Spacecraft formation flying is currently an important and thriving area of research, with plenty of unique challenges to overcome in the field of spacecraft dynamics, and a wide variety of useful applications if these challenges may be overcome. The guidance of the relative motion of a spacecraft formation is an area of particular interest.Conventional space missions typically require a guidance system which outputs the desired orbit of a single spacecraft. However, in a formation, the position of one spacecraft relative to another is of greater interest, and thus the guidance system must handle the more difficult task of determining the desired relative motion of the formation.Many models for spacecraft formation flying exist, but all have their limitations, either in accuracy due to assumptions made in their derivation like using circular orbits or neglecting important orbit perturbations, or in computational efficiency by requiring numerical integration. This thesis presents a novel set of analytical equations of motion describing the position of a follower spacecraft relative to a leader spacecraft in formation which is valid for eccentric orbits and which incorporates the so-called J 2 perturbation. This set of three equations, one for each priniciple direction in the local-vertical-local-horizontal reference frame, is then validated for accuracy by comparison with a numerical simulator. Finally, the equations are verified in a number of practical applications, focussing on their use as a guidance system in spacecraft formation guidance and control simulations.iii Acknowledgements First and foremost I would like to thank my supervisor Steve Ulrich for giving me the opportunity to pursue this work, for his support and encouragement along the way, and most of all for his patience, understanding and kindness throughout this project. Certainly none of this would have been possible without his help. I would also like to thank my family who are all always there for me, especially my parents, John and Lorna Kuiack for their love, and unending support. Finally I would like to thank Giuliana Velarde for helping me stay motivated and on track, and for her many hours spent editing my work.