"Mapping the Effects of Distant Perturbations on Particle-Planet Interactions"

W. F. Bottke, Jr., R. Greenberg, A. Carusi, G. B. Valsecchi

(1997) Icarus 125, 288-301

Monte-Carlo codes generally treat planetesimal-planet encounters using the two-body scattering approximation, which becomes inaccurate for low velocity encounters (i.e., near the planets escape velocity). However, Monte-Carlo codes using the two-body approximation frequently produce results consistent with more accurate codes using numerical integration (Wetherill and Cox 1985a,b). To better understand why this breakdown occurs, and to test a hypothesis from Greenberg et al. (1988) which may explain the unexpected accuracy of Monte-Carlo codes, we numerically integrate test body trajectories using a unique set of orbital elements defined by the geometry of the two-body approximation. This new coordinate system is ideal for examining the effects of distant planetary perturbations on particle trajectories all the way to encounter with the planet.

Our results show that the failure of the two-body approximation is caused by distant planetary perturbations modifying the approach geometry of the test bodies; behavior at encounter follows two-body scattering even at very low relative velocities. By testing particle swarms encountering a planet, we found that some test bodies, whose approach orbit was shifted by distant planetary perturbations, were replaced by similarly-shifted nearby test bodies. The "particle replacement" mechanism explains why Monte-Carlo codes frequently yield outcome results comparable to numerical integration results. Thus, our results verify that Monte-Carlo models can yield statistically accurate results, even if individual particles do not behave as assumed in those code.

For more information, contact Bill Bottke:bottke@astrosun.tn.cornell.edu