二阶后牛顿光线方程

近来相继提出一系列的空间天体测量计划，要求考虑在多参考系中二阶后牛顿部分对光线传播的贡献，也就是说，必须讨论在最近完成的扩展的DSX体系下的二阶后牛顿(2PN)光线方程．DSX体系是在20世纪90年代初建立的，用来讨论对N个任意形状和组成、自转可变形物体的一套完整的一阶后牛顿(1PN)天体力学理论．在此建议采用迭代的方法来推导2PN光线方程．从度规和Christoffel记号出发推导太阳系中的2PN光线方程．当忽略掉更高阶的项时，2PN光线方程将回到在很多教科书中广泛出现的1PN光线方程．利用这套方程就可以计算太阳系的光线传播．

The Second-order Post-Newtonian Equations of Light Ray

A series of space astrometric missions are proposed recently, in some of these projects the second-order contribution to light propagation in multiple systems should be considered, i.e.. the second-order post-Newtonian(2PX) equations of light ray have to be discussed under the recent extension of the DSX scheme which was founded in early 1990's to discuss a complete first-order post-Newtonian(lPN) celestial mechanics for N arbitrarily composed and shaped, rotating deformable bodies. In this paper, the iterative method is taken to establish and calculate the 2PN equations of light ray. The 2PN equations of light ray in the solar-system have been deduced from the metric tensor and Christoffel symbols. When the higher-order terms are neglected, the 2PN equations of light ray reduce to the 1PX equations which widely appeared in many textbooks. Using these equations light propagation in the solar system can be calculated.