Coupling between the spin precession and polar motion of a synchronously rotating satellite: application to Titan

  • Rose-Marie BalandEmail author
  • Alexis Coyette
  • Tim Van Hoolst
Original Article


We here develop, in an angular momentum approach, a consistent model that integrates all rotation variables and considers forcing both by the central planet and a potential atmosphere. Existing angular momentum approaches for studying the polar motion, precession, and libration of synchronously rotating satellites, with or without an internal global fluid layer (e.g., a subsurface ocean) usually focus on one aspect of rotation and neglect coupling with the other rotation phenomena. The model variables chosen correspond most naturally with the free modes, although they differ from those of Earth rotation studies, and facilitate a comparison with existing decoupled rotation models that break the link between the rotation motions. The decoupled models perform well in reproducing the free modes, except for the Free Ocean Nutation in the decoupled polar motion model. We also demonstrate the high accuracy of the analytical forced solutions of decoupled models, which are easier to use to interpret observations from past and future space missions. We show that the effective decoupling between the polar motion and precession implies that the spin precession and its associated mean obliquity are mainly governed by the external gravitational torque by the parent planet, whereas the polar motion of the solid layers is mainly governed by the angular momentum exchanges between the atmosphere (e.g., for Titan) and the surface. To put into perspective the difference between rotation models for a synchronously rotating icy moon with a thin ice shell and classical Earth rotation models, we also consider the case of the Moon, which has a thick outer layer above a liquid core. We also show that for non-synchronous rotators, the free precession of the outer layer in space degenerates into the tilt-over mode.


Cassini state Precession Polar motion Titan Internal ocean Angular momentum formalism 



We thank Benoît Noyelles for allowing us to mutually compare our results. We also thank Antony Trinh for fruitful discussions about Earth rotation. We thank the anonymous reviewer for his comments and suggestions that have helped to improve our paper. The research leading to these results has received funding from the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office.

Conflict of interest The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Royal Observatory of BelgiumBrusselsBelgium
  2. 2.UNamur, Namur Institute for Complex System (naXys)NamurBelgium

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