Introduction of tidal models in lunar ephemerides
Daniel Baguet  1@  , Nicolas Rambaux  1  , Agnes Fienga  2  , Anthony Mémin  2  , Arthur Briaud  2  , Hauke Hussmann  3  , Alexander Stark  3  , Xuanyu Hu  4  , Jacques Laskar  1  , Mickaël Gastineau  1  
1 : Institut de Mécanique Céleste et de Calcul des Ephémérides
Observatoire de Paris, Sorbonne Université, Centre National de la Recherche Scientifique
2 : Géoazur
Institut National des Sciences de l'Univers, Observatoire de la Cote d'Azur, COMUE Université Côte d'Azur (2015-2019), Université Côte d'Azur, Centre National de la Recherche Scientifique, Institut de Recherche pour le Développement
3 : DLR, Department of Planetary Geodesy, Berlin
4 : Technische Universität Berlin, Institute of Geodesy and Geoinformation Science, Berlin

Since the start of the Artemis program, interest in lunar studies has been renewed. The Lunar Laser Ranging (LLR) experiment measures the Earth-Moon distance at a few centimeters accuracy and the Moon's librations at a one milliarcsecond accuracy [1], providing a refined description of the tidal deformation of the Moon. The ephemeris INPOP of the Paris Observatory is a joint numerical integration of the orbits of the Moon and the planets as well as the lunar rotation, which is fitted to the LLR data. Studying the lunar tides allows us to probe the internal composition of the Moon. For example, recent results from tidal constraints highlight the presence of a solid inner core [2]. The tidal response depends on the density and the rheology of the layers, and on the dissipation due to the viscosity of the lunar interior (e.g. [3], [4]). The tidal Love number k2 and the dissipation inside the Moon depend on the forcing frequencies, which are mainly exerted by the Earth and the Sun.
In INPOP the tidal deformation accounts for a k2 independent of the excitation frequency and a unique time delay [1]. The formulation in Fourier series of the distortion coefficients (also called variation of the Stokes coefficients) by Williams and Boggs (2015) [3] allows us to describe the tidal gravitational variation by taking into account the frequency dependency. We introduce the distortion coefficients as Fourier series in order to test the impact of the variation of the Love number and of the dissipation on libration measurements.



1. Viswanathan, V. et al. Monthly Notices of the Royal Astronomical Society 476, 1877–1888 (2018).

2. Briaud, A., Ganino, C., Fienga, A., Mémin, A. & Rambaux, N. The lunar solid inner core and the mantle overturn. Nature 617, 743–746 (May 2023).

3. Williams, J. G. & Boggs, D. H. Journal of Geophysical Research (Planets) 120, 689–724 (2015).

4. Briaud, A. et al. Icarus 394, 115426 (2023).

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