Forced and Free Libration of the Galilean Satellites

Numerical simulations of the coupled orbital and rotational dynamics of the Galilean satellites show the presence of both free and forced librations. Jupiter's large mass implies periods of the free librations of the Galilean satellites shorter than the Moon's. While the period of the Moon's free zero longitude libration is 2.9 yr, the same period is only about 13 days for Io, 53 days for Europa, 185 days for Ganymede and 900 days (2.5 yr) for Callisto. Our simulations also reproduce the pole wobble of the Moon with a period of 75 yr and show analogous variations for the Galilean satellites' poles with periods of about 230 days for Io, 1756 days (4.8 yr) for Europa, ~30 yr for Ganymede and ~300 yr for Callisto. Simulations including tides will be carried out to determine the most likely rotational state of the Galilean satellites as the end state of the tidal evolution.