The Problem of Two Bodies with a Finite Velocity of Gravity

Abstract

From the moment of Newton’s discoveryof the law of universal gravitation, ordinary differentialequations were used to study the motion of bodies,since it was assumed that the velocity of gravitationis infinite. However, in reality the velocity of gravityis finite, which is consistent with the theory of relativityof Einstein, which postulated that the velocity ofgravity matches the velocity of light, and the studiesconducted by S. Kopeikin and E. Fomalont on the fundamentallimit of the velocity of gravity. Due to thedelay of the gravitational field for studying the motionof bodies, the mathematical apparatus based on differentialequations with a delay argument is the mostacceptable one. These equations are used to constructand study the mathematical model of the motion of twobodies. It is shown that the motion of these bodies withidentical masses (with finite velocity of gravity!) is notcarried out in accordance with Kepler’s laws.