The 3:2 spin-orbit resonant motion of Mercury View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2006

AUTHORS

Anne Lemaitre , Sandrine D’Hoedt , Nicolas Rambaux

ABSTRACT

Our purpose is to build a model of rotation for a rigid Mercury, involving the planetary perturbations and the non-spherical shape of the planet. The approach is purely analytical, based on Hamiltonian formalism; we start with a first-order basic averaged resonant potential (including J 2 and C 22, and the first powers of the eccentricity and the inclination of Mercury). With this kernel model, we identify the present equilibrium of Mercury; we introduce local canonical variables, describing the motion around this 3:2 resonance. We perform a canonical untangling transformation, to generate three sets of action-angle variables, and identify the three basic frequencies associated to this motion. We show how to reintroduce the short-periodic terms, lost in the averaging process, thanks to the Lie generator; we also comment about the damping effects and the planetary perturbations. At any point of the development, we use the model SONYR to compare and check our calculations. More... »

PAGES

213-224

Book

TITLE

Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications

ISBN

978-1-4020-5324-5

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4020-5325-2_12

DOI

http://dx.doi.org/10.1007/978-1-4020-5325-2_12

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1017231669


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