Master thesis and internship[BR]- Master's thesis : Computation of satellite orbits around asteroids using the ManLab software[BR]- Integration Internship : ULiège

Abstract

The computation of periodic orbits in non-Keplerian dynamics is a critical issue for space missions, mostly for those around irregular asteroids. The purpose of this thesis is to use a novel, frequency domain, approach to solve the problem. The approach is based on the Harmonic Balance Method, a well known method for the analysis of nonlinear vibrations, but never used before in astrodynamics. In this thesis, it was used the Harmonic Balance Method implemented in ManLab, an interactive path-following and bifurcation analysis software. The study starts with a theoretical explanation about the circular restricted three body problem and about the dynamical problem around asteroids. For the latter, the available gravitational model are displayed in order to correctly select the one of interest. After this first theoretical introduction, the classical methods used in the field are briefly discussed, and the theory behind the Harmonic Balance Method and its ManLab implementation is introduced. After this preliminary introduction the two problems are analyzed. For the circular restricted three body problem, the analysis focus on the description of the bifurcations of the families of orbits around the first Lagrangian point. For the problem around an asteroid a fictitious spherical asteroid, for which some periodic orbits were computed and compared with the ones obtained through time integration and through the classical Harmonic Balance Method.