A model of orbital diffusion

It has been reported (Chapman et al. 1989, in Asteroids II, edited by R, P. Binzel, T. Gehrels, and M. S. Matthews, Univ. of Arizona Press, Tucson, p. 386) that the shapes of asteroid families tend to be asymmetric, with a re lative flattening along the line toward the Sun. This article addresses tha t observation. We develop a simple model for this, with an initially locali zed cluster circularly orbiting the Sun in the ecliptic plane, and acted up on by a background of weak stochastic forces. The model's linearized equati ons of motion are such that a component of random force, perpendicular to t he radius, acts back to affect the radial motion. The result is a flattenin g, over time, toward the Sun. (C) 2001 Academic Press.