Differential equations of motion of celestial bodies

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.

The research raises the problem of determining and measuring the interaction of planets on the trajectory of their orbits around the Sun. Its solution becomes possible only based on an adequate mathematical model. For this purpose, Newton's law of universal gravitation was adapted to the case of moving masses in a wide range of velocities in flat Euclidean space and physical time. The finite speed of propagating the gravitational field is considered. Differential equations of planets’ motion are obtained.