Classification of Satellite Resonances in the Solar System

Abstract

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io–Europa, Europa–Ganymede, and Enceladus–Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas–Tethys and Titan–Hyperion MMRs, and their resonant arguments are the only ones to exhibit substantial librations. Could there be a causal connection between the libration amplitude and the presence of a separatrix? Our suspicions were aroused by Goldreich & Schlichting, who demonstrate that sufficiently deep in a MMR, eccentricity damping could destabilize librations. However, our investigation reveals that libration amplitudes in both the Mimas–Tethys and Titan–Hyperion MMRs are fossils. Although the Mimas–Tethys MMR is overstable, its libration amplitude grows on the tidal damping timescale of Mimas's inclination, which is considerably longer than a Hubble time. On the other hand, the Titan–Hyperion MMR is stable, but tidal damping of Hyperion's eccentricity is too weak to have affected the amplitude of its libration.