Design and Comparison of Relative Dynamics Models about Cislunar Near Rectilinear Halo Orbits

This work presents a comparison between relative models of the Earth-Moon non-Keplerian dynamics regimes, in the perspective of modeling the close relative dynamics between two orbiting objects and of designing Guidance, Navigation and Control algorithms for space debris avoidance operation of future space exploration missions on cislunar Near Rectilinear Halo Orbits. According to the Artemis missions program, NASA will bring back humankind to the Moon in the next years thanks to the Gateway space station. In the Earth-Moon three body environment near the L1-L2 lagrangian points, the classic two body relative models are no more suitable, since the Moon gravitational influence is about 25-40% of the total one acting on a spacecraft. This raises the necessity of developing different relative models for space debris monitoring and safety applications. The work is distinguished for formulating a common benchmark for comparison of Restricted Three Body Problem (R3BP) and Restricted Two Body Problem (R2BP) relative models, showing the range of applicability and their limitations analyzed in terms of displacement with respect to an ephemeris propagation. Quantitative results are then provided to verify models performance at different space debris avoidance location along the orbit. Furthermore, a new R2BP relative model is developed with an innovative strategy which use local osculating Keplerian trajectories respect to a fictitious planet, showing an optimal trade-off between dynamics simplicity and relative errors accuracy. Finally, since the evolution of the relative geometry between Sun, Earth and Moon has a non-negligible influence, an epoch sensibility analysis is conducted by comparing several propagations with different revolutions of the reference orbit in an 18 years Saros Period. R2BP and R3BP models error oscillation behavior due to a change in epoch is then discussed