The dynamics of the outer edge of Saturn's A ring perturbed by the satellites Janus and Epimetheus

Abstract

We present an analytical model to study the dynamics of the outer edge of Saturn's A ring. The latter is influenced by 7:6 mean motion resonances with Janus and Epimetheus. Because of the horseshoe motion of the two co-orbital moons, the ring edge particles are alternately trapped in a corotation eccentricity resonance (CER) or a Lindblad eccentricity resonance (LER). However, the resonance oscillation periods are longer than the 4-year interval between the switches in the orbits of Janus and Epimetheus. Averaged equations of motion are used, and our model is numerically integrated to describe the effects of the periodic sweeping of the 7:6 CERs and LERs over the ring edge region. We show that four radial zones (ranges 136 715-136 723, 136 738-136 749, 136 756-136 768, and 136 783-136 791 km) are chaotic on decadal time-scales, within which particle semimajor axes have periodic changes due to partial libration motions around the CER fixed points. After a few decades, the maximum variation of semimajor axis is about 11 km (respectively 3 km) in the case of the CER with Janus (respectively Epimetheus). Similarly, particle eccentricities have partial oscillations forced by the LERs every 4 yr. For initially circular orbits, the maximum eccentricity reached is ~0.001. We apply our work to 'Peggy', an object recently discovered at the ring edge, confirming that it is strongly perturbed by the Janus 7:6 LER. The CER has currently no effect on that body, nevertheless the fitted semimajor axes are just outside the chaotic zone of radial range 136 756-136 768 km.