Computation of low energy Earth-to-Moon transfers with moderate flight time

We consider a problem of constructing a spacecraft transfer trajectory with low cost and moderate flight time from the Earth to the Moon. We adopt the planar circular restricted three-body problem (PCR3BP) as the spacecraft model, and reduce computation of optimal transfers to a nonlinear boundary value problem (BVP). Using a computer software called AUTO, we numerically solve the nonlinear BVP and continue its solutions to obtain optimal transfers. Especially, we find a transfer trajectory having the same cost but 22% shorter flight time or having 7.5% lower cost, compared to the traditional Hohmann type transfer. Moreover, we show that these transfers are unstable in an appropriate meaning and closely relate to chaotic dynamics of the PCR3BP.