Nixon, C. et al. Titan’s cold case files – outstanding questions after Cassini-Huygens. Planet. Space Sci. 155, 50–72 (2018).
Iess, L. et al. The tides of Titan. Science 337, 457–459 (2012).
Durante, D., Hemingway, D., Racioppa, P., Iess, L. & Stevenson, D. Titan’s gravity field and interior structure after Cassini. Icarus 326, 123–132 (2019).
Downey, B. G. & Nimmo, F. Titan’s spin state as a constraint on tidal dissipation. Sci. Adv. 11, eadl4741 (2025).
Tobie, G., Mocquet, A. & Sotin, C. Tidal dissipation within large icy satellites: applications to Europa and Titan. Icarus 177, 534–549 (2005).
Kalousová, K. & Sotin, C. Dynamics of Titan’s high-pressure ice layer. Earth Planet. Sci. Lett. 545, 116416 (2020).
Iess, L. et al. Gravity field, shape, and moment of inertia of Titan. Science 327, 1367–1369 (2010).
Castillo-Rogez, J. C. & Lunine, J. I. Evolution of Titan’s rocky core constrained by Cassini observations. Geophys. Res. Lett. 37, L20205 (2010).
Néri, A., Guyot, F., Reynard, B. & Sotin, C. A carbonaceous chondrite and cometary origin for icy moons of Jupiter and Saturn. Earth Planet. Sci. Lett. 530, 115920 (2020).
Rappaport, N. J. et al. Can Cassini detect a subsurface ocean in Titan from gravity measurements? Icarus 194, 711–720 (2008).
Segatz, M., Spohn, T., Ross, M. & Schubert, G. Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus 75, 187–206 (1988).
Sohl, F., Hussmann, H., Schwentker, B., Spohn, T. & Lorenz, R. D. Interior structure models and tidal Love numbers of Titan. J. Geophys. Res. Planets 108, 5130 (2003).
Mitri, G. et al. Shape, topography, gravity anomalies and tidal deformation of Titan. Icarus 236, 169–177 (2014).
Baland, R.-M., Tobie, G., Lefèvre, A. & Van Hoolst, T. Titan’s internal structure inferred from its gravity field, shape, and rotation state. Icarus 237, 29–41 (2014).
Idini, B. & Nimmo, F. Resonant stratification in Titan’s global ocean. Planet. Sci. J. 5, 15 (2024).
Goossens, S., van Noort, B., Mate, A., Mazarico, E. & van der Wal, W. A low-density ocean inside Titan inferred from Cassini data. Nat. Astron. 8, 846–855 (2024).
Stiles, B. W. et al. Determining Titan’s spin state from Cassini RADAR Images. Astron. J. 135, 1669–1680 (2008).
Baland, R.-M., Van Hoolst, T., Yseboodt, M. & Karatekin, O. Titan’s obliquity as evidence of a subsurface ocean? Astron. Astrophys. 530, A141 (2011).
Bills, B. G. & Nimmo, F. Rotational dynamics and internal structure of Titan. Icarus 214, 351–355 (2011).
Baland, R.-M., Yseboodt, M. & Van Hoolst, T. The obliquity of Enceladus. Icarus 268, 12–31 (2016).
Béghin, C. et al. Analytic theory of Titan’s Schumann resonance: constraints on ionospheric conductivity and buried water ocean. Icarus 218, 1028–1042 (2012).
Lorenz, R. D. & Le Gall, A. Schumann resonance on Titan: a critical re-assessment. Icarus 351, 113942 (2020).
Le Maistre, S. et al. Spin state and deep interior structure of Mars from InSight radio tracking. Nature 619, 733–737 (2023).
Buccino, D., Border, J. S., Folkner, W. M., Kahan, D. & Le Maistre, S. Low-SNR Doppler data processing for the InSight radio science experiment. Remote Sens. 14, 1924 (2022).
Ray, R. D., Eanes, R. J. & Lemoine, F. G. Constraints on energy dissipation in the Earth’s body tide from satellite tracking and altimetry. Geophys. J. Int. 144, 471–480 (2001).
Bagheri, A., Khan, A., Al-Attar, D., Crawford, O. & Giardini, D. Tidal response of Mars constrained from laboratory-based viscoelastic dissipation models and geophysical data. J. Geophys. Res. Planets 124, 2703–2727 (2019).
Petricca, F. et al. Partial differentiation of Europa and implications for the origin of materials in the Jupiter system. Nat. Astron. 9, 501–511 (2025).
Petricca, F. et al. Exploring the tidal responses of ocean worlds with PyALMA. Icarus 417, 116120 (2024).
Yao, C., Deschamps, F., Lowman, J. P., Sanchez-Valle, C. & Tackley, P. J. Stagnant lid convection in bottom-heated thin 3-D spherical shells: influence of curvature and implications for dwarf planets and icy moons. J. Geophys. Res. Planets 119, 1895–1913 (2014).
Castillo-Rogez, J. C., Efroimsky, M. & Lainey, V. The tidal history of Iapetus: spin dynamics in the light of a refined dissipation model. J. Geophys. Res. Planets 116, E09008 (2011).
Hilairet, N. et al. High-pressure creep of serpentine, interseismic deformation, and initiation of subduction. Science 318, 1910–1913 (2007).
Poirier, J. P., Sotin, C. & Peyronneau, J. Viscosity of high-pressure ice VI and evolution and dynamics of Ganymede. Nature 292, 225–227 (1981).
Durham, W. B., Stern, L. A. & Kirby, S. H. Rheology of water ices V and VI. J. Geophys. Res. Solid Earth 101, 2989–3001 (1996).
Zarriz, A., Journaux, B. & Powell-Palm, M. J. On the equilibrium limit of liquid stability in pressurized aqueous systems. Nat. Commun. 15, 10666 (2024).
Lunine, J. I. & Stevenson, D. J. Clathrate and ammonia hydrates at high pressure: application to the origin of methane on Titan. Icarus 70, 61–77 (1987).
Tobie, G., Lunine, J. & Sotin, C. Episodic outgassing as the origin of atmospheric methane on Titan. Nature 440, 61–64 (2006).
Lainey, V. et al. Resonance locking in giant planets indicated by the rapid orbital expansion of Titan. Nat. Astron. 4, 1053–1058 (2020).
Wisdom, J. et al. Loss of a satellite could explain Saturn’s obliquity and young rings. Science 377, 1285–1289 (2022).
Asphaug, E. & Reufer, A. Late origin of the Saturn system. Icarus 223, 544–565 (2013).
Journaux, B. et al. Large ocean worlds with high-pressure ices. Space Sci. Rev. 216, 7 (2020).
Sotin, C., Kalousová, K. & Tobie, G. Titan’s interior structure and dynamics after the Cassini-Huygens mission. Annu. Rev. Earth Planet. Sci. 49, 579–607 (2021).
Hendrix, A. R. et al. The NASA Roadmap to Ocean Worlds. Astrobiology 19, 1–27 (2019).
Kalousová, K. et al. Evolution of impact melt pools on Titan. J. Geophys. Res. Planets 129, e2023JE008107 (2024).
Arrigo, K. R. Sea ice ecosystems. Annu. Rev. Mar. Sci. 6, 439–467 (2014).
Cappuccio, P. et al. Ganymede’s gravity, tides and rotational state from JUICE’s 3GM experiment simulation. Planet. Space Sci. 187, 104902 (2020).
Kivelson, M., Khurana, K. & Volwerk, M. The permanent and inductive magnetic moments of Ganymede. Icarus 157, 507–522 (2002).
Showman, A. P., Stevenson, D. J. & Malhotra, R. Coupled orbital and thermal evolution of Ganymede. Icarus 129, 367–383 (1997).
Jia, X., Kivelson, M. G., Khurana, K. K. & Walker, R. J. Improved models of Ganymede’s permanent and induced magnetic fields based on Galileo and Juno data. J. Geophys. Res. Planets 130, e2024JE008309 (2025).
Sotin, C. et al. Oceanus: a New Frontiers orbiter to study Titan’s potential habitability. 19th EGU General Assembly (2017).
Evans, S. et al. MONTE: the next generation of mission design and navigation software. CEAS Space J. 10, 79–86 (2018).
Buccino, D. R., Kahan, D. S., Yang, O. & Oudrhiri, K. Extraction of Doppler observables from open-loop recordings for the Juno radio science investigation. In Proc. 2018 United States National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM) (IEEE, 2018).
Jacobson, R. A. The orbits of the main Saturnian satellites, the Saturnian system gravity field, and the orientation of Saturn’s pole. Astron. J. 164, 199 (2022).
Justus, C., Duvall, A. & Johnson, D. Engineering-level model atmospheres for Titan and Neptune. In Proc. 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit (American Institute of Aeronautics and Astronautics, 2003).
Lebonnois, S., Burgalat, J., Rannou, P. & Charnay, B. Titan global climate model: a new 3-dimensional version of the IPSL Titan GCM. Icarus 218, 707–722 (2012).
Petricca, F., Genova, A., Goossens, S., Iess, L. & Spada, G. Constraining the internal structures of Venus and Mars from the gravity response to atmospheric loading. Planet. Sci. J. 3, 164 (2022).
Cascioli, G. et al. Constraining the Venus interior structure with future VERITAS measurements of the gravitational atmospheric loading. Planet. Sci. J. 4, 65 (2023).
Journaux, B. et al. Holistic approach for studying planetary hydrospheres: Gibbs representation of ices thermodynamics, elasticity, and the water phase diagram to 2,300 MPa. J. Geophys. Res. Planets 125, e2019JE006176 (2020).
Vance, S., Bouffard, M., Choukroun, M. & Sotin, C. Ganymede’s internal structure including thermodynamics of magnesium sulfate oceans in contact with ice. Planet. Space Sci. 96, 62–70 (2014).
Bollengier, O., Brown, J. M. & Shaw, G. H. Thermodynamics of pure liquid water: sound speed measurements to 700 MPa down to the freezing point, and an equation of state to 2300 MPa from 240 to 500 K. J. Chem. Phys. 151, 054501 (2019).
Bagheri, A. et al. The tidal–thermal evolution of the Pluto–Charon system. Icarus 376, 114871 (2022).
Jackson, I. & Faul, U. H. Grainsize-sensitive viscoelastic relaxation in olivine: towards a robust laboratory-based model for seismological application. Phys. Earth Planet. Inter. 183, 151–163 (2010).
Bierson, C. J. The impact of rheology model choices on tidal heating studies. Icarus 414, 116026 (2024).
Amorim, D. O. & Gudkova, T. Constraining Earth’s mantle rheology with Love and Shida numbers at the M2 tidal frequency. Phys. Earth Planet. Inter. 347, 107144 (2024).
Petricca, F. et al. Characterization of icy moon hydrospheres through joint inversion of gravity and magnetic field measurements. Geophys. Res. Lett. 50, e2023GL104016 (2023).
Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).
Cascioli, G., Mazarico, E., Dombard, A. J. & Nimmo, F. Leveraging the gravity field spectrum for icy satellite interior structure determination: the case of Europa with the Europa Clipper Mission. Planet. Sci. J. 5, 45 (2024).
Lainey, V., Arlot, J.-E., Karatekin, O. & Van Hoolst, T. Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature 459, 957–959 (2009).
Iess, L. et al. Measurement and implications of Saturn’s gravity field and ring mass. Science 364, eaat2965 (2019).
McCarthy, C. & Cooper, R. F. Tidal dissipation in creeping ice and the thermal evolution of Europa. Earth Planet. Sci. Lett. 443, 185–194 (2016).
Solomatov, V. S. Scaling of temperature- and stress-dependent viscosity convection. Phys. Fluids 7, 266–274 (1995).
Lorenz, R. D. et al. Titan’s rotation reveals an internal ocean and changing zonal winds. Science 319, 1649–1651 (2008).
Meriggiola, R., Iess, L., Stiles, B., Lunine, J. & Mitri, G. The rotational dynamics of Titan from Cassini RADAR images. Icarus 275, 183–192 (2016).
Béghin, C. The atypical generation mechanism of Titan’s Schumann resonance. J. Geophys. Res. Planets 119, 520–531 (2014).
Colombo, G. Cassini’s Second and Third Laws. In: Measure of the Moon. Astrophysics and Space Science Library, Vol 8, 12–22 (Springer, 1967).
Yoder, C. The free librations of a dissipative Moon. Philos. Trans. R. Soc. Lond. A Math. Phys. Sci. 303, 327–338 (1981).
Williams, J. G., Boggs, D. H., Yoder, C. F., Ratcliff, J. T. & Dickey, J. O. Lunar rotational dissipation in solid body and molten core. J. Geophys. Res. Planets 106, 27933–27968 (2001).
Tokano, T. Tidal winds on Titan caused by Saturn. Icarus 158, 499–515 (2002).
Charnay, B., Tobie, G., Lebonnois, S. & Lorenz, R. D. Gravitational atmospheric tides as a probe of Titan’s interior: application to Dragonfly. Astron. Astrophys. 658, A108 (2022).
Kamata, S. et al. Tidal deformation of Ganymede: sensitivity of Love numbers on the interior structure. J. Geophys. Res. Planets 121, 1362–1375 (2016).
McKinnon, W. B. Convective instability in Europa’s floating ice shell. Geophys. Res. Lett. 26, 951–954 (1999).
Choukroun, M. & Grasset, O. Thermodynamic model for water and high-pressure ices up to 2.2 GPa and down to the metastable domain. J. Chem. Phys. 127, 124506 (2007).
Tobie, G., Choblet, G. & Sotin, C. Tidally heated convection: constraints on Europa’s ice shell thickness. J. Geophys. Res. Planets 108, 5124 (2003).
Ojakangas, G. W. & Stevenson, D. J. Thermal state of an ice shell on Europa. Icarus 81, 220–241 (1989).
Renaud, J. P. & Henning, W. G. Increased tidal dissipation using advanced rheological models: implications for Io and tidally active exoplanets. Astrophys. J. 857, 98 (2018).
Bagheri, A. et al. Tidal insights into rocky and icy bodies: an introduction and overview. Adv. Geophys. 63, 231–320 (2022).
Peltier, W. R. The impulse response of a Maxwell Earth. Rev. Geophys. 12, 649–669 (1974).
Bills, B. G. Improved estimate of tidal dissipation within Mars from MOLA observations of the shadow of Phobos. J. Geophys. Res. Planets 110, E07004 (2005).
Gao, P. & Stevenson, D. J. Nonhydrostatic effects and the determination of icy satellites’ moment of inertia. Icarus 226, 1185–1191 (2013).
Moore, W. B. & Schubert, G. The tidal response of Ganymede and Callisto with and without liquid water oceans. Icarus 166, 223–226 (2003).
Mazarico, E., Barker, M. K., Neumann, G. A., Zuber, M. T. & Smith, D. E. Detection of the lunar body tide by the Lunar Orbiter Laser Altimeter. Geophys. Res. Lett. 41, 2282–2288 (2014).
Xiao, H. et al. Mercury’s tidal Love number h2 from co-registration of MLA profiles. Geophys. Res. Lett. 52, e2024GL112266 (2025).
Durante, D. et al. Analysis of Cassini altimetric crossovers on Titan. Remote Sens. 16, 2209 (2024).
Steinbrügge, G. et al. Assessing the potential for measuring Europa’s tidal Love number h2 using radar sounder and topographic imager data. Earth Planet. Sci. Lett. 482, 334–341 (2018).
Steinbrügge, G., Stark, A., Hussmann, H., Sohl, F. & Oberst, J. Measuring tidal deformations by laser altimetry. A performance model for the Ganymede Laser Altimeter. Planet. Space Sci. 117, 184–191 (2015).
Van Hoolst, T., Baland, R.-M. & Trinh, A. On the librations and tides of large icy satellites. Icarus 226, 299–315 (2013).
Thomas, P. et al. Enceladus’s measured physical libration requires a global subsurface ocean. Icarus 264, 37–47 (2016).
Hemingway, D. J. & Nimmo, F. Looking for subsurface oceans within the moons of Uranus using librations and gravity. Geophys. Res. Lett. 51, e2024GL110409 (2024).
Petricca, F., Landau, D., Melwani Daswani, M. & Castillo-Rogez, J. Gravity and radio science investigation at the moons of Uranus to reveal subsurface oceans and characterize interior structures. J. Geophys. Res. Planets 130, e2024JE008715 (2025).
Van Hoolst, T., Rambaux, N., Karatekin, O., Dehant, V. & Rivoldini, A. The librations, shape, and icy shell of Europa. Icarus 195, 386–399 (2008).
Styczinski, M., Melini, D. & Tharimena, S. drsaikirant88/PyALMA3: author list correction. Zenodo https://doi.org/10.5281/zenodo.10476128 (2024).