Numerical Stability Analysis of Small Body Orbiter Trajectories. Application to Beacon Missions

The purpose of this thesis is to investigate numerical methods to categorize regular orbits for small body orbiter missions in support of robust small body mission design. To investigate the orbital stability of small body orbiters, Fast Laypunov Indicators (FLI) and chaoticity maps were applied in the work of Villac and Broschart in 2009. While Villac and Broschart implemented chaoticity maps with the general FLI definition and the spherical harmonic model for the gravity field model, we are interested in the degree chaoticity maps depending on the numerical methods and model parameters. Therefore, we extend the work to the other gravity field model, the polyhedral method, and different indicators. Simulation results show that chaoticity maps from the normalized FLI is reliable due to the trivial change on maps among different indicators and model parameters. In the end, we investigate a beacon mission concept for small body orbiter missions. With regular orbits from chaoticity map analysis, we are able to maintain the orbiter in long term stable orbits and to ensure the success of missions.