Apse Alignment of Narrow Eccentric Planetary Rings

The boundaries of the Uranian epsilon, alpha, and beta rings can be fitted byKeplerian ellipses. The pair of ellipses that outline a given ring share acommon line of apsides. Apse alignment is surprising because the quadrupolemoment of Uranus induces differential precession. We propose that rigidprecession is maintained by a balance of forces due to ring self-gravity,planetary oblateness, and interparticle collisions. Collisional impulses playan especially dramatic role near ring edges. Pressure-induced accelerations aremaximal near edges because there (1) velocity dispersions are enhanced byresonant satellite perturbations, and (2) the surface density declines steeply.Remarkably, collisional forces felt by material in the last 100 m of a 10 kmwide ring can increase equilibrium masses up to a factor of 100. New ringsurface densities are derived which accord with Voyager radio measurements. Incontrast to previous models, collisionally modified self-gravity appears toallow for both negative and positive eccentricity gradients; why all narrowplanetary rings exhibit positive eccentricity gradients remains an openquestion.Comment: Accepted to Ap