Energy analysis and trajectory design for low-energy escaping orbit in Earth–Moon system

Due to the limits of size and weight of probes, analysis and design of the low-energy escaping orbit play a significant role in saving the energy in space exploration. In this paper, we research the mechanism of the evolution of the probe orbital energy and develop a design method for the low-energy escaping orbits in the Earth–Moon system. A dynamic model accounting for the Sun–Earth–Moon-probe elliptical four-body problem is presented by considering Moon’s eccentricity and Sun’s direct gravitational influence. Considering the influences from phase of Earth, Moon and Sun, the equations of the probe orbital energy and its variation are derived and theoretical analysis is implemented based on corresponding energy expressions. Then, the Poincaré mapping technique is utilized to search two types of low-energy families of escaping orbits and the results of numerical simulation confirm the theoretical predictions. The dynamic model proposed in this paper is more accurate and has practical value comparing with the circular restricted three-body problem, and the escaping strategy can save over 25 % of energy relative to the hyperbolic escaping.