The Librations of Titan

Titan, the largest satellite of Saturn, rotates synchronously with its orbital motion. As a result of Titan's non-spherically symmetric mass distribution, the 1:1 spin-orbit resonance is stable, but small variations in the rotation rate around the equilibrium state are possible and measurements of these librations have been reported several times (Lorenz et al. 2008, Stiles et al 2008, Stiles et al. 2010, Meriggiola et al. 2012). The librations contain information on the interior of Titan, and in particular can be used to constrain several properties of the ice shell of Titan (Van Hoolst et al. 2013).

The measurements of the rotation variations are based on determinations of the shift in position of Cassini SAR radar images taken during different flybys. The results, however, do not agree and the spin variations are smaller for the latest studies. Theoretical estimates show that variations in the rotation rate can occur for several reasons (Van Hoolst et al. 2013, Richard et al. 2014). First, Titan's rotation changes with a period equal to Titan's orbital period as a result of the gravitational torque exerted by Saturn. Second, dynamic variations in the atmosphere of Titan induce changes in Titan's rotation with a main period equal to half the orbital period of Saturn. Third, free librations with periods of the order of a year might be excited, and fourth, deviations from a Keplerian orbit perturb the rotation at additional frequencies.

Here, we report on different theoretical aspects of the librations and compare theoretical predictions with observational results. We consider the influence of the rheology of the ice shell and take into account Cassini measurements of the external gravitational field and of the topography of Titan. We also evaluate the librations induced by Titan's hydrocarbon seas and use the most recent results of Titan's atmosphere dynamics.