Stable 1:2 Resonant Periodic Orbits in Elliptic Three-Body Systems

Abstract

The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion resonance are presented. Using the method of differential continuation, the locations of the resonant periodic orbits of such systems are identified and through an extensive study of their phase-parameter space, it is found that the majority of the resonant periodic orbits are unstable. For certain values of the mass and the orbital eccentricity of the inner planet, however, stable periodic orbits can be found. The applicability of such studies to the 1:2 resonance of the extrasolar planetary system GJ876 is also discussed.

19 pages, 10 figures, 4 color figures, Submitted for publication, For better quality figures send an email

References in corpus (4)

• Short-Term Dynamical Interactions Among Extrasolar Planets
• A Mass for the Extrasolar Planet Gl 876b Determined from Hubble Space Telescope Fine Guidance Sensor 3 Astrometry and High-Precision Radial Velocities
• Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions
• The Dynamical Simulations of the Planets Orbiting GJ 876

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• Planar resonant periodic orbits in Kuiper belt dynamics
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• Modeling Radial Velocity Data of Resonant Planets to Infer Migration Histories
• Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
• Continuation of periodic orbits in two-planet resonant systems