The interior structure of a satellite determines its response to rotational and tidal forcing, which in turn affects its equilibrium shape and tidal heating. The unusual shape of the Moon given its present rotational and orbital state has been explained as due to a fossil figure preserving a record of remnant rotational and tidal deformation. However, previous studies assume infinite rigidity and ignore deformation due to changes in the rotational and orbital potentials as the Moon evolves to the present state. In the first part of the talk, I will present a new self-consistent model that takes into account finite rigidity. The new model reveals a fossil figure consistent with an early epoch of true polar wander and an early low-eccentricity, synchronous lunar orbit.

Icy satellites of the outer solar system have emerged as potential habitable worlds due to the presence of subsurface oceans. Tidal heating is a dominant long-term energy source for icy satellites. Therefore, in addition to directly affecting the interior structure, the presence of subsurface oceans is closely related to how an icy satellite’s thermal, rotational, and orbital states evolve. The long-term survivability of subsurface oceans depends on contributions to tidal heating from the ocean itself. Therefore, there is a need for developing ocean tidal heating models. In the absence of such a model, determining the long-term evolution and survivability of subsurface oceans in icy satellites will remain challenging. In the second part of the talk, I will present a new theoretical treatment for ocean tidal heating that takes into account the effects of ocean loading, self-attraction, and deformation of the solid regions. These effects modify both the forcing potential and the ocean thicknesses for which energy dissipation is resonantly enhanced, potentially resulting in orders of magnitude changes in the dissipated energy flux.