The occurrence conditions and trajectory constructions for low energy cislunar transfers

The paper deals with the occurrence conditions and trajectory constructions for low-energy transfers in the cislunar space, from the views of libration point theories and nonlinear dynamical techniques. The classical concept of "libration" is unavailable for spatial bicircular model (SBCM) because of the time-dependent perturbations. So the equivalent equilibrium is defined according to the geometry of instantaneous Hill's boundary, i.e., LL₁ or LL₂ The altitudes of periapsis and eccentricities of all the lunar capture trajectories are presented via the Poincare map, and the minimum energy to capture on the lunar surface is deduced which is quite different from ones obtained in circular restricted three-body problem (CR3BP) and Hill Models. The asymptotical behaviors of invariant manifolds flown from libration point or Halo orbit are destroyed by SBCM: the durations flown in and out of the libration point or Halo orbit have shifted from infinite to finite, and the directions have changed from reversible to nonreversing. The minimum energy cislunar transfer is acquired by the trajectory transiting LL₁ point, and the (M,N)- loopy transiting trajectories are attained by transiting LL₁-Halo orbits. Similarly, the minimum energy of weak stability boundary (WSB) transfer is induced by the trajectory transiting LL₂ point, and the earth's escape and lunar capture windows for WSB transfers are yielded by transiting LL₂-Halo orbits. All three transfer manners, as low-thrust, impulse and WSB, are applied to the transfer from Earth to Moon and the insertion of the distant retrograde orbit (DRO).