A Systematic Study of the Stability of Symmetric Periodic Orbits in the Planar, Circular, Restricted Three-Body Problem |
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Authors: | Alessandra Celletti Andrea Chessa John Hadjidemetriou Giovanni Battista Valsecchi |
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Affiliation: | (1) Dip. Matematica, Università di Roma 'Tor Vergata', Via della Ricerca Scientifica, I-00133 Roma, Italy;(2) Department of Physics, University of Thessaloniki, 54006 Thessaloniki, Greece;(3) Istituto di Astrofisica Spaziale e Fisica Cosmica del C.N.R., Via Fosso del Cavaliere 100, 00133 Roma, Italy |
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Abstract: | We investigate symmetric periodic orbits in the framework of the planar, circular, restricted, three-body problem. Having fixed the mass of the primary equal to that of Jupiter, we determine the linear stability of a number of periodic orbits for different values of the eccentricity. A systematic study of internal resonances, with frequency p/q with 2p 9, 1 q 5 and 4/3 p/q 5, offers an overall picture of the stability character of inner orbits. For each resonance we compute the stability of the two possible periodic orbits. A similar analysis is performed for some external periodic orbits.Furthermore, we let the mass of the primary vary and we study the linear stability of the main resonances as a function of the eccentricity and of the mass of the primary. These results lead to interesting conclusions about the stability of exosolar planetary systems. In particular, we study the stability of Earth-like planets in the planetary systems HD168746, GI86, 47UMa,b and HD10697. |
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Keywords: | periodic orbits linear stability three-body problem exosolar systems |
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