**DPS 35th Meeting, 1-6 September 2003**

*Session 4. Other Planetary Satellites I*

Oral, Chairs: L. Bruesch and M. L. Delitsky, Tuesday, September 2, 2003, 1:30-3:00pm, DeAnza III
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## [4.05] Numerical Simulations of the Orbits of Prometheus and Pandora

*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.