THE STABILITY OF MULTI-PLANET SYSTEMS

A system of two small planets orbiting the Sun on low-eccentricity, lo w-inclination orbits is stable with respect to close encounters if the initial semi-major axis difference, a, measured in mutual Hill radii, R(H), exceeds 2 root 3, due to conservation of energy and angular mom entum. We investigate the stability of systems of more than two planet s using numerical integrations. We find that systems with Delta < 10 a re always unstable, with the time, t, of first close encounter given a pproximately by log t = b Delta + c, where b and c are constants. It i s likely that systems with Delta > 10 are also unstable. The slope b d epends weakly on the number of planets, but is independent of planetar y mass, m, if we measure Delta in units that are proportional to m(1/4 ) rather than the usual R(H) proportional to m(1/3). Instability in mu lti-planet systems arises because energy and angular momentum are no l onger conserved within each two-planet subsystem due to perturbations by the additional planet(s). These results suggest that planetary embr yos will not become isolated prior to the final stage of terrestrial-p lanet formation simply due to a failure to achieve close encounters. O ther factors leading to isolation cannot be ruled out at this stage. ( C) 1996 Academic Press, Inc.