Probabilities of Collisions of Asteroidal and Cometary Particles With Planets: Analytical Technique

Details Probabilities of Collisions of Asteroidal and Cometary Particles With Planets: Analytical Technique Probabilities of Collisions of Asteroidal and Cometary Particles With Planets: Analytical Technique

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998dda....30.0701g&link_type=abstract

American Astronomical Society, DDA meeting #30, #07.01; Bulletin of the American Astronomical Society, Vol. 30, p.1143

Mathematics

Probability

1

Scientific paper

Close approaches between the minor bodies of the Solar System and the major planets have thus far been considered mainly by Opik-type Monte-Carlo codes. Assuming that both the planets and the test bodies are on independent keplerian orbits, with uniformly precessing apsides and nodes around the Sun (the orbits are considered unperturbed unless they enter a planet's sphere of influence), those codes compute the probability that a given test body will encounter that sphere without actually integrating the orbit of each body. Here, based on our recent papers (1997, ApJ 488, 268; ApJ 474, 496), we propose a convenient analytical technique to evaluate the probability that a given test body with orbital parameters a,e,i will encounter the Hill sphere of a given planet. As an application, we compute the probabilities of close encounters with the planets for small cometary and asteroidal particles drifting toward the Sun due to the Poynting-Robertson drag. This enables us to evaluate the role that the gravitational scattering of interplanetary particles by planets plays in the dynamics of the zodiacal dust cloud. Both for large and small particles produced by bodies crossing Earth's orbit, we compute the distributions in velocity and orbital parameters a,e,i (for `large' particles, as opposite to `small' ones, the P-R drift does not change their a,e). We discuss how to extend this technique to tackle (i) mutual collisions of asteroids and (ii) mutual collisions of interplanetary particles.

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