Letter to the Editor

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

¹ Institut für Erdmessung (IfE), Leibniz Universität Hannover, Scheiderberg 50, 30167 Hannover, Germany
e-mail: hofmann@ife.uni-hannover.de
² QUEST – Centre for Quantum Engineering and Space Time Research, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

Received: 30 August 2010
Accepted: 19 October 2010

Abstract

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 für Erdmessung (IfE) LLR model taking the effect of a fluid lunar core into consideration. The temporal variation in the gravitational constant Ġ/G₀ and the strong equivalence principle, parameterized by the Nordtvedt parameter η, 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 Ġ/G₀ = (−0.7 ± 3.8) × 10^-13  yr^-1 and η = (−0.6 ± 5.2) × 10^-4.