INVESTIGATION OF THE MOTION OF A SATELLITE, ACCORDING TO GENERAL THEORY OF RELATIVITY

In this paper we investigate the energy integral which is obtained in the problem of the motion of a material point in a central field within the frame of the general theory of relativity. Applied are the method of the small parameter in a combination with the balance method. Derived is a compact formula, describing the trajectory of the motion. This formula gives a correct quantitative description of the basic relativistic effects. We prove the shortening of the major axis of the orbit in comparison with the case where we do not take into account relativistic effects. This result can be useful for analysing the structure of planet systems around massive stars.