An algorithm for determining collision probabilities between smallsolar system bodies

Abstract

The introduction of surveys (e.g. Spacewatch, OCA-DLR) dedicated to the discovery of asteroids and other small bodies is likely to increase the number of known objects to many times the current figure of roughly 30 000. Previous methods for determining collision probabilities amongst these objects (e.g. those due to Öpik, Wetherill, Greenberg and Kessler) all have idiosyncrasies which make them inappropriate for analyses of interactions between large numbers of solar system bodies. Here we present an adaptation of the Wetherill and Greenberg methods, which avoids approximations made by Öpik but which remains accurate and fast enough in its implementation to allow the direct analysis of the collision probabilities and impact velocities of thousands of potentially colliding objects.