About the Deviation of Electromagnetic Pulses in an Earth-Fixed Rotating Reference Frame

Abstract

The position of an artificial Earth satellite or the Moon is determined by laser ranging. Laser measurements of distances are carried out from ground stations to satellites equipped with corner reflectors or to the reflectors located on the surface of the Moon. The time interval between the emission and reception of ultrashort laser pulses at the same station make it possible to determine the position of the satellite or the Moon at the moment of reflection. In this case, the signal emitted from the station and the reflected signal from the satellite follow different paths. In this case, an angle is formed between the direction of the emitted and reflected signals at the location point. It is this deviation of laser signal paths that is the subject-matter of this paper. Since the Earth-fixed rotating reference frame is noninertial, calculations are performed with consideration for the theory of relativity. The spherical shape of the Earth and the Keplerian orbits of satellites are considered without taking into account the Earth’s gravitational field. The signal deviation significantly depends both on the satellite orbital parameters and the Earth’s rotation rate. The mathematical calculations allow the authors to generalize and compare the results of studies of this effect obtained from various available publications. They were also used in numerical calculations on the example of a high-orbit and high-eccentricity satellite RadioAstron and all of the 24 GLONASS low-orbit satellites with minor eccentricities. The magnitudes of both the effect itself and its variations depending on the changes in the satellite orbit parameters are calculated. The accuracy of modern instruments is sufficient to record the effect, and the result obtained will increase the efficiency of their application. In the future, it is planned to evaluate the factors of the Earth oblateness and its gravitational potential.