Mecânica celeste: uma análise dinâmica do problema restrito de três corpos para astros do sistema solar

Abstract

The Restricted Problem of Three Bodies was proposed as a simplification for the more general problem, which physicists tried most did not reach an exact solution. However, even though it is a simplified system, the French physicist Henri Poincaré has shown that he has no analytical solution. The study of this mechanical problem has crucial importance to understand the behavior of systems existing in nature that are modeled by their characteristics, such as systems of stars linked by their gravitational potential. The dynamic analysis of the system is done by the interpretation of the equations of motion, however the typical equations of the restricted problem of three bodies, have their variables coupled, making a direct solution impossible by the usual methods, to overcome this problem numerical methods are used that help in search for approximate solutions. The objective of this work is to provide a detailed description of the characteristics of this system, seeking to give a numerical treatment using the Runge-Kutta Classic method, using routines in the MATLAB software, to find approximate solutions to the equations of motion, from which the dynamic evolution of the system.