Abstract 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.

Abstract The micro-canonical phase-space volume for the three-body problem is a topic of intrinsic interest. Within the flux-based statistical theory, it provides a means to predict the scale of disintegration times for non-hierarchical systems. While the bare phase-volume diverges, Dandekar et al. (Celest Mech Dyn Astron 134(6): 55, 2022. https://doi.org/10.1007/s10569-022-10108-1) (Paper I) showed that a regularized version can be defined. Building on Paper I, which determined the regularized phase-volume for a given energy $${{\bar{\sigma }}}(E)$$ σ ¯ ( E ) , this paper extends the analysis to its distribution over angular momentum, $${{\bar{\sigma }}}(E,L)$$ σ ¯ ( E , L ) . Through analytical integrations, we reduce the problem to a 3d numerical integration, a step-up in complexity from the 2d integration required for $${{\bar{\sigma }}}(E)$$ σ ¯ ( E ) . We provide regularized phase-volume values for several mass sets across a range of E and L, validated through an L-integration test. Notably, the values remain positive for all tested parameters, lending further support to the validity of the chosen regularization procedure. For high values of L at fixed masses and E, we observe a strong suppression of $${{\bar{\sigma }}}(E,L)$$ σ ¯ ( E , L ) .