Comparative planetology: probing the interiors of rocky planets through tidal deformation

Tidal deformation provides one of the most powerful observational probes of the deep interiors of rocky planets and moons. Measurements of tidal Love numbers are sensitive to internal density structure, the presence of liquid layers, mantle rigidity and viscosity, and the thermal state of planetary interiors. They have therefore become key observables for investigating the internal structure of terrestrial bodies such as Mercury and the Moon (Williams et al., 2014; Verma and Margot, 2016; Steinbrügge et al., 2018; Thor et al., 2021). Recent and upcoming spacecraft missions, including the BepiColombo mission, are expected to significantly improve the precision of tidal measurements, opening new perspectives for comparative tidal studies across rocky planetary bodies.

One-dimensional (1D), radially symmetric interior models have become a standard framework for interpreting tidal observables. These models enable efficient probabilistic investigations of planetary interiors and have successfully reproduced first-order tidal responses for bodies such as Mercury and the Moon. However, the interpretation of tidal measurements remains strongly dependent on assumptions regarding internal density structure, mantle rheology, temperature, and the possible presence of liquid or partially molten layers. As observational precision improves, lateral variations in crustal thickness, mantle temperature, rigidity, or viscosity may also become increasingly relevant for interpreting not only the amplitude of tidal Love numbers, but also the spatial patterns of tidal deformation.

Here, we present ongoing work aimed at developing a comparative framework for investigating tidal deformation across rocky planets and moons. This approach combines probabilistic interior modeling with frequency-dependent viscoelastic tidal calculations to explore how different rheological formulations influence tidal observables over a broad range of forcing periods. The objective is to assess how tidal measurements can be used to constrain not only the radial structure of planetary interiors, but also their thermal and rheological state.

We investigate the tidal response associated with Hookean elastic, Maxwell, Andrade, and Sundberg–Cooper rheologies for planetary interiors characterized by distinct thermal states and internal structures. Preliminary results indicate that while the real part of the Love numbers is primarily controlled by bulk radial structure and core size, the imaginary component and tidal quality factor exhibit strong sensitivity to mantle rheology and forcing frequency. In particular, Andrade and Sundberg–Cooper rheologies generate broader dissipation spectra than classical Maxwell models, suggesting that multi-frequency tidal observations may provide important constraints on the viscoelastic properties of planetary mantles. This is consistent with previous studies showing that anelastic and transient rheologies can significantly modify tidal dissipation relative to Maxwell models (Renaud and Henning, 2018; Walterová et al., 2023).

Comparative analyses of Mercury and the Moon further illustrate how forcing frequency, mantle viscosity, and core properties jointly control the amplitude and spectral behavior of tidal deformation. These results emphasize the importance of considering both rheological complexity and frequency dependence when interpreting tidal measurements from terrestrial bodies. Such a comparative approach is particularly relevant because different rocky bodies sample different tidal forcing periods, thermal states, and interior configurations, thereby offering complementary constraints on planetary evolution.

Future high-precision observations from planetary missions may therefore provide new opportunities to constrain not only the radial structure of rocky planets and moons, but also the physical state and long-term evolution of their interiors. In this context, comparative tidal geophysics provides a promising framework for linking geodetic observations, mantle rheology, and planetary evolution across terrestrial bodies.

References

Williams, J. G., Konopliv, A. S., Boggs, D. H., Park, R. S., Yuan, D. N., Lemoine, F. G., ... & Zuber, M. T. (2014). Lunar interior properties from the GRAIL mission. Journal of Geophysical Research: Planets, 119(7), 1546-1578.

Renaud, J. P., & Henning, W. G. (2018). Increased tidal dissipation using advanced rheological models: Implications for Io and tidally active exoplanets. The Astrophysical Journal, 857(2), 98.

Steinbrügge, G., Padovan, S., Hussmann, H., Steinke, T., Stark, A., & Oberst, J. (2018). Viscoelastic tides of Mercury and the determination of its inner core size. Journal of Geophysical Research: Planets, 123(10), 2760-2772.

Thor, R. N., Kallenbach, R., Christensen, U. R., Gläser, P., Stark, A., Steinbrügge, G., & Oberst, J. (2021). Determination of the lunar body tide from global laser altimetry data. Journal of Geodesy, 95(1), 4.

Verma, A. K., & Margot, J. L. (2016). Mercury's gravity, tides, and spin from MESSENGER radio science data. Journal of Geophysical Research: Planets, 121(9), 1627-1640.

Walterová, M., Běhounková, M., & Efroimsky, M. (2023). Is there a semi‐molten layer at the base of the lunar mantle?. Journal of Geophysical Research: Planets, 128(7), e2022JE007652.