Note on Mercury’s rotation: the four equilibria of the Hamiltonian model
| Autor: | Nicolas Rambaux, Anne Lemaitre, Sandrine D’Hoedt |
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| Rok vydání: | 2006 |
| Předmět: |
Physics
Hamiltonian model Applied Mathematics Degenerate energy levels chemistry.chemical_element Astronomy and Astrophysics Rigid body Mercury (element) Computational Mathematics symbols.namesake Classical mechanics chemistry Space and Planetary Science Modeling and Simulation Harmonics Physics::Space Physics symbols Astrophysics::Earth and Planetary Astrophysics Hamiltonian (quantum mechanics) Mathematical Physics Eigenvalues and eigenvectors Linear stability |
| Zdroj: | Celestial Mechanics and Dynamical Astronomy. 96:253-258 |
| ISSN: | 1572-9478 0923-2958 |
| DOI: | 10.1007/s10569-006-9041-x |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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