Velocity evolution of planetesimals:: Unified analytical formulas and comparisons with N-body simulations

Analytical formulas are derived for the rates of evolution of the mean square orbital eccentricities and inclinations of a general population of planetesimals. For planetesimals on crossing orbits, the derivations based upon the local-velocity formalism of P. Hornung et al. (1985, Icarus 64, 295-307) and upon the Hill-variable formalism of S. Ida et al. (1993, Mon. Not. R. Astron, Soc.) and H. Tanaka and S. Ida (1995, Icarus 120, 371-386) are reconciled and some minor errors in the earlier work are corrected. The corrected analytical theory is compared with a series of N-body simulations of one- and two-component planetesimal systems. For planetesimals on noncrossing orbits, the contribution to velocity evolution is found to be about two times as large as was previously estimated,In addition, N-body simulatiuons show that the rate of dynamical friction is about 30% less effective at driving two-component systems toward equipartition of random kinetic energy than is estimated by the theory. When these adjustments are made to the theory, we find remarkable agreement with the N-body simulations. These results essentially support previously published estimates for the time scale of runaway accretion of planetary embryos. (C) 2000 Academic Press.