Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007dps....39.2609h&link_type=abstract
American Astronomical Society, DPS meeting #39, #26.09; Bulletin of the American Astronomical Society, Vol. 39, p.462
Astronomy and Astrophysics
Astronomy
Scientific paper
Current literature on ring-satellite interactions tells us that the long-term orbital stability of a satellite that orbits near a planetary ring is uncertain. This is because the satellite's perturbations at its Lindblad and corotation resonances in the ring tend to alter the satellite's eccentricity e, but it is unclear whether e-damping or e-excitation is the result, since that depends on whether particle motions at the corotation resonances are unsaturated (Goldreich & Tremaine 1982). Further, the stability of the satellite's inclination I seems grim, since the satellite's inclination is excited by its many vertical resonances in the ring (Borderies et al 1984). Consequently, it is unclear whether the small gap-embedded satellites Pan (which inhabits the Encke gap in Saturn's A ring) and Daphnis (which inhabits the Keeler gap) should in fact reside in nearly circular orbits that are coplanar with the ring.
To address this uncertainty, the following considers the satellite's secular gravitational perturbations of the ring, which can also alter the satellite's e and I. The Lagrange planetary equations are used to show that a small gap-embedded satellite can launch spiral density and spiral bending waves that propagate radially outwards from the gap's outer edge. These one-armed waves propagate via the secular part of the ring's self-attraction, and they tend to have low amplitudes and long wavelengths, 100's of km in Saturn's A ring. The excitation of these waves also damps the satellite's e and I at rates that depend on the satellite's mass, ring surface density, the gap width, and the planet's oblateness (Hahn 2007). These analytic predictions are also confirmed using the `rings-model' of Hahn (2003) to simulate a ring-satellite system. Whether this secular interaction can stabilize a satellite's e and I will be determined, and whether these low-amplitude waves have any observational consequences will also be discussed.
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