Dynamical behaviors and relative trajectories of the spacecraft formation flying

To describe the relative motion of spacecraft formation flying, this paper presents a method based on relative orbital elements, which is suitable to elliptical orbit with arbitrary eccentricity. The long time formation flying conditions are theoretically derived taken into account the relationship between relative motion and relative orbital elements. These conditions include that both the orbital periods of all participating spacecrafts should be the same and other relative orbital elements should be small enough. The expected relative distance of the spacecrafts would determine the magnitudes of such relative orbital elements. Theoretical analysis and numerical simulation results show that the spacecrafts with sufficient small relative orbital elements can keep long time formation flying without any active control when the orbital perturbations are not considered. The results also show that Hillʹs equation is only suitable for describing a short time formation flying.