Theory of the Libration of the Moon
Abstract
In 1693, Jean Dominique Cassini disclosed his finding that the rotational motion of the Moon could be neatly described by the superposition of two uniform motions, a prograde rotation of the Moon about its polar axis and a retrograde precession of the Moon's equator along the ecliptic. The description of these motions is now called Cassini's laws. The theoretical explanation of Cassini's laws shows that physical librations with amplitudes less than 0″.5, as seen from the Earth, must also exist. Until 1970, the physical librations were just marginally discernible, and the dynamical theory was developed to a level far superior to the quality of the observations. In 1970 the resolution of libration observations jumped by a factor of 10^{4} over earlier techniques, and existing theories became inadequate for analyzing the observations. This paper presents a new semianalytic libration theory that is of use for analyzing observations. In this development the Moon is assumed to be either rigid, elastic or anelastic, and its gravity potential is represented through its fourthdegree harmonics. The Moon is considered to be moving about the Earth in an orbit that is perturbed by the Sun (the ALE of Deprit, Henrard and Rom), and by the planets and the figures of the Earth and Moon (from the ILE, principally derived by Brown). The direct effects of the rotation of the plane of the ecliptic and the figure of the Earth are also considered. Tables for physical libration variables are tabulated which are truncated at 0″.010.
 Publication:

Moon and Planets
 Pub Date:
 August 1981
 DOI:
 10.1007/BF00911807
 Bibcode:
 1981M&P....25....3E
 Keywords:

 Earth Orbits;
 Libration;
 Lunar Rotation;
 Perturbation Theory;
 Planet Ephemerides;
 Angular Momentum;
 Angular Velocity;
 Computer Techniques;
 Coordinates;
 Fourier Series;
 Orbital Mechanics;
 Tables (Data);
 Lunar and Planetary Exploration; Moon