Performance analysis of impulsive station-keeping strategies for cis-lunar orbits with the ephemeris model

Future long-term lunar missions, such as cis-lunar space stations and communication/navigation constellations, have been proposed by different space agencies. For such long-term missions, reliable station-keeping strategies are of great importance to counteract unfavourable effects of perturbations, navigation errors, etc. In this study, representative cis-lunar orbits with favourable characteristics, including near rectilinear halo orbits (NRHOs), distant retrograde orbits (DROs), and halo orbits, are considered as nominal orbits of long-term lunar missions for station-keeping analysis. Both the target point method and the discrete linear quadrant regulator (DLQR) control are applied to these nominal orbits in the ephemeris model. Under some practical constraints caused by the navigation and orbital control systems, Monte-Carlo simulations are carried out to evaluate performances of the station-keeping strategies. Then, effects of solar radiation pressure (SRP) and nonspherical lunar gravity on the station-keeping performances are demonstrated by Monte-Carlo simulations with low-fidelity nominal orbits constructed in ephemeris models without SRP or nonspherical lunar gravity. Finally, comparisons between different impulse intervals are made to find the balance between the station-keeping cost and position deviation. It is found that the stability index of the nominal orbit has no direct effect on the station-keeping cost, but plays an important role in the selection of the impulse interval. The DROs and NRHOs allow a much longer impulse interval than the unstable halo orbits. The results can provide useful references for selections of the nominal orbit and station-keeping strategy in future long-term lunar missions.