# The Problem of Two Bodies with a Finite Velocity of Gravity

## DOI:

https://doi.org/10.31713/MCIT.2019.14## Keywords:

two-body problem, two-body problem with finite gravity velocity## 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.

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## How to Cite

*Modeling, Control and Information Technologies: Proceedings of International Scientific and Practical Conference*, (3), 160–164. https://doi.org/10.31713/MCIT.2019.14