The Problem of Two Bodies with a Finite Velocity of Gravity

Abstract

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.