The stability of the solar system

Astronomy and Astrophysics – Astronomy

Scientific paper

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Celestial Mechanics, Dynamic Stability, Many Body Problem, Solar System, Elliptical Orbits, Natural Satellites, Orbit Perturbation, Three Body Problem

Scientific paper

Empirical criteria are presented for the stability of a hierarchical dynamical n-body system and applied to the problem of the long-term stability of hierarchical planetary and satellite systems in the solar system. The criterion of Zare (1976, 1977) for the stability of a three-body system consisting of a binary around which a third body orbits is introduced, and a statistical empirical approach to the question of the stability of hierarchical dynamic systems of three or more bodies is presented which is based on Zare's criterion and involves the establishment of a set of parameters expressing the disturbances to elliptical orbits. When applied to hierarchical three-body subsets of the solar system and satellite systems, the criterion is observed to be well satisfied, with certain exceptions including the retrograde satellites of Jupiter.

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