Using chaos to guide a spacecraft to the Moon

Significant results were already achieved in the guidance of spacecraft by using the characteristics of the chaotic system. The space agency NASA, in 1987, made use of the sensitive dependence on initial conditions in the classical three-body problem to maneuver ISEE-3 spacecraft towards a comet by means of small correction, which requires only a small amount of fuel. Later, the spacecraft Hiten was sent to the Moon by using a ballistic lunar capture transfer that was accomplished by the use of regions of chaotic motion in the phase space. However, these methods imply long transport times. This happens because in chaotic Hamiltonian systems, besides the coexistence of interwoven chaotic and quasi-periodic regions, the phase space is divided into layered components which are separated from each other by Cantori. Typically, a trajectory initialized in one layer of the chaotic region wanders in that layer for a long time before it crosses the Cantori and wanders in the next region. In this article, we show how the transport time for a Hamiltonian chaotic system can be substantially reduced by using a targeting method that was originally devised for a chaotic scattering. The method takes explicit advantage of the sensitive dependence on initial conditions. It finds, from an ensemble of trajectories, the trajectory that passes closest to the overlapping parts of certain resonance regions that form natural barriers to the transport. By using small perturbations, we construct the final trajectory that conducts from source to the target regions, and passes through the layers of the chaotic Hamiltonian system. As an example, the technique is applied in the planar, circular, restricted three-body problem to model the dynamics of a spacecraft moving in the Earth–Moon system. Comparisons are made between our method and other targeting strategies.