We investigate the impact of viscoelastic tidal deformation of the Moon on the motion of a polar orbiter. The dissipative effects in the Moon’s interior, i.e., tidal phase lags, are modeled as Fourier series sampled at given frequencies associated with linear combinations of Delaunay arguments, the fundamental parameters describing the lunar motion around the Earth and the Sun. We implement the tidal model to evaluate the temporal lunar gravity field and the induced perturbation on the orbiter. We validate the numerical scheme via a frequency analysis of the perturbed orbital motion. We show that, in the case of the Lunar Reconnaissance Orbiter at a low altitude of less than 200 km, the main lunar tides and hence the potential Love numbers around the monthly and some multiple frequencies are dynamically separable. The omission of those effects in practice introduces a position error at the level of a few decimeters within 10 days.

Jupiter’s moon Ganymede might be in possession of a subsurface ocean located between two ice layers. However, from Galileo data it is not possible to unambiguously infer the thickness and densities of the individual layers. The upcoming icy satellite mission JUICE (JUpiter ICy moons Explorer) will have the possibility to perform more detailed investigations of Ganymede’s interior structure with the radio science experiment 3GM and the GAnymede Laser Altimeter (GALA). Here we investigate the possibility to derive the rotational state of the outer ice shell by using topography measured by laser altimetry. We discuss two different methods to invert synthetic laser altimetry data. Method 1 is based on a spherical harmonics expansion and Method 2 solves for B-splines on a rectangular grid. While Method 1 has significant limitations due to the omission of high degrees of the global expansion, Method 2 leads to stable results allowing for an estimate of the in-orbit measurement accuracy. We estimate that GALA can measure the amplitude of Ganymede’s librations with an accuracy of 2.5–6.6 µrad (6.6–17.4 m at the equator). This allows for determining the thickness of an elastic ice shell, if decoupled from the deeper interior by a subsurface ocean, to about an accuracy of 24–65 km.

We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k₂. Based on these constraints we predict the tidal Love number h₂ to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase-lag is predicted to be 4° at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16 mW/m². We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h₂ and k₂ provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700 km, and with the expected determination of h₂ from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase-lag with an accuracy better than ≈0.5° would further allow constraining the temperature at the core-mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core.