太阳系二阶后牛顿天体力学初步研究

项目名称： 太阳系二阶后牛顿天体力学初步研究

项目编号： No.11273044

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 陶金河

作者单位： 中国科学院上海天文台

项目金额： 80万元

中文摘要： 本项目在Damour, Soffel和Xu的一阶后牛顿天体力学的基础上，研究由任意形状和组成、可形变的、弱自引力的、低速运动和缓慢自转的天体组成的N体系统（如太阳系）的广义相对论二阶后牛顿近似理论，主要包括：全局参考系和局部参考系的度规表达式，引力场的方程，参考系和规范的选取，相对论多极矩的定义，引力势的表达式，参考系的变换关系，引力势的变换关系，天体运动方程和电磁波传播方程等等。二阶后牛顿天体力学是未来建立高精度的二阶后牛顿天文参考系的理论基础，具有重要的理论意义，在天文和天体物理相关领域也有广泛的应用。

中文关键词： 广义相对论；二阶后牛顿；长期岁差；天体力学；深空探测

英文摘要： The project is on the basis of the Damour, Soffel and Xu's first post-Newtonian celestial mechanics, to investigate and research the second post-Newtonian approximate theory of general relativity for a system of N arbitrarily composed and shaped, deformable, weakly self-gravitating, and slowly moving and rotating bodies (such as the solar system), mainly including: the metric expressions of both global and local reference systems, the equations of gravitational field, the chioce of reference systems and their gauges, the definitions of relativistic multipole moments, the expressions of gravitational potentials, the transformations among the reference systems, the transformations among the gravitational potentials, and the motion equations of celestial body and the electromagnetic wave propagation equation, and so on. The second post-Newtonian celestial mechanics is the theoretical basis for establishing the future high precise second post-Newtonian astronomical reference systems, it possesses important theoretical significance, and will be widely applied in astronomy and astrophysics.

英文关键词： general relativity；second post-Newtonian；long-term precession；celestial mechanics；deep space exploration