Abstract
Many missions are now being proposed that make use of formations of satellites rather than just single platforms. While a small number of missions require no fixed formation geometry, the majority of missions use a well defined configuration of satellites. In this thesis I present a technique for modelling the motion of satellite formations in Low Earth Orbit (LEO). The relative motion model is based on an epicycle absolute orbit model, and avoids the linearisation problem by not relying on solution of the relative equations of motion. I present expressions for the relative motion and then show how they may be split up to describe the motion as a combination of the uniform motion of a formation origin, the motion of the formation as a whole about this origin and the motion of the individual satellites within the formation. I then show how this model may be used to determine properties of the formation such as its lifetime, and also to set properties of the formation, such as introducing a condition of no relative secular drift. I then invert the process of modelling the relative motion based on a given set of orbital parameters, and define a process for determining the orbital parameters required to produce a required relative motion. I consider a straightforward set of designs that rely on simple assumptions about the formation shape when planning the formation motion, and then more complex designs that consider the dynamics and configuration when determining the required orbital parameters. Finally, I present techniques for collision risk identification and mitigation, deriving the condition under which collisions occur in terms of the relative orbital parameters, and then showing how the risk may be mitigated with minimal change to the geometric properties of the formation.