Substantiation of the results of the laser location of the trajectory of the moon moving away from the Earth

Abstract

Progress in astronomical measurements of the trajectories of the movement of celestial bodies reveals new effects that require justification. In particular, it refers to the slight drift of the Moon from the Earth. A solution to this problem is possible only based on an adequate mathematical model. To perform this, it was adapted Newton’s law of universal gravitation to the case of moving masses in flat space and physical time. At the same time, the final speed of propagation of the gravitational field can be considered. The differential equations of motion of the three-mass Sun-Earth-Moon cosmic system are obtained. In the heliocentric coordinate system, transient processes of the movement of the named celestial bodies are simulated, which testify to the presence of the Moon moving away from the Earth and the influence of the effects of movement on its course. The significant dependence of the final result on numerical methods of integration, computer calculation tools, and the values of space-velocity initial conditions is shown. The results of the simulation of transient processes are attached.