On the fates of minor bodies in the outer solar system

The equations of motion of roughly one thousand test particles in the outer solar system for up to 22.5 million years have been integrated. The test particles are placed on initially circular orbits about the sun and feel the gravitational influence of the sun and four (or in some cases two) of the giant planets. The initial conditions of the planets are obtained from their current orbital elements, and their mutual gravitational interactions are fully included. Test particles that undergo a close approach to a planet are removed from the integration. Interior to Jupiter the creation of gaps in the test-particle semimajor-axis distribution appears to be associated with resonances in the outer asteroid belt. Exterior to Neptune there is a dynamical erosion of the region just beyond the giant planets (i.e., at the inner edge of the Kuiper belt). The majority of the test particles between the giant planets are perturbed to a close approach to a planet on timescales of millions of years. These results suggest that there are very few initially circular orbits between the giant planets that are stable against a close approach to a planet over the lifetime of the solar system.