Dynamics behavior and simulation of relative trajectories of satellite formation flying

To overcome the restriction of Hill's equation, this paper presents the orbital elements method for describing the relative motion of satellite formation flying. Theoretical conditions are derived for long term formation flying that includes the relationship between the relative distances and velocities and the relative orbital elements. The analysis proves that the orbital periods of formatted satellites must be equal. Simulation of the relative trajectories with various orbital elements and a qualitative theoretical analysis illustrate the advantages of the orbital elements method. The proposed method can be used for large eccentricity elliptical orbits and can be applied for orbit design of spacecraft formation flying. The results show that satellites formatted using closed orbital elements will remain in their orbits with little active control. The theoretical results show that the application of Hill's equation is restricted to short-time formation flying in circular orbits.