Numerical Results on a Simple Model for the Confinement of Saturn’s F Ring
In this paper we discuss a simple model for the confinement of Saturn’s F ring and present some preliminary numerical results. The model involves the gravitational interaction of independent test particles with Saturn, including its second zonal harmonic, the shepherd moons Prometheus and Pandora, and Titan, the largest of Saturn’s satellites. We perform accurate long-time integrations (3.2 × 106 revolutions of Prometheus) to check if the particle has escaped or remains trapped in the region between the shepherds. A particle escapes if its orbit crosses the region between the shepherds, or if it displays a physical collisions (lies with Hill’s region) with them. We find a wide region of initial conditions of the test particle that remain confined. We carry out a frequency analysis and use the ratio of the standard deviation over the average main frequencies as stability index. This indicator separates clearly the set of trapped initial conditions of the test particles, displaying some localised structures for the most stable ones. Retaining only those particles which are more stable according to our indicator, we obtain a narrow elliptic ring displaying sharp edges which agrees with the nominal location of Saturn’s F ring.
KeywordsTest Particle Stability Index Time Dependent Perturbation Kepler Motion Ring Particle
This work was initiated during LB’s sabbatical year at the Universitat de Barcelona, which was partially supported by DGAPA (UNAM) and Min. Educación (SAB2010-0123, Spain). We acknowledge financial support provided by the projects IN–110110 (DGAPA–UNAM), 79988 and 144684 (CONACyT), 334309729-9729-4-9 (Min. Ciencia e Innovación), MTM2009-09723 (Min. Ciencia e Innovación) and 2009 SGR 67 (Generalitat de Catalunya). It is a pleasure to thank Carles Simó for his encouragement, valuable comments, questions and discussions.
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