Minimum Δv for the transfer to permanent lunar orbits with hyperbolic approach

In this paper, the minimum ΔV of the two-impulse transfer from the low Earth orbit to the permanent lunar capture orbit is investigated in the frameworks of the planar circular restricted three-body problem and the two-body model, respectively. For the restricted three-body problem, the near-optimal lunar capture is adopted to find the capture point and the corresponding permanent lunar orbit. Then, we derive the theoretical minimum ΔV on two-impulse Earth-Moon transfer in the restricted three-body problem. For the two-body model, we apply the optimization to designing the patched-conic transfer. Then, using the numerical integration, we obtain the corresponding permanent lunar capture orbit and the minimum ΔV of the transfer. At last, some examples of both methods are discussed and compared. The results we obtained provide a reference for the low energy transfer from the low Earth orbit to the permanent lunar orbit.