Testing Relativistic Gravity with Lunar Laser Retroreflectors and PEP

Testing relativistic gravity with lunar laser retroreflectors and PEP G. Bargiacchi1, R. Campagnola1, M. Muccino1,2, L. Porcelli1, S. Dell’Agnello1, E. Battista1, S. Capozziello3,4,5, M. Maiello1, R. March1, R. Rodriquez 1, L. Salvatori1, M. Tibuzzi1, M. Trigilio1,2, B. Villalba1,2 1 Istituto Nazionale di Fisica Nucleare—Laboratori Nazionali di Frascati (INFN-LNF), Via E. Fermi 54, P.O. Box 13, 00044 Frascati, RM, Italy 2 Aerotecno s.r.l., Via dei Savorelli 3, 00165 Rome, RM, Italy 3 Istituto Nazionale di Fisica Nucleare—Sezione di Napoli (INFN-NA), Via Cintia snc, 80126 Napoli, NA, Italy 4 Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138 Napoli, NA, Italy 5 Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte S. Angelo, Via Cinthia snc, Ed. N, 80126 Napoli, NA, Italy Email: [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] Keywords: General relativity, gravitational physics, lunar laser retroreflectors, Planetary Ephemeris Program Since 1969, Lunar Laser Ranging (LLR) technique, i.e., the time-of-flight measurements of short laser pulses fired from ground stations to Laser Retroreflector Arrays (LRAs) of cube-corner retroreflectors (CCRs) on the Moon, has supplied significant information on the internal structure of the Moon, a large amount of ephemerides data, and important tests of General Relativity (GR) [1] thanks to the Apollo (USA) and Lunokhod (USSR) CCR LRAs deployed on the Moon. Nowadays, after the significant improvement of LLR station capabilities by more than two orders of magnitude, LRAs dominate the error budget due to lunar librations due to eccentricity and inclination of the Moon orbit [2,3]. To improve this situation, next-generation libration-free retroreflectors are necessary. To this end, the Satellite/lunar/GNSS laser ranging/altimetry and cube/microsat Characterization Facilities Laboratory (SCF_Lab) at the Istituto Nazionale di Fisica Nucleare—Laboratori Nazionali di Frascati (INFN-LNF), in collaboration with the University of Maryland (UMD) and supported by the Italian Space Agency (ASI), developed MoonLIGHT (Moon Laser Instrumentation for General relativity High-accuracy Tests), a single, uncoated CCR of 100 mm diameter, unaffected by lunar librations [2,3,4]. Since landers of NASA’s Commercial Lunar Payload Services (CLPS) do not guarantee accurate landing accuracies, INFN-LNF proposed to ESA the MoonLIGHT Pointing Actuator (MPAc) instrument, a specifically devised, designed, and manufactured robotic actuator, which, once its host craft has landed on the Moon, will align the front face of MoonLIGHT towards the Earth [5]. ESA signed with NASA an MoU to launch MPAc to the Reiner Gamma swirl with IM-3, the third mission granted by NASA to Intuitive Machines (IM) [6], currently foreseen in late 2025 or early 2026. The flight model of MPAc was qualified, delivered and accepted by ESA, NASA and IM in 2023 and is in storage in Houston at IM. As far as concern the landing accuracy on the Moon, on the 2nd of June 2024 the INstrument for landingRoving Laser Retroreflector Investigations (INRRI), developed by INFN, successfully landed onboard China’s CE-6 lander on the far side of the Moon. By collaboration of Italian and Chinese scientists, the instrument's design and rigorous testing ensured its survival in the lunar far side environment. Following the Chang'e-6 landing, INRRI's location was confirmed. An initial observation of INRRI validated the functionality of INRRI. The successful deployment of INRRI on the CE-6 lander marked a milestone as it serves as the first permanent, high-precision control point on the lunar far side, supporting lunar surface mapping, orbit determination, and navigation for future lunar missions. Among all the possible applications, MPAc will be beneficial for geophysical purposes. In fact, MoonLIGHT will support improved studies of inertia moments, tides, core-mantle boundary, determination of fluid and/or solid core, librations, etc. Remarkably, the deployment of MPAc on the Moon will contribute to attain lunar orbit range accuracy below a few millimetres, with a significant improvement compared to the current centimetre value. Simulations on the magnitude of the accuracy improvements from LLR data have been obtained by using the Planetary Ephemeris Program (PEP) [7], a software developed and maintained since the 1960s by the Harvard-Smithsonian Center for Astrophysics (CfA), MA, USA. PEP is a software that in particular uses LLR data on Apollo, Lunokhod and modern MoonLIGHT laser retroreflectors for precision test of GR and beyond by comparison of GR predictions with observations. The use of PEP with previous and new more accurate data will improve, in turn, the accuracy on the constraints of Weak and Strong Equivalence Principles (WEP/SEP), the relative variation with time of the gravitational constant, the geodetic precession, Yukawa deviations from Newtonian gravity through the inverse square law, and will put more stringent constraints on departures from GR, enabling constraints on new theories beyond GR, like spacetime torsion [8], f(R) gravity [9], nonminimally-coupled gravity [10,11], Lorentz-invariance violations, etc. Indeed, PEP includes a detailed mathematical model of the solar system with a large number of adjustable parameters, including some that describe fundamental physics. By estimating these parameters based on the available data, we can restrict the range of allowable theories in physics and cosmology, enabling constraints on departures from standard physics. As a matter of fact, PEP constantly keeps improving GR tests and pushes constraints on fundamental physics observables in search for new physics. In this regard, gravitational tests and constraints from LLR measurements have already been investigated, as in [11], where nonminimally coupled gravity is proved to be a workable alternative to address issues for which GR is not fully adequate, consistently with the bound on WEP arising from 48 years of LLR data. Furthermore, various proposals in the literature suggest employing LLR to detect discrepancies from Einstein's theory in the positions of the Lagrangian points in the Earth-Moon and Sun-Earth systems [12,13,14,15] and to investigate possible violations of the equivalence principle. [16]. However, improvements of LLR data expected from LLR of next generation, such as in the MoonLIGHT experiment, are paving the way for more accurate constraints and tests of alternative physics. In this framework, the use of PEP not only in its traditional form but also with the implementation of extended theories of GR and alternative cosmological models, other than the standard one, proves intriguing and cutting-edge to shed light on the debated and puzzling framework of gravitational and cosmological theories. [1] Murphy T.W. Jr. et al. (2012) Classical and Quantum Gravity, 29, 184005. [2] Ciocci E. et al. (2017) J. Adv. in Space Res. 60, 1300-1306. [3] Porcelli L. et al. (2021). Next generation lunar laser retroreflectors for fundamental physics and lunar science, Topical White Paper submitted to the Committee on the Biological and Physical Sciences Research in Space 2023-2032 of The National Academies of Sciences of the USA. [4] Huang K. et al. (2024) Astronomical Techniques and Instruments, 1(6), 295-306. [5] Muccino M. et al. (2025) Remote Sensing, 17, 813. [6] https://www.nasa.gov/news-release/nasa-selectsintuitive-machines-for-new-lunar-science-delivery/. [7] Shapiro I., Reasenberg R.D., Chandler J.F. (1988) Phys. Rev. Lett., 61, 2643-2646. [8] March R. et al. (2011) PRD, 83, 104008. [9] Capozziello S. et al. (2019) IJMPD, 28, 10, 1930016. [10] March R. et al. (2022) PRD, 105, 044048. [11] March R. et al. (2024) PRD, 109, 124013. [12] Battista E. and Esposito G. (2014) PRD, 89, 084030. [13] Battista E. et al. (2015) PRD, 91, 084041. [14] Battista E. et al. (2015) PRD, 92, 064045. [15] Tartaglia et al. (2018) Mod.Phys.Lett.A, 33, 1850136. [16] Battista et al. (2025), in prep.