The Relativistic Orbit Observables in Lunar Laser Ranging

Abstract

The several relativistic observables in the lunar orbit measureable by present-day lunar laser ranging data are analytically calculated in a unified treatment. Because the solar tidal deformation of the lunar orbit plays such a central role in altering amplitudes and frequencies in the lunar motion, the relativistic equations of motion are solved using procedures similar to those G. W. Hill introduced into classical lunar theory and which treat the orbit's tidal deformation in a partially nonperturbative manner. The tidal deformation, itself, is relativistically altered in magnitude. The amplitude of relativistic perturbations of monthly period are found to be significantly amplified by interaction with the orbit's tidal deformation. This amplification enhances the sensitivity of the lunar orbit as an observational probe of the gravitational to inertial mass ratio of the Earth (and Moon). The "evection" amplitude is also altered by general relativity at an observational level. Relativistic corrections to the perigee precession rate are found which include not only 4% enhancement of the well-discussed de Sitter "geodetic precession" term, but also a direct contribution from the solar tidal acceleration which is 10% as large. An orbit is found beyond the lunar orbit (at about 1.8 lunar orbit radii) for which the interaction between the tidal deformation and any "monthly" perturbation is resonant and strongly amplifies the latter. Ranging to a satellite in such an orbit could perhaps be useful in future high precision tests of relativistic gravity.Solar radiation pressure acceleration of the Moon is found to be at the threshold of observability in both the secular and periodic terms of lunar motion.