(untitled) (Моделювання, керування та інформаційні технології, 2019)
From the moment of Newton’s discovery of the law of universal gravitation, ordinary differential equations were used to study the motion of bodies, since it was assumed that the velocity of gravitation is infinite. However, in reality the velocity of gravity is finite, which is consistent with the theory of relativity of Einstein, which postulated that the velocity of gravity matches the velocity of light, and the studies conducted by S. Kopeikin and E. Fomalont on the fundamental limit of the velocity of gravity. Due to the delay of the gravitational field for studying the motion of bodies, the mathematical apparatus based on differential equations with a delay argument is the most acceptable one. These equations are used to construct and study the mathematical model of the motion of two bodies. It is shown that the motion of these bodies with identical masses (with finite velocity of gravity!) is not carried out in accordance with Kepler’s laws.