basic method for estimating such parameters should therefore be useful for asteroid and related investigations.
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 II. APPLICATION OF THE PROBABILISTIC estimating collision rates and velocities of all asteroids in the COLLISION MODEL TO MULTIPLE TARGETS main belt with each other. The results obtained are compared with those obtained by previous investigators using other meth-Previously, a new method was described (Paper 1) and ods. The new method yields main belt collision probabilities then used to estimate the collision probability of a single about 10-15% higher than earlier results, and the impact veloctarget object with a large set of asteroids that can collide ity distribution is shifted downward by about 20%. Analysis with it. It will now be shown how this same method can of the velocity components shows that the most significant also be used to estimate the collisional probability of a difference is in the component normal to the plane of the large population of asteroids with each other.
ecliptic, with the new method yielding a higher likelihood of this Z component having a low magnitude. The nonnormal Just as before, a simulation of the long-term relative distribution of the Z component in previous results may be due motion of a large, representative set of asteroids is conto underestimating the collision probability for nearly coplanar ducted. Once more the assumption is made that the distrior nearly tangent orbits. For these frequently occurring cases, bution of distances between arbitrary pairs of asteroids the new method may well have advantages, because it is singuover a long time interval is equivalent to the distribution larity-free and does not depend on an elaborate and very sensiobtained by sampling an ensemble of such systems at a tive analytical model of the geometry of close encounters. Β© 1998 given time. This again implies that these systems can be Academic Press characterized as essentially random processes which are