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S. Musotto, F. Varadi, G. Schubert, W. Moore (UCLA)
Numerical simulations of the orbits of the Galilean satellites are being carried out using realistic physical models in order to better understand their coupled orbital and thermal evolution. We are able to isolate from the simulated orbits the so-called free libration of the Laplace angle which is the primary quantity in the classical description of the tidal evolution of the Laplace resonance. The amplitude and period of the libration could only be estimated in the past through J. Lieske's motion theory in which they are two of the parameters fitted to observations. Our direct numerical simulations, together with standard digital signal processing, confirm Lieske's values. However, the commonly used formulae for tidal dissipation are incorrect because they do not take into account the large deviations from Keplerian ellipses due to the gravity field of Jupiter. While the formulae assume very small variations in eccentricity on the orbital time scale, those are, in fact, about one quarter of the orbital average. We will address this important issue.