Mathematics – Probability
Scientific paper
Aug 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989a%26a...220..293n&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 220, no. 1-2, Aug. 1989, p. 293-300.
Mathematics
Probability
42
Collisions, Hill Method, Many Body Problem, Protoplanets, Solar Gravitation, Distribution Functions, Probability Theory
Scientific paper
Particle orbits are studied numerically in the framework of the three-body problem, and the collisional rate between the protoplanet and an ensemble of planetesimals with various orbital elements is found. After reviewing Hill's equations and showing their application to the present problem, a distribution function is described for planetesimals under the assumption of a Gaussian type distribution of their eccentricities and inclinations. An exact expression for the total collision rate between the protoplanet and the planetesimals is found in an integral form, and the collision probability is deduced analytically in the limit of high-speed collisions.
Ida Shigeru
Nakagawa Yasuhiro
Nakazawa Kazuhiro
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