Low-energy cislunar and trans-lunar transfer trajectories from the view of libration points

There exist cislunar and trans-lunar libration points near the Moon, which are referred as the LL\ and LL\ points respectively and can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from Sun, Earth and Moon is employed to investigate the energy-minimal and practical transferring trajectories. Different from the circular restricted three body problem (CR3BP), the equivalent gravitational equilibria are defined according to the geometry of instantaneous Hill's boundary due to the gravitational perturbation from Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincare mapping for all the lunar captured 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 lunar surface is deduced in the spatial bi-circular model (SBCM). It is presented that the asymptotical behaviors of invariant manifolds approaching to or from the libration points or Halo orbits are destroyed in the time- inpendent model. The energy-minimal and practical cislunar transferring trajectories are acquired by transiting LL\ and LL2 points. Copyright