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 squa re orbital eccentricities and inclinations of a general population of plane tesimals. 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 rec onciled and some minor errors in the earlier work are corrected. The correc ted analytical theory is compared with a series of N-body simulations of on e- and two-component planetesimal systems. For planetesimals on noncrossing orbits, the contribution to velocity evolution is found to be about two ti mes as large as was previously estimated,In addition, N-body simulatiuons s how that the rate of dynamical friction is about 30% less effective at driv ing two-component systems toward equipartition of random kinetic energy tha n is estimated by the theory. When these adjustments are made to the theory , we find remarkable agreement with the N-body simulations. These results e ssentially support previously published estimates for the time scale of run away accretion of planetary embryos. (C) 2000 Academic Press.