Dynamics of the Uranian Rings

Some of the problems of the shepherding satellite model of Goldreich ant tremaine are discussed. The following topics are studied: (1) optical depths of the all the observed narrow rings; (2) satellite and ring separation timescales; (3) ring edge sharpness; (4) shock formation in narrow rings; (5) the existence of small satellites near the Uranian rings; and (6) the apse and node alignments of the eccentric and inclined rings.