Application of spin-orbit theory to a class of orbit-orbit resonances: The case of Titan-Hyperion

The orbit-orbit interaction of two satellites of greatly unequal mass is studied under the condition that the more massive satellite moves in a circular (unperturbed) orbit that lies entirely inside the orbit of the smaller (perturbed) body. It is shown that this system is equivalent in every respect to a special case ofspin-orbit coupling. On this basis, conditions for resonance are derived, as well as libration periods and bandwidths. Application is made to Saturn's resonant pair of satellites, Titan and Hyperion, which approximate the conditions of this problem. The calculated libration period of 646 days is in reasonably good agreement with the observed 640-day period.Most of this work was done at the Jet Propulsion Laboratory, Pasadena, during the summer of 1974.