Chaotic Motions of F-Ring Shepherds

Abstract

Recent HST images of the Saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20 degrees. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.35 inverse years for satellite masses based on a nominal density of 1.3 gm/cm^3. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are anti-aligned. In this context we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occured shortly after their apsidal lines were anti-aligned.