Mathematics – Probability
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.p23e0109o&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #P23E-0109
Mathematics
Probability
6265 Planetary Rings
Scientific paper
We examine gravitational capture probability of colliding particles in planetary rings and accretion rates of small particles onto an embedded moonlet, using analytic calculation, three-body orbital integration, and N-body simulation. Taking into account a Rayleigh distribution of particles' orbital eccentricities and inclinations, we derive an analytic expression for the capture probability, which reproduces numerical results when rp < 0.01 and v/ve > 1 (rp is the ratio of the sum of the physical radii of colliding particles to their mutual Hill radius, and v/ve is the ratio of their relative random velocity to their mutual escape velocity). Numerical results of three-body orbital integration that accounts for the Rayleigh distribution of particles eccentricities and inclinations show a rather steep decrease of the capture probability when v/ve > 1. The probability is also found to decrease rather abruptly when rp > 0.7 as shown by our previous work (Ohtsuki 1993, Icarus 106, 228), although the probability is non-negligible even for rp=0.8 when v/ve < 1 and collisions are sufficiently dissipative. Numerical results of N-body simulation for accretion of small particles by a moonlet show agreement with the above three-body results in the initial stage of accretion, but the accretion rate is reduced as particles start to fill the moonlet's Hill sphere.
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