An observational constraint on Titan’s tidal dissipation

A satellite’s spin state holds clues to its interior properties. A satellite’s spin axis precesses about its orbit normal due to torques on its permanent triaxial figure. At the same time, the orbit normal precesses about the Laplace plane normal (defined as the average precessional plane) due to torques from the planet’s oblateness, the Sun, and when applicable other satellites. Tidal torques drive the system to equilibrium, which for a circular orbit corresponds to synchronous rotation and an equilibrium spin vector, called a Cassini state. In a Cassini state, the precessional periods of the spin axis and orbit normal are the same, and the spin vector lies approximately in the plane defined by the orbit normal and Laplace plane normal, which we call the Cassini plane. There is a small angular offset between the spin axis and the Cassini plane which depends on the degree of dissipation in the body. Therefore, accurate observations of the spin states of satellites in our solar system can shed light on their tidal dissipation properties. Using the equations of motion of a body’s spin axis under the influence of tidal and precessional torques, we derive a relation between the tidal dissipation factor, k2/Q, and the spin vector. The observed spin orientations of the Moon and Titan can be used to estimate their values for k2/Q. The low value of Q derived for Titan suggests a recent excitation of its eccentricity such as by a close encounter with a putative now-lost satellite.