2003/01/17 by Nader Haghighipour, J. Couetdic, Jocelyn Couetdic +4 · 2 citations
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Astrophysics #Astrophysics and Star Formation Studies #Celestial mechanics #Classical mechanics #Eccentricity (behavior) #Elliptic orbit #Exoplanet #Massless particle #Mathematical physics #Mean motion #Orbital eccentricity #Periodic orbits #Phase space #Physics #Planet #Planetary system #Resonance (particle physics) #Stellar, planetary, and galactic studies #Three-body problem #astro-ph #math-ph #math.MP
paper · pdf · doi:10.1086/378119
published as Astrophys.J.596:1332-1340,2003 · 19 pages, 10 figures, 4 color figures, Submitted for publication, For better quality figures send an email
arxiv created 2003/01/17 · openalex publication_date 2003/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 massless 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 GJ 876 is also discussed.