Abstract
This article presents the results of testing the hypothesis of the dependence of gravity on the velocity of motion of bodies. The numerical simulation clearly confirmed the correspondence of the calculated and observed values of the precession of orbit pericentres in binary systems including pulsars, as well as planets of the solar system. Based on the revealed dependence of the gravitational force on the velocity, the article describes a new effect of the precession of the centres of binary systems, which should be found as a result of further practical research.