Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Abstract

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here, we show current results for relativistic parameters like a possible temporal variation of the gravitational constant G˙/G0=(−5.0±9.6)×10−15yr−1, the equivalence principle with Δmg/miEM=(−2.1±2.4)×10−14, and the PPN parameters β−1=(6.2±7.2)×10−5 and γ−1=(1.7±1.6)×10−4. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein’s theory is found and the results set improved limits for the different effects.

Characteristics of differential lunar laser ranging

“…where ε is white noise added according to the accuracy of DLLR. All variables used in our LUNAR software (Hofmann 2017;Biskupek 2015) is in quadruple-precision floating-point format. According to the distance between the Earth and Moon (between 363,000 and 406,000 km), this precision enables us to directly use the above formulation for simulating DLLR data which has a predicted accuracy of about 30 µm.…”

“…The positions are considered in the Barycentric Celestial Reference System (BCRS). Here, tse, tsr, and tr are given in the Barycentric Dynamical Time (TDB) (Biskupek 2015); tse is initially given in the Coordinated Universal Time (UTC) which requires the transformation from UTC to TDB (Petit & Luzum 2010).…”

“…With more than 50 years of tracking the Moon from Earth, LLR contributes to many scientific research fields related to the Earth-Moon system. For geodesy, LLR can be used to calculate the Earth orientation parameters (EOPs) that are related to the precession, nutation, rotation ∆UT 1, and polar motion (Singh et al 2021;Biskupek 2015). It can potentially provide a good verification for the estimation of ∆UT 1 from very long baseline interferometry (VLBI).…”

“…stant, G, with time, the geodetic precession, the equivalence principle (EP) for the Earth and Moon in the gravitational field of the Sun, and of the galactic dark matter as well as the parametrized post-Newtonian (PPN) parameters, etc. (Biskupek et al 2021;Zhang et al 2020;Williams et al 2012;Viswanathan et al 2018). For selenophysics, LLR is sensitive to the lunar orbit, solid tides, and orientation (Müller et al 2019;Williams et al 2014).…”

Current and Future Tests of General Relativity

“…Despite the spectacular aspects of the areas mentioned, which are often exclusively mentioned in public talks and also as "selling points" for gravity research, one should not forget that solar system and near-Earth gravity research is by no means closed, and that GR is also becoming a tool for studying the Earth's environment. Relativistic Geodesy and inertial sensing are closely linked to GR and rely on its predictions, and can, conversely, be used for high-precision tests of GR [6]. Present and future perspectives for further solar-system tests are discussed in [7].…”