On the original distribution of the asteriods. I.

Abstract

The depletion of an initially uniform distribution of asteroids extending form Mars to Saturn, caused by the gravitational perturbations of Jupiter and Saturn, is calculated by numerical integration of the asteroid orbits. Almost all (about 85%) the asteroids between Jupiter and Saturn are ejected in the first 6000 years Most of the asteroids between the $\text{2}\text{3}$ Jupiter resonance (4.0 A.U.) and Jupiter are ejected in the first 2400 years with the exception of the stable librators (e.g., the Hilda group). Interior to the $\text{2}\text{3}$ resonance the depletion was small, and interior to the $\text{1}\text{2}$ resonance (3.3 A.U.) no asteroids were ejected in the first 2400 years.