Relativity parameters determined from lunar laser ranging

Abstract

Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters \ensuremath{\beta} and \ensuremath{\gamma}, and G\ifmmode \dot{}\else \.{}\fi{}/G. Recent data can be fitted with a rms scatter of 3 cm. (a) Using the Nordtvedt effect to test the principle of equivalence, it is found that the Moon and Earth accelerate alike in the Sun's field. The relative accelerations match to within 5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$. This limit, combined with an independent determination of \ensuremath{\gamma} from planetary time delay, gives \ensuremath{\beta}. Including the uncertainty due to compositional differences, the parameter \ensuremath{\beta} differs from unity by no more than 0.0014; and, if the weak equivalence principle is satisfied, the difference is no more than 0.0006. (b) Geodetic precession matches its expected 19.2 marc sec/yr rate within 0.7%. This corresponds to a 1% test of \ensuremath{\gamma}. (c) Apart from the Nordtvedt effect, \ensuremath{\beta} and \ensuremath{\gamma} can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8\ensuremath{\beta}+1.4\ensuremath{\gamma} can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both \ensuremath{\beta} and \ensuremath{\gamma} match the values of general relativity to within 0.005, and the linear combination \ensuremath{\beta}+\ensuremath{\gamma} matches to within 0.003, but caution is advised due to the lack of theoretical understanding of these sensitivities. (d) No evidence for a changing gravitational constant is found, with |G\ifmmode \dot{}\else \.{}\fi{}/G|\ensuremath{\le}8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$/yr. There is significant sensitivity to G\ifmmode \dot{}\else \.{}\fi{}/G through solar perturbations on the lunar orbit. \textcopyright{} 1996 The American Physical Society.