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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

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2006.02.007 Byline: Anne-Sophie Libert, Jacques Henrard Keywords: Celestial mechanics; Extrasolar planets; Planetary dynamics; Resonances Abstract: Using a high-order (order 12) expansion of the perturbative potential in powers of eccentricities [Libert, A.-S., Henrard, J., 2005. Celest. Mech. Dynam. Astron. 93, 187-200], we study the secular effects of two coplanar planets which are not in mean motion resonances. The main results concern eccentricity variations, oscillation amplitude of the angular difference of the apsidal lines ([DELTA]I) and frequency of such an oscillation. We show that this analytical approach describes correctly the behaviour of most of the exosystems and underlines the known limitations of the linear Laplace-Lagrange theory. Apsidal configuration of I Andromedae, HD 168443, HD 169830, HD 38529, HD 74156 and HD 12661 are examined. We also point out the great sensitivity of the I Andromedae system to the initial values (e.sub.1(0), e.sub.2(0) or [DELTA]I(0)). Author Affiliation: Departement de Mathematique FUNDP, 8 Rempart de la Vierge, 5000 Namur, Belgium Article History: Received 15 June 2005; Revised 13 February 2006