Diffusive chaos in the outer asteroid belt.

Abstract

We present an analytic theory of motion near resonances in the planar elliptic restricted three-body problem. The theory predicts the location and extent in semimajor axis and eccentricity (a,e) space of the chaotic motion, the Lyapunov time, and the time for objects on chaotic orbits to be removed from the system. The latter is given by the time for test bodies with small initial eccentricities to diffuse to the eccentricity at which they suffer close encounters with the perturbing body. The theory predicts gaps in the outer asteroid belt similar to the Kirkwood gaps seen in the inner belt, in agreement with our recent numerical results. It also predicts that asteroids in a number of high order mean motion resonances will possess very short Lyapunov times ( ~ 10,000 years) but removal times comparable or longer than the life time of the solar system; Helga, Ulla, and Wingolfia may afford examples of such bodies. Finally, we explore the relationship between the Lyapunov time and the removal time. We explain the simple power law relation found in previous numerical work, and show where it does and does not apply.