Mapping the effects of distant perturbations on particle-planet interactions

William F. Bottke, Richard J. Greenberg, Andrea Carusi, Giovanni B. Valsecchi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Monte-Carlo codes generally treat planestesimal-planet encounters using 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 accurate codes using numerical integration. To better understand why this breakdown occurs at low velocities, and to test a hypothesis from Greenberg et al. (1988, Icarus 75, 1-29) that 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 orbits were shifted by distant planetary perturbations, were then 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. Moreover, we found that the relative velocity of a test body at encounter is not the critical parameter in determining the "breakdown" of two-body scattering outcome statistics; instead, we found that the semimajor axis of the test body relative 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, our results verify that Monte-Carlo models can yield statistically accurate results, even if individual particles do not behave as assumed in those codes.

Original languageEnglish (US)
Pages (from-to)288-301
Number of pages14
JournalIcarus
Volume125
Issue number2
StatePublished - Feb 1997

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planets
planet
perturbation
interactions
encounters
scattering
trajectory
geometry
approximation
numerical integration
test
particle
effect
low speed
breakdown
body mass
code
replacement
orbital elements
particle trajectories

ASJC Scopus subject areas

  • Space and Planetary Science
  • Astronomy and Astrophysics

Cite this

Bottke, W. F., Greenberg, R. J., Carusi, A., & Valsecchi, G. B. (1997). Mapping the effects of distant perturbations on particle-planet interactions. Icarus, 125(2), 288-301.

Mapping the effects of distant perturbations on particle-planet interactions. / Bottke, William F.; Greenberg, Richard J.; Carusi, Andrea; Valsecchi, Giovanni B.

In: Icarus, Vol. 125, No. 2, 02.1997, p. 288-301.

Research output: Contribution to journalArticle

Bottke, WF, Greenberg, RJ, Carusi, A & Valsecchi, GB 1997, 'Mapping the effects of distant perturbations on particle-planet interactions', Icarus, vol. 125, no. 2, pp. 288-301.
Bottke, William F. ; Greenberg, Richard J. ; Carusi, Andrea ; Valsecchi, Giovanni B. / Mapping the effects of distant perturbations on particle-planet interactions. In: Icarus. 1997 ; Vol. 125, No. 2. pp. 288-301.
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