There exist cislunar and trans-lunar libration points near the Moon, which are referred as the LL_1 and LL_2points respectively and can generate the different types of low-energy trajectories transferring from Earth toMoon. The time-dependent analytic model including the gravitational forces from Sun, Earth and Moon isemployed to investigate the energy-minimal and practical transferring trajectories. Different from the circularrestricted three body problem (CR3BP), the equivalent gravitational equilibria are defined according to thegeometry of instantaneous Hill's boundary due to the gravitational perturbation from Sun. The relationshipbetween the altitudes of periapsis and eccentricities is achieved from the Poincaré mapping for all the lunarcaptured trajectories, which acts as an initial guess for the whole low-energy trajectories from Earth to Moon.Compared with CR3BP and Hill model, the minimal energy required by the capturing trajectory to the lunarsurface is deduced in the spatial bi-circular model (SBCM). It is presented that the asymptotical behaviors ofinvariant manifolds approaching to or from the libration points or Halo orbits are destroyed in the timeinpendentmodel. The energy-minimal and practical cislunar transferring trajectories are acquired by transitingLL_1 and LL_2 points.
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