Dynamics and control of cluster orbits for distributed space missions

Space missions in which the payload functions are distributed among several satellites may benefit from the use of cluster orbits where the satellites fly in a tightly locked formation with a relatively small Delta V required to maintain the cluster. By properly selecting the initial Keplerian orbit elements, the satellites can achieve the desired close separation and cluster orientation. However, a perturbation analysis shows that the formation is quickly disrupted due to natural perturbing forces such as solar radiation pressure, atmospheric drag, and Earth gravity harmonics. The formation-keeping algorithm faces two challenges: (1) a tight tolerance for controlling the orbit of each satellite, and (2) minimizing the total propellant expenditure for all the satellites. This paper consists of two parts. Part I describes a method for determining the cluster orbital elements, and the relative geometry and dynamics of satellites under a two-body force field with the secular J(2) influence. Part II examines the disruption of the formation due to all the major natural perturbations, and the feasibility of a formation-keeping strategy. The proposed strategy blends four state-of-the-art techniques: differential GPS measurements, micro electromechanical systems, frozen orbits, and auto-feedback control. Results show that it only requires 10 to 30 mls per year per satellite in Delta V to control a 1 km radius cluster for LEO.