Generation of launch windows for high-accuracy lunar trajectories

The purpose of this paper is to systematically establish in arbitrary timespan a full set of instantaneous ground launch windows for certain accurate three-dimensional asymmetric free return circumlunar trajectories tailored to human lunar missions for China, and in general propose a novel methodology useful for determining ground launch windows for other Earth-to-Moon trajectories. Using time-varying spherical trigonometry, an analytical design method for finding ground launch windows is developed with two-body model assumption. Windows appear when the Moon at arrival time and the Earth parking orbit nodes on lunar orbit plane have similar right ascensions. The numerical first guesses obtained almost instantly are within minutes of accurate solutions and refined to highly accurate trajectories by differential corrections of only one phase. A translunar launch window plot visualizing all monthly and daily launch windows differentiating two types of translunar injections is created. The method proposed can be used for automated generation of complete trajectory sets, and provide the basis for the preparation of launch timetables satisfying lunar mission requirements.