1. Exoplanetary systems: The role of an equilibrium at high mutual inclination in shaping the global behavior of the 3-D secular planetary three-body problem
- Author
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Libert, Anne-Sophie and Henrard, Jacques
- Subjects
Astronomy ,Earth sciences - Abstract
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2007.05.007 Byline: Anne-Sophie Libert, Jacques Henrard Keywords: Celestial mechanics; Extrasolar planets; Planetary dynamics; Resonances Abstract: On the basis of a high-order (order 12) expansion of the perturbative potential in powers of the eccentricities and the inclinations, we analyze the secular interactions of two non-coplanar planets which are not in mean-motion resonance. The model is based on the planetary three-body problem which can be reduced to two degrees of freedom by the well-known elimination of the nodes [Jacobi, C.G.J., 1842. Astron. Nachr. XX, 81-102]. We introduce non-singular canonical variables which bring forward the symmetries of the problem. The main dynamical features depend on the location and stability of the equilibria which are easily found with our analytical model. We find that there exists an equilibrium when both eccentricities are zero. When the mutual inclination is small, this equilibrium is stable, but for larger mutual inclination it becomes unstable, generating a large chaotic zone and, by bifurcation, two regular regions, the so-called Kozai resonances. This analytical study which depends on only two parameters (the ratio of the semi-major axes and the mass ratio of the planets) makes possible a large survey of the problem and enables us to identify and quantify its main dynamical features, periodic orbits, regular and chaotic zones, etc. The results of our analytical model are illustrated and confirmed by numerical integrations. Author Affiliation: Departement de Mathematique FUNDP, 8 Rempart de la Vierge, 5000 Namur, Belgium Article History: Received 25 January 2007; Revised 20 April 2007
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- 2007