Like our Moon, the large icy satellites of Jupiter are thought to be in a Cassini State, an equilibrium rotation state characterized by a synchronous rotation rate and a precession rate of the rotation axis equal to that of the normal to the orbit. In these equilibrium states (up to four Cassini States are possible for a solid and rigid satellite), the spin axis of the satellite, the normal to its orbit and the normal to the inertial plane remain coplanar with an obliquity that remains theoretically constant. However, as the gravitational torque exerted on the satellite shows small periodic variations, the orientation of the rotation axis will also vary with time and nutations in obliquity will appear.

Here we present a dynamical model for the study of the Cassini States. This model includes the coupling between the polar motion and the spin axis precession/nutation which is neglected in the classical studies. We study the influence of the triaxiality of Ganymede on its four possible Cassini States, use a Toy model of the Moon to illustrate the nutations in obliquity obtained with the dynamical model, and investigate the influence of the presence of a subsurface ocean on the Cassini State I of Europa.

Longitudinal librations are periodic changes in the rotation angle of a planet or satellite. Their observation and subsequent interpretation have profoundly increased our understanding of the interior structure of Mercury. Likewise, libration is thought to provide important constraints on the interior structure of icy satellites. Here we study the libration of Mercury and large icy satellites rotating synchronously with their orbital motion and explain how it depends on the interior structure.

The state of knowledge about the structure and composition of icy satellite interiors has been significantly extended by combining direct measurements from spacecraft, laboratory experiments, and theoretical modeling. Interior models of icy bodies will certainly benefit from future missions to the outer solar system, providing new and improved constraints on the surface chemistry, bulk composition and degree of internal differentiation, possible heterogeneities in radial mass distribution, the presence and extent of liquid reservoirs, and the amount of tidal heating for each target body. Here we summarize geophysical constraints on the interior structure and composition of selected Jovian and Saturnian icy satellites and investigate conditions under which potentially habitable liquid water reservoirs could be maintained. Future geophysical exploration which includes gravitational and magnetic field sounding from low-altitude orbit and close flyby, combined with altimetry data and in-situ monitoring of tidally-induced surface distortion and time-variable magnetic fields, would impose important constraints on the interiors of outer planet satellites.