CHAOTIC ORBITS AND LONG-TERM STABILITY - AN EXAMPLE FROM ASTEROIDS OF THE HILDA GROUP

This paper calculates Lyapunov times, T(L), for certain members of the Hilda minor planets, a group that librates at the 3:2 mean motion resonance with Jupiter. We find that many are definitely chaotic, but that the resulting escape times T(c), obtained from a relation that we recently published [Lecar et al., AJ, 104, 1230 (1992)] does not conflict with their being present today. On the other hand, we show that bodies with libration amplitudes 10 to 20 deg larger than the maximum currently found would have escaped during the lifetime of the solar system. We interpret this behavior as ''observational'' support for the relation between T(L) and T(c) that LFM inferred from numerical simulations. Consideration of T(L)'s for real and hypothetical objects with low proper eccentricities at and near the Hilda group lends further support.