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[4.09] Differential Continuation of Stable Resonant Periodic Orbits in Three-Body Systems

J. Couetdic (Ecole Centrale Paris), F. Varadi, W.B. Moore (IGPP/UCLA), N. Haghighipour (DTM/Carnegie)

We present an differential continuation method designed to study the locations of the resonant periodic orbits in the phase-parameter space of the three-body problem. We study systems with a star, and two planets orbiting around the first object in a mean-motion resonance. The method is based on the use of the so-called Plücker coordinates instead of the classical Newton method. A variant of the same method is also used with great efficiency for the search of initial resonant periodic orbits for the continuation. This method enables the investigation of those systems through an extensive study of their phase-parameter space. Our results on the stable orbital configurations in the 2:1 resonance provide constraints on the existence of terrestrial planets in extra-solar planetary systems.

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Bulletin of the American Astronomical Society, 36 #2
© 2004. The American Astronomical Soceity.