Comparison with other methods shows that the algorithm does not suffer from the same limitations as those of Öpik and Wetherill, and while its assumptions are similar to those of Greenberg the choice of reference frame makes the algorithm faster. Although this algorithm is much slower than use of Öpik's simple equations, it is still fast enough to carry out large numbers of comparisons, typically allowing several comparisons to be made per second on a desktop PC at 4 significant figure accuracy (cf. Vedder 1996, 1998; Dell'Oro & Paolicchi 1997).
At this precision large-scale surveys of collision rates in the solar system become possible, and the entire population of known asteroids can be analysed in a matter of hours. This opens the door to realistic simulations of collision rates in many new classes of problem, for example detailed particle generation rates resulting from collisions in the zodiacal cloud, asteroid belt and Edgeworth-Kuiper belt. The source code is available on request from the first author.
SPM and FM thank the organizing committee of the Maratea NATO Advanced Study Institute "Small Bodies in the Solar System" for support whilst part of this work was carried out; the work was also supported by the EU-HCM contract CHRX-CT94-0445 (FM) and DENI (SPM). The authors thank M. Carpino, J. Fernández and A. Fitzsimmons for helpful comments and discussions, and especially P. Farinella for detailed comments and suggestions which have greatly improved the manuscript.
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