Stability of spatial orbits around Earth-Moon triangular libration points

The stability of spatial orbits around the triangular libration points in the ephemeris model of the Earth-Moon system is studied. Five contributions are made: (1) practical stable spatial orbits in the ephemeris Earth-Moon system lasting thousands of years or even longer are first reported, and spatial stable regions are identified. (2) The mechanism that shapes the boundaries of the spatial stable regions is investigated, and is found to be related to resonances among the precession rates of the lunar orbit, the precession rates of the small body, the mean orbital motion of the Sun, and the libration frequency of the co-orbital motion. (3) Influence on the spatial stable regions from the solar radiation pressure is studied. It is found that the spatial stable region generally shrinks with increasing solar radiation pressure strength. Dust grains with sizes of millimetres in magnitude or smaller generally escape in hundreds of years while objects with larger sizes can stay for thousands of years or even longer; (4) difference between the bi-circular problem model and the ephemeris model in describing the spatial stable regions is presented. (5) The observation of possible objects in the spatial stable orbits is discussed. With the public's growing interest in the cislunar space, the current study is a good attempt to enhance the understanding of the practical orbital dynamics in the cislunar space.