The occurrence conditions and trajectory constructions for low energy cislunar transfers

The paper deals with the occurrence conditions andtrajectory constructions for low-energy transfers in the cislunar space,from the views of libration point theories and nonlinear dynamicaltechniques. The classical concept of ``libration'' is unavailable forspatial bicircular model (SBCM) because of the time-dependent perturbations.So the equivalent equilibrium is defined according to the geometry ofinstantaneous Hill's boundary, i.e., LL_1 or LL_2. The altitudes ofperiapsis and eccentricities of all the lunar capture trajectories arepresented via the Poincare map, and the minimum energy to capture on thelunar surface is deduced which is quite different from ones obtained incircular restricted three-body problem (CR3BP) and Hill Models. Theasymptotical behaviors of invariant manifolds flown from libration point orHalo orbit are destroyed by SBCM: the durations flown in and out of thelibration point or Halo orbit have shifted from infinite to finite, and thedirections have changed from reversible to nonreversing. The minimum energycislunar transfer is acquired by the trajectory transiting LL_1 point,and the (M,N)- loopy transiting trajectories are attained by transitingLL_1-Halo orbits. Similarly, the minimum energy of weak stabilityboundary (WSB) transfer is induced by the trajectory transitingLL_2 point, and the earth's escape and lunar capture windows for WSBtransfers are yielded by transiting LL_2-Halo orbits. All threetransfer manners, as low-thrust,impulse and WSB, are applied to the transfer from Earth to Moon and theinsertion of the distant retrograde orbit (DRO).