High-order Correction In The Radar Echo Delay Using Post Newtonian Approximation

Ever since Einstein found Einstein equation 100 years ago, a lot of experiments have been done to test the predictions of Einstein's general relativity. However, because Einstein's theory of gravity cannot be quantized and unified with the other three fundamental forces,so we still need to test classical gravitational theories to higher orders. There are many experiments in the solar system that can test Einstein's general relativity, including the light propagation in the solar system. Due to the gravitational pull, light ray will change direction when it passes by the sun, so the propagation time between two points A and B will be longer. In principle,we can calculate the time that the light travels from a location A to location B, however the calculation is not simple at all, so we need to use the post Newtonian approximation to solve the problem. Then we not only get the result at the order we want,but also test the general theory of relativity.In this thesis, we first introduce the Post-Newtonian approximation and the Parametrized Post-Newtonian(PPN) formalism. Next, we give an introduction to the eikonal function and the world function, which we can also use to calculate the light travel time with PPN parameters. Then the transformation of the coordinates between the standard form and the general isotropic one is deduced for the Schwarzschild metric. This thesis applies the general equation of motion and the method of Post-Newtonian approximation,to derive the echo time required for radar signals propagating from one point to another to the second order in the standard form. This calculated time is also called light travel time.The deduced relationship can help us to transform the calculated result deduced from the standard form to the one in general isotropic one. Finally, we use the formula to calculate the time delay to the order of(Gm/c~2)~2or(Gm/Rc~2)~2.