Long burn arc powered explicit guidance algorithm for Earth-to-Moon missions

Earth-to-Moon missions with low thrust-to-weight ratios present unique challenges for exoatmospheric guidance, and the existing algorithms are ineffective for the unprecedentedly long burn arcs and high orbital eccentricities. To address these challenges, a Long Burn Arc Powered Explicit Guidance (LBA-PEG) algorithm is developed and compared with the existing algorithms. In the proposed LBA-PEG algorithm, a fully numerical thrust prediction method is developed to accurately predict the highly nonlinear thrust effects over long burn arcs. Moreover, a real-time Newton correction method is proposed to correct the orbit injection point, remedying the position-velocity coupling induced by high orbital eccentricities. The comparison between the proposed algorithm and the existing algorithm shows that the proposed algorithm surpasses the existing ones by significantly enhancing fuel efficiency and improving tolerance to thrust decrease. The proposed LBA-PEG algorithm can adapt to a 65% thrust decrease, which is 12%–22% larger than that of the existing algorithms, and it can still reliably converge and complete the guidance mission even when the length of the burn arc exceeds 90°. The proposed LBA-PEG highlights the algorithm's adaptability for long burn arc missions, especially in critical scenarios such as manned Earth-to-Moon missions.