Resolução numérica de sistemas de equações diferenciais aplicada ao problema dos três corpos

Abstract

The three-body problem seeks to determine the motion of three point-mass objects that interact mutually through Newton’s gravitational force, given initial conditions for the velocity and position of each body. Due to the complexity of the interaction among the three bodies and the system’s high sensitivity to initial conditions, the model is non-linear and can only be approached analytically in specific cases. For all other situations, the only alternative is the application of numerical methods. However, these methods are based on approximations, which makes finding a numerical solution to the problem particularly challenging. In this work, numerical methods aimed at solving a system of nonlinear differential equations that model the three-body problem will be studied and implemented, with an analysis of the numerical stability and accuracy of these methods and results found in the literature.