Formation design and geometry for Keplerian elliptic orbits with arbitrary eccentricity

The well-known Hill-Clohessy-Wiltshire equations that are used for the design of formation flight relative orbits are based on a circular reference orbit. Classical solutions like the projected circular relative orbit no longer hold in the presence of eccentricity. This paper develops a parameterization for linearized relative motion near a Keplerian elliptic orbit of arbitrary eccentricity. The eccentricity-induced effects are studied and exploited to obtain desired shapes of the relative orbit. These solutions will result in lower formation-keeping costs than the traditional Hill's solutions, because they accurately represent effects of eccentricity on formation dynamics, while maintaining much of the desired geometry afforded by solutions assuming circular reference orbits.

Formation design and geometry for Keplerian elliptic orbits with arbitrary eccentricity Conference Paper