Mathematics – Probability
Scientific paper
Feb 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985azh....62..141z&link_type=abstract
(Astronomicheskii Zhurnal, vol. 62, Jan.-Feb. 1985, p. 141-152) Soviet Astronomy (ISSN 0038-5301), vol. 29, Jan.-Feb. 1985, p. 8
Mathematics
Probability
1
Eccentric Orbits, Planetary Evolution, Solar Orbits, Terrestrial Planets, Fokker-Planck Equation, Inclination, Probability Density Functions, Protoplanets, Root-Mean-Square Errors
Scientific paper
Consideration is given to the evolution of eccentricity and inclination in the orbit of an accumulating terrestrial planet following collisions or encounters with a swarm of bodies. It is shown that encounters, being more numerous, have a more powerful influence on the evolution of the orbits. Differential equations are derived describing the variation of the mean square of the inclination with the growth of the planetary mass. The eccentricity and incllnation of the planetary orbits were found to be smaller than the corresponding quantities for bodies of the swarm. The difference was equal to about the sq rt of m bar prime/m, the average mass of bodies in the swarm divided by the mass of the planet. A solution is obtained to the Fokker-Planck equation for the distribution of the eccentricity and inclination. The results are compared with observations of planetary embryos and the known evolutionary history of the solar system.
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