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Classification of Satellite Resonances in the Solar System

Luan, Jing and Goldreich, Peter (2017) Classification of Satellite Resonances in the Solar System. Astronomical Journal, 153 (1). Art. No. 17. ISSN 1538-3881. doi:10.3847/1538-3881/153/1/17.

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Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io–Europa, Europa–Ganymede, and Enceladus–Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas–Tethys and Titan–Hyperion MMRs, and their resonant arguments are the only ones to exhibit substantial librations. Could there be a causal connection between the libration amplitude and the presence of a separatrix? Our suspicions were aroused by Goldreich & Schlichting, who demonstrate that sufficiently deep in a MMR, eccentricity damping could destabilize librations. However, our investigation reveals that libration amplitudes in both the Mimas–Tethys and Titan–Hyperion MMRs are fossils. Although the Mimas–Tethys MMR is overstable, its libration amplitude grows on the tidal damping timescale of Mimas's inclination, which is considerably longer than a Hubble time. On the other hand, the Titan–Hyperion MMR is stable, but tidal damping of Hyperion's eccentricity is too weak to have affected the amplitude of its libration.

Item Type:Article
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Luan, Jing0000-0001-6048-1959
Additional Information:© 2016. The American Astronomical Society. Received 2016 February 27; revised 2016 October 18; accepted 2016 October 30; published 2016 December 21. We thank the anonymous referee who provided valuable comments and questions, which helped us to greatly improve the paper. We thank Katherine Deck for alerting us to differences in librational stability between e- and e'-type MMRs (Deck & Batygin 2015) and Eugene Chiang for helpful comments on our presentation.
Group:Astronomy Department
Subject Keywords:planets and satellites: dynamical evolution and stability
Issue or Number:1
Record Number:CaltechAUTHORS:20170213-152600459
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Official Citation:Jing Luan and Peter Goldreich 2017 AJ 153 17
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74268
Deposited By: George Porter
Deposited On:13 Feb 2017 23:44
Last Modified:11 Nov 2021 05:25

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