The recent crossing of the 7:3 resonance between Ganymede and Callisto

Abstract

Io, Europa and Ganymede are locked in the well-known Laplace resonance, while Callisto is not, even though it is very close to the 7:3 mean motion resonance with Ganymede. When considering the estimated tidal dissipation in the Jovian system and the consequent orbital migration rate of the moons, it follows that the 7:3 resonance should have been encountered around two million years ago. Through accurate numerical simulations, we investigated the dynamical effects of the 7:3 resonance crossing on the recent orbital evolution of the Galilean moons. We found that the most probable dynamical pathway is that Ganymede and Callisto were not captured into resonance, not even temporarily, while their eccentricities experienced a downward kick because of the resonance crossing, reducing their mean values of about 16% and 5%, respectively. Since this kind of evolution requires a value of the eccentricity of Ganymede before the resonant encounter slightly larger than today's, it follows that tidal dissipation within the moon must be low. In fact, a null free eccentricity of Ganymede would have led to an almost certain capture into the 7:3 resonance that would have survived until today. As a result of the resonance encounter, the amplitude of the free libration of the Laplace resonant angle increased, providing an explanation for its current value. Moreover, we found evidence that a three-body resonance crossing between the three outer moons occurred within the last few tens of thousands of years.