Substantiation of the anomalies of the measurement results for trajectories of gravitational maneuver of space vehicles

Abstract

In astronomical research, the problem of measuring the trajectories of the gravitational maneuver of space vehi- cles in the gravitational field of large celestial bodies arises. The known measurement results differ from those predicted by classi- cal celestial mechanics. A practical solution to this anomaly is possible only based on an adequate mathematical model. For this purpose, we have adapted Newton’s law of universal gravitation to the case of moving masses in a possible range of speeds in flat space and physical time. At the same time, the finite speed of propagation of the gravitational field is taken into account. The dif- ferential equations of motion of cosmic bodies have been obtained. In the heliocentric and planetocentric coordinate systems, tran- sient processes in the cosmic three-mass system are simulated – star, planet, and man-made spacecraft (Sun-Mercury-space probe). To more deeply identify the essence of gravitational interaction, transient processes of both acceleration and deceleration of the space vehicle were simulated depending on the specified space-velocity initial conditions for the differential equations of motion. The results of the simulation of transient processes are attached.