Equivalence principle and the Moon

The perturbation of the lunar motion caused by a hypothetical violation of the equivalence principle is analytically worked out in terms of power series in the manner of Hill and Brown. The interaction with the quadrupolar tide is found to amplify the leading order term in the synodic range oscillation by more than 62%. Confirming a recent finding of Nordtvedt, we show that this amplification has a pole singularity for an orbit beyond the lunar orbit. This singularity is shown to correspond to the critical prograde orbit beyond which, as found by Hénon, Hill’s periodic orbit becomes exponentially unstable. It is suggested that ranging between prograde and retrograde orbits around outer planets might provide future high precision orbital tests of the equivalence principle. It is argued that, within the context of string-derived non-Einsteinian theories, the theoretical significance of orbital tests of the universality of free fall is to measure the basic coupling strength of some scalar field primarily through composition-dependent effects. Present Lunar Laser Ranging data yield, within such models, the value γ¯=(-0.9±1.3)×${10}^{\mathrm{-}7}$ for the effective Eddington parameter γ¯≡γ-1 measuring this coupling strength. © 1996 The American Physical Society.