Width of Cassini's Division in Saturn's Rings

Abstract

IT is commonly implied and sometimes explicitly stated in textbooks that the period of revolution corresponding to an orbit at the centre of Cassini's division in the rings of Saturn is half the period of Mimas, the closest massive satellite of Saturn, and that perturbations due to Mimas are responsible for the gap. In fact, the half period point of Mimas is 200 km beyond the outer edge of ring B rather than at the centre of the gap¹. Moreover, the perturbations of Mimas are actually quite small—probably too small to account for the width of the gap, even if one disregards the mismatch between T_M/2 and the revolution period at the centre of the gap. In fact, there is a simple way to obtain an approximate expression for the width of the gap produced in a ring of light particles by the perturbations of a massive body at the half-frequency point, assuming that both the massless particles in the ring and the outer body move in a central field produced by a very massive body.