Progress in Lunar Laser Ranging Tests of Relativistic Gravity

TL;DR

LLR provides a solar-system testbed for relativistic gravity, including EP and SEP, PPN $β$, $γ$, geodetic precession, and the time variation of $G$. By analyzing data through April 2004 (15,553 normal points) and incorporating Cassini γ, the paper reports tight constraints: $[(M_G/M_I)_e-(M_G/M_I)_m]_{EP}=(-1.0\pm1.4)\times10^{-13}$ and $[(M_G/M_I)_e-(M_G/M_I)_m]_{SEP}=(-2.0\pm2.0)\times10^{-13}$, with $η=(4.4\pm4.5)\times10^{-4}$, and $β-1=(1.2\pm1.1)\times10^{-4}$. The time variation of $G$ is limited to $\dot{G}/G=(4\pm9)\times10^{-13}\ \mathrm{yr}^{-1}$ and the geodetic precession deviation to $K_{gp}=-0.0019\pm0.0064$, all consistent with GR. These results inform scalar-tensor gravity theories and guide future LLR experiments, including Apache Point.

Abstract

Analyses of laser ranges to the Moon provide increasingly stringent limits on any violation of the Equivalence Principle (EP); they also enable several very accurate tests of relativistic gravity. We report the results of our recent analysis of Lunar Laser Ranging (LLR) data giving an EP test of Δ(M_G/M_I)_{EP} =(-1.0 +/- 1.4) x 10^{-13}. This result yields a Strong Equivalence Principle (SEP) test of Δ(M_G/M_I)_{SEP} =(-2.0 +/- 2.0) x 10^{-13}. Also, the corresponding SEP violation parameter ηis (4.4 +/- 4.5) x 10^{-4}, where η=4β-γ-3 and both βand γare parametrized post-Newtonian (PPN) parameters. Using the recent Cassini result for the parameter γ, PPN parameter βis determined to be β-1=(1.2 +/- 1.1) x 10^{-4}. The geodetic precession test, expressed as a relative deviation from general relativity, is K_{gp}=-0.0019 +/- 0.0064. The search for a time variation in the gravitational constant results in \dot G/G=(4 +/- 9) x 10^{-13} yr^{-1}, consequently there is no evidence for local (~1AU) scale expansion of the solar system.