In Part I, several early papers are reviewed. In Part II, a theory of fragmentation is developed, based not on statistical treatment of many collisions as has been done earlier, but rather on the physics of a single collision. In Part III, the fragmentation theory is applied to the original distribution of asteroid masses found by Anders, to show that this distribution will migrate toward that presently observed. In Part IV, we consider the tendency for fragmentation to produce a steady state mass distribution, and conclude that B, the slope in a log-log mass distribution, will tend toward a value 2 3 except at masses less than roughly 10 8 gm, where certain physical effects produce a steeper slope. In Part V, we estimate the total number of parent bodies (i.e., those belonging to Anders' initial mass distribution) required to provide the present number of asteroidal fragments, and conclude that in the zone 2.15 to 2.6 a.u., 5 to 30 such bodies, each of mass greater than several times 10 20 gm, have been broken. In Part VI, we attempt to relate the buildup of particles in the asteroid belt to the time history of meteoritic flux observed on the Earth. Anders' model of meteorite origin among the “Mars asteroids” is used. A critical factor is the half-life against perturbation by Mars into Earth-crossing orbits, found to be about 1 × 10 9 years. This produces an exponential depletion of the meteorite pool. The short cosmic ray exposure ages of meteorites is attributed to (1) this depletion effect, (2) grinding and refragmentation, especially of stones, and (3) a possibly statistical excess of recent major collisions. The flux near the Earth has increased nearly linearly but with a superimposed sawtooth effect caused by discrete collisions and the relatively short perturbation half-life. The total cratering flux, composed of large fragments and a possible nonsteroidal component but excluding anomalous early effects, is now roughly a factor 2 above its average value over solar system history unless recent major cillisions have occurred, a conclusion of importance in interpreting planetary surfaces. In Part VII, these results are contrasted with other literature, in particular an earlier suggestion that the flux has increased exponentially by a factor 50 over its average value. Part VIII applies the results of this paper in an attempt to explain properties of meteorites as observed on Earth, and predicts the terrestrial flux of asteroidal meteorites.
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