Determination of dependence of gravitational interaction force of bodies on their velocity

The article conducts a numerical verification of the hypothesis about the empirical dependence of the gravitational interaction force between bodies on the velocity of each body. The criterion used to evaluate the tested dependence of gravitational force on the velocity of bodies is the correspondence between the calculated values of the precession of the pericenters of binary systems obtained in the case of the tested dependence and the actual values known from astronomical observations. Numerical modeling has clearly shown that the force of gravitational attraction depends differently on the velocities of the “source” of gravity (the body creating the gravitational field) and the “receiver” of gravity (the body on which the force of attraction acts). The article shows that the identified dependence of the gravitational force on the velocities of the “source” and “receiver” of gravity is the only solution that ensures consistency with the actually observed precession of the pericenters of binary star systems and the Sun–planet system. It is shown that a numerical model of the motion of the components of a binary system corresponding to the identified dependence yields an empirical formula for the precession of the pericenters of binary systems that coincides with that obtained in general relativity and in Gerber’s theory. Based on the identified dependence of gravitational force on velocity, the article describes a new effect of precession of the centers of mass of binary systems, which should be discovered through further astronomical observations.