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N.J. Cooper, C.D. Murray (Queen Mary, University of London)
We present the results of a numerical study of the orbits of Prometheus and Pandora. The full equations of motion have been integrated numerically for a variety of starting epochs between 1981 and 2004 using the Runge-Kutta-Nystrom RKN12(10)17M algorithm of Dormand et al. (1987). Included in the simulations are the effects of the 8 major satellites of Saturn, together with Janus and Epimetheus. Perturbations due to the Sun and Jupiter are also taken into account, along with the effects of Saturn's oblateness, up to terms in J6.
The results show that the anti-correlation in the temporal variation of the mean longitudes of Prometheus and Pandora, demonstrated by Goldreich and Rappaport (Icarus 162 (2003), 391) in their two-satellite simulations, survives the addition of the other satellites to the model. Chaos is also apparent through extreme sensitivity to initial conditions and a positive value for the Lyapunov characteristic exponent. The simulations also clearly show the influence of the nearby 3:2 corotation eccentricity resonance due to Mimas on the mean longitude of Pandora, as predicted by theory and as detected by French et al. in their HST observations (Icarus 162 (2003), 143). The smaller effect due to the corresponding 3:2 inner Lindblad resonance is also detectable, though apparently much less significant.
We investigate the possible role of the other satellites in the short-term evolution of the orbits of Prometheus and Pandora and consider the effects of various nearby resonances. Finally, we estimate the possible uncertainties in the orbits of Prometheus and Pandora during the Cassini tour, and discuss how the proposed sequence of observations for these satellites by Cassini may be expected to improve the precision of their orbits.
The authors thank the U.K. Particle Physics and Astronomy Research Council for financial support.
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.