Relativistic Motion of the Test Body in Photogravitational Field of Star: Application to the Solar System

Abstract

The regularities of the motion for every test body in photogravitational field of a star, which can significantly di˙er from the regularities of motion of a body in gravitational field, have been obtained. The following e˙ects of STR and GTR to the terms of order v2/c2 have been considered: the light pressure, the Poynting-Robertson e˙ect, the longitudinal and transverse Doppler e˙ect, the increase in mass of the moving test body, the e˙ects of the space-time curvature which arise due to the gravitational fields of the star and gas-dust ball surrounding the star. We have showed that the longitudinal Doppler e˙ect and the aberration of light (the e˙ects of order v/c) lead to the spiral motion of the test body around the star. Taking into account other e˙ects of order v2/c2 accelerates approximately by factor two the body fall on the spiral onto the star. The spiral can be seen as the decreasing in size ellipse with decreasing eccentricity and periastron, which can shift against the motion in orbit due to the influence of the gravitational field of gas-dust ball.