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H. Hussmann, T. Spohn (Institute of Planetology, University of Muenster, Germany)
The inner Galilean Satellites Io, Europa, and Ganymede are locked in the three-body Laplace resonance. Different conceivable scenarios have been suggested for the formation of the resonance. One possibility involves expansion of Io's orbit due to tidal torques exerted by Jupiter. The rate of expansion depends on the Jovian dissipation factor QJ. In this scenario Io has been closer to Jupiter in the past. However, the initial distance of Io to Jupiter is unknown. Because of their small mass and small eccentricities, tidal evolution of the inner four satellites of Jupiter, Metis, Adrastea, Amalthea, and Thebe can be neglected. Thus we expect the small satellites to be at present close to the distance to Jupiter where they were formed. With Io being closer to the small satellites in the past, perturbations were stronger than at present. As a first step we calculate the orbital evolution of the inner satellites, with Io as an external perturber using a Lie-series method for the numerical integration. The model resembles the elliptical restricted three-body problem, with the inner satellites being test particles. To investigate the phase space and possible mean motion resonances we calculated the orbits over 105 years using different values of Io's semi-major axis and eccentricity. For Io's present eccentricity, we get chaotic behaviour of Thebe, the outermost of the small satellites, with Io being as close as 3.42 RJ. Tidal evolution of Io from 3.42RJ to its current 5.91RJ will require a Jovian dissipation factor of QJ= 3.0 X 105, if dissipation in Io is neglected. Due to the resonances (especially 3:2 and 2:1, at 4.1 and 4.9 RJ, respectively) Thebe's eccentricities are enhanced but do not ecceed a value of 0.04.
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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.