Theory of physical libration of the Moon caused by a liquid core: Cassini’s motion

Abstract

This is the first part of a study to develop a modern theory of physical libration of the Moon caused by a liquid core. We use a special approach to studying Moon’s rotation relying on Poincaré’s planetary model and special forms of equations of motion in Andoyer and Poincaré variables. We construct expansions of the force function of the problem (the second harmonic of the selenopotential) in Andoyer and Poincaré variables for a high-precision description of disturbed orbital motion of the Moon. We investigate the main regularities in lunar rotational motion taken as a body with a solid nonspherical mantle and an ellipsoidal liquid core. The motion of the ideal liquid of the core is simple according to Poincaré. The Cassini laws can be dinamically interpreted for the motion of a synchronous satellite with a liquid core. The Cassini angle (the inclination of the rotation axis relative to the normal to the ecliptic plane) determined by us is very consistent with its determinations from laser observations.