@article{Slyusarchuk_2019, title={The Problem of Two Bodies with a Finite Velocity of Gravity}, url={https://itconfdoc.nuwm.edu.ua/index.php/ITConf/article/view/83}, DOI={10.31713/MCIT.2019.14}, abstractNote={<p>From the moment of Newton’s discovery<br>of the law of universal gravitation, ordinary differential<br>equations were used to study the motion of bodies,<br>since it was assumed that the velocity of gravitation<br>is infinite. However, in reality the velocity of gravity<br>is finite, which is consistent with the theory of relativity<br>of Einstein, which postulated that the velocity of<br>gravity matches the velocity of light, and the studies<br>conducted by S. Kopeikin and E. Fomalont on the fundamental<br>limit of the velocity of gravity. Due to the<br>delay of the gravitational field for studying the motion<br>of bodies, the mathematical apparatus based on differential<br>equations with a delay argument is the most<br>acceptable one. These equations are used to construct<br>and study the mathematical model of the motion of two<br>bodies. It is shown that the motion of these bodies with<br>identical masses (with finite velocity of gravity!) is not<br>carried out in accordance with Kepler’s laws.</p>}, number={3}, journal={Modeling, Control and Information Technologies: Proceedings of International scientific and practical conference}, author={Slyusarchuk, Vasyl}, year={2019}, month={Nov.}, pages={160–164} }