Testing General Relativity with Laser Ranging to the Moon

This paper assesses some possibilities inherent in precise laser ranging to the moon for testing Einstein's theory of gravitation. The anticipated accuracy of the determination of the light transit time for a laser pulse returned by an optical corner reflector on the lunar surface is about two parts in ${10}^{10}$. Such high precision opens the possibility of detecting general relativistic effects in both the light propagation itself and in the lunar motion. The detailed analysis presented here indicates that, although the effects on light propagation are probably not detectable, there are general relativistic effects in the lunar motion which appear to be observationally accessible with the expected laser-ranging data. Observation of the dominant effect would provide a significant test of the correctness of the geodesic equation, to $O\left(\frac{1}{c^2}\right)$ beyond the Newtonian approximation, for describing the motion of bodies in a gravitational field.