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Solar Semi-Secular Resonances and the Orbital Evolution of Rhea and Titan

Presentation #221.03 in the session Planets and Satellites Dynamics (Poster + Lightning Talk)

Published onOct 23, 2023
Solar Semi-Secular Resonances and the Orbital Evolution of Rhea and Titan

Recent observational results show that orbital evolution rates of Rhea and Titan do not conform to classical tidal theory (Lainey et al. 2020). In order to understand these moons’ orbital evolution preceding the present epoch, it is imperative to simulate the preceding interactions that could have influenced the moons’ orbits and surface characteristics. While numerous current and past mean-motion resonances among the moons have attracted much attention, solar semi-secular resonances offer an alternate window in the past evolution of the moons, and Rhea in particular. Rhea currently has nodal and apsidal precession periods of about 35 years, and in the past, it should have migrated through the location where its precession periods were equal to Saturn’s orbital period, leading to strong Solar perturbations. Cuk et al. (2016) found that this “evection” resonance, in which a moon’s pericenter is locked to the Sun, could have excited the orbit of Rhea’s hypothetical precursor and potentially caused the instability and re-accretion of the inner system. While Rhea may be able to damp its eccentricity after passing the evection resonance, it should have also acquired a large inclination at the same time, Cuk et al. (2016) argued that Rhea must have re-accreted after the evection resonance passage. We revisit this issue in light of the resonance-lock theory of Saturn’s tides (Fuller et al. 2016). We identify the exact mechanism exciting the inclinations as the equality between the moon’s nodal precession period (relative to Saturn’s equinox) and Saturn’s perihelion-to-perihelion orbital period. The magnitude of this resonance is proportional to Saturn’s obliquity and its periodically varying eccentricity. While extrapolations from current trends imply that Rhea could not have crossed the solar semi-secular resonances without acquiring a large inclination, there are combinations of past migration rates of Rhea and Titan that have Rhea cross the resonance before Titan’s migration causes Saturn’s spin axis to tilt (Saillenfest et al. 2021). We will discuss these and other dynamical constraints of these moons’ orbital histories at the meeting.

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