A problem in resonance

Abstract

Saturn's satellite Hyperion experiences large perturbations by Titan, the largest of Saturn's satellites, because of the closeness of Hyperion's orbital period to three-quarters of that of Titan.

The motion of Hyperion is a superposition of periodic fluctuations (both free and forced) onto a motion which is periodic in a suitable uniformly rotating frame of reference, and in which Hyperion would be at a maximum distance from Saturn at each conjunction with Titan.

Successive attempts to determine the mass of Titan from observed perturbations of Hyperion have suffered from omissions in the theory of terms subsequently found to be significant.

An attempt is in progress which, it is believed, comprises all long-period changes in the osculating elements which are of second degree in the mass of Titan, and of third degree in the eccentricity of its orbit. Results so far obtained indicate that the period of the free motion of the orbit plane of Hyperion is better determined by Woltjer's reduction of the observations than by his theoretical calculations.