Shepherding of the Uranian Rings. I. Kinematics

The possible kinematical relationships between the Uranian rings and all ten newly discovered satellites of Uranus are examined. Observational evidence is presented for interactions between 1986U7 and 1986U8 and the epsilon, delta, and gamma rings. The likelihood that these two satellites are shepherding the epsilon ring and are responsible for some of its internal structure is assessed, and the results are used to propose a reduction in the ring radius scale. It is also proposed that 1986U7 and 1986U8 are the inner and outer shepherds for the epsilon ring, that 1986U7 is the outer shepherd for the delta ring, and that 1986U8 is an outer shepherd for the gamma ring. The results of theoretical investigations of planetary ring dynamics are then applied to these associations, and their dynamical significance is evaluated. The resonant torques which the satellites exert on each ring are calculated and compared to the viscous torque which transports angular momentum outward through the ring and to the atmospheric-drag torque which causes the ring's orbit to decay.