Problema extendido de tres cuerpos, restringido y circular

Abstract

[en] The Extended Circular Restricted Three-Body Problem studies the motion of three bodies which are only exposed to their mutual interaction force $F \sim r^{\alpha}$ . In this problem, the mass of one of the 3 bodies is much smaller than the others, so this third bodie will not disturb the motion of the others. To study the motion of the third body, first we will study the others’ motion, and then we will add the third body, supposing that these two bodies have a circular motion. This body will have its motion under the field that the other 2 bodies generate, so we will study this field. In particular, we will obtain the equilibrium points of the field, and we will discuss analytically their existence. Furthermore, we will obtain the regions of the plane in which the motion will be possible, providing a qualitative description of their boundary. Finally, some of these regions will be simulated, thanks to a program which creation is away of this project.