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

TL;DR

Lunar Laser Ranging experiments provide highly precise tests of the Equivalence Principle by measuring Earth-Moon distance variations, confirming the principle to an accuracy of about 1 part in 10^13, and constraining related gravitational parameters.

Contribution

This paper presents the most precise LLR-based test of the Equivalence Principle and related gravitational parameters, demonstrating the robustness of the results and discussing potential future improvements.

Findings

No significant violation of the Equivalence Principle detected.

The SEP violation parameter η is constrained to (4.4 ± 4.5)×10^{-4}.

PPN parameter β is measured as β - 1 = (1.2 ± 1.1)×10^{-4}.

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.