小行星主带上单个行星的质量上限

The Upper Boundary of Mass for An Imaginary Planet in the Main Asteroid Belt

介绍了N体模拟的Hermite算法,并利用该算法研究了不同质量行星在小行星主带上轨道的演化情况．采用的演化模型是太阳系N体模型(N=7),即把水星、金星、地球的质量加到太阳上,忽略冥王星,同时在小行星主带附近增加一个假想行星,系统演化时间为1亿年．数值模拟显示能够稳定存在于小行星主带上的单个天体的质量上限其量级为10^(25)kg．模拟同时还显示在某些情况下,假想行星与木星之间的低阶共振可以增强系统的稳定性．

The stability of an imaginary planet located in the present main asteroid belt is studied, with a 7-body model （the Sun, Mars, Jupiter, Saturn, Uranus, Neptune and an imaginary planet）. The fourth order Hermite scheme P（EC）^3 is used, which has very little secular energy error for the integration of periodic orbits with constant time-step. The evolution of orbits are followed up to 108 years. Numerical results show that, the lower order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper boundary of the imaginary planet＇s mass that can be survived in the main belt is around 10^25 kg, near Earth＇s mass.