Dynamical Stability and Dynamical Evolution of Extra-Solar Planetary System

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Since the discovery of a planet Of 51 Peg, 76 planets orbiting nearby stars have been discovered from the Doppler observations. Among them v Andromedae has three planets and, GJ876, HD83443, HD1683443, HD82943, HD74156, and 47 Uma have two planets. In the planetary systems of HD83443, HD1683443, HD74156, and 47 Uma the mutual distance between two planets are very large compared with their mutual Hill radius and then they are dynamically stable. In other three planetary stems the mutual distances are small and their eccentricity large, which means that a close approach may take place and become unstable. We mainly investigated the long-term dynamical stability of these planetary systems and obtained the following results : 1)These planetary systems are stabilized by the corotation of the pericenters and/or 2 : 1 mean motion resonance. 2)The stability of outer two planets of v Andromedae is maintained by the corotation of the pericenters, which avoid the close approaches of two planets. The disturbance to the most inner planet from two outer planets is weak and the planetary system of the v Andromedae is stable. 3-1) When two planets of GJ876 have minimum mass estimated from the observation, this planetary system. The is stabilized only of 2 : 1 mean motion resonance. 3-2)When the two planets have much larger masses, they are stabilized by 2 : 1 mean motion resonance and the corotation of the pericenters