Sharp edges of planetary rings

Abstract

The ring systems of Saturn and Uranus exhibit a number of sharp edges across which the optical depth drops from order unity to near zero. At least two and perhaps all of these features are associated with the location of orbital resonances between a satellite and a ring particle. It is remarkable that the optical depth varies on a distance scale which is much finer than that over which angular momentum can be transferred between a satellite and the ring material. We illustrate here with qualitative argument the results of a numerical simulation concerning the outer edge of the B ring. More details can be found in Borderies, Goldreich and Tremaine (1982).