Relativistic tests with lunar laser ranging

Abstract This paper presents the recent version of the lunar laser ranging (LLR) analysis model at the Institut für Erdmessung (IfE), Leibniz Universität Hannover and highlights a few tests of Einstein’s theory of gravitation using LLR data. Investigations related to a possible temporal variation of the gravitational constant, the equivalence principle, the PPN parameters β and γ as well as the geodetic precession were carried out. The LLR analysis model was updated by gravitational effects of the Sun and planets with the Moon as extended body. The higher-order gravitational interaction between Earth and Moon as well as effects of the solid Earth tides on the lunar motion were refined. The basis for the modeled lunar rotation is now a 2-layer core/mantle model according to the DE430 ephemeris. The validity of Einstein’s theory was studied using this updated analysis model and an LLR data set from 1970 to January 2015. Within the estimated accuracies, no deviations from Einstein’s theory are detected. A relative temporal variation of the gravitational constant is estimated as G ˙ / G 0 = ( 7.1 ± 7.6 ) × 10 − 14 y r − 1 , the test of the equivalence principle gives Δ ( m g / m i ) E M = ( − 3 ± 5 ) × 10 − 14 and the Nordtvedt parameter η = ( − 0.2 ± 1.1 ) × 10 − 4 , the PPN-parameters β and γ are determined as β − 1 = ( − 4.5 ± 5.6 ) × 10 − 5 and γ − 1 = ( − 1.2 ± 1.2 ) × 10 − 4 and the geodetic precession is confirmed within 0.09%. The results for selected relativistic parameters are obtained by introducing constraints from an LLR solution without estimating relativistic quantities. The station coordinates are constrained for the estimation of