The problem of the Kirkwood gaps in the asteroid belt

Abstract

is shown to be valid for both the restricted problem and for the problem with Jupiter's orbit eccentric. (The units are so chosen that the semimajor axis and the mean motion of Jupiter's orbit are unity.) L = L* and R* are the values of L and of the disturbing function after elimination of the short-period terms. r/aL* is zero at n* - L*-3 (p+q)/p. A distribution of the asteroids that is a smooth function of F in the vicinity of the commensurability becomes V-shaped as a function of L* or n* with zero value at the com- mensurability. This is confirmed by the observed distribution. It is conjectured that the crowding of com- mensurabilities in the 3/2 and 4/3 regions accounts for the observed distribution in that part of the asteroid belt.