It has been repeatedly suggested, on the basis of visual and radar observations, that meteors often appear in pairs or larger groups, within short time intervals. They usually have some similar characteristics (brightness, path, etc.) so they easily attract the observer's attention. This phenomenon could be a result of chance and only an analysis of its frequency can give an answer whether there is any a priori reason for it. The possible reality of this grouping has been studied by some authors. However, their observing data contained only meteors brighter than +8m, and did not yield unambiguously acceptable evidence for existence of real pairs in this range and said nothing about the region of very small meteors.

The paper consists of three sections:

1. (1) In continuation of a previous paper by the author, on 154 minor meteor streams, elements of orbits and other data are presented for an additional 95 minor streams (most of them less active). These streams have been found both by the studies of the photographic orbits of meteor bodies known before, and from the visual radiants of faint showers.

2. (2) The problems of a possible family of six minor meteor streams associated with the Lexell comet 1770-I, and the connection between nine other minor streams and long-period comets, are examined. The assumption is made that nearly-parabolic comets may be accompanied by meteor streams of considerable width.

3. (3) Radiants and elements of the orbits for 30 meteor bodies of the Cyclids are described, as were established by photographic data. Perturbed motion of one such meteor body is investigated by numerical integration of differential equations of motion on the electronic computer BESM-2, using Cowell's method of quadratures and taking account of perturbations from six planets (Venus–Uranus) and of high-order terms through to the 4th order. Over the time interval studied of 45 years the orbit of the Cyclids has been stable. Perturbing action of the Earth does not lead to any substantial changes in the elements of the orbits. Even at close approaches of the order of 0–003 AU the changes in the angular elements are not greater than about 1°.

A search for major streams has been performed among the orbits of meteors observed with the six station meteor radar of the Harvard-Smithsonian Radio Meteor Project at a limiting radio magnitude of about + 10 on the visual scale.

The analysis of the Geminid shower from observations made in December 1961, 1962, 1963 and 1964, shows some evidence that meteors belonging to this stream are detected at an earlier date than the bright photographic meteors. From observations made on December 28–31 of the same years during the hours in which the Geminid radiant is within the collecting area of the six station system, 15 orbits were identified as possible members of the shower.

It is suggested that the stream might be active for a period longer than the previous observations indicated.

Hourly rates of meteor echoes are presented, and it is shown that the peak activity occurred at solar longitude 234°. 457 in 1965, and 234°. 466 in 1966 (mean equinox 1950·). The exponent s is calculated from distribution of echo durations and its variation with date is given.

In connection with the expected passage of the Earth through the densest part of the Leonid meteoric stream in November, 1966, the Commission on Comets and Meteors of the Astronomical Council of the U.S.S.R., and the All-Union Astronomical-Geodetic Society, organized visual, photographic and radar observations of the shower at many points in the Soviet Union.

The investigation is based on a system of elements, obtained from the best observations made in England during the maximum of the meteor shower 1866. This system represents the most probable orbit of that part of the stream, which passed perihelion during the years 1864–67 and was later given the name of Ortho-Leonids. Seventeen points (meteor groups) have been chosen on this orbit, and differential equations of their motion have been integrated on the electronic computer BESM-2 by Cowell's method of quadratures, taking account of perturbations from eight planets (Venus–Pluto), with a variable step from 0·001 to 40 days and taking account of differences through to the 4th order. The motions of two groups (XI and XII) have been investigated in an interval of 300 years (1700–2000), and the motions of the rest of the groups for a space of 135 years (1866–2000). All the close approaches of these groups to the Earth, Jupiter, Saturn and Uranus have been determined. The results of integration are given in the tables, which clearly represent the evolution of the orbit of every group. It has been found that the basic factors determining the evolution of separate groups, and of the stream as a whole, are the close approaches to the outer planets. The perturbations by these planets, especially by Jupiter and Saturn, determine the conditions for an encounter of the meteor groups with the Earth, and cause a change in the activity of the Leonid shower at different apparitions. Apparitions of the Leonids have been investigated for the last millennium, and in more detail for the last 180 years. It has been stated that the orbit of the Ortho-Leonid stream remained stable over the interval of 1000 years; its stability has been confirmed by calculations during the last 300 years, and the limits of changes of its elements have been computed. The perturbing influence of the Earth on the motion of meteor bodies in its sphere of action has been investigated. It turns out that at exceptionally deep penetrations of meteor bodies into this sphere of action, at a distance of some 1000 km from the Earth, its perturbations can essentially transform the orbit of a meteor body, e.g. reduce its period of revolution by some years, and materially change the eccentricity of the orbit, its inclination, etc. Conditions for an encounter of the stream with the Earth in the period 1898–2000 have been clarified, and forecasts have been made for the times of maximum activity of the shower in the years 1966–68. In 1967 the maximum activity of the Leonids is predicted to occur from November 17, 18h to November 18, 1h UT.

The aim of our investigation was the determination of the epoch of the Leonid maximum for the return in 1966. We applied the same method, which has been used by Stoney and Downing (1899) for the investigation of motion of Leonids in 1899, e.g. method of variation of elements. Our attention has been concentrated on the motion of the position of the line of nodes, which is one of the important characteristics for the epoch of maximum activity of the shower. We started with the Adams elements – deduced from the splendid appearance of Leonids 1866, as did Stoney and Downing. We chose a 40-day interval for the integration step of perturbations as the most convenient, because all the positions of the great planets are tabulated with this interval in Washington tables (Eckert et al., 1951). Only the perturbations due to Jupiter, Saturn and Uranus during the years 1866–1966 have been considered as decisive for the motion of the Leonids' nodes. The computations for the epoch 1866–99 – divided into five parts – have been compared with those obtained by Stoney and Downing, with the results shown in Table 1.

The basic material of this discussion is being published under the title ‘On Maintaining the Meteoritic Complex’.* The assumed meteoritic influx on the Earth is derived from measurements of penetration of space vehicles, radio and photographic meteors, meteorite falls, Apollo asteroids, lunar craters, and comets (see Figure 1). I assume that the much higher impact rates from acoustic measures of dust and from collections do not measure the true influx rate. The total flux is some 2 × 10−16 g cm−2 sec−1 on the surface of a corresponding non-gravitating sphere. I take the equivalent space density of some 2 × 10−22 gm cm−3 as applicable over a volume of some 3·5 AU radius about the Sun and i<20° of the ecliptic, giving a total mass of 4·5 × 1019 gm for particles of mass < 102gm. For Earth-crossing orbits the total mass is some 1·3 × 1019 gm. I adopt 2·5 × 1019 gm for the total mass.

All known dissipating or destructive factors are included in determining the ‘ecology’ of the meteoritic material. Direct light pressure quickly eliminates particles of the order of 1μ or less in dimension while the solar wind drives away all gases. The Poynting-Robertson effect (PR-effect) is effectively increased by some 22% because of the pseudo PR-effect of the solar wind. Direct sublimation of earthy solids is significant only near the Sun while sputtering losses produced by the solar wind are real but effectively small (~ 10%) compared to spiralling rates by the PR-effect. Magnetic-field, charge and rotation effects may quite possibly be significant but are not yet subject to precise calculations.

Space erosion has been demonstrated for stony meteorites and cometary meteoroids (see Table 1). A totally destructive collision is assumed to occur when a particle of mass m is struck by another with mass ≥m/3200. Gravitational elimination effects for the Earth and Venus (time ~ 108 yr), Mars (time ~ 6 × 109 yr) and Jupiter (time ~ 106 yr) are, following öpik, assumed to be negligible for the small Zodiacal Cloud particles, compared to the dissipative effects included above.

The mean lifetimes for small particles of mass m are calculated crudely and presented in Table 2 along with the assumed distribution function in mass. The corrected (factor 1/1·3) PR-lifetime is indicated by τPR, erosion by particles of mass < m/3200 by τe, collisional destruction by particles of mass ≥ m/3200 by τc, and the mean lifetime including all these effects by τ.

The mean lifetime is much less dependent on mass than might be expected. Averaging all the particles according to mass distribution and τ, the weighted mean lifetime for all material of m< 102gm comes out 8 × 104 yr. Combining this mean lifetime with a total mass of 2·5 × 1019 gm, the average total-input rate to maintain the Zodiacal Cloud in quasi-equilibrium becomes some 10 tons sec−1. Note that this input rate may be considerably overestimated because I have not included the contributions to the cloud by broken fragments.

It appears quite possible that comets can supply the needed 10 tons sec−1 injected into orbits totally within that of Jupiter. Fragile carbonaceous chondrites and ‘half-baked asteroids’ (see Appendix), however, may compete with comets in contributing to the fireballs and possibly to the visual meteors. The stony meteorites may be maintained by collisional spallation from Earth-crossing asteroids induced by smaller bodies, the Apollo asteroids being derived from the asteroid belt by the gravitational effects of Mars. The data and theory are not yet adequate to provide a definitive solution to the problem of asteroidal vs. cometary origin for the Apollo asteroids.

One asks whether McCrosky's fireballs might have originated directly from comets, not primarily from Apollo asteroids. Jupiter crossings (τ ~ 106 yr) might have eliminated most of the orbits with aphelia beyond Jupiter's. A rough calculation failed by a factor of 3–5 in accounting for the reduction in numbers of orbits with large aphelion distances among McCrosky's fireballs as compared to the number among photographic meteors. This leaves the question essentially unsolved but also allows the possibility that a considerable fraction of McCrosky's fireballs may be of direct cometary origin, in typical short-period comet orbits, rather than Apollo-asteroid fragments.

A collisional model for interplanetary debris, formulated earlier by the writer, is applied presently to the problem of asteroids and their debris. Following observational evidence, a population-index type-number density function is assumed. The integro-differential equation describing the evolution of a system of colliding brittle particles derived earlier is satisfied for this special case. The result is a stable steady state solution subject to certain boundary conditions. It is found that catastrophic collisions dominate over the erosion process in the present steady state model.

Using a root mean-squared average collision velocity of 5 km/sec, the population index, α, for asteroids is calculated to be α = 1·837. This value of α is rather insensitive to the physical parameters and is within the margin of error of an empirical least squares fit by the writer α = 1·80 ± ·04 to the distribution of asteroids reported by Kuiper et al. If the largest three asteroids are statistically interpreted, the distribution of asteroids in the asteroidal belt is consistent with the present collisional model. This would imply that most asteroids are fragments from some parent object(s).

The theoretical distribution is normalized to the observed number of asteroids in the survey by Kuiper et al., and using the present theory various statistical properties of the population of asteroids and their debris are calculated. The total mass of objects in the asteroidal belt is almost entirely concentrated in the masses of the three largest objects. The total asteroidal mass, crushed yearly, is of the order of 1012 kg and the rate of mass loss to radiation forces is about 7 × 1010 kg/yr.

The mean lifetime of large asteroids is found to be of the order of 108–109 years. The lifetime of objects is limited by the probability of catastrophic collisions; erosion and radiation damping only have a minor influence on the particle lifetimes.

The erosion rate of the largest objects is of the order of 1m /106 yr, and this rate decreases for smaller objects. Comparison with erosion rates estimated by Whipple indicates that the lifetimes, with respect to erosion, of objects smaller than about 1 kg may be dominated by collisions with cometary particles.

The observed properties of non-gravitational effects in the motion of the short-period comets are described in connection with the possible mass-loss processes in their nuclei. The impulses on the nuclei have been found to be about 1 cm/sec to 3 m/sec per revolution. The contributions to the observed dynamic anomalies of gas- and dust-matter ejections from the nucleus into the comet's atmosphere are estimated. The existence of meteor showers is related to the characteristics of cometary activity. Methods of further investigations are suggested.

Halliday: We are now approaching the end of a busy week – one which has been both scientifically profitable and completely enjoyable for us all. I have been asked to make some comments in the form of a brief summary of our discussions during the first half of the symposium, covering the field of meteor physics. So many topics were presented that my summary must necessarily be incomplete, but I hope it may serve to introduce some further exchange of ideas this morning.

Whipple: It is quite impossible for me to make a proper summary of the many major contributions on meteors presented at this most exciting symposium, and I shall make no attempt to do so. I can better point out trends and possible goals. First a reminiscence. It is more than 30 years ago when I first began seriously to study the problems of meteors. A major expectation then concerned hyperbolic meteor orbits, or meteoroids originating in interstellar space. We knew, of course, that many meteors came from comets and supposed that some of the sporadic meteors came from asteroids. These problems appear now to be largely solved, although the negative results with regard to hyperbolic meteors are definitive only at the 1% level. With our more precise instrumentation and continued observations I would not be too surprised if we might someday find an interstellar meteor. The expectation might be as high as 10−4 among observed meteors. The contribution of the asteroid belt, particularly carbonaceous chondrites or whatever similar fragile bodies are indicated by McCrosky's observations of the fireballs, is truly uncertain. Both Ceplecha and Kresák have shown some strong evidence that we cannot discount possible asteroidal contributions among the photographic meteors.