A New Approach to Evaluate Collision Probabilities Among Asteroids, Comets, and Kuiper Belt Objects

A new method to evaluate the longterm collision probabilities between orbiting objects has been developed. It is designed to work with any orbital evolution model to estimate the collision probabilities of a system (asteroids, comets, Kuiper Belt objects, or planetesimals) as the system evolves in time. Contrary to Opik's classical method based on uniform sampling in space, this method is based on uniform sampling in time. Since orbital elements are updated frequently rather than based on some assumptions, this dynamical approach is more general than Opik's. When applied to an Opik system - a system of objects with fixed semimajor axes (a), eccentricities (e), and inclinations (i), and randomly distributed right ascensions of the ascending node (Omega), arguments of pericenter (omega), and mean longitudes (lambda), this method yields results that are consistent with those obtained using Opik's method.