Long-term satellite formation keeping must account for the effects of orbital perturbations. While long-term formation keeping around the Earth has been thoroughly studied, lunar formations are yet to be further explored. In comparison to the Earth, the Moon introduces a more complex gravitational field, and requires taking into account additional gravitational perturbations.
In this work, the rates of the differential orbital elements of two lunar satellites in formation are expanded up to second order. These rates are then simplified, assuming the chief satellite is on a frozen lunar reference orbit. Additional assumptions are made to simplify the variational equations further, while retaining second-order terms. Numerical simulations are performed to illustrate the feasibility of using simplified rates of the differential orbital elements under various perturbation mitigation techniques, for a nominal orbit which deviates from the assumed frozen reference orbit. These simulations are carried out for a variety of scenarios, including frozen and near-frozen chief orbits, based on an actual lunar formation flying mission. The analysis validates the feasibility of using perturbation mitigation techniques for future lunar formation flying missions.