THE KEPLER PROBLEM
Abstract
This paper examines the Kepler problem as a special case of the motion of bodies in a central force field. It presents Kepler's fundamental laws, which describe the motion of planets around the Sun, and discusses their physical meaning and significance for modern science. Particular attention is paid to the analytical solution of the two-body problem and the impossibility of obtaining an exact solution for systems with three or more bodies. In this regard, numerical methods for solving equations of motion are considered, specifically the use of the MATLAB environment for modeling orbital motion. An algorithm is presented for reducing a system of differential equations to first-order form and their subsequent numerical solution. The paper emphasizes the importance of the Kepler problem for the development of astronomy, mechanics, and space exploration.