Testing the equivalence principle with lunar laser ranging residuals from different planetary and lunar ephemerides

Abstract

Lunar laser ranging (LLR) provides a sensitive test of the equivalence principle (EP) through a possible synodic perturbation in the Earth--Moon distance. In this work, we develop an independent LLR data-reduction framework and investigate this signature in the post-fit O--C residuals obtained with the EPM21, INPOP21, and DE430 planetary and lunar ephemerides. The same observation model and parameter-adjustment procedure are applied to the three ephemerides, allowing their residual-based results to be compared within a consistent framework. To account for the nonuniform distribution of LLR observations over the synodic angle $D$, the residuals are fitted with cosine and sine harmonics up to the third order. Signal-injection tests are also performed to quantify the attenuation of a possible $\cos D$ signal during the parameter adjustment. After correcting for signal attenuation, solar radiation pressure, and the thermal response of the lunar retroreflectors, the preferred EPM21, INPOP21, and DE430 solutions yield $\Delta(m_g/m_i)_{\rm EM}=(0.900\pm3.183)\times10^{-14}$, $(0.496\pm3.624)\times10^{-14}$, and $(2.669\pm7.048)\times10^{-14}$, respectively. The EPM21 and INPOP21 results are based on observations from 1970 to 2024, whereas the DE430 solution was obtained using observations up to 2016. All three estimates are consistent with zero within their uncertainties. This work demonstrates that residual-based analysis can provide an independent and transparent EP test, while also offering guidance for assessing sampling and ephemeris-dependent effects in future high-precision LLR studies.