Other
Scientific paper
Feb 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996icar..119..261c&link_type=abstract
Icarus, Volume 119, Issue 2, pp. 261-268.
Other
139
Scientific paper
A system of two small planets orbiting the Sun on low-eccentricity, low-inclination orbits is stable with respect to close encounters if the initial semi-major axis difference, Delta, measured in mutual Hill radii, R_H, exceeds 2\sqrt{3}, due to conservation of energy and angular momentum. We investigate the stability of systems of more than two planets using numerical integrations. We find that systems with Delta < 10 are always unstable, with the time, t, of first close encounter given approximately by log t = bDelta + c, where b and c are constants. It is likely that systems with Delta > 10 are also unstable. The slope b depends weakly on the number of planets, but is independent of planetary mass, m, if we measure Delta in units that are proportional to m^1/4 rather than the usual R_H ~ m^1/3. Instability in multi-planet systems arises because energy and angular momentum are no longer conserved within each two-planet subsystem due to perturbations by the additional planet(s). These results suggest that planetary embryos will not become isolated prior to the final stage of terrestrial-planet formation simply due to a failure to achieve close encounters. Other factors leading to isolation cannot be ruled out at this stage.
Boss Alan P.
Chambers John E.
Wetherill George W.
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