Fast design and optimization of the low energy lunar escaping trajectory

In this paper, a fast design and optimizing method of the low energy lunar escaping trajectory is introduced in the earth-moon elliptical four body system. Firstly, to find the optimal escaping conditions rapidly, the energy demand of the spacecraft is analyzed and it's found that when Moon is getting near its perigee and Sun becomes co-linear with Earth and Moon the escaping will consume the least amount of fuel. Then, given the appropriate launching opportunity the Manifold Degeneration Method is introduced to optimize the escaping energy. Finally, the computing process of the escaping trajectory design and optimization which contains 5 steps is given. According to the simulation results, the computing process proposed is effective in searching the optimal escaping trajectory and over 25% of the launching impulse can be saved with the optimal escaping orbit.