Three Body Problem and Formation of Binary System

Abstract

The singularities of differential Newtonian equation of motion in three body problem cause the loss of accuracy and the considerable increase of the computer time. These singularities could be eliminated during the process of regularization to transform the independent variables and the coordinate of Newtonian equations of motion. In this study, we calculated the positions and velocities of three body along the time scale to find out the unique solution of regularized Newtonian equations of motion with the 5th order Runge-Kutta method by assuming the suitable initial velocities and positions. As the results of these calculations it is shown that the triple stellar system eventually distintegrated, two of them formed a binary, and the last one escaped from this system with a hyperbolic orbit. This may suggest one possible explanation for the binary formation.