Regular motions in extra-solar planetary systems
Abstract
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes oscillates around a constant value. It introduces the Hamiltonian equations of the $N$-planet problem and Poincaré's reduction of them to $3N$ degrees of freedom with a detailed discussion of the non-osculating ``canonical'' heliocentric Keplerian elements that should be used with Poincaré relative canonical variables. It also includes Beaugé's approximation to expand the disturbing function in the exoplanetary case where masses and eccentricities are large. The paper is concluded with a discussion of systems captured into resonance and their evolution to symmetric and asymmetric stationary solutions with apsidal corotation.
- Publication:
-
Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems
- Pub Date:
- January 2006
- DOI:
- 10.48550/arXiv.astro-ph/0402335
- arXiv:
- arXiv:astro-ph/0402335
- Bibcode:
- 2006cwod.book..255F
- Keywords:
-
- Astrophysics
- E-Print:
- 25 pages, 11 figures, to be published in "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Systems" (B.A.Steves, ed.), Kluwer Acad. Publ