Variations of the gravitational constant from lunar laser ranging data

Thirty seven years of lunar laser ranging (LLR) data provided a large number of results which contributed to a better understanding of the dynamics of the Earth-Moon system and to the highly accurate determination of relativistic quantities such as the equivalence principle.Spatial and temporal variations of Newton's coupling parameter, G, may occur intrinsically in alternative theories of gravity or because of lack of local Lorentz invariance in metric gravity.Here, we use LLR data to determine possible secular and quadratic temporal variations of the gravitational constant.Measurements of these parameters yield /G = (27)10 -13 yr -1 (realistic errors) and G/G = (45)10 -15 yr -2 .The determination of the preferred-frame parameters quantifying a possible spatial anisotropy of G gave 1 = (-4 9) 10 -5 and 2 = (2 2) 10 -5 .This ensemble of parameters may be useful for constraining post-Newtonian theories of gravitation.