Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Context. Forty years of lunar laser ranging (LLR) data provide an excellent basis to determine various parameters of the Earth-Moon system as well as parameters related to gravitational physics. Aims. We update the Institut fur Erdmessung (IfE) LLR model taking the effect of a fluid lunar core into consideration. The temporal variation in the gravitational constant (G) over dot/G(0) and the strong equivalence principle, parameterized by the Nordtvedt parameter eta, are investigated. Methods. A set of LLR observations from 1970 to 2009 was analysed and the parameters were determined by a least squares adjustment in two runs. After solving for classical Newtonian parameters (e.g. initial conditions for the lunar orbit and rotation) in the first run, relativistic parameters were determined in the second run. Results. The upper limits to the gravitational constant and the Nordtvedt parameter were found to be (G) over dot/G(0) = (-0.7 +/- 3.8) x 10(-13) yr(-1) and eta = (-0.6 +/- 5.2) x 10(-4).