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N.J. Rappaport (JPL), P. Goldreich (Caltech)
In 2002, Rappaport and Goldreich demonstrated that the motions of Prometheus and Pandora are chaotic. The chaos arises from the gravitational interactions between the satellites. Sudden changes in mean motions occur every 6.2 years when the periapsis of Pandora's orbit is aligned and on the same side of Saturn with the apoapsis of Prometheus' orbit, and the gravitational interactions between the two bodies are greatly enhanced.
We followed up this work by a search for the origin of the chaos. We found that the chaos is due to overlapping of the four resonances associated with the same 121:118 ratio of mean motions and the four possible combinations of periapsis longitudes of Prometheus and Pandora. Mean motion of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 degrees per year, respectively.
Furthermore, we demonstrated that the whole system can be represented by a single degree of freedom model that captures the full chaotic dynamics.
References: (1) Rappaport, N.J., and P. Goldreich 2002: The Chaotic Dynamics of Prometheus and Pandora, BAAS 34, 883. (2) Goldreich, P., and N. Rappaport 2003: Chaotic motions of Prometheus and Pandora, Icarus 162, 391-399.
This research was supported by NASA Planetary Geology and Geophysics grant 344-30-53-02 and by NSF grant AST-0098301.
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.