Weiss, J.W., Porco, C.C., and Tiscareno, M.S. (2008). "Edge-Waves in Ring Gaps and the Determination of Masses of Embedded Satellites." American Astronomical Society, DDA meeting #39, #18.02.


Abstract
Moons embedded in planetary-ring gaps generate radial waves on the gap-edges. The scale and morphology of these waves can be used to deduce properties of the moons, particularly their masses. However, existing analytic theory describing the relationship between the moon's mass and the edge-wave amplitudes neglects non-linear effects during encounters as well as possible effects of pre-encounter inclinations and eccentricities of the moon and particles. We will present our numerical integrations of ring-satellite encounters in which we explore the effects of the non-linearity, eccentricities, and inclinations.

We find that in the Saturnian system, Pan's mass can accurately be deduced using the existing analytic theory. Daphnis is more dynamically interesting, being more inclined, more eccentric, and closer to its gap-edge than Pan. The proximity of Daphnis to the Keeler gap's edges results in significant non-linear effects, leading to the analytic calculation over-estimating the mass of Daphnis by 30%.

The eccentricity and inclination both cause time-variable structure on the gap-edge, meaning single observations are not sufficient for determining the mass of the satellite. Additionally, Daphnis' inclination induces an inclination in the gap-edge which conversely act to decrease Daphnis' inclination with a damping timescale of several thousands of years.