Abstract: Extremely low lunar orbits (eLLOs), defined as those with altitudes below 50 km, are of great significance for ultra-high-resolution lunar remote sensing and fine scientific exploration. However, due to significant non-spherical perturbations from lunar mascons and drastic variations in lunar surface elevation, spacecraft in such orbits face a considerable risk of lunar impact, imposing stringent requirements on orbit-maintenance strategies for eLLOs. This paper fully considers practical engineering constraints in eLLO missions, including attitude pointing for correction maneuvers, correction control frequency, and control time intervals. Based on the eccentricity-vector translation characteristics of eLLOs with the safe-zone theory, the eccentricity vector translation theorem is combined with the well-established analytical two-impulse control method for low Earth circular orbits. This method enables arbitrary adjustment of the eccentricity vector while maintaining the semi-major axis and the upper limit of orbital altitude, thereby satisfying the altitude constraints of eLLOs. To mitigate the potential lunar impact risk during the interval between two successive tangential impulses, the first tangential maneuver is constrained to be an orbit-raising maneuver. However, this may prolong the free-drift duration during the wait for the maneuver window, potentially leading to a premature lunar impact. To address this issue, the paper further proposes compensation correction strategies, including free-drift correction and curve-trend correction of the eccentricity vector, which effectively mitigate potential lunar impact risks. Furthermore, this paper establishes a rolling planning framework for autonomous orbit maintenance, realizing autonomous control throughout the entire mission process. The proposed method is applied to an 18 km eLLO maintenance mission. Compared with a traditional maintenance strategy based on convex optimization, the proposed approach features a simpler thruster pointing mode, reduces the number of thruster firings by 8.33%, and decreases potential lunar impacts from 12 to 0, demonstrating the high reliability and engineering feasibility of the proposed method and strategy.

Key words: extremely low lunar orbit, non-spherical perturbation, orbit maintenance, impulsive control, eccentricity vector