Averaged Equation of Satellite Relative Motion in an Elliptic Orbit

The precision model of relative motion is a necessity for satellite formation flying, but these models are complex for analysis and design, especially in elliptic orbit. For some satellite formation flying applications, the long-term formation maintenance and fuel-saving is more important for satellite life. Using the averaged analysis method over an orbit period, the averaged equation of satellite relative motion in an elliptic orbit is presented in this paper. Firstly, based on the homogeneous solutions of T-H equations, a simple averaged equation of relative motion is derived. Secondly, the improved averaged equation of relative motion which is described by the instantaneous orbit elements difference is developed for considering the orbital perturbation. The effectiveness of the proposed models is verified by four simulation cases which consider the orbit perturbation or not. The proposed model can eliminate the periodicity movement of satellite relative motion, and it is convenient for long-term formation flying designing and configuration controlling.