The autonomous formation flying of multiple spacecraft to replace a single large satellite will be an enabling technology for many future missions. In this research, the current status of formation flying missions and technologies is determined, and the Darwin nulling interferometry mission, which aims to detect and characterise extrasolar planets, is selected as the research focus. Darwin requires high precision formation flying of multiple telescopes near the Sun-Earth L2 point. A comprehensive account of current research in astrobiology is presented which provides the motivation for a Darwin-type mission. Astrobiology is integral to the definition of formation manoeuvres and target identification. The system design issues associated with developing a higher resolution, Planet Imager mission are also explored through a preliminary mission design. Relative dynamics models for satellite formation flying control in Low Earth Orbit (LEO) and L2 are developed and methods of incorporating the Earth oblateness perturbation (J2) into the equations of relative motion to improve model fidelity are investigated. The linearised J2 effect is included in the Hill equations in time averaged and time varying form. The models are verified against the Satellite Tool Kit (STK) numerical orbit propagator, and applied to optimal control system design and evaluation for formation keeping tasks. The ‘reference orbit’ modelling approach applied in LEO is applied to the development of a new formation flying model at L2. In this case, linearised equations of motion of the mirror satellites relative to the hub are derived and performance evaluated for different initial conditions. These and other higher order models are compared to STK. The linearised model is applied to controller design for station keeping and formation manoeuvring tasks suitable for a Darwin-type mission, and the role of the model in developing controllers for a load levelling guidance system is explored.