Main belt asteroid collision probabilities and impact velocities

A new method for estimating asteroid collision probabilities and impact velocities (Vedder 1996, Icarus, 123, 436-449) is extended from single to multiple targets. It is then applied to estimating collision rates and velocities of all asteroids in the main belt with each other. The results obtained are compared with those obtained by previous investigators using other methods. The new method yields main belt collision probabilities about 10-15% higher than earlier results, and the impact velocity distribution is shifted downward by about 20%. Analysis of the velocity components shows that the most significant difference is in the component normal to the plane of the ecliptic, with the new method yielding a higher likelihood of this Z component having a low magnitude. The nonnormal distribution of the Z component in previous results may be due to underestimating the collision probability for nearly coplanar or nearly tangent orbits. For these frequently occurring cases, the new method may well have advantages, because it is singularity-free and does not depend on an elaborate and very sensitive analytical model of the geometry of close encounters. (C) 1998 Academic Press.