Galilean satellites: Evolutionary paths in deep resonance |
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| Institution: | 1. Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA;2. Southwest Research Institute, Boulder, CO 80302, USA;3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA;4. Department of Earth Sciences, ETH Zurich, Switzerland;5. Environmental Science and Engineering, California Institute of Technology, Pasadena, CA 91125, USA;6. Ashima Research, Pasadena, CA 91106, USA;1. EOST, UMR-CNRS 7516, Université de Strasbourg, 5 rue René Descartes, 67084 Strasbourg, France;2. IPG Paris, Paris Sorbonne Cité, UMR-CNRS 7154, 1 rue Jussieu, 75005 Paris, France;1. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS – Université Bourgogne Franche-Comté, 9 Av. A. Savary, BP 47870, F-21078 Dijon Cedex, France;2. Université de Toulouse, UPS-OMP, Institut de Recherche en Astrophysique et Planétologie, Toulouse, France;3. CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France;4. Ligne AILES-Synchrotron SOLEIL, L’Orme des Merisiers, F-91192 Gif-sur-Yvette Cedex, France;5. Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France |
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| Abstract: | The Laplace resonance among the inner three Galilean satellites (mean motions n1 − 3n2 + 2n3 = 0) has stable configurations in “deep resonance,” i.e., where mean motions taken by pairs are in ratios very close to 2:1. The present satellite configuration, with the resonance variable φ ≡ λ1 − 3λ2 + 2λ3 stable at 180°, is unstable near this exact commensurability. But there is a continuous path of stable conditions branching from φ = 180° to higher and lower values of φ and toward very deep resonance, according to a theory extended to third order in orbital eccentricity. This path provides a track for tidal evolution of the system. Thus, scenarios involving evolution (probably episodic) from deep resonance are viable, and eliminate the requirement by the alternative equilibrium hypothesis for rapid tidal dissipation in Jupiter. Evolution out from deep resonance is consistent with the free eccentricity of Ganymede, the free libration of φ, and observational constraints on Io's secular acceleration. Also, the relatively large forced eccentricities in deep resonance may have controlled geophysical processes in the satellites by much greater tidal heating and global stress than at present. |
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