CHAOTIC ORBITS AND LONG-TERM STABILITY - AN EXAMPLE FROM ASTEROIDS OFTHE 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 res onance with Jupiter. We find that many are definitely chaotic, but tha t the resulting escape times T(c), obtained from a relation that we re cently published [Lecar et al., AJ, 104, 1230 (1992)] does not conflic t with their being present today. On the other hand, we show that bodi es with libration amplitudes 10 to 20 deg larger than the maximum curr ently found would have escaped during the lifetime of the solar system . We interpret this behavior as ''observational'' support for the rela tion between T(L) and T(c) that LFM inferred from numerical simulation s. Consideration of T(L)'s for real and hypothetical objects with low proper eccentricities at and near the Hilda group lends further suppor t.