二阶后牛顿光线轨迹方程

The Second-order Post-Newtonian Orbit Equation of Light

根据DSX体系的后牛顿近似理论,直接由Lagrange方程导出了轴对称稳态时空中光子的二阶后牛顿轨迹方程,并求得在赤道平面内传播的光线偏转角.在可测量精度范围内,得到的结论与Schwarzschild和Kerr度规下的情况相吻合.

The photon＇s orbital equation is often used to discuss the movement of manmade satellite, small planet and photon in the solar system. It is also applied to the studies of astronomical measure such as VLBI, GPS and XNAV etc. In this paper, based on the second-order post-Newtonian approximation under the DSX scheme of GTR, it is educed that the second-order post-Newtonian orbit equation of light in axis-symmetrical stationary space-time using Lagrange equation. From here, the orbit equation and deflection angle of light propagating in equatorial plane are got. The conclusions are consistent with that of Schwarzchild and Kerr metric in the precision Of measure. Because the oblateness of star is considered, it is more accurate than that of Kerr metric. The great advantage of the second-order post-Newtonian approximation under the DSX scheme of GTR is satisfy linear superposition. So, the conclusions in the paper can be applied to deal with the motion of light in multiple systems, but in this situation Kerr metric is of no effect.