Franco-Rodriguez, Jorge Adalberto
June 26, 2014
Gravitational Two-Body problem, Three-Body problem, N-Body problem
The prediction of the movement of a group of N gravitationally attracting bodies around its center of mass CM, given their initial positions and velocities, is what has been called the N-body problem, since Isaac Newton formulated it in his magnum work Phylosophiae Naturalis Principia Mathematica, commonly known as his "Principia" published in 1687. So far it has only been fully resolved the problem of two bodies from the classical view (Johan Bernoulli in 1710). For N > 2 in some cases only approximate, or not general, “solutions” exist. Operating on scalar equations derived from Newton's Laws allowed establishing in a simple, general and novel way the equations of the problem of two bodies moving gravitationally stable at the same angular velocity around their center of mass (CM). By studying under this general optic the three-body-equal-mass problem moving at equal angular speed the conditions of equal forces on CM and equal angles between contiguous forces, displayed as the unique solution for this particular case. Later, the equal-angle-force solutions were obtained for unequal masses. Such solutions were also reached under Least Action Principle corroborating such results. Finally, analysis of this problem was done by reducing the three-body problem to an equivalent two-body one providing same unique solutions. Thus, on the base of the solution of such particular case for N = 3, all possible stable cases of the three-body problem become solved.....