# Regular motions in extra-solar planetary systems

@inproceedings{FerrazMello2004RegularMI, title={Regular motions in extra-solar planetary systems}, author={Sylvio Ferraz-Mello and Tatiana A. Michtchenko and Claudineia Brazil and OA Universidad Nacional de Cordoba Argentina}, year={2004} }

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 Poincar\'e's reduction of them to $3N$ degrees of freedom with a detailed discussion of the non-osculating ``canonical'' heliocentric Keplerian elements…

## 26 Citations

Secular dynamics of a coplanar, non‐resonant planetary system under the general relativity and quadrupole moment perturbations

- Physics, Geology
- 2009

We construct a secular theory of a coplanar system of N planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual…

Modeling the 3-D secular planetary three-body problem: Discussion on the outer υ Andromedae planetary system

- Physics, Geology
- 2006

Dynamic portrait of the planetary 2/1 mean‐motion resonance – II. Systems with a more massive inner planet

- Physics, Geology
- 2008

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant…

The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects

- Physics, Geology
- 2007

We describe numerical tools for the stability analysis of extrasolar planetary systems. In par- ticular, we consider the relative Poincare variables and symplectic integration of the equations of…

On the dynamics of extrasolar planetary systems under dissipation: Migration of planets

- Physics, Geology
- 2010

We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general…

Planetary migration and extrasolar planets in the 2/1 mean-motion resonance

- Physics, Geology
- 2004

In this paper, we present a new set of corotational solutions for the 2/1 commensurability, including previously known solutions and new results. Comparisons with observed exoplanets show that…

Orbital stability of coplanar two-planet exosystems with high eccentricities

- Physics, Geology
- 2016

The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when…

Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12

- Physics, Geology
- 2006

This paper considers the dynamics of two planets, as the planets B and C of the pulsar PSR B1257+12, near a 3/2 mean-motion resonance. A two-degrees-of-freedom model, in the framework of the general…

On the habitability of the OGLE-2006-BLG-109L planetary system

- Physics, Geology
- 2009

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired…

Regular and chaotic orbits in the dynamics of exoplanets

- Physics, Geology
- 2016

Abstract
Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets…

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