High-order analytical solution of relative motion equation for satellite formation flying in elliptical orbit

The paper studied relative motion equation for satellite formation flying with large separations. The configuration is traditionally designed by the periodic solutions of the C-W equation in circle reference orbit or Lawden equation in elliptic reference orbit. Hence, the linear solutions are more suitable for the configuration with small scale formation than large scale formation. However, in some specific situations, it is necessary to use satellites with large separations. Then the paper studied relative motion based on the nonlinear equations in an elliptic reference orbit. The solution is expanded as series form with respect to the eccentricity of the reference orbit, in-plane amplitude and out-of-plane amplitude. Taking the Lawden periodic solution as starting point, the high-order analytical solution is constructed by Lindstedt-Poincare method. Particularly, as the eccentricity is zero, the analytical solution degenerated to express the relative motion in circle reference orbit. Finally, the practical convergence of the analytical solution is discussed in order to examine its validity and applicability.