Lunar reference systems and their realisations using INPOP ephemerides

¹ Sorbonne Université, Observatoire Paris, Université PSL, CNRS, Laboratoire Temps Espace, LTE, 75014 Paris, France
² Observatoire de la Côte d’Azur, Université Côte d’Azur, CNRS, Géoazur, IRD, 250 avenue A. Einstein 06560 Valbonne, France
³ Tor Vergata University of Rome, Department of Physics, Via della Ricerca Scientifica 1, 00133 Rome, Italy
⁴ Institute of Geodesy and Geoinformatics, Wrocław University of Environmental and Life Sciences, Norwida 25, Wrocław, 50-375, Poland
⁵ Northumbria University, Newcastle-upon-Tyne, UK

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 June 2025
Accepted: 16 September 2025

Abstract

Context. The definition of a reference system plays a crucial role in quantifying geodetic effects and in surface body cartography. Today, the development and specification of the lunar reference system is stimulated by future space missions, some of which will be manned, and by the needs of lunar space navigation.

Aims. This paper aims to describe the lunar reference system in use and determine the accuracy of its realisation in space and time. At present, two lunar reference systems are defined: the Principal Axis system (PA system), based on the Moon’s principal axes of inertia, and the Mean Earth/Polar Axis (ME system), defined by the Earth’s mean position on the Moon surface. A first step towards a relativistic definition of the lunar time scale is also introduced in agreement with that proposed by the International Astronomical Union (IAU) and other recent realisations.

Methods. We based the realisation of a PA lunar reference system on the choice of an ephemeris, which relied on the coordinates of the laser retro-reflectors on the Moon surface. We related the ME system and frame to the PA system and frame through a rotation transformation. This study provides a new method to determine the transformation procedure between the two systems, based on a series decomposition of librations and pole motion.

Results. We used the comparisons of the position of the lunar laser retro-reflectors obtained with different ephemerides to estimate the internal and external uncertainties of the different realisations of the PA and ME systems. It also includes comparisons between Euler angles and the propagation of their uncertainties.

Conclusions. This work provides the full expression of the transformation and a new series of libration and polar motion for the lunar motion. We also introduce possible realisations of lunar timescales, applicable depending on their use. The proposed procedure, with opportunities for future improvements, can help set new standards for lunar reference systems and their realisations.