MAPPING THE EFFECTS OF DISTANT PERTURBATIONS ON PARTICLE-PLANET INTERACTIONS

Monte-Carlo codes generally treat planestesimal-planet encounters usin g the two-body scattering approximation, which can be inaccurate when relative velocities are low; however, Monte-Carlo codes using the two- body approximation frequently produce results consistent with more acc urate codes using numerical integration, To better understand why this breakdown occurs at low velocities, and to test a hypothesis from Gre enberg et al. (1988, Icarus 75, 1-29) that may explain the unexpected accuracy of Monte-Carlo codes, we numerically integrate test body traj ectories using a unique set of orbital elements defined by the geometr y of the two-body approximation. This new coordinate system is ideal f or examining the effects of distant planetary perturbations on particl e trajectories all the way to encounter with the planet. Our results s how that the failure of the two-body approximation is caused by distan t 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 pl anet, we found that some test bodies, whose approach orbits were shift ed by distant planetary perturbations, were then replaced by similarly shifted nearby test bodies. The ''particle replacement'' mechanism ex plains why Monte-Carlo codes frequently yield outcome results comparab le to numerical integration results, Moreover, we found that the relat ive velocity of a test body at encounter is not the critical parameter in determining the ''breakdown'' of two-body scattering outcome stati stics; instead, we found that the semimajor axis of the test body rela tive to the size of the planet's Hill sphere (or the synodic period of the test body when mass is included) is much more diagnostic. Thus, o ur results verify that Monte-Carlo models can yield statistically accu rate results, even if individual particles do not behave as assumed in those codes. (C) 1997 Academic Press.