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

• Published in: Celestial mechanics and dynamical astronomy Vol. 131; no. 2; pp. 1 - 50
• Main Authors: Baland, Rose-Marie, Coyette, Alexis, Van Hoolst, Tim
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2019; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Angular momentum; Astrophysics and Astroparticles; Atmosphere; Atmospheric models; Classical Mechanics; Coupling; Decoupling; Dynamical Systems and Ergodic Theory; Earth rotation; Geophysics/Geodesy; Ice cover; Icy satellites; Jupiter; Libration; Lunar rotation; Mathematical models; Model accuracy; Moon; Nutation; Obliquity; Oceans; Original Article; Physics; Physics and Astronomy; Planetary rotation; Precession; Rotation; Space missions; Titan; Angular momentum formalism; Internal ocean; Precession; Cassini state; Titan; Polar motion
• ISSN: 0923-2958; 1572-9478
• DOI: 10.1007/s10569-019-9888-2

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.