Determination of orbital elements for the formation assembly problem

In this paper, we derive general relationships between the coordinates of the spacecraft in the Hill frame and their actual orbital elements for a closely placed formation with the help of Euler transformation matrices. Then, with the help of the results, we represent the orbital elements as a function of relative coordinates with respect to a reference spacecraft for an Earth-based scenario. The knowledge of orbital elements of the satellites in a formation help to plan ahead the necessary maneuvers to establish a desired configuration pattern.