Anne
Lemaitre
Mathematical Sciences
University of Namur
Département de mathématique, FUNDP, 8, Rempart de la Vierge, 5000, Namur, Belgique
D’Hoedt
Sandrine
http://link.springer.com/10.1007%2Fs10569-006-9041-x
Mercury is observed in a stable Cassini’s state, close to a 3:2 spin-orbit resonance, and a 1:1 node resonance. This present situation is not the only possible mathematical stable state, as it is shown here through a simple model limited to the second-order in harmonics and where Mercury is considered as a rigid body. In this framework, using a Hamiltonian formalism, four different sets of resonant angles are computed from the differential Hamiltonian equations, and each of them corresponds to four values of the obliquity; thanks to the calculation of the corresponding eigenvalues, their linear stability is analyzed. In this simplified model, two equilibria (one of which corresponding to the present state of Mercury) are stable, one is unstable, and the fourth one is degenerate. This degenerate status disappears with the introduction of the orbit (node and pericenter) precessions. The influence of these precession rates on the proper frequencies of the rotation is also analyzed and quantified, for different planetary models.
en
articles
2019-04-11T14:27
253-258
Note on Mercury’s rotation: the four equilibria of the Hamiltonian model
false
research_article
2006-11
2006-11-01
https://scigraph.springernature.com/explorer/license/
Springer Nature - SN SciGraph project
96
Applied Mathematics
Nicolas
Rambaux
dimensions_id
pub.1018348031
doi
10.1007/s10569-006-9041-x
3-4
readcube_id
576ba8068f4828933a72583dc0a7a92f321235ed93af94542ba2e3a76d216d90
0923-2958
Celestial Mechanics and Dynamical Astronomy
0008-8714