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# Lunar Laser Ranging Tests of the Equivalence Principle with the Earth and Moon

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### Abstract

A primary objective of the Lunar Laser Ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. Time series of the highly accurate measurements of the distance between the Earth and Moon provide unique information used to determine whether, in accordance with the Equivalence Principle (EP), both of these celestial bodies are falling towards the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Current LLR solutions give $$(-1.0 \pm 1.4) \times 10^{-13}$$ for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, $$\Delta(M_G/M_I)$$. This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of $$\Delta(M_G/M_I)_{\tt SEP} = (-2.0 \pm 2.0) \times 10^{-13}$$. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter $$\eta$$ of $$(4.4 \pm 4.5)\times10^{-4}$$, where $$\eta = 4\beta -\gamma -3$$ and both $$\gamma$$ and $$\beta$$ are parametrized post-Newtonian (PPN) parameters. The PPN parameter $$\beta$$ is determined to be $$\beta - 1 = (1.2 \pm 1.1) \times 10^{-4}$$. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR ranging accuracy will further advance the research of relativistic gravity in the solar system, and, most notably, will continue to provide highly accurate tests of the Equivalence Principle.

### Most cited references42

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(2003)
According to general relativity, photons are deflected and delayed by the curvature of space-time produced by any mass. The bending and delay are proportional to gamma + 1, where the parameter gamma is unity in general relativity but zero in the newtonian model of gravity. The quantity gamma - 1 measures the degree to which gravity is not a purely geometric effect and is affected by other fields; such fields may have strongly influenced the early Universe, but would have now weakened so as to produce tiny--but still detectable--effects. Several experiments have confirmed to an accuracy of approximately 0.1% the predictions for the deflection and delay of photons produced by the Sun. Here we report a measurement of the frequency shift of radio photons to and from the Cassini spacecraft as they passed near the Sun. Our result, gamma = 1 + (2.1 +/- 2.3) x 10(-5), agrees with the predictions of standard general relativity with a sensitivity that approaches the level at which, theoretically, deviations are expected in some cosmological models.
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### Author and article information

###### Journal
19 July 2005
2009-01-02
10.1142/S021827180901500X
gr-qc/0507083