Computer Science
Scientific paper
Apr 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005tvnv.conf..263d&link_type=abstract
Transits of Venus: New Views of the Solar System and Galaxy, Proceedings of IAU Colloquium #196, held 7-11 June, 2004 in Preston
Computer Science
2
Scientific paper
One of the main characteristics of Mercury is its 3:2 spin-orbit resonance, combined with a 1:1 resonance between the orbital node of its orbit and the angle describing the precession of the rotation axis, both measured on the ecliptic plane. We build an analytical model, using Hamiltonian formalism, that takes into account this phenomenon thanks to the introduction of three resonant variables and conjugated momenta. We calculate the equilibria corresponding to four different configurations, which means four completely different values of the (ecliptic) obliquity; in particular, we focus on the present (stable) situation of Mercury, and thanks to several canonical transformations, we obtain, near the equilibrium, three pairs of angle-action variables, and consequently, three basic frequencies. Let us note that the model is as simple as possible: the gravitational potential is limited to the second degree terms (the only ones for which a value can be presently given), and the orbit of Mercury is Keplerian. The numerical values obtained by our simplified model are validated by the coherence with existing complete numerical models.
D'Hoedt Sandrine
Lemaître Aristide
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