Dynamical Stability and Dynamical Evolution of Extra-Solar Planetary System

自从发现了一颗51Peg的行星以来，从多普勒观测中已经发现了76颗围绕附近恒星运行的行星。其中，V仙女座有三颗行星，GJ876、HD83443、HD1683443、HD82943、HD74156和47 Uma有两颗行星。在HD83443、HD1683443、HD74156和47 Uma四个行星系中，两颗行星之间的距离比它们相互的Hill半径大得多，因此它们是动态稳定的。在其他三个行星茎中，相互距离较小，偏心率较大，这意味着可能发生近距离接近并变得不稳定。我们主要研究了这些行星系统的长期动力稳定性，得到了以下结果：1)这些行星系统是由近心自转和/或2：1平均运动共振稳定的。2)仙女座外围两颗行星的稳定性是通过中心附近的自转来维持的，避免了两颗行星的近距离接近。两颗外行星对最内侧行星的扰动很弱，仙女座五的行星系统是稳定的。3-1)当GJ876的两颗行星从观测中估计出质量最小时，这个行星系统。只有2：1的平均运动共振才是稳定的。3-2)当两颗行星的质量大得多时，它们被2：1的平均运动共振和近地中心的自转所稳定

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