DIFFUSIVE CHAOS IN THE OUTER ASTEROID BELT

We present an analytic theory of motion near resonances in the planar elliptic restricted three-body problem. The theory predicts the locati on and extent in semimajor axis and eccentricity (a,e) space of the ch aotic motion, the Lyapunov time, and the time for objects on chaotic o rbits to be removed from the system. The latter is given by the time f or test bodies with small initial eccentricities to diffuse to the ecc entricity at which they suffer close encounters with the perturbing bo dy. The theory predicts gaps in the outer asteroid belt similar to the Kirkwood gaps seen in the inner belt, in agreement with our recent nu merical results. It also predicts that asteroids in a number of high-o rder mean motion resonances will possess very short Lyapunov times (si milar to 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 la w relation found in previous numerical work, and show where it does an d does not apply. (C) 1997 American Astronomical Society.