后牛顿近似计算雷达回波延迟的高阶修正

发布时间：2018-01-03 12:26

本文关键词：后牛顿近似计算雷达回波延迟的高阶修正　出处：《华中科技大学》2015年硕士论文　论文类型：学位论文

【摘要】：爱因斯坦提出广义相对论100年来,人们已经做了大量的实验验证了经典广义相对论理论的各种预言。但是由于爱因斯坦引力理论目前还无法进行量子化,我们还无法把引力理论与其它三种基本相互作用统一起来,因此有必要继续对爱因斯坦引力理论进行更精确的检验。太阳系中有很多可以检验广义相对论的实验,包括在太阳系中传播的光线。由于太阳引力的作用会使得通过太阳附近的光线发生偏折,因此从A点传播到B点的光线所经历的时间由于引力效应会发生延迟。这个延迟效应原则上是可以计算出来的,但是通常却无法得到一个能直接运用的解析表达式,所以我们需要采取一些近似方法。本文主要利用后牛顿近似方法计算雷达回波延迟近似到二阶。这样我们便可以利用理论计算结果和更精确的实验结果进行比较,从而甄别不同的引力理论。本文首先简单介绍了后牛顿近似方法及后牛顿参数,然后介绍了如何利用光程函数计算出光在引力场中的传播时间,以及world函数与光的传播时间的关系。接下来本文推导出了史瓦西度规标准形式与各向同性度规之间的坐标变换关系。进一步,本文利用用后牛顿近似方法,由测地线方程推导出来了广义运动方程,并在标准形式下计算了雷达信号(光信号)从一点传播到另一点所需的时间,这个计算结果精确到了星体引力半径的二阶(Gm/c~2)~2,即计算精度达到了(Gm/Rc~2)~2阶。通过坐标变换关系,我们可以比较不同坐标系下得到的结果的一致性。
[Abstract]:Einstein's general theory of relativity in 100 years, people have done a lot of experimental verification of the classical general relativity theory. But because the predictions of Einstein's theory of gravity is not quantized, we are unable to put the theory of gravitation and the other three fundamental interactions of unity, it is necessary to test more accurate on Einstein's theory of gravity. In the solar system have a lot of experimental test of general relativity, including the spread of light in the solar system. Due to the influence of the sun's gravity will make the line near the sun through the light deflection occurs, so the experience from point A to point B light propagation time delays will occur due to gravitational effect this delayed effect principle can be calculated, but often cannot get a direct use of the analytical expressions, so we need to take a Some approximate methods. This paper mainly uses the Newton approximation method to calculate radar echo delay approximate to two order. So we can compare the calculation results with theoretical and experimental results more accurate, so as to identify different theory of gravitation. This paper introduces the Newton approximate Newton method and parameters, and then introduces how to use the the optical path function to calculate the propagation time of light in gravitational field, and the relationship between the propagation time of world function and light. Then the paper deduced coordinate between the Schwarzschild metric standard form and isotropic metric transformation. Further, by using the approximate method used by Newton, by the geodesic equation derived from the generalized the motion equation, and calculate the radar signal in the standard form (optical signal) from one point to another point spread the time required for the calculation results to the leading stars The two order (Gm/c~2) ~2 of the radius of force is, that is, the computation accuracy is up to (Gm/Rc~2) ~2 order. Through the coordinate transformation relation, we can compare the consistency of the results obtained in different coordinate systems.

【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P131

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