Dynamical Influences on the Orbits of Prometheus and Pandora

Abstract

We present the results of a numerical and analytical study of the orbits of the Saturnian satellites Prometheus and Pandora, including the perturbing effects of other moons. The full equations of motion have been integrated numerically between 1980 and 2010, taking into account Saturn's oblateness up to terms in J6. Included in the simulations are the effects of the eight major satellites of Saturn, together with the co-orbital satellites, Janus and Epimetheus. The results show that the anticorrelation in the temporal variation of the mean longitudes of Prometheus and Pandora, demonstrated in previously published two-satellite simulations, survives the addition of the other satellites to the model. Chaos is apparent through sensitivity to initial conditions and a positive value for the maximum Lyapunov characteristic exponent. There is evidence that the other satellites also contribute to the chaotic motion on a longer timescale. The effects of the nearby Mimas 3 : 2 resonance on the orbit of Pandora are clearly detectable. We find evidence that Janus and Epimetheus have a secondary role in the dynamical evolution of Prometheus and Pandora and discuss possible mechanisms. We show from theory that two independent sets of second-order resonances due to Epimetheus sweep across the orbits of Prometheus and Pandora every 4 years, when the orbit of Epimetheus switches position with its co-orbital companion. However, no effects related to this have so far been identified. Comparison of integrated results with extrapolations of current published ephemerides suggest uncertainties on the order of 104 km in the down-track positions of Prometheus and Pandora, equivalent to 4° in mean longitude, during the Cassini tour.