Use of an Analytical Theory for the Physical Libration of the Moon to Detect Free Nutation of the Lunar Core

A brief review of modern observational achievements and the theoretical basis of physical libration of the Moon is presented. Special attention is given to the inferred existence of a lunar core and determination of its parameters. The creation of a theory of physical libration of the Moon, which requires analyses of semi-empirical series of long-term laser observations and the use of the highly accurate DE421 dynamical ephemeris, is related to this. A large role in this area has been played by the analytical theory of physical libration of the Moon constructed by Yu.V. Barkin, which made it possible for the first time to derive parameters of the free nutation of the lunar core from observations. This paper is based on a talk given at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).