Synchronous locking of tidally evolving satellites

Satellite spin states evolve under the action of solid body torques and tidal forces. The tidal effects result in a damping of fast spin rates and, ultimately, in the locking of the spin into what are known as Cassini states. The dynamical equations for the satellite spin vector are derived, non-dimensionalized, and discussed. The non-dimensional parameters that determine the ultimate fate of the system are identified. A review of Cassini states is given, and then the effect of a permanent triaxial deformation on the evolution of the spin vector is explored. We find that for the parameter ranges of most real Solar System satellites which have been despun to synchronous rotation, occupation of Cassini state 1 is the only possible endpoint. The existence of a non-axially symmetric deformation destabilizes the higher obliquity Cassini state 2. We discuss the possibility of tumbling occurring during the spin-down and argue that this does not effect our basic conclusions. The non-occupancy of Cassini state 2 (except for the Moon, for which state 1 does not exist) is not a function of initial conditions or spin configuration occupied at synchronous lock, as previously hypothesized. (C) 1996 Academic Press, Inc.