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Abstract
Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two noncoplanar planets which are not in meanmotion resonance. By means of Lie transformations (which introduce an actionangle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3D secular threebody problem and compute the longterm time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear LaplaceLagrange theory and point out the great sensitivity of the 3D secular threebody problem to its initial values. This analytical approach is applied to the exoplanetary system μ Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration δ ω̄ observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes.
Original language  English 

Pages (fromto)  209229 
Number of pages  21 
Journal  Celestial Mechanics and Dynamical Astronomy 
Volume  100 
Issue number  3 
DOIs  
Publication status  Published  1 Mar 2008 
Keywords
 3D threebody problem
 Analytical expansion
 Extrasolar planets
 Laplace plane
 Secular motion
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Projects
 1 Finished

EXTRA: Exoplanetary systems and resonances
LIBERT, A., HENRARD, J. & LEMAITRE, A.
1/10/04 → 30/09/08
Project: PHD