Progress in Lunar Laser Ranging Tests of Relativistic Gravity

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. These analyses give an EP test of $\Delta (M_G/M_I{)}_{\mathrm{E}\mathrm{P}}=(-1.0\pm 1.4)\times {10}^{-13}$. This result yields a strong equivalence principle (SEP) test of $\Delta (M_G/M_I{)}_{\mathrm{S}\mathrm{E}\mathrm{P}}=(-2.0\pm 2.0)\times {10}^{-13}$. Also, the corresponding SEP violation parameter $\eta$ is $(4.4\pm 4.5)\times {10}^{-4}$, where $\eta =4\beta -\gamma -3$ and both $\beta$ and $\gamma$ are post-Newtonian parameters. Using the Cassini $\gamma$, the $\eta$ result yields $\beta -1=(1.2\pm 1.1)\times {10}^{-4}$. The geodetic precession test, expressed as a relative deviation from general relativity, is $K_{\mathrm{g}\mathrm{p}}=-0.0019\pm 0.0064$. The search for a time variation in the gravitational constant results in $\dot{G}/G=(4\pm 9)\times {10}^{-13}{\mathrm{y}\mathrm{r}}^{-1}$; consequently there is no evidence for local ($\sim 1\mathrm{A}\mathrm{U}$) scale expansion of the solar system.