Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........49s&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF CALIFORNIA, LOS ANGELES, 1982.Source: Dissertation Abstracts International, Volume: 43-01, Sectio
Astronomy and Astrophysics
Astrophysics
1
Scientific paper
A kinetic theory is developed for calculating the velocity evolution of planetesimal populations in order to improve recent models of terrestrial planet formation. The theory is based on a Boltzmann equation in a rotating reference frame which describes the evolution of the planetesimal's orbital eccentricities and inclinations in terms of the distribution of random velocities relative to the reference circular orbit defined by the orbital angular momentum. The effects of mutual gravitational interactions and inelastic collisions are respectively modeled with a Fokker-Planck equation and a modified Boltzmann collision integral. The three dominant mechanisms for change in the random kinetic energy are found to be (1) energy dissipation by inelastic collisions, (2) energy transfer from large bodies to small bodies by gravitational encounters, and (3) energy transfer from circular reference orbit motion to random motion by viscous stirring. For the orbital case of a uniform mass distribution of planetesimals, the calculated velocity evolution is in good agreement with the numerical simulations done by G. W. Wetherill (Ann. Rev. Astron. Astrophys. 18, 77, 1980). For populations consisting of two different mass components, however, the present work predicts larger velocities for the smaller bodies and smaller velocities for the larger bodies compared to previous analytical theories because they neglected mechanism (2). A more rigorous derivation of mechanism (3) yields a larger viscous stirring rate of small bodies by gravitational encounters with large bodies which also leads to a larger velocity for the small bodies as well as nearly equal rates of radial drift associated with the angular momentum transport for both components. Calculations of the velocity evolution of two -component populations with simultaneous mass growth by accumulation indicate that when a significant fraction of the mass is contained in the smaller bodies, the equilibrium velocities are attained rapidly enough to keep pace with the mass evolution. When most of the mass is contained in the large bodies, however, the random velocities exceed their equilibrium values because the equilibration time is comparable to the mass growth time.
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