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

James G. Williams; Slava G. Turyshev; Dale H. Boggs

doi:10.1142/S021827180901500X

paper

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

arXiv:gr-qc/0507083 · doi:10.1142/S021827180901500X

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 $(- 1.0 \pm 1.4) \times 1 0^{- 13}$ for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, $Δ (M_{G} / M_{I})$ . This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of $Δ (M_{G} / M_{I})_{SEP} = (- 2.0 \pm 2.0) \times 1 0^{- 13}$ . 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 $η$ of $(4.4 \pm 4.5) \times 1 0^{- 4}$ , where $η = 4 β - γ - 3$ and both $γ$ and $β$ are parametrized post-Newtonian (PPN) parameters. The PPN parameter $β$ is determined to be $β - 1 = (1.2 \pm 1.1) \times 1 0^{- 4}$ . 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.

arXiv comment50 pages, 18 figures, 4 tables

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

Abstract

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