instrumental trouble was later eliminated by the installation of more powerful motors, it was nevertheless present during all the period of time covered by the meteors included in this paper.

The shutter flutter was semiregular in character and exhibited widely different amplitudes, ranging mostly from zero to 5°, with a fundamental period of but with occasional lapses into cycles half or twice that length. When two or more cycles of the flutter are covered by the photographic trail, its effect can easily be eliminated with relative confidence (Whipple and Jacchia, 1957b). For shorter trails, however, the process becomes more questionable, and a few meteors had to be rejected for this reason. The uncertainty in the correction for shutter flutter is, by a reasonable estimate, of the same order of magnitude as that arising from observational scatter; the two effects also depend in very similar manner on the duration of the meteor.

Speed of rotation of the shutters. The rotating shutters of the Super-Schmidt cameras are driven by synchronous motors fed by a 60-cycle a.c. current whose frequency is regulated by a quartz crystal. Theoretically the shutter speed should not vary more than 0.01 percent but occasional dips in speed as high as 0.1 percent have been observed. The shutter speed, always checked at the start and at the end of an observing night, and occasionally at intervals during the night, is recorded to the nearest tenth of one rpm. It is safe to assume that no error larger than 0.05 percent can come from this source.

Orbital data

Table 1 presents orbital data for the 413 photographic meteors. The column heads have the following meanings:

Trail No.: Number of trail photographed at the Doña Ana station.

Day: Day of the month in Universal Time given to

Yr.: Year of observation minus 1900.

Mo.: Number of the month of the observation.

Sh. No.: Identification of associated meteor shower, if any, as indicated in tables 3 and 4; the letter “Q” after the number indicates a questionable association.

a: Semimajor axis, in a.u.

e: Eccentricity.

q: Perihelion distance, in a.u.

q': Aphelion distance, in a.u.

ω: Argument of perihelion; angle from the ascending node to perihelion along direction of motion, in degrees. Equinox 1950.0.

: Longitude of the ascending node along the ecliptic from the vernal equinox of 1950.0, in degrees.

i: Inclination of the orbit plane to the ecliptic 1950.0, in degrees.

π: Longitude of perihelion π = ω + , in degrees.

True radiant: Radiant after correction for the earth’s attraction in degrees and minutes: α, right ascension; δ, declination; equinox 1950.0.

V∞: Velocity with respect to the stations, corrected for atmospheric drag, in km/sec.

VG: Velocity with respect to the center of the earth, corrected for earth’s attraction, in km/sec.

VH: Heliocentric velocity, fully corrected, in km/sec.

λ: Elongation of the true radiant from the apex of the earth’s motion, in degrees.

sin Q: Q is the angle between the apparent great circles of motion as seen from the two stations.

C.W.: Cosmic weight, a weighting factor intended to be inversely proportional to the probability that meteoroids of constant mass in their observed orbits will, in one revolution, collide with the earth and produce photographable meteors. C.W. is calculated from the expression,

where p=a(1—e^2); p and a are expressed in a.u. and the velocities in units of 100 km/sec (see Whipple, 1954).

K: A criterion designed to distinguish statistically between cometary and asteroidal orbits. The K criterion is defined by the expression log_10 where the aphelion distance is measured in a.u. The term q'/(1—e) is proportional to the inverse square of the aphelion velocity. In most cases K>0 for comets and K<0 for asteroids, but the values of K are not well known for asteroids of q<l.

Mp: Photographic absolute magnitude.

t: Duration of longer photographed trails in seconds of time. Trails both limited by the edge of film are designated by G.

Qual.: Quality class of velocity and orbit determination, defined in table 2 and in text (below).

TABLE 1.—Basic orbital data

Classification on the basis of quality

When all sources of possible error are added, the velocities of good meteors turn out to be correct to approximately 0.1 percent, those of fair meteors to some 0.4 percent, and those of poor meteors (comprising less than 10 percent of the total) to approximately 1 or 2 percent.

We have tried to assign to each meteor a grade of reliability by which it is classified. Table 2 gives for each quality class in table 1 the most probable value of the relative error and the maximum error to be expected if all causes of error were working in the same direction.

TABLE 2.—Errors for meteors of various quality classes in table 1

Frequency distributions of orbital elements

On page 97 ff. we discuss certain minor selection factors operating in the choice of the meteoric trails reduced in the present program. A number of strong selection factors, however, enter into the statistical distributions of the orbital elements and, indeed, into the correlations among them. Certain of these factors are included in the quantity, cosmic weight (C.W.). Thus meteors of small orbital inclination or with apsides near the earth’s orbit are distinctly favored. Also, the photographic technique appears to favor meteors of higher velocity, exclusive of the geometric factors involved. On the other hand, the effect of the cross-sectional area of the earth is to favor the slow meteors.

Perturbational effects, especially of Jupiter, play important roles in determining the distribution of orbital elements. A selective effect probably operates in the case of meteoric streams, resulting from the fact that the earth moves on a line through the stream. This effect is not well understood and deserves major consideration. Because of the complexity of this problem, however, no attempt will be made here to discuss it. A few of the statistical interrelationships among the observed orbital elements will be treated in the following sections and some of the major selectional factors will be discussed briefly.

Perihelion distance versus argument of perihelion.—Figure 1 is a plot of the perihelion distance against the argument of perihelion ω for the observed meteors. A rather amazing correlation results from the fact that meteors must, by definition, be observed at the nodes of their orbits at heliocentric distances near 1 a.u. The effect of this requirement is peculiarly conspicuous in the figure because the eccentricities of the orbits are generally large and the aphelion distance much greater than 1 a.u. The concentration near the two parabola-like curves in figure 1 would be even more complete were meteoric observations from a point near the equator possible on a 24-hour basis. A complete discussion would involve the detailed effects resulting from night versus day, northern versus southern hemisphere, and ascending versus descending node. We merely show the diagram as a warning that correlations among orbital elements of meteors as well as among distribution functions must be evaluated carefully in terms of selection effects.

FIGURE 1.—Argument of perihelion ω plotted against perihelion distance q (all meteors).

Inclinations of orbits having aphelia within Jupiter’s orbit.—One of the authors (Whipple, 1940) investigated the perturbations in the angular elements of meteors derived from Comet Encke and showed that the Taurid meteor shower is associated with this comet. Some of the conclusions apply broadly to all meteors in orbits with aphelion distances less than the perihelion distance of Jupiter. With the secular perturbations in node, for Comet Encke the inclination varies over the range from 4° to 16° (with respect to the plane of Jupiter’s orbit, not far from that of the earth). For similar orbits of small perihelion distance, the condition heliocentric distance r = 1 a.u. at the node permits encounters with the earth only when the inclination is relatively low, approximately 4.6°.

On the other hand, the rate of change of the node at this orientation is a maximum and strongly influences the chance of encounter with the earth. Hence, any theory dealing with the distribution of inclinations or with the dependence of inclination upon perihelion distance, for orbits with aphelia lying within Jupiter’s orbit, must be carefully studied if the observed distribution or correlation is to be of significance. The ramifications of these perturbational relationships are too involved for the present paper. They are mentioned only to indicate that the mean inclinations of the very short-period meteor orbits in space may be seriously underestimated because of the peculiarities of the perturbations of Jupiter.

Inclination versus perihelion distance.—Figure 2 depicts the observed distribution of meteors with respect to perihelion distance and inclination. As is to be expected from geometrical selection effects, a high concentration of observed meteors occurs near q=1 a.u. and near i=0 . No conspicuous gaps occur in the diagram except in the neighborhood of q=0, and possibly near i=90° for small q.

Although there is no dearth of comets with small perihelion distances, the meteoric distribution cuts off sharply at q=.05 a.u. with only 3 sporadic meteors having q<0.1 a.u. The remarkable δ-Aquarid shower shows a high concentration near q=0.06 a.u. with a minimum value of 0.047 a.u. Six of the 7 sporadic meteors with q<0.15 a.u. are of short period with aphelion distance <5 a.u. The inclinations are all moderate, <40°.

We conclude that the sun’s energy, possibly heat or corpuscular radiation, eliminates meteors rapidly within a distance of .05 a.u. and effectively reduces the numbers with q<0.1 a.u. The existence of the dense δ-Aquarid stream, however, with q<0.1 a.u. suggests strongly that these effects do not arise from direct melting or destruction but from some slow process such as etching by corpuscular radiation or by sublimation in the range 0.05<q<0.10 a.u.

FIGURE 2.—Orbital inclination i plotted against perihelion distance q. Major showers (mean values) are indicated by circled dots.

A possibly significant scarcity of meteors, both shower and sporadic, near inclination 90° may be associated with the minimum of comet frequencies in this same range. The effect may well be of a perturbational character and deserves more thorough study.

Inclination versus aphelion distance.—In figure 3 orbital inclinations are plotted against q'–½ , where q' is the aphelion distance expressed in a.u. This parameter was chosen in preference to q' or q'–1 to avoid the crowding of points at one end of the diagram.

FIGURE 3.—Orbital inclination i plotted against aphelion distance q'. The variable in abscissa is q'–½; heliocentric distances of the major planets are marked at the bottom. Major showers (mean values) are indicated by circled dots.

At great aphelion distances the distribution is rather uniform with inclination although there is some scarcity of low inclination orbits. The effect of Jupiter’s perturbations shows strikingly for aphelia between Jupiter and the asteroids, where retrograde orbits are absent and the mean inclination falls rapidly as the aphelion distance decreases. The apparent concentration near the orbit of Mars does not seem to be real (see data of Hawkins and Southworth, 1958).

No concentration at all is evident in the region of the asteroid belt. This fact is a powerful argument against an asteroidal origin of an appreciable number of the meteors in this collection. The concentrations of major showers near the ranges 0.1 to 0.2 and 0.4 to 0.6 in q'–½ are of some interest. The former concentration may, of course, be fortuitous. The latter indicates a strong dependence of shower comets on Jupiter’s perturbations, with some longevity in orbital characteristics attained by those showers with aphelia inside of Jupiter’s orbit. It appears to be very difficult for comet aphelia to be reduced much below 2 a.u.; the Geminids represent an extreme case. Figure 3 is very similar to a corresponding figure for comets except for the dearth of comets with very small aphelion distance. Such comets, of course, would be very short lived and it is difficult to see how they could develop. Meteors, on the other hand, subject to physical forces, can theoretically attain quite small aphelion distances.

Aphelion distance versus longitude of aphelion.—We have already seen that aphelia for meteors are highly concentrated near Jupiter’s orbit. In figure 4 the aphelion distance is plotted as a. function of longitude of aphelion with the corresponding radius-vector of Jupiter indicated as a curve. There is a slight tendency for the distribution of meteoric aphelia to fall off just beyond Jupiter’s orbit. It is not clear, however, that this effect is statistically significant.

Among the asteroids the concentration of aphelia in the direction of Jupiter’s aphelion is extremely marked. The effect exists because the perturbations of Jupiter are greater when the asteroidal aphelion is closer to the orbit of Jupiter and the consequent forward motion of the line of apsides is more rapid. Thus the aphelia tend to concentrate in the direction of Jupiter’s aphelion. We should expect such an effect for meteor orbits that lie entirely within Jupiter’s orbit. No such tendency is indicated in figure 4. Apparent concentrations appear to be possibly significant some 90° from Jupiter’s line of apsides. Three possible explanations for this lack of a well-explained perturbational effect are as follows:

(1) Physical forces change the lines of apsides for meteors more rapidly than do Jupiter’s perturbations.

(2) Meteors of small aphelion distance may be contributed by a relatively small number of comets (or other bodies) and show a random distribution because of the small statistical selection of sources.

(3) The lifetimes of meteoroids may be extremely short, appreciably smaller than the revolution period of apsides.

Explanation (1) is purely hypothetical insofar as physical perturbations of meteoroids are concerned. The major physical forces that have been considered are the Poynting-Robertson effect, corpuscular radiation from the sun, and encounters with meteoritic dust. There is no evidence that electromagnetic forces act appreciably on meteoroids while the forces listed above should not generally shift the lines of apsides appreciably. In other words, if physical forces are responsible for the lack of concentration of lines of apsides, these forces must be of a character not yet considered seriously.

The number of recognized meteor streams is relatively small and a few major sources, such as extraordinarily large comets, may indeed play a significant role in providing the observed meteors. Nevertheless, if meteoroids had long lifetimes we should expect the Jupiter effect to be manifest in the distribution of the lines of apsides.

Hence, it seems necessary to conclude that meteors are injected into their orbits without a significant correlation with the lines of apsides of Jupiter’s orbit, and that their lifetimes are relatively short. For Comet Encke, with an aphelion distance of 4.1 a.u., the line of apsides revolves in some 13,000 revolutions. The Taurid meteors can be traced back in history by their association with Encke’s comet through some 1,500 revolutions, not much more than 10 percent of a complete revolution in the line of apsides. Although aphelia near Jupiter will move somewhat more rapidly than that of Comet Encke, nevertheless we clearly should expect no concentration of the lines of apsides for meteors. if the ordinary meteor lifetime averages less than perhaps 2,000 to 3,000 revolutions.

FIGURE 4.—Aphelion distances q' plotted against the longitude of aphelion π + 180°. Only meteors with q'< 8 a.u. are shown in the diagram. The curve represents Jupiter’s heliocentric distance. Major showers (mean values) are indicated by circled dots.

Since meteors (see p. 125) originate almost entirely from comets, and since the lines of apsides of comets with aphelia near Jupiter or within its orbit appear not to be concentrated by perturbations by Jupiter, we appear to have a satisfactory explanation of figure 4 in terms of short lifetimes for meteors. The fact that some 60 percent of the meteors exist in identifiable streams or associations is added evidence for their short lifetimes because a number of forces, both physical and gravitational, tend to disturb the stream motions and hide the evidence for comet origin.

Geocentric velocity versus elongation of the radiant.—For certain types of meteoritic orbits our only reliable information is the elongation of the radiant. Hence we present the meteor data in figure 5, where the ordinate is geocentric velocity, VG (corrected for earth’s attraction), and the abscissa is the elongation, λ, of the corrected radiant from the apex of the earth’s motion about the sun. Small values of λ correspond to the high-velocity meteors that make head-on encounters with the earth, while large values correspond to relatively slow meteors that “catch up” with the earth. The continuous curve in figure 5 indicates the parabolic limit in VG . For elongations up to about 60° the observed values describe a curve parallel to the parabolic one, with a rather narrow scatter. Above about 60° in λ the effect of short-period orbits occurs and extends the range of velocities over an area much below the parabolic limit in geocentric velocity. The asteroids with perihelia inside the earth’s orbit would occur near the lower edge of the distribution in figure 5, with a concentration near elongation 90°.

Sources of meteors

With the precise material presented in the previous pages, we may now consider possible sources of these photographic meteors.

Interstellar meteors.—Meteoroids of immediate interstellar origin should travel in hyperbolic orbits about the sun. Table 1 lists 7 meteors with hyperbolic velocities and 2 with parabolic velocities. Among the 7 hyperbolic meteors none is of quality as high as 1.5, while the one parabolic case is of quality 1. Hence, among the 251 meteors of highest quality, there are no hyperbolic and only one parabolic velocities measured. Four of the 7 hyperbolic cases lie among the 36 meteors of poorest quality.

All meteors with nearly hyperbolic velocities have been carefully restudied to search for errors in the calculations and to determine whether uncertainties in the instant of the meteor might lead to a spurious determination of a hyperbolic velocity. In all cases an elliptical solution can be obtained by use of an instant within the common interval of exposure.

No evidence exists that the velocities of identified shower meteors differ significantly from those of the comets with which they are associated. This fact can be used to indicate that the systematic errors in meteoric velocities are small, not exceeding the errors indicated on page 114.

Any hypothesis that hyperbolic meteors are selectively avoided in the photographic meteor program because of their greater apparent velocities appears to be unfounded. Strong evidence indicates that a given body moving at high velocity through the atmosphere produces more light than a similar body at a lower velocity, and that the luminosity dependence is more than linear with the velocity. For meteors of the same intrinsic brightness the camera’s ability to register the meteor varies roughly as the inverse product of distance and velocity. Since faster meteors occur at somewhat higher altitudes than slower meteors, the product is the inverse velocity raised to a power slightly less than unity. Hence the luminosity and the geometric factors combine to favor the photography of more rapidly moving meteors in preference to slower moving ones.

The criteria of selection used here for meteor trails favored the slower meteors because those of highest angular velocity tend to produce fewer shutter breaks; this effect was partially compensated by the inclusion of more of the faster meteors than would have been allowable by strict application of the selection criteria. Hyperbolic meteors, moreover, need not enter the atmosphere with high velocities. The fact that observed borderline cases occur almost entirely in the high-velocity range casts further doubt on the existence of hyperbolic meteors.

The observing program ran continuously through the hours of darkness for more than 2 years; hence any selection factor stemming from a lack of observations in the late night hours versus the early evening hours appears not to be serious.

We conclude, therefore, that hyperbolic meteors constitute, at most, less than 1 percent of our sample—the most precise photographic material yet available—and that there is no strong evidence for the existence of any hyperbolic meteors. This conclusion agrees with that obtained by radio techniques in the researches of McKinley (1951) in Canada, and of Lovell (1949) and associates (see Almond, Davies, and Lovell, 1953) in England.

FIGURE 5. Geocentric velocity VG against the elongation λ of the corrected radiant from the apex of the earth’s motion (all meteors). The curve represents the parabolic velocity at earth’s perihelion.

The occurrence of hyperbolic meteors remains to be demonstrated.

Lunar meteoroids.—It has been suggested recently by Urey (1960) that the encounter between large meteorites and the moon might produce an appreciable number of secondary meteorites from lunar material, which subsequently would have a moderate probability of falling on the earth. In the present collection of 413 meteor orbits only one has a geocentric velocity (VG, corrected for earth attraction) below 9 km/sec. This is meteor No. 4952, which fell on October 19, 1952, with VG=3.41 km/sec. Its hypothetical velocity of ejection from the moon would have been increased by the effect of the earth potential at the moon (1.0 km/sec) and the lunar velocity of escape (2.38 km/sec), so that it would have required a lunar ejection velocity of 4.4 km/sec. The study by Hawkins and Southworth (1958) of randomly selected fainter meteors indicates 6 meteors with velocities of ejection from the moon less than 9 km/sec.

Further criteria are not available for any of these meteors except one. For number 4952, Jacchia (unpublished) finds that its behavior in the upper atmosphere is normal as compared with the average of the other slow meteors.

Of the few meteors that have aphelion distances less than 1.4 a.u.—only 3 out of the 413—all have aphelia less than 1.1 a.u. This fact strongly suggests that the earth, in some manner or other, is responsible for this concentration. This concept is strengthened by the data of Hawkins and Southworth, which indicate that of 12 meteors with aphelia less than 1.3 a.u., 7 have aphelia less than 1.1 a.u. About half the meteors of small q' have geocentric velocities much too great to ascribe to lunar ejection—2 out of 3 among the 413 presented here and 6 out of 12 from the data of Hawkins and Southworth. These ratios suggest that the earth perturbs meteor orbits, possibly by “capture” phenomena as has happened for comets and meteors with aphelia near Jupiter. The capture phenomenon and the concomitant encounter phenomenon are both favored by low orbital inclinations and apsides near the earth’s orbit. Hence the few data available do not answer the question as to whether lunar ejection is likely or not for the very few possible examples.

The lunar ejection theory for meteorites is greatly weakened by the fact that the collisional cross-section of the earth is much greater than that of the moon, by approximately a factor of 16, if we neglect the additional gravitational factors at low relative velocities. Unless the process of formation and ejection of secondary meteorites by encounters between primary meteorites and the moon is extremely efficient, one would expect only a small fraction of the total number of meteorites found on the earth to be of lunar origin. The low velocity of encounter with the atmosphere, required by a lunar ejection mechanism, is not a great compensating factor.

In summary, we find little or no evidence to support the hypothesis of meteoric ejection from the moon, although for photographic meteors the hypothesis is not excluded at approximately the 1 percent level.

Comets and asteroids.—In earlier sections we have shown that no appreciable fraction of the meteors discussed here could have come from sources outside the gravitational control of the sun, or from encounters between larger meteoritic bodies with the moon. Observationally, each of these sources is within the 1 percent level of probability and no evidence proves the existence of either source.

There remain two obvious sources of meteors: comets and asteroids. The only proven source of meteors is cometary. Whipple and Hawkins (1959) identify 12 meteor streams with 9 comets, the association of the η Aquarids and Orionids with Halley’s comet being somewhat uncertain. Tentative identifications of other meteor streams with as many as 20 comets have been made and are fairly probable; the list grows continuously with increasing orbital information on meteors. Incidentally, the present orbital information on meteors now exceeds both in quantity and quality that on comets.

These positive and tentative identifications leave a major fraction of the observed meteors without a known source. In the search for possible asteroidal sources, we must consider the character of asteroid orbits.

If an asteroid is to contribute meteors, its perihelion must lie near or within the earth’s orbit. Only 7 asteroids have been observed to pass within the earth’s orbit; hence our sample for comparison is extremely small. The mean aphelion distance of these asteroids is 2.2 a.u. and the inclinations are generally small. Since we know of only 1 asteroid, Hidalgo, that passes beyond Jupiter’s orbit (neglecting, of course, the Trojans), it seems to be a proper assumption that meteors of asteroidal origin should have aphelia well within Jupiter’s orbit, perhaps concentrated in the major portion of the asteroid belt or its inner reaches. No asteroidal aphelion is known to lie within the orbit of Mars.

No meteor orbit in the present collection appears to be sufficiently like that of any individual asteroid to suggest a specific genetic association. If, then, we eliminate as of asteroidal origin all meteors with aphelia very close to the orbit of Jupiter and beyond, as well as those definitely associated with known comets, we will have reduced the asteroidal source to less than approximately 40 percent. If we choose aphelion distance near and beyond the environment of Jupiter as a criterion for cometary origin, and if we assume in addition that all meteors in streams or associations are of cometary origin, then we reduce the potential asteroidal contribution to less than 11 percent. Since the percentage of the meteors identifiable with streams will increase as a larger number of accurate meteor orbits becomes available, it seems quite safe to conclude, on the basis of these assumptions, that the asteroidal contribution to the present collection of photographed meteors cannot possibly exceed 10 percent. Let us now seek evidence that any of the remaining 10 percent are actually of asteroidal origin.

A somewhat more vivid picture of the distribution of aphelion distances is shown in figure 6, where the meteoric data have been divided into two groups: sporadic, and showers plus associations. The frequency distributions have been compared with the total number of comet passages in the list by Baldet and De Obaldia (1952), except that the orbits listed as parabolic have been excluded because of the generally poor orbital determinations (comparison is properly made between the distribution of all cometary passages and the observed meteoric distribution).[2] The histogram is in terms of the argument (q')–½ and the meteor groups reduced to a common basis of 1000. The three sets of curves are very similar in general character, and suggest that the meteoric orbits are shifted towards somewhat smaller values of q' than the comet orbits. In particular, there is a marked absence of very great aphelion distances among the meteors, while the comets show the well-known heavy concentration near the parabolic limit.

The influence of Jupiter’s perturbations is markedly shown in all three curves, the most striking feature of the distribution function. One has the impression that meteoric orbits are pressing against the Jupiter barrier (Whipple, 1951, 1955; Öpik, 1951). The sporadic meteors include a considerable number of longer period, in comparison to the shower meteors, but otherwise the two distributions are so nearly identical in form that it is difficult to draw any other conclusion than that the two classes of orbits are similar, and that the bodies are probably of the same origin.

A number of other orbital data are available for a comparison among the three groups of elements, for sporadic meteors, showers plus associations, and comets. The distributions of inclinations are similar in character, as noted earlier, and the lines of apsides appear not to give any clues of importance. The K criterion, used earlier by one of the authors (Whipple, 1954) apparently will not be particularly valuable until we have far greater information concerning the asteroids that cross the earth’s orbit. Furthermore, it is not certain that the K criterion is more significant than the distribution of aphelion distances. So many selection factors enter into the cometary statistics as well as the meteor statistics that an exact equality of distributions is hardly to be expected. Other elements than those discussed seem not to add appreciably to a solution of the problem but are entirely consistent with a cometary origin for photographic meteors.

A comparison of the present collection of meteor orbits with those of comets indicates a cometary origin for at least 90 percent of the meteors. If we assume that meteors in streams and associations are of cometary origin, the general similarity of their distribution function with those of the sporadic meteors would indicate no significant difference in origin; therefore, a cometary origin appears likely for practically all meteors. One of the authors (Jacchia, unpublished) can find no significant difference in physical characteristics among meteors with very small orbits of low inclination among typical stream meteors, or among meteors with distinctly cometary orbits. Striking evidence exists that photographic meteors are produced by extremely fragile objects (Jacchia, 1955; McCrosky, 1955), and the forward motions in meteoric trains (Cook and Whipple, unpublished) provide strong indications that photographic meteors may be of extremely low density. Such evidence makes it doubtful that the photographic meteoroid is comparable to the iron or stony meteorites that fall on the earth.

[2] More precisely, the frequencies could be property corrected for the cosmic weight. This has been done but has not been presented here since the histograms are not markedly changed by this weighting factor.

FIGURE 6.—Distribution of aphelion distances for comets, shower meteors, and sporadic meteors. Ordinates are numbers of objects reduced to a standard population of 1,000 in intervals of 0.04 of q' –½ . Comets for which only parabolic orbits had been computed were eliminated from the comet distribution.

The writers are of the opinion that the asteroidal contribution to the photographic meteors probably does not exceed 1 percent of the total and may well be less.

Meteor streams and associations

The selection of meteor streams and associations given in tables 3 and 4 is not intended to be definitive. The dividing line between the terms “stream” and “association” is not rigidly defined. The intent here is to indicate the nature of the streams and associations to be found by intercomparison of a limited amount of rather precise data, the 413 orbits of the meteors listed in table 1, and the 144 brighter orbits previously published (Whipple, 1954). Other investigators might apply more rigid rules or might be constrained to include even more members in the associations.

TABLE 3.— Code for identifying known meteor showers listed in table 1

The large variations that occur in the orbits of certain comets, such as Lexell or Brooks II, must also certainly occur among the orbits of meteors both before and after their ejection from comets. Refined analysis in many cases will undoubtedly indicate widespread variations in the orbital elements of meteors originally produced by the same comets.

We find a number of low inclination streams with components in which the line of nodes is shifted by 180°. This phenomenon was first observed for the Taurid meteors in association with Comet Encke (Whipple, 1940).

TABLE 4.— Identification of tentative meteor associations listed in table 1

[EXPLANATION: (N), northern branch of the stream; (S), southern branch of the stream; parentheses, small camera meteors not included in table 1 but listed in Whipple (1954).]

The fact that 268 out of 413 meteors can be placed in associations—even though the criterion may be somewhat loose—is proof that streaming is a major phenomenon among meteors. This is not surprising when we consider that, on astronomical time scales, the lifetimes of small bodies must be quite finite. On the other hand, the orbital evidences of origin for meteors crossing the orbit of Jupiter would be lost long before an appreciable percentage of the bodies would be eliminated by encounter or major perturbational effects. For orbits lying entirely within that of Jupiter the expectations are not so clearcut. Asteroidal families have long been recognized by their orbital characteristics and presumably must persist over periods of time measured possibly in hundreds of millions of years. The Poynting-Robertson effect alone would destroy such associations, in terms of possible identification, in much shorter times for meteors in the photographic range with masses measured in grams. More research along these lines is urgently needed in order to clarify the time scales applicable to the lifetimes of meteors. We can see that these are measured in terms of a very few thousand revolutions, but other approaches to the problem are highly desirable.

Table 5 gives some tentative identifications of known comets with the meteor associations indicated in table 4. Five of these cometary associations appear quite valid and six others fairly probable. Three are in the extremely doubtful category. As a larger number of precise meteor orbits become available, the number of such identifications will undoubtedly increase. A more definitive identification of meteor streams and cometary associations can be made from a combination of the other photographic evidence available, particularly the concurrent publications by Hawkins and South worth (1961) and by McCrosky and Posen (1961).

TABLE 5.— Possible associations between comets and meteor associations of table 4

Acknowledgments

The writers are indebted to a great many people for the success of this meteor program. An outstanding accomplishment was the design of the unique optical system by James G. Baker and its production by the Perkin-Elmer Corporation. Even so, the optical glass could not have been produced without the aid of the Optics Division of the National Bureau of Standards. In the observational program, the extremely able and devoted efforts of Richard E. McCrosky and Gunther Schwartz are particularly notable. In analysis and reduction, R. E. Briggs and J. R. B. Carmichael have given staunch support. We have profited greatly from technical advice by R. E. McCrosky, A. F. Cook, and G. S. Hawkins. To the above-mentioned collaborators and to many others who have contributed markedly, we wish to express our sincere appreciation and gratitude.

This research was supported by the Office of Naval Ordnance, the Office of Naval Research, the Air Force Cambridge Research Center, Geophysics Research Directorate, the U.S. Army Office of Ordnance Research, and the Smithsonian Astrophysical Observatory.

References

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Abstract

Orbital results are presented for 413 long-trail meteors doubly photographed with the Baker Super-Schmidt cameras in New Mexico and reduced by precise methods. The error in velocity probably does not exceed 0.1 percent for 173 meteors, or 0.4 percent for 181 others.

With such exact material it is now possible to determine definitively the source of meteors in the visual range. The obvious possibilities are interstellar, cometary, asteroidal, and secondary lunar sources.

Meteors of interstellar origin would move in hyperbolic orbits about the sun. The 251 orbits of precision 0.2 percent in velocity include no hyperbolic cases; for 7 hyperbolic orbits among the less precise cases, a long-period solution exists within the possible range of each. Hence more than 99 percent, if not all, must have been gravitational members of the solar system. The orbital data alone indicate that more than 90 percent of these, probably more than 99 percent, must be cometary in origin, while the physical data from decelerations and light curves show no unusual characteristics for the remainder. The number of meteoroids produced by the encounter of meteorites with the moon cannot exceed the 1 percent level of probability among the current selection. Thus comets seem to supply essentially all the visual meteors and probably also smaller meteoroids.

A number of statistical correlations among meteor orbital elements are shown and commented on. Also a preliminary study of meteor streams and associations is made. Several new cometary associations with meteor streams are suggested.