On the formation of the orbit-orbit resonance of Titan and Hyperion

We consider two possibilities for the formation of the orbit-orbit resonance of Titan and Hyperion. The first involves an approximate determination of the region in phase space corresponding to a stable libration at the 4:3 resonance. This calculation indicates that a condition of libration is a reasonably probable ( > 10%) dynami- cal state of the system. The second possibility concerns the evolution of the system from an initially circulatory state to a libratory state through tidal interaction. Our conclusion, based on numerical integrations, is consistent with other, semianalytical studies, and indicates that tides could have played a significant role in both the origin and the evolution of the Titan-Hyperion resonance only if the effective Q for the Titan-Saturn interaction were of the order of (2-4) X 1 0 . In an appendix, we show that the presence of Hyperion makes it unlikely that bodies can survive for long in orbits near the L4 and L5 ("Trojan") points of Titan.