A note on the computation of multi-revolution NRHO under the ephemeris model

Abstract

Near Rectilinear Halo Orbits (NRHOs) are vital to manned lunar and deep space exploration, which nowadays are of great interest for different space agencies and in particular with regard to the future space station. However, the required computation of multi-revolution NRHO under the ephemeris model is difficult, especially for the NRHOs with low periapsis relative to the secondary body. This paper explores this issue from the perspective of multiple shooting, first analyzing the influence of the state transition matrices by means of their condition number and then, focusing on a good selection of trajectory segments with suitable patch points. The methodology considerably improves the convergence and the computation under the ephemeris model. Numerical simulations show that at least 30 revolutions can be achieved for NRHOs with perilune radius of less than 12,000 km around L1 or period less than 8.8 days around L2; meanwhile, the number of segments used can be as low as 2 for each single revolution. As for the position of patch points, the first and last points of each revolution should be apart from the Moon, and the distance can be reduced only when the number of segments increases. The proposed method requires no dedicated optimization algorithm or commercial software to produce the multi-revolution NRHOs.