On the Motion Period of the Rotation Axis Pole in the Case of an Elastic Moon

Abstract

Numerous studies present results of investigating the rotational and translational-rotational motion of a viscoelastic Earth and its Moon. However, they primarily focus on the dynamics of the Earth--Moon system. Further contemporary studies of the Moon will necessarily involve investigating how the elastic properties of the Moon manifest in its physical libration (in the modern era). The following lines of research are particularly noteworthy: effects of the liquid and solid nuclei of the Moon, as well as the Moon mantle elasticity, on its rotational motion, taking into account a highly precise description of the orbital motion of the Moon and the motion being driven by resonance. This paper identifies significant effects to be taken into account when interpreting observation results. We used the Liouville problem equations stated in Andoyer variables along with the perturbation theory to describe the rotational motion of the Moon. We show that accounting for the elastic properties of the Moon in its model means that its pole oscillation period becomes significantly longer than the period yielded by the classic solid Moon model. The paper presents the Chandler period values for comparison, calculated according to the formulas provided. The investigation results are relevant to the updated Russian lunar program for the 2021--2040 period.