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R. Malhotra (U of Arizona)
In the past decade, more than 100 jovian mass planets have been detected in orbit about sun-like stars in our galactic neighborhood; ten of these include systems with two or more planets. It is likely that these systems contain additional bodies that are presently below the detection threshold. Dynamical stability considerations can constrain or suggest the possible orbital configurations of the unseen bodies. For systems with only a single detected planet, the Hill stability criterion or the resonance overlap criterion define zones of exclusion around the planet's orbit where other bodies are unstable. For a multiple planet system, no global criterion for stability is known. In this paper, I show that it is possible to do much better than the usual patch-work of single--planet analytic stability criteria, by using the classical Laplace-Lagrange secular theory for a multiple-planet system to locate the secular resonances and the magnitude of eccentricity excitation of test particles. Zones of high eccentricities (planet-crossing or star-grazing values) can then be identified and excluded as possible locations of undetected bodies. Applications of this analysis to several exo-planet systems will be presented, as well as comparison with long term numerical integrations from the recent literature.
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Bulletin of the American Astronomical Society, 36 #4
© 2004. The American Astronomical Soceity.