Analytical design methods for determining Moon-to-Earth trajectories

To support Chinaʹs lunar exploration mission requirements of high-latitude landing and anytime return, i.e., the capability of safely returning the crew exploration vehicle at any time from any lunar parking orbit, an analytical model for determining a transearth trajectory is presented. With a finite sphere of influence model, families of analytical Moon-to-Earth return trajectories are generated and analyzed to observe the characteristics in their Moon departures and Earth encounters. The requirement of high-latitude landing for the return phase trajectory is considered in the modified analytical model. No initial guess is required to generate the analytical solution. The results presented here are limited to a single impulsive maneuver. The difference between the results of the analytical model and a high-fidelity model is compared. This difference is relatively small and can be easily eliminated by a simple differential correction procedure. The solution can be used to establish the orbital launch window for Moon-to-Earth return and to serve as an initial estimate for future optimization procedures.