Dynamics of narrow rings

The ring models described here were developed to account for the dynamical problems posed by the narrow rings of Uranus. Some of these rings are now known to be eccentric, inclined, nonuniform in width, optically thick, and narrow, with very sharp edges. The eccentric rings have common pericenters and large, positive eccentricity gradients. The theory of shepherding satellites successfully accounts for most of these features and can also account for some features of the narrow Saturnian rings, in particular, waves, kinks, and periodic variations in brightness. Outstanding problems include the putative relation between eccentricity and inclination displayed by eight of the nine Uranian rings, and the magnitudes of the tidal torques acting on the shepherding satellites. The horseshoe-orbit model, although viable, probably has more application to the narrow rings from which the Saturnian coorbital satellites formed. The angular momentum flow rate due to particle collisions is a minimum at the Lagrangian equilibrium points L(4) and L(5), and one can expect accretion to be rapid at these points.