Statistical properties of encounters among asteroids: A new, general purpose, formalism

The statistical properties of asteroid mutual encounters have been studied by several authors, with the main purpose of estimating collisional rates ( and thus mean collisional lifetimes) and the distribution of encounter velo cities. In this paper we present a new approach, conceptually not really di fferent with respect to the classical ones, but implemented with a rather d ifferent mathematical formalism and consequently more flexible. When a comp arison is possible our results are very similar to those obtained by means of other techniques. We exploited the peculiar flexible features of the present formalism to stu dy-in a quantitative way-what happens when special dynamical conditions occ ur, such as a clustering of longitudes of perihelia (as in the so-called Kr esak effect) or of the longitudes of the sample around the longitude (varia ble in time) of Jupiter, as in the case of Trojans. These dynamical situati ons have never been explored in the past using statistical approaches, and the development of the present one can avoid the use of heavy N-body integr ations. Concerning the Trojan asteroids, the results of our analysis, altho ugh discussed here in a simplified version, are satisfactorily compared wit h those emerging from a detailed numerical integration of the orbits (Marza ri et al., 1996, Icarus 119, 192-201). Finally, we used our approach to analyze the statistical properties of impa cts among very large samples of objects with a moderate amount of computer time, thanks to the numerical algorithm, based on a Monte Carlo technique o f integration. We have tested this numerical procedure by comparing our res ults with previous ones published in the literature; we find an amazing agr eement with the more standard and refined numerical methods. (C) 1998 Acade mic Press.