The Moon undergoes periodic tidal forcing due to its eccentric and oblique orbit around the Earth¹. The response to this tidal interaction drives temporal changes in the lunar gravity field and is sensitive to the satellite’s internal structure^{2, 3–4}. We use data from the NASA GRAIL spacecraft^{5, 6, 7, 8–9} to recover the time-varying lunar gravity field, including a degree-3 gravitational tidal Love number, k₃. Here, we report our estimated value of k₃ = 0.0163 ± 0.0007, which is about 72% higher than that expected for a spherically symmetric moon¹⁰. Such a large k₃ can be explained if the elastic shear modulus of the mantle varies by about 2–3% between the nearside and farside⁴, providing an observational demonstration of lateral heterogeneities in the deep lunar interior. This asymmetric structure suggests preservation of a predominantly thermal anomaly of roughly 100–200 K in the nearside mantle that formed surface mare regions 3–4 billion years ago¹¹ and could influence the spatial distribution of deep moonquakes¹².

Juice (JUpiter ICy moons Explorer) 3GM Radio Science Experiment will map the gravitational field of Ganymede with unprecedented accuracy and measure tidally-induced variations. These measurements will allow the characterization of its putative ocean and may resolve lateral variations in internal structure. Lateral variations cause an additional tidal signal that depends on their wavelength and amplitude. We show that shell thickness variations of (Formula presented.) the mean thickness produce an additional tidal signal (Formula presented.) times smaller than the main tidal signal, detectable given the accuracy of Juice. Using a Bayesian framework, we show that measuring differences between (Formula presented.) and (Formula presented.) constrain equator to pole shell thickness differences. Also measuring the degree-3 spherical harmonic signal due to degree 2 forcing constrain degree-1 and degree-3 structure. This demonstrates tidal tomography's potential to map three dimensional structure and supports its consideration for future missions.

Body tides reveal information about planetary interiors and affect their evolution. Most models to compute body tides rely on the assumption of a spherically symmetric interior. However, several processes can lead to lateral variations of interior properties. We present a new spectral method to compute the tidal response of laterally heterogeneous bodies. Compared to previous spectral methods, our approach is not limited to small-amplitude lateral variations; compared to finite element codes, this approach is more computationally efficient. While the tidal response of a spherically symmetric body has the same wavelength as the tidal force; lateral heterogeneities produce an additional tidal response with a spectra that depends on the spatial pattern of such variations. For Mercury, the Moon, and Io, the amplitude of this signal is as high as 1%-10% of the main tidal response for long-wavelength shear modulus variations higher than ∼10% of the mean shear modulus. For Europa, Ganymede, and Enceladus, shell-thickness variations of 50% of the mean shell thickness can cause an additional signal of ∼1% and ∼10% for the Jovian moons and Encelaudus, respectively. Future missions, such as BepiColombo and JUICE, might measure these signals. Lateral variations of viscosity affect the distribution of tidal heating. This can drive the thermal evolution of tidally active bodies and affect the distribution of active regions.