Design of two-impulse Earth-Moon transfers using differential correction approach

In this paper, a novel optimized algorithm of two-impulse Earth-Moon transfers in the circular restricted three-body problem (CR3BP) is proposed based on differential correction approach. In this innovative approach, the initial and final states of transfer orbit are estimated reasonably by fully considering the periapsis map (PM) condition. Then the Newton-Raphson method is utilized iteratively to deduce the differential equations of transfer orbit and further to yield the accurate initial state. Thus, the planar two-impulse Earth-Moon transfer can be accomplished. In addition, a simple design procedure is developed to solve the problem that arises from more unknown parameters in the spatial CR3BP. Therefore, the proposed method can be applied not only for the planar CR3BP but also the spatial CR3BP. Numerical results show the two-impulse Earth-Moon transfers need less energy than the Hohmann transfers and shorter flight time than the Weak Stability Boundary (WSB) transfers. Moreover, the proposed method can effectively enable a large set of two-impulse Earth-Moon transfers to be computed numerically.