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 four-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 km) are chaotic on decadal timescales, within which particle semi-major axes have periodic changes due to partial libration motions around the CER fixed points. After a few decades, the maximum variation of semi-major axis is about eleven (resp. three) kilometres in the case of the CER with Janus (resp. Epimetheus). Similarly, particle eccentricities have partial oscillations forced by the LERs every four years. 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 (Murray et al. 2014), confirming that it is strongly perturbed by the Janus 7:6 LER. The CER has currently no effect on that body, nevertheless the fitted semi-major axes are just outside the chaotic zone of radial range 136756-136768 km.