Georgia Institute of Technology College of Sciences

An analysis of the dynamics of a mass-less spacecraft (or point mass) around an in-homogeneousTrojan body in a system composed of three primaries lying at the vertexes of an equilateral triangle, with their mutual positions fixed over the course of the motion is here presented. To this end two suitable models are identified to represent the system, depending on the distance from the primary. The first model, adopted for use close to the asteroid, where the dynamics is dominated by this sole body, is the Restricted Two Body Problem. In this model the in-homogeneities of the asteroid are taken into account as they have a dominant effect on the dynamics of the spacecraft. The second model is the Lagrangian Circular Restricted Four Body Problem (CR4BP), which is adopted far from the asteroid, where the gravitational perturbations of the Sun and Jupiter are dominant while the in-homogeneities of the asteroid are negligible. Low-thrust propulsion perturbations are incorporated into this model. The possibility to determine the range of validity of each model using an application of a Weak Stability Boundary (WSB) theory is investigated and applied. Applications are shown for the main example of Lagrangian configuration in the Solar system, the Sun-Jupiter-Trojan-spacecraft system.