Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

  • H. A. Folonier
  • S. Ferraz-MelloEmail author
  • E. Andrade-Ines
Original Article
Part of the following topical collections:
  1. Close Approaches and Collisions in Planetary Systems


This paper deals with a new formulation of the creep tide theory (Ferraz-Mello in Celest Mech Dyn Astron 116:109, 2013—Paper I) and with the tidal dissipation predicted by the theory in the case of stiff bodies whose rotation is not synchronous but is oscillating around the synchronous state with a period equal to the orbital period. We show that the tidally forced libration influences the amount of energy dissipated in the body and the average perturbation of the orbital elements. This influence depends on the libration amplitude and is generally neglected in the study of planetary satellites. However, they may be responsible for a 27% increase in the dissipation of Enceladus. The relaxation factor necessary to explain the observed dissipation of Enceladus (\(\gamma =1.2{-}3.8\times 10^{-7}\ \mathrm{s}^{-1}\)) has the expected order of magnitude for planetary satellites and corresponds to the viscosity \(0.6{-}1.9 \times 10^{14}\) Pa s, which is in reasonable agreement with the value recently estimated by Efroimsky (Icarus 300:223, 2018) (\(0.24 \times 10^{14}\) Pa s) and with the value adopted by Roberts and Nimmo (Icarus 194:675, 2008) for the viscosity of the ice shell (\(10^{13}{-}10^{14}\) Pa s). For comparison purposes, the results are extended also to the case of Mimas and are consistent with the negligible dissipation and the absence of observed tectonic activity. The corrections of some mistakes and typos of paper II (Ferraz-Mello in Celest Mech Dyn Astron 122:359, 2015) are included at the end of the paper.



We thank Gwenaël Boué and Michael Efroimsky for their detailed reading of the original manuscript and for their enlightening suggestions. We also thank C. Beaugé and G.O. Gomes for several discussions. This investigation is funded by FAPESP, Grants 2016/20189-9, 2014/13407-4, 2016/13750-6 and 2017/10072-0, and by the National Research Council, CNPq, Grant 302742/2015-8. Preliminary results of this investigation were presented at the 9th Humboldt Colloquium on Celestial Mechanics, in Bad Hofgastein (Austria), March 2017.

Supplementary material

10569_2018_9872_MOESM1_ESM.pdf (333 kb)
Supplementary material 1 (pdf 332 KB)


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Instituto de Astronomia Geofísica e Ciências AtmosféricasUniversidade de São PauloSão PauloBrasil

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