The Bicircular Model Near the Triangular Libration Points of the RTBP

Abstract

We present a study of a simplified model of the Restricted Four Body Problem consisting of Earth, Moon, Sun and a massless particle, as a model of the dynamics of a spacecraft. The region where we look for the motion is a vicinity of the triangular libration points of the Restricted Three Body Problem. The model we discuss here is the so called Bicircular Problem. The main question is the existence of zones where the motion has good stability properties. The answer is positive, but the stable motions can not be confined to a small distance of the ecliptic plane. Both numerical simulations and analytical results are presented. Some tentative explanations offer a possible way to study many other kinds of problems. Some applications to space missions are mentioned.