Long-term behavior of the spatial orbit near the Moon in restricted three-body problem

In the Earth-Moon-spacecraft circular restricted three-body problem (CRTBP), the evaluation of the orbits near the Moon can distinctly reflect the complexity of the dynamical system. In this paper, the long-term behavior of the spatial orbit near the Moon is investigated in the CRTBP. The Poincare section, where the section points are defined as the lunar apsides, is an effective tool. The distribution of the long-term capture solutions and the orbital elements of the section points display the long-term behavior of the spatial lunar orbits from the qualitative and quantitative angles, respectively. As two kinds of important long-term lunar orbits, the quasi-periodic and periodic orbits are also investigated. Using the continuation scheme, we obtain the spatial lunar periodic orbit families. The characters of the periodic orbit families are discussed in detail. In addition, some applications of the spatial lunar periodic orbits are given. The method to investigate the long-term behavior of the spatial lunar orbits we present is simple and direct. We can easily locate the lunar quasi-periodic orbit and obtain the spatial periodic orbit family.