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.