NUMERICAL STUDY OF ORBITAL STABILITY IN THE RELATIVISTIC RESTRICTED THREE-BODY PROBLEM

This paper presents a numerical study of the relativistic restricted three-body problem within the framework of General Relativity. Using the Lagrangian and Hamiltonian formalisms, the equations of motion with relativistic corrections up to the order of 1/c2 were derived and solved numerically in Wolfram Mathematica. The developed model allows one to analyze orbital stability under small relativistic perturbations. Numerical simulations were performed using the Runge–Kutta integration method for three systems: “Earth–Sun–Moon,” “Earth–Sun– Mercury,” and an equal-mass configuration. The results confirm the stability of circular orbits and reproduce the observed relativistic precession of Mercury’s perihelion. For the equal-mass system, the calculations reveal a transition from quasi-periodic to chaotic motion, depending on the initial conditions. The study demonstrates the reliability and efficiency of the Mathematica environment for modeling nonlinear relativistic dynamics and shows that the proposed approach can be useful for further research in celestial mechanics and gravitational physics.

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