Ellipsoidal equilibrium figure and Cassini states of rotating planets and satellites deformed by a tidal potential in the spatial case

Autor(es)

Folonier, Hugo A. ^{[1, 2]} ; Boue, Gwenael ^[2] ; Ferraz-Mello, Sylvio ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Astron Geofes & Ciencias Atmosfer, BR-05508090 Sao Paulo - Brazil

^[2] Sorbonne Univ, PSL, Observ Paris, ASD IMCCE, CNRS UMR8028, 77 Ave Denfert Rochereau, F-75014 Paris - France

• Tipo de documento: Artigo Científico
• Fonte: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY; v. 134, n. 1 FEB 2022.
• Citações Web of Science: 0

Resumo

The equilibrium figure of an inviscid tidally deformed body is the starting point for the construction of many tidal theories such as Darwinian tidal theories or the hydrodynamical Creep tide theory. This paper presents the ellipsoidal equilibrium figure when the spin rate vector of the deformed body is not perpendicular to the plane of motion of the companion. We obtain the equatorial and the polar flattenings as functions of the Jeans and the Maclaurin flattenings, and of the angle theta between the spin rate vector and the radius vector. The equatorial vertex of the equilibrium ellipsoid does not point toward the companion, which produces a torque perpendicular to the rotation vector, which introduces terms of precession and nutation. We find that the direction of spin may differ significantly from the direction of the principal axis of inertia C, so the classical approximation vertical bar omega approximate to C omega only makes sense in the neighborhood of the planar problem. We also study the so-called Cassini states. Neglecting the short-period terms in the differential equation for the spin direction and assuming a uniform precession of the line of the orbital ascending node, we obtain the same differential equation as that found by Colombo (Astron J 71:891, 1966). That is, a tidally deformed inviscid body has exactly the same Cassini states as a rotating axisymmetric rigid body, the tidal bulge having no secular effect at first order. (AU)

• Processo FAPESP: 16/13750-6 - O Brasil no espaço: Astrofísica e Engenharia
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• Processo FAPESP: 19/11276-3 - Extensão da teoria da maré de fluência Newtoniana ao caso espacial
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• Processo FAPESP: 16/20189-9 - Evolução dinâmica devida à maré em exoplanetas e satélites diferenciados
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