International conference on multidisciplinary science

THE KEPLER PROBLEM

Alieva Jamila

Associate Professor of the Department of Applied Mathematics, Andijan State University, PhD

Akbarova Nigora

Master's student in Mechanics and Mathematical Modeling at Andijan State University

Keywords: Kepler problem, Kepler's laws, planetary motion, central field, celestial mechanics, numerical methods, differential equations, MATLAB, orbital motion, two-body model, astronomy.

---

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.

---

References

1. С.В. Поршнев Компьютерное моделирование физических процессов в пакете MATLAB 2011.736с.

2. Mechanical vibrations / Singiresu S. Rao. 5th edition

3. И.А. Елизаров, Ю.Ф. Мартемьянов, А.Г. Схиртладзе, А.А. Третьяков Моделирование систем 2011.