Solution set calculation of the Sun-perturbed optimal two-impulse trans-lunar orbits using continuation theory

The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission. A model for computing the two-impulse trans-lunar orbit, which strictly satisfies the boundary constraints, is established. The solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial continuation. By taking the solution set of a circular restricted three-body model as the initial values of the design variables, the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology. A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer window. Moreover, there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost. A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.