Numerical Simulations of the Orbits of the Galilean Satellites

Long-term numerical simulations of the orbits of the Galilean satellites are carried out using a realistic physical model. The free libration of the Laplace angle, which plays a central role in the classical description of the tidal evolution of the Laplace resonance, is isolated from the simulated orbits. The amplitude and the period of the libration agree well with the values obtained by J. Lieske. In addition, we point out that tidal dissipation models need to take into account the large variations in Ioʹs eccentricity due to Jupiterʹs oblateness.