Weak dynamical effects in the Uranian ring system

Abstract

ABSTRACTA number of weak gravitational forces were examined for their kinematic effects on the Uranian ring system, in an attempt to account for residual errors of ~2 km in the ring positions and a few times 10-3deg/day in the apse precession rates. The principal conclusions are as follows: (1) perturbations by the five known satellites are too small to have observable effects with the best current estimates of the satellite masses. (2) Limits can be set on the masses of inter-ring “shepherd” satellites from their influence on precession rates and their radial perturbations on the rings. For example, the maximum mass of a shepherd satellite between rings 4 and 5 is ~ 1019gm. (3) Using the best available ring parameters, there is no convincing evidence that the rings are associated with resonances with known satellites. The only close association is of rings 5, α and γ with three-body resonances due to Miranda and Ariel. It is more likely that the putative shepherd satellites may occupy resonances. (4) The known satellites can cause anomalous residuals by changing the position of Uranus relative to the system barycenter during the occultation. The maximum change, so far, during the 1977 March 10 event, was 1.6 km. This effect will be investigated with the MIT Uranus ring model.