Effects of physical librations of the Moon on the orbital elements of a lunar satellite

Physical librations of the Moon are small cyclic perturbations with periods of one month and longer, and amplitudes of 100 arc seconds or less. These cause the selenographic axes fixed in the true Moon to have a different orientation than similar axes fixed in the mean Moon.Physical librations have two types of effects of present interest. If the orbital elements of a lunar satellite are referred to selenographic axes in the true Moon as it rotates and librates, then the librations cause changes in the orientation angles (node, inclination, and periapsis argument of the satellite) large enough that long-period perturbation theory cannot be used without compensation for such geometrical effects. As a second effect, the gravitational potential of the Moon is actually wobbled in inertial space, a condition not included in the potential expression used in perturbation theory.This paper gives data on the magnitude of the physical librations, the geometrical effects on the orbital elements and the equivalent changes in the coefficients in the potential. It is shown that geometrical effects can be accommodated either by using an inertial axes system or by compensating for the lunar librations and precession when the selenographic axes are used. Further, it is shown that physical effects are small and negligible for all but the most exacting endeavors.