Towards a theory for the uranian rings

Interparticle collisions, radiation drag and differential precession all tend to disrupt the rings of Uranus. The first two effects lead to radial spreading which would disrupt a free ring in ≲ 10^8 yr. We propose that the rings are confined in radius by gravitational torques from a series of small satellites that orbit within the ring system. Differential precession tends to destroy the apse alignment of the elliptical ε ring. We suggest that apse alignment is maintained by the self-gravity of the ring. The resulting mass of the ε ring is ~5 × 10^(18) g. Its radial confinement requires (for example) a pair of satellites of mass ~10^(19) g, in circular orbits roughly 500 km away on either side of the ring