Weiss J.W., Porco,C.C., Tiscareno, M.S., Burns, J.A., Dones, L. (2005). "The Determination of the Masses of Ring-Embedded Moons from their Effects on Nearby Ring Particles." American Astronomical Society, DPS meeting #37, #61.03.
High resolution Cassini images of Saturn's Encke and Keeler gaps, and the moons contained in them, have uncovered complex patterns in the gaps edges that do not conform to the simplest models generally used for these systems. We will present the results of our numerical studies of the interactions between moons in ring gaps and particles on the edges of the gaps. Analytical treatments of these interactions use an impulse approximation to model the behavior in addition to assuming that both particle and moon start on circular orbits. Our numerical integrations of test particles interacting with a moon provide a means of relaxing these assumptions and testing the derived relationship between moon mass and amplitude of the waves on the gap's edge.|
We will show that for moon-gap configurations where the moon is several Hill's sphere radii from the edge of the gap, the analytic expression giving wave amplitude as a function of mass and edge-moon separation, results in reasonably accurate measurements of the moon's mass. However, if the edge-moon distance is only a few Hill's sphere radii -- such as in the Keeler gap --the analytic predictions yield mass estimates that are substantially too high. That is, the gap moons can be smaller for a given disturbance in the gap's edge than previously thought.
We also show that in cases where the moon and/or ring particles are on eccentric orbits, the orbital phases at the time of closest approach profoundly affect the particle's behavior which can lead to distinctly non-sinusoidal waveforms at the gap's edges. This kind of behavior has been observed in the Encke gap (Porco et al., 2005, Science). For gap edges within a few Hill sphere radii of their moons, such as the Keeler gap, the effect is even more pronounced. The edge waves undergo significant changes in apparent radial location and amplitude, yielding complicated patterns not unlike those observed in the edges of the Keeler gap. (See abstract by Tiscareno et al.)