On Ganymede's synchronous rotation in the presence of a subsurface ocean

We investigate the librations of Ganymede's core and shell on different time scales around its synchronous spin-orbit resonant state. Our study is based on dynamical models of the moon being composed of a thin external shell and an inner solid core, separated by a potential internal ocean. Here, we assume that the two layers are interacting via a gravitational torque and a viscous torque. External tidal torques on each layer are also considered. We derive and analyze the fundamental equations of motion using analytical and numerical methods for initial conditions close to resonance and several parameters. A core subject of our study is to provide estimates of the damping time scales for the free librations and the geometry of the dynamical attractor in phase space. In addition, we analyze the separate torques, i.e., their isolated effects on the short- and mid-term evolution. We derive explicit solutions that enable us to perform an accurate investigation of the system parameters, i.e., their influence on the amplitudes and frequencies. Analytical estimates of the damping time scales are provided on the basis of the real parts of the eigenvalues and are validated by numerical simulations. Finally, we test our findings, being based on a well-established class of dynamical models, also with an alternative approach based on creep tide theory. On the basis of this model we provide relaxation time scales of the elastic layers and compare the different dynamical phases with the model based on rigid layers. With this we are able to provide a plausible range of damping time scales (ranging from 3 to 100 years), relaxation factors (ranging from 0.5 to 30 years) libration amplitudes of the damped solutions (15 m), and periods of the damped solutions (7.2 days). Our study enables us to constrain the order of magnitudes of the parameters that describe the composition of the layers, their rheological properties, and the current dynamical state of Ganymede being consistent with mid-term simulations. This work may serve as a framework for the interpretation of measurements done by the JUICE mission to constrain critical parameters that can only be observed indirectly: core and shell geometry, their densities, existence and thickness of an internal ocean, to name a few.