In general, the lunar landing stage can be divided into two distinct phases: de-orbit and descent, and the descent phase usually comprises two sub-phases: braking and approach. And many optimization problems of minimal energy are usually focused on descent phases. In these approaches, the energy of de-orbit burning is not considered. Therefore, a possible low perilune altitude can be chosen to save fuel for the descent phase. Perilune altitude is typically specified between 10 and 15km because of the mountainous lunar terrain and possible guidance errors. However, it requires more de-orbit burning energy for the lower perilune altitude. Therefore, in this paper, the perilune altitude of the intermediate orbit is also considered with optimal thrust programming for minimal energy. Furthermore, the perilune altitude and optimal thrust programming can be expressed by a function of the radius of a parking orbit by using continuation method and co-state estimator.
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