Resonances and Capture Probability in the Ida/Dactyl System
J-M. Petit (CNRS, France), A. Lemaitre (FUNDP, Belgique)
In a previous work, Petit et al. (1997, Icarus, in press) have shown that the Galileo family of Dactyl's orbits contains orbits which are close or within the mean motion resonances (resonances between Ida's rotation frequency and Dactyl's orbital frequency). These may play an important role in the long term dynamical evolution of Ida/Dactyl. Using an averaged Hamiltonian with a z-symmetrical potential for orbits in the equatorial plane, we compute the probability of capture into resonance in the presence of dissipation. For these orbits, the agreement between the Hamiltonian approach and numerical integrations is rather good. The capture probability is maximum in the 5:1 resonance. For this simplified problem, the fate of an orbit is rather simple. Either it jumps across the resonance, or it is captured into the resonance. In the later case, the eccentricity starts to grow until it reaches a value allowing for very close encounter with the primary, leading finally to a hyperbolic trajectory.
Numerical integrations of Galileo family orbits a few degrees off the equatorial plane with a z-assymmetrical potential exhibit very different behaviours. The probability of capture is larger, but these captures are mostly temporary. Inside a resonance, the eccentricity can rise as before until a close encounter. It can also escape the resonance by crossing the separatrix, either by being trapped in a secondary resonance (between the longitude of pericenter frequency and the libration frequency) or by following a constant action line forcing the eccentricity to increase and then decrease again We will present some possible explanation of these effects with the locations of the secondary resonances and the constant action lines.