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.
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References
Beletsky, V.V.: Essays on the Motion of Celestial Bodies. Birkhauser Verlag (2000)
Bills, B.G., Comstock, R.I.: Forced obliquity variations of Mercury. J. Geophys. Res. 110, E04006 (2005)
Correia, A., Laskar, J.: Mercury’s capture into the 3:2 spin-orbit resonance as a result of its chaotic dynamics. Nature 429, 848–850 (2004)
Deprit, A.: Free rotation of a rigid body studied in the phase plane. Am. J. Phys. 35(5), 424–428 (1967)
D’Hoedt, S., Lemaitre, A.: The spin-orbit resonant rotation of Mercury: a two degree of freedom Hamiltonian model. Celest. Mech. Dynam. Astron. 89, 267–283 (2004a)
D’Hoedt, S., Lemaitre, A.: The spin-orbit resonance of Mercury: a Hamiltonian approach. In: Kurtz, DW (ed.) Proceedings of the International Astronomical Union 196, pp. 263–270. (2004b)
D’Hoedt, S., Lemaitre, A., Rambaux, N.: 2006, Note on Mercury’s rotation: The four equilibria of the Hamiltonian model, Celest. Mech. Dynam. Astron. 96 (2006) in press.
Henrard, J., Lemaitre, A.: The untangling transformation. Astron. J. 130, 2415–2417 (2005)
Kaula, W.M.: Theory of Satellite Geodesy: Applications of Satellites to Geodesy. Blaisdell Publishing, NY (1996)
Meyer, K.R., Hall, G.R.: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences, vol. 90. Springer-Verlag, Berlin (1992)
Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)
Peale, S.J.: The free precession and libration of Mercury. Icarus 178, 4–18 (2005a)
Peale, S.J.: The proximity of Mercury’s spin to Cassini’s state 1 from adiabatic invariance. Icarus 181, 338–347 (2005b)
Rambaux, N., Bois, E.: Theory of the Mercury’s spin-orbit motion and analysis of its main librations. Astron. Astrophy. 413, 381–393 (2004)
Yseboodt, M., Margot, J.L.: Evolution of Mercury’s obliquity. Icarus 181, 327–337 (2005)
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Lemaitre, A., D’Hoedt, S., Rambaux, N. (2006). The 3:2 spin-orbit resonant motion of Mercury. In: Celletti, A., Ferraz-Mello, S. (eds) Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5325-2_12
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DOI: https://doi.org/10.1007/978-1-4020-5325-2_12
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