Lunar tidal Deformation from earth-based and orbital Laser Ranging – LDLR

Three methods are used in this project
1) Monte Carlo exploration of the space domain for thicknesses and viscocities for the different Moon layers. Statistical filtering by comparisons of these visco-elastic modelings with observed tidal Love numbers and dissipation
2) Improvement of the lasr altimetric measurements of Love numbers from the LRO mission by assessing sensitivity of the LRO orbits to the visco-elastic contributions to the gravity field and to sun illumination and Moon albedo
3) Improvement of the lunar laser ranging measurements of Love numbers from earth-based observations by introducing visco-elastic Love numbers in the modelings of the Moon rotation in the planetary and rotational ephemerides INPOP.

So far, the project succeed in providing new constraints on possible scenarii for the Moon internal structure. By exploring different hypotheses on the thicknesses of the different layers as well as their viscosities we
were able to produce four different types of models all consistent with the previous studies but giving additional information on the LVZ and the viscosity of the fluid core. This quantity never has been obtained by previous studies and gives a new ins-sight of the Moon interior. Even if we are not able to
rule or confirm the existence of a Moon inner core, we are able to give stringent constraints on the fluid core viscosity and the LVZ. A first paper is currently under the process of submission to Icarus for publication and a second one is in preparation regarding the impact of our estimation of the LVZ viscosity on its chemical composition.

The next steps are:
1) To fit lunar ephemerides including the visco-elastic contribution of the Moon gravity and frequency-depend deformation at the Moon reflectors to the most recent LLR data
2) testing the impact of using visco-elastic Love numbers and up to date Moon ephemerides in the analysis of real altimetric data in using updated lunar ephemerides
3) introduce lateral heterogeneities through a finite element model (spectral model). We will validate our spectral model by comparing output Love numbers to the Love numbers estimated using our reference model. We expect these heterogeneities to explain the discrepancy obtained between LA h2 and
INPOP h2 by the crustal thickness asymmetry or/and by viscoelastic behaviours.

One paper has been published and one is submitted for publication.
1) Thor, R. N., R. Kallenbach, U. R. Christensen, P. Glaser, A.
Stark, G. Steinbrugge, and J. Oberst (2021), Determination of
the lunar body tide from global laser altimetry data, Journal of
Geodesy, 95(1), doi:10.1007/s00190-020-01455-8.

2)Briaud, A., Fienga, A., Melini, D. Rambaux, N., Memin, A.,
Spada, G.,Saliby, C. , 2021, Constraints on the Moon's low viscosity
zone and core from the tidal deformations, Icarus, submitted.

Knowledge about the deep interior of the Moon puts tight constraints on its formation and ultimately on the evolution of the Earth-Moon system. Measurements of the tidal response of the Moon resulting from the gravitational field of the Earth provide unique evidence on its inner working and can be obtained from orbiting spacecraft and Earth-based observations. Furthermore, the Moon dynamical monitoring is the most accurate ever made in the solar system thanks to the deployment of laser retro-reflectors (LRR) on its nearside surface leading to a centimeter accuracy over the past 40 years. Such accuracy requires a high accurate modeling of its orbit but also of its rotation, inducing a unique development in the inner structure for an object different from the Earth. This project aims at a synthesis of the a large amount of observations and modelings obtained from Earth-based Lunar Laser Ranging (LLR) and orbit-based laser altimetry (LA) to achieve an improved and consistent determination of the tidal deformation of the Moon by estimating its gravitational Love numbers and consequently constraining the present dissipation in the Earth-Moon system.
Besides, planetary deformations are usually characterised with the help of a triplet of adimensional numbers, the Love numbers, giving the horizontal and vertical displacement of the surface (l and h) and the gravitational response to a potential of degre n for k. With the Love numbers, our modele can implement elastic and viscoelastic rheologies as well as effects induced by the asymmetric thickness of the Moon crust.
This project is based on the association of the DLR team expert in Laser altimetry and the INPOP team, expert in LLR data analysis and planetary and lunar ephemerides construction.
The following steps will be followed: i) improvements of the LA data analysis in considering improvements in the orbit determination of the spacecraft (in our case, LRO) and in using different versions for the libration modelings with INPOP and visco-elastic and asymmetric Love numbers in the data analysis procedure. By doing so, one will evaluate the sensitivity of the LA data analysis algorithm to inner structure assumptions. ii) In the INPOP libration modeles, one will add more complexity in the tides modeling in introducing high-order Love numbers, visco-elastic Love numbers and Love numbers obained in introducing asymmetry of the crustal thickness provided by our new modele of deformation including viscoelasticity and spatial heterogeneity in the crust.
The expected results will be i) a better description of the tidal deformation of the Moon and the dissipation for the earth-moon system together with a better constraint on the visco-elastic rheology of the moon considering the lateral asymmetry of the crustal thickness detected by GRAIL ii) the set up of a method for constraining accurately inner structure of any planet in using high accurate LA observations. This final result will open a lot of possible applications to space missions such as Bepi-Colombo, JUICE or future mars missions.