The range of validity of the two-body approximation in models of terrestrial planet accumulation. I - Gravitational perturbations

Details The range of validity of the two-body approximation in models of terrestrial planet accumulation. I - Gravitational perturbations The range of validity of the two-body approximation in models of terrestrial planet accumulation. I - Gravitational perturbations

Oct 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984icar...60...40w&link_type=abstract

Icarus (ISSN 0019-1035), vol. 60, Oct. 1984, p. 40-55.

Mathematics

39

Gravitational Effects, Planetary Evolution, Protoplanets, Terrestrial Planets, Two Body Problem, Accumulations, Perturbation Theory, Planetary Nebulae, Three Body Problem, Planets, Two-Body Problem, Models, Terrestrial Planets, Perturbations, Gravity Effects, Eccentricity, Inclination, Planetesimals, Calculations, Mathematical Models, Monte Carlo Methods, Orbits, Evolution, Analysis, Velocity, Escape, Trajectories

Scientific paper

The validity of the two-body approximation in calculating gravitational perturbations resulting from close encounters of planetesimals is evaluated. Gravitational perturbations in semimajor axis, eccentricity, and inclination resulting from encounters out to Tisserand sphere of influence radii are computed by two- and three-dimensional numerical integration and the results are compared with those obtained by treating the encounter as a two-body problem. It is concluded that the two-body approximation fails to describe the outcome of individual encounters because the two-body 'gravitational focusing' cross section is not valid in this low-velocity region. The Arnold extrapolation, whereby a few very close encounters are used to estimate the effect of many more distant encounters, is found to be a useful approximation in this velocity range.

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