ORBITAL STABILITY IN THE TWO-BODY PROBLEM AND KEPLER'S LAWS: A DIDACTIC APPROACH

Résumé

The two-body problem is a fundamental concept in celestial mechanics and theore- tical physics, addressing the motion of two particles that interact exclusively through a central force, such as gravity. This article explores the stability of the two-body problem, investigating whether the trajectories of the particles remain confined to a specific region of space over time. The analysis is based on Kepler’s laws and the equations of motion derived from Newton’s second law. Understanding the stability of this problem is crucial both for the accurate prediction of the behavior of celestial bodies and for practical applications in aerospace engineering and astrophysics.

Keywords: Two-body problem, Orbital stability, Kepler's laws.