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

Lainey, Valéry and Gomez Casajus, Luis and Fuller, Jim and Zannoni, Marco and Tortora, Paolo and Cooper, Nicholas and Murray, Carl and Modenini, Dario and Park, Ryan S. and Robert, Vincent and Zhang, Qingfeng (2020) Resonance locking in giant planets indicated by the rapid orbital expansion of Titan. Nature Astronomy, 4 (11). pp. 1053-1058. ISSN 2397-3366. doi:10.1038/s41550-020-1120-5.

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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 distance, 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 theory, 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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URLURL TypeDescription ReadCube access Paper
Lainey, Valéry
Gomez Casajus, Luis0000-0002-7972-4006
Fuller, Jim0000-0002-4544-0750
Zannoni, Marco0000-0002-4151-9656
Cooper, Nicholas0000-0003-4901-0210
Park, Ryan S.0000-0001-9896-4585
Robert, Vincent0000-0002-4517-5213
Zhang, Qingfeng0000-0003-4086-9678
Alternate Title:New tidal paradigm in giant planets supported by rapid orbital expansion of Titan
Additional Information:© 2020 Nature Publishing Group. Received 01 August 2019; Accepted 30 April 2020; Published 08 June 2020. 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). 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. Author Contributions: 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. The authors declare no competing financial interests.
Group:Astronomy Department
Funding AgencyGrant Number
International Space Science Institute (ISSI)UNSPECIFIED
Agenzia Spaziale Italiana (ASI)2017-10-H.O
Rose Hills FoundationUNSPECIFIED
Alfred P. Sloan FoundationFG-2018-10515
Science and Technology Facilities Council (STFC)ST/M001202/1
Paris ObservatoryUNSPECIFIED
National Natural Science Foundation of China11873026
Subject Keywords:Exoplanets; Giant planets; Rings and moons
Issue or Number:11
Record Number:CaltechAUTHORS:20200327-111401612
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Official Citation: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).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102142
Deposited By: George Porter
Deposited On:27 Apr 2020 18:30
Last Modified:16 Nov 2021 18:09

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