Design of low energy escape trajectory and delta-V reduction

In this paper, we propose a new method of designing efficient escape trajectories from a gravity field of a planet. In particular, we study to design escape trajectories from the Martian moon Phobos with these processes in the context of the three-dimensional Sun-Mars-Spacecraft Circular Restricted Three-Body Problem (CR3BP). Our method consists of two design steps for realizing low-energy transit trajectories. The first step is to design reference trajectories escaping from a vicinity of Phobos. In this step, we use a halo orbit as a hub, and numerically propagate trajectories which is along both stable and unstable manifolds. Each stable and unstable invariant manifold asymptotically approaches to a halo orbit forward and backward in time respectively. Therefore, it is possible to systematically design transit trajectories passing through the vicinity of the halo orbit with some lower energy using the properties of the invariant manifolds. The second step is to modify such designed trajectories to reduce its thrust (?V) of departing for practical missions. Therefore, we apply a method called differential correction to renew trajectories by iterating analytical approximations. We target to states of a spacecraft whose ?V is to be lower, and the number of thrusting a spacecraft is reduced in order to improve its mission operability. Finally, we illustrate that we can obtain the efficient escaping trajectories from the Mars vicinity.