Maneuver Design Using Relative Orbital Elements

Relative orbital elements provide a geometric interpretation of the motion of a deputy spacecraft about a chief spacecraft. The formulation yields an intuitive understanding of how the relative motion evolves with time, and by incorporating velocity changes in the local-vertical, local-horizontal component directions, the change in relative motion due to impulsive maneuvers can be evaluated. This paper utilizes a relative orbital element formulation that characterizes relative motion where the chief spacecraft is assumed to be in a circular orbit. Expressions are developed for changes to the relative orbital elements as a function of the impulsive maneuver components in each coordinate direction. A general maneuver strategy is developed for targeting a set of relative orbital elements, and this strategy is applied to scenarios that are relevant for close proximity operations, including establishing a stationary relative orbit, natural motion circumnavigation, and station-keeping in a leading or trailing orbit.