Cislunar L₄ and L₅ axial orbits and their applications

Cislunar L₄ or L₅ axial orbit families are continuous asymmetrical periodic orbits from the figure-8 orbit around L₄ or L₅ Lagrange point of the Earth–Moon system to the halo-family around the Moon. They provide special locations of lunar relay satellites for the lunar south pole due to their offset locations. In this paper, we investigate the orbital characters and applications of cislunar L₄ and L₅ axial orbits. A construction method of cislunar L₄ and L₅ axial orbit families is proposed according to their topological feature in the torus space. Then, lunar relay performances, including coverage and eclipse, are analyzed for different cislunar L₄ and L₅ axial orbits. Numerical computation indicates that 3:1 resonant L₄ and L₅ axial orbits are the optimal options in terms of the stability, coverage and eclipse avoidance. Lunar relay performances of a two-satellite constellation deployed in these orbits are compared with that in a near rectilinear halo orbit (NRHO). Numerical results show that the constellation of axial orbits can provide longer contact duration to the lunar equator and southern hemisphere than that of the NRHO. Finally, a station-keeping strategy and a transfer design of cislunar L₄ and L₅ axial orbits are developed, and their fuel costs are studied.