Influence of a subsurface ocean on the Cassini States and the polar motion of the Galilean satellites

The Galilean satellites are in an equilibrium rotation state called Cassini State and characterized by a synchronous rotation and a precession rate of the rotation axis that is equal to that of the normal to the orbit. Moreover, the spin axis of the satellite, the normal to its orbit and the normal to the inertial plane remain coplanar and the obliquity (angle between the normal to the orbit and the spin axis) remains theoretically constant over time. For satellites with a slow orbital precession rate like the Galilean moons, up to four Cassini states are possible, characterized by an obliquity close to 0 (CSI), /2 (CSII and IV) and (CSIII). The Galilean satellites are assumed to be in CSI.We here study the influence of a subsurface ocean on the CSI of triaxial satellites using an angular momentum approach. In our model, the motion of the spin motion in space is coupled with the polar motion of the satellite and we extend our model by considering terms up to order 2 in small quantities. Moreover, and contrary to what is usually done in the classical Cassini States studies, we here do not average the external gravitational torque over short period terms. In addition to the mean obliquity value of the different satellites, we therefore also compute the nutations (small periodic variations), both in obliquity and in longitude, that arise due to the periodic variations of the gravitational torque acting on the satellites and study the influence of a subsurface ocean on the obliquity and polar motion of these satellites.