The physical librations of the moon,including higher harmonic effects

The equations of the physical libration of the Moon are developed using a representation of the Earth-Moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. TheImproved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10 six-yearly (argument), 1.2 three-yearly, 0.5 annual, and 0.1 monthly; on pole direction they are on the order of 0.5 six-yearly and 1.0 monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.