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. Transients in the three-mass system of a star and two planets close to the Sun-Mercury-Venus system are simulated. To reveal deeply the essence of physical interaction, a hyperbolized transition process is simulated under artificially close moving masses.
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