A study of the restricted three-body problem and the James-Webb orbit

Abstract

In this Bachelor Thesis we are going to put some ground work on the study of orbits in the system Sun-Earth that could receive a telescope like the James Webb. The James Webb is the latest launched telescope by NASA and has some different characteristics than previous telescopes like the Hubble. We are going to search for the perfect orbit to fulfill the needs these characteristics demand. In order to do that, we are going to study the restricted three body problem (rtbp) where the two primaries are the Sun and the Earth and the third body (which we consider that doesn’t affect the two primaries) is our telescope. This problem, using a carefully selected rotational coordinate system, is going to get us some differential equations that will define the movement of the third body. This equations have 5 fixed points and we are interested in seeing the stability and position with respect to the two primaries of this points, there is also a family of periodic orbits that we are going to find integrating the equations using the Taylor’s method and also numerically find the stability of these orbits.