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


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.

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.

Change history

  • 16 June 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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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).

Author information




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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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

Supplementary Information

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

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Source Data Fig. 2

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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 (2020).

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