Stability of the Galilean Satellites in Deep Orbital Resonance

The Galilean satellites are locked in the Laplace resonance, which is responsible for forcing their significant orbital eccentricites. The eccentricites in turn result in tidal energy dissipation within the satellites that is responsible for the great thermal activity on Io, including both volcanism observed by Voyager and heat flux measured from Earth. The resonance results from the nearly 2:1 commensurability of orbital periods (or equivalently of mean motions) taken by pairs. These geometrical relations enhance the mutual gravitational effects. Yoder pointed out that tides raised on Io tend to drive the system out of resonance (toward greater nu and correspondingly smaller eccentricities) while tides raised on Jupiter tend to drive the system towards deeper resonance (smaller nu and larger forced eccentricities). The possible behavior of the system in deep resonance is investigated.