Solution Domain Analysis of Earth-Moon Quasi-Symmetric Free-Return Orbits

The solution domain of the Earth-Moon quasi-symmetric free-return orbits (EMQSFRO) is analyzed using a novel strategy proposed in this paper applying the Jet Propulsion Laboratory (JPL) ephemeris dynamic model. EMQSFRO is constrained by altitude at the time of trans-lunar injection (TLI), lunar swing-by altitude and Earth atmosphere re-entry angle. A vehicle on such an orbit can return to Earth without need of additional impulse after TLI. The present research on EMQSFRO and its technical applications are first summarized. Then a novel direct design strategy for EMQSFRO is proposed using a sequential quadratic programming algorithm, which applies the orbital parameters in the Moon perilune inertial coordinate system as design variables, and computes the objective orbital parameters in the TLI and re-entry time using the forward and backward numerical integral method. A simulation example indicates that the method has excellent convergence performance and precision. According to further simulation results, the solution domain cross-profile characteristics of four kinds of the EMQSFRO are discovered, which can give a deeper insight into the dynamic principle of EMQSFRO generation and supply references to the orbit design of aerospace missions.