Determination of orbit reachable domain due to initial uncertainties

A general method is developed to find the 3D envelope of the reachable domain(RD), which is caused by the initial orbit uncertainties, for ellipse reference orbits. A reference plane changed with the time is defined and the nominal orbit is regarded as a baseline. Then the function of the distance from the baseline to RD envelope is established in the reference plane along the nominal trajectory. So the RD envelope boundaries problem turns into an issue of solving nonlinear equations. Subsequently the error caused by using the linear dynamic model partially is evaluated. A variable parameter self-adaptation homotopy algorithm is developed to solve the nonlinear equations obtained. The simulation results of a satellite released example show that the method proposed is feasible and effective.