论文标题
太阳系的计算机辅助证明了100，000年的稳定性
A computer assisted proof for 100,000 years stability of the solar system
论文作者
论文摘要
我们提供了一项分析证明，并在未来100，000年内对八个主要行星和冥王星的动态稳定性进行了计算机计算的辅助。这意味着在此期间，行星的半高轴不会发生重大变化。轨道的偏心率和倾斜度也将保持足够小。标准线性四步数值方法用于整合汞，金星，地球，火星，木星，土星，天王星，海王星和冥王星的轨道。九个行星的动力学用轨道元素写成，表现出54个一阶普通微分方程的系统。数值方法的步进大小 - 大约六天，已经进行了6,290,000次。我们估计四舍五入错误的总积累，与天文数据中可能的不确定性以及计算机计算的准确性有关的偏差。
We present an analytical proof assisted by computer calculations for the dynamical stability of the eight main planets and Pluto for the next 100,000 years. It means that the semi-major axes of the planets will not change significantly during this period. Also the eccentricities and inclinations of the orbits will remain sufficiently small. A standard linear four-step numerical method is used to integrate approximately the orbits of Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Written in orbital elements, the dynamics of the nine planets manifests a system of 54 first-order ordinary differential equations. The step-size of the numerical method -- about six days, has been performed 6,290,000 times. We estimate the total accumulation of rounding-off errors, deviations related to possible uncertainty in the astronomical data and the accuracy of the computer calculations.
