The Role of Three-Body Resonances on the Dynamical History of the Saturnian Satellite System

The orbital evolution of Saturnian moons is not well established. The classical theory based on equilibrium tides states that the rate of migration of a given moon would depend directly on its mass and inversely proportional to high power (11/2) of its semimajor axis. Recent results obtained from data analysis from both Earth-based astrometry and Cassini data showed that the theory of equilibrium tides does not correspond to the observed orbital evolution of the moons, especially Rhea and Titan. Gravitational perturbations between moons via pairs of mean motion resonances (MMRs) play a major role in accelerating/decelerating the rate of outward/inward migration of each moon. Current existence of MMRs between Mimas-Tethys and Enceladus-Dione pairs indicates that these moons exhibit convergent migration consistent with equilibrium tide theory. Therefore, the dynamical evolution of the Saturnian system clearly does not fit a single, simple paradigm. Up to now, only MMRs involving two moons were considered to investigate the past and current orbital configuration of the Saturnian satellite system. In this talk, we show, via direct numerical integrations, that three-body resonances among Saturnian satellites were quite common in the past, and could result in a relatively long-term, but finite capture time (10 Myr or longer). We find that these three-body resonances are always of the eccentricity type, and do not appear to affect the moons’ inclinations. While some three-body resonances are located close to two-body resonances (but involve the orbital precession of the third body), others are isolated, with no two-body arguments being near resonance. Three-body resonances have a potential to explain some of the system’s unsolved problems, including the high eccentricity of Mimas (e ∼ 0.02) and the evolution of Enceladus and Dione through their many sub-resonances into the present configuration. The dynamical past of Enceladus’s orbit is crucial for fully understanding the history and nature of its tidal heating and geological activity.