Symplectic Maps for the N - body Problem with Applications to Solar System Dynamics

The mapping method of Wisdom (1982) is generalized to encompass all gravitational n-body problems with a dominant central mass. The method is used to compute the evolution of the outer planets for a billion years, providing independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic. The stability of the symplectic mapping method for the n-body problem introduced recently by Wisdom and Holman (1991) is analysed in a novel application of the methods of non-linear dynamics. Test particle stability in the outer solar system is surveyed. Clusters of test particles near the triangular Lagrange points of Jupiter, Saturn, Uranus, and Neptune survive the full integration, here 20 million years. Nearly all particles started on circular orbits between the outer planets are removed by close encounters with the planets during the course of 4.5 billion years integrations. Numerous test particles between Neptune and 43 AU are removed by close encounters with Neptune. The distribution of encounter times suggests that the times to first encounter can reach several billion years. The flux of new encounters decays slowly, roughly as the inverse of time. An estimate of the mass of the Kuiper belt is given. Thesis Supervisor: Jack Wisdom Title: Professor