Translunar Trajectory Analysis and Design for the European Student Moon Orbiter

This kind of transfer is based on the Weak Stability Boundary (WSB) of a system of two or three bodies – the Sun, the Earth and the Moon in the case of lunar transfers – where the gravitational attraction of the Sun and of the Earth-Moon system is in an unstable equilibrium: at certain times and positions the Sun's influence is stronger on the spacecraft and at other times and positions it is the Earth-Moon system; this instability causes a change in the trajectory of the spacecraft.
The WSB region is about 1.5 million km far from the Earth and varies with the orbital parameters of the orbit about the Moon. When a spacecraft leaves the Earth on an intended WSB trajectory, it will first follow a conventional Hohmann transfer, but on the way back to Earth it does not complete the Hohmann orbit as expected: the Sun's gravity increases the spacecraft's energy and as a result the perigee of its orbit is raised to an altitude approximately the same as the altitude of the Moon orbit about the Earth.
The spacecraft is then able to reach the Moon almost by itself, where a thrust will have to be applied to stay in a lunar orbit, because the Moon capture that might occur will be unstable.
Transfers via WSB were first described by Dr Belbruno in 1987. Since then, they were extensively investigated, demonstrating a relationship with invariant manifolds, using Dynamical Systems theory and studying the perturbation of the Sun. The first mission to make use of a WSB transfer was Hiten, a Japanese spacecraft launched in 1991 whose original objective was to orbit the Earth and to serve as a communication relay for Hagoromo, which was sent to the Moon.