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Resonance locking in giant planets indicated by the rapid orbital expansion of Titan

A Publisher Correction to this article was published on 16 June 2020


Saturn is orbited by dozens of moons, and the intricate dynamics of this complex system provide clues about its formation and evolution. Tidal friction within Saturn causes its moons to migrate outwards, driving them into orbital resonances that pump their eccentricities or inclinations, which in turn leads to tidal heating of the moons. However, in giant planets, the dissipative processes that determine the tidal migration timescale remain poorly understood. Standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance1, implying negligible migration for outer moons such as Saturn’s largest moon, Titan. Here, we use two independent measurements obtained with the Cassini spacecraft to measure Titan’s orbital expansion rate. We find that Titan rapidly migrates away from Saturn on a timescale of roughly ten billion years, corresponding to a tidal quality factor of Saturn of Q 100, which is more than a hundred times smaller than most expectations. Our results for Titan and five other moons agree with the predictions of a resonance-locking tidal theory2, sustained by excitation of inertial waves inside the planet. The associated tidal expansion is only weakly sensitive to orbital distance, motivating a revision of the evolutionary history of Saturn’s moon system. In particular, it suggests that Titan formed much closer to Saturn and has migrated outward to its current position.

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Fig. 1: Saturnian tidal quality factor.
Fig. 2: Tidal migration timescales.
Fig. 3: Moon orbital evolution.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Data for Figs. 1 and 2 are available as Source Data with the paper.

Code availability

All astrometric data derived from ISS-images can be reproduced using our CAVIAR software available under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License ( The MONTE space navigation code was obtained through a license agreement between NASA and the Italian Space Agency; the terms do not permit redistribution. MONTE licenses may be requested at The availability of NOE software is limited due to NASA restrictions.


  1. Goldreich, P. & Soter, S. Q in the Solar System. Icarus 5, 375–389 (1966).

    Article  ADS  Google Scholar 

  2. Fuller, J., Luan, J. & Quataert, E. Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems. Mon. Not. R. Astron. Soc. 458, 3867–3879 (2016).

    Article  ADS  Google Scholar 

  3. Lainey, V. et al. Strong tidal dissipation in Saturn and constraints on Enceladus’ thermal state from astrometry. Astrophys. J. 752, 14 (2012).

    Article  ADS  Google Scholar 

  4. Lainey, V. et al. New constraints on Saturn’s interior from Cassini astrometric data. Icarus 281, 286–296 (2017).

    Article  ADS  Google Scholar 

  5. Charnoz, S. et al. Accretion of Saturn mid-sized moons during the viscous spreading of young massive rings: solving the paradox of silicate-poor rings versus silicate-rich moons. Icarus 216, 535–550 (2011).

    Article  ADS  Google Scholar 

  6. Ćuk, M., Dones, L. & Nesvorný, D. Dynamical evidence for a late formation of Saturn’s moons. Astrophys. J. 820, 97 (2016).

    Article  ADS  Google Scholar 

  7. Witte, M. G. & Savonije, G. J. Tidal evolution of eccentric orbits in massive binary systems. a study of resonance locking. Astron. Astrophys. 350, 129–147 (1999).

    ADS  Google Scholar 

  8. Ogilvie, G. I. & Lin, D. N. C. Tidal dissipation in rotating giant planets. Astrophys. J. 610, 477–509 (2004).

    Article  ADS  Google Scholar 

  9. Fuller, J. Saturn ring seismology: evidence for stable stratification in the deep interior of Saturn. Icarus 242, 283–296 (2014).

    Article  ADS  Google Scholar 

  10. Salpeter, E. E. On convection and gravitational layering in Jupiter and in stars of low mass. Astrophys. J. Lett. 181, L83 (1973).

    Article  ADS  Google Scholar 

  11. Wilson, H. F. & Militzer, B. Solubility of water ice in metallic hydrogen: consequences for core erosion in gas giant planets. Astrophys. J. 745, 54 (2012).

    Article  ADS  Google Scholar 

  12. Tortora, P. et al. Rhea gravity field and interior modeling from Cassini data analysis. Icarus 264, 264–273 (2016).

    Article  ADS  Google Scholar 

  13. Iess, L. et al. The gravity field and interior structure of Enceladus. Science 344, 78–80 (2014).

    Article  ADS  Google Scholar 

  14. Iess, L. et al. Measurement and implications of Saturn’s gravity field and ring mass. Science 364, aat2965 (2019).

    Article  ADS  Google Scholar 

  15. Durante, D., Hemingway, D. J., Racioppa, P., Iess, L. & Stevenson, D. J. Titan’s gravity field and interior structure after Cassini. Icarus 326, 123–132 (2019).

    Article  ADS  Google Scholar 

  16. Evans, S. et al. Monte: the next generation of mission design and navigation software. CEAS Space J. 10, 79–86 (2018).

    Article  ADS  Google Scholar 

  17. Cooper, N. J. et al. The Caviar software package for the astrometric reduction of Cassini ISS images: description and examples. Astron. Astrophys. 610, A2 (2018).

    Article  Google Scholar 

  18. Zhang, Q. F. et al. First astrometric reduction of Cassini imaging science subsystem images using an automatic procedure: application to Enceladus images 2013-2017. Mon. Not. R. Astron. Soc. 481, 98–104 (2018).

    Article  ADS  Google Scholar 

  19. Choblet, G. et al. Powering prolonged hydrothermal activity inside Enceladus. Nat. Astron.1, 841–847 (2017).

    Article  ADS  Google Scholar 

  20. Howett, C. J. A., Spencer, J. R., Pearl, J. & Segura, M. High heat flow from Enceladus’ south polar region measured using 10-600 cm−1 Cassini/CIRS data. J. Geophys. Res. Planets 116, 3003 (2011).

    Article  ADS  Google Scholar 

  21. Sinclair, A. T. A re-consideration of the evolution hypothesis of the origin of the resonances among Saturn’s satellites. In IAU Colloq. 74: Dynamical Trapping and Evolution in the Solar System (eds Markellos, V. V. & Kozai, Y.) Vol. 106, 19–25 (IAU, 1983).

  22. Dermott, S. F., Malhotra, R. & Murray, C. D. Dynamics of the Uranian and Saturnian satellite systems—a chaotic route to melting Miranda? Icarus 76, 295–334 (1988).

    Article  ADS  Google Scholar 

  23. Fuller, J. & Lai, D. Dynamical tides in compact white dwarf binaries: influence of rotation. Mon. Not. R. Astron. Soc. 444, 3488–3500 (2014).

    Article  ADS  Google Scholar 

  24. Colombo, G., Franklin, F. A. & Shapiro, I. I. On the formation of the orbit-orbit resonance of Titan and Hyperion. Astron. J. 79, 61 (1974).

    Article  ADS  Google Scholar 

  25. Polycarpe, W. et al. Strong tidal energy dissipation in Saturn at Titan’s frequency as an explanation for Iapetus orbit. Astron. Astrophys. 619, A133 (2018).

    Article  Google Scholar 

  26. Crida, A. & Charnoz, S. Formation of regular satellites from ancient massive rings in the Solar System. Science 338, 1196–1199 (2012).

    Article  ADS  Google Scholar 

  27. Neveu, M. & Rhoden, A. R. Evolution of Saturn’s mid-sized moons. Nat. Astron. 3, 543–552 (2019).

    Article  ADS  Google Scholar 

  28. Fuller, J., Hambleton, K., Shporer, A., Isaacson, H. & Thompson, S. Accelerated tidal circularization via resonance locking in KIC 8164262. Mon. Not. R. Astron. Soc. 472, L25–L29 (2017).

    Article  ADS  Google Scholar 

  29. Burkart, J., Quataert, E. & Arras, P. Dynamical resonance locking in tidally interacting binary systems. Mon. Not. R. Astron. Soc. 443, 2957–2973 (2014).

    Article  ADS  Google Scholar 

  30. Burkart, J., Quataert, E., Arras, P. & Weinberg, N. N. Tidal resonance locks in inspiraling white dwarf binaries. Mon. Not. R. Astron. Soc. 433, 332–352 (2013).

    Article  ADS  Google Scholar 

  31. Bar-Sever, Y. E. et al. Atmospheric media calibration for the deep space network. Proc. IEEE 95, 2180–2192 (2007).

    Article  ADS  Google Scholar 

  32. Lainey, V. Quantification of tidal parameters from Solar System data. Celest. Mech. Dyn. Astron. 126, 145–156 (2016).

    Article  ADS  Google Scholar 

  33. French, R. G. et al. Astrometry of Saturn’s satellites from the Hubble Space Telescope WFPC2. Publ. Astron. Soc. Pacif. 118, 246–259 (2006).

    Article  ADS  Google Scholar 

  34. Jacobson, R. A. The small Saturnian satellites—chaos and conundrum. In AAS/Division of Dynamical Astronomy Meeting Vol. 45, 304.05 (AAS, 2014).

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V.L.’s research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This work has been supported by the ENCELADE team of the International Space Science Institute (ISSI). Support for this work was provided by the Italian Space Agency (L.G.C., M.Z., P.T. and D.M.) through agreement 2017-10-H.O in the context of the NASA/ESA/ASI Cassini/Huygens mission. J.F.’s research is funded in part by a Rose Hills Innovator Grant and the Sloan Foundation through grant FG-2018-10515. N.C. and C.M. thank the UK Science and Technology Facilities Council (grant number ST/M001202/1) for financial assistance. N.C. thanks the Scientific Council of the Paris Observatory for funding. Q.Z.’s research was supported by the National Natural Science Foundation of China (grant number 11873026).

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Authors and Affiliations



All authors contributed to the writing of the manuscript. V.L. developed and fitted to the observations the full numerical model presented for the astrometric approach. P.T. led the radiometric data analysis approach. L.G.C. and M.Z. carried out the radiometric data analysis. J.F. provided theoretical interpretation, constructed figures and performed supplementary calculations. D.M. contributed to software development. N.C., C.M., V.R. and Q.Z. provided extra astrometric data. R.P. provided extra expertise in the astrometric analysis.

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Correspondence to Valéry Lainey.

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The authors declare no competing financial interests.

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Peer review information Nature Astronomy thanks Stefano Bertone, Aurelien Crida, Shigeru Ida, Francis Nimmo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Discussion, Supplementary Tables 1 and 2, Supplementary Figures 1–4

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Lainey, V., Casajus, L.G., Fuller, J. et al. Resonance locking in giant planets indicated by the rapid orbital expansion of Titan. Nat Astron 4, 1053–1058 (2020).

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