Relativity parameters determined from lunar laser ranging

Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters {β} and {γ}, and G ̇ \.{}{}/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×{}10^-13. This limit, combined with an independent determination of {γ} from planetary time delay, gives {β}. Including the uncertainty due to compositional differences, the parameter {β} 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 {γ}. (c) Apart from the Nordtvedt effect, {β} and {γ} can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8{β}+1.4{γ} can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both {β} and {γ} match the values of general relativity to within 0.005, and the linear combination {β}+{γ} 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 ̇ \.{}{}/G|{≤}8×{}10^-12/yr. There is significant sensitivity to G ̇ \.{}{}/G through solar perturbations on the lunar orbit. {} 1996 The American Physical Society.