Calculating deviation of laser pulses at ranging artificial Earth satellites considering its gravitational field

Accurate laser location of artificial Earth satellites (AES) makes it possible to obtain valuable information on the dynamic parameters of the Earth, its gravitational fields, and to clarify the global coordinates of the system. The effect of laser pulses deviation at the ranging AES is studied. The angle of deviation is formed between directions of emitted and returned signals at the point of the laser station’s location. The main contribution into the value of the angle is conditioned by relativity theory effects connected with non-inertiality of the station frame on the rotating Earth surface. In this article, the value of the deviation angle is calculated considering the Earth’s gravitational field that was not considered in previous works. Exactness of necessary approximations enables modelling a motion of AES by Keplerian orbits. The gravitational field of the Earth is described by the Schwarzschild solution, in the framework of which equations for the laser pulse trajectories are presented. All the calculations are made in the coordinates of the proper frame of the station. The obtained variation of the main deviation angle value is less for three orders with respect to the one that can be detected by the modern devices. Therefore, we can state that it should not be taken into account. Such a conclusion is very important for developments in this field because simpler methods, including analytical ones, are permissible. The efficiency of the numerical calculations of the effect for concrete AES remains high as well