DYNAMIC STABILITY IN THE OUTER SOLAR-SYSTEM AND THE DELIVERY OF SHORT-PERIOD COMETS

Test particle stability in the outer solar system is surveyed. Roughly 7000 test particles are numerically integrated for durations ranging from 20 to 800 million yr. The initial conditions of the test particles fall into two categories: (1) orbits initially near the Lagrange L4 and L5 points of the Jovian planets, and (2) circular orbits in the invariable plane with semimajor axes of 5-50 AU. Clusters of test particles near the triangular Lagrange points of Jupiter, Saturn, Uranus, and Neptune survive the full integration. However, the stable regions near Saturn's L4 and L5 points exclude the actual Lagrange points. Nearly all particles between the outer planets are removed by close encounters with the planets during the course of these integrations. Numerous test particles between Neptune and 43 AU are removed by close encounters with Neptune, some quite late in the integrations. The particles which have late encounters reach Neptune by a path that roughly preserves semimajor axis while the eccentricity varies irregularly. 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. This gives new insight into the dynamics of the delivery of short period comets from the hypothesized Kuiper belt. An estimate of the mass of the Kuiper belt is given.