Abstract
The topic of this research focuses on developing analytic models, simulations and relative orbit control for multiple spacecraft in constellations or formations in Low Earth Orbits (LEO). The motivation for this research lies in the recent development and focus on describing the relative motions of spacecraft flying in LEO and also the numerous advantages proposed formation flying missions could provide. Since the complexity of modelling, the dynamics and executing control on a group of satellites is far greater than that of one satellite, this research only investigates a small number of very specific problems in this area. The focus of the approach is to develop the orbit modelling of a single satellite, to describe the relative motion of multiple satellites in neighbouring orbits, using the analytical epicycle equations. The first part of the thesis focuses on the problem of formation and constellation assembly, where inclination differences in the initial conditions causes drift in the relative phases of the satellites. After deriving an analytical model and executing firings, real world data is shown to prove the accuracy of the method. In the second part, the modelling of relative orbits of kilometre-sized satellite formations is investigated. Such formations could only be viable if accurate description and prediction of the relative orbits of the spacecraft is available. The analytic formulation also gives a better understanding of ways to establish formations and maintain them with the least fuel requirement. Finally, in the third part, the orbit acquisition, phasing and maintenance of constellations of satellites is discussed in the context of Surrey's Disaster Monitoring Constellation. The centralized control scheme allows for global optimization and fuel balancing algorithms, which can also be used for formation flying as well. The results presented show that small satellite formations and constellations benefit significantly from an analytical description. Reformulating the epicycle equations for multi-satellite applications provides satisfactory accuracy for most small satellite formation missions. Key words: spacecraft formation flying, satellite constellations, epicycle.