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 relative flattening along the line toward the sun. This article addresses that observation. We develop a simple model for this, with an initially localized cluster circularly orbiting the Sun in the ecliptic plane, and acted upon by a background of weak stochastic forces. The model's linearized equations of motion are such that a component of random force, perpendicular to the radius, acts back to affect the radial motion. The result is a flattening, over time, toward the Sun.
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