THE LONG-TERM DYNAMICS OF DACTYLS ORBIT

Asteroid Ida's satellite Dactyl was observed over 5 1/2 hr by the Gali leo spacecraft imaging system, The observed motion fits a family of or bits parameterized by the mass of Ida. We have tested the stability of these orbits by numerically integrating motion about a realistically shaped model for Ida. Those with pericenter distance q less than or si milar to 65 km (corresponding to Ida's density greater than or similar to 3.1 g cm(-3)) are unstable over time scales of a few days to a few months, placing a strong upper limit on Ida's density. Moreover, at t he opposite extreme of density, orbits corresponding to densities less than 2.3 g cm(-3) are chaotic and become unstable after about 1000 ye ars. For density between 2.3 and 2.5 g cm(-3), Galileo family orbits a re chaotic but there is no indication of instability over thousands of years. Dactyl likely formed at the same time as Ida, so its orbit mus t be stable over time scales much longer than we have been able to exp lore numerically. As a start toward understanding long-term stability, we have investigated the character of orbits commensurate with the ro tation of Ida within the Galileo family. We found that the overlap of high-order resonances for low densities of Ida explains the chaotic be havior of orbits. The low-order p:1 and p:2 resonances, corresponding to a high density for Ida, are distinct and stable and are all consist ent with the longitudinal position of Dactyl at the epoch of the Galil eo encounter, However, there is no evidence of preferential stability of resonant orbits against collison with Ida or escape over 6000 years . If a resonant orbit is actually occupied, it may have been selected by a longer-term stability or by dissipative processes. (C) 1997 Acade mic Press.