Low-energy Earth – Moon – Earth flight trajectory design using optimization procedures

The problem of designing a low-energy Earth Moon Earth spacecraft flight trajectory using optimization procedures is considered. The proposed approach combines rough and ready analytical methods with numerical population-based optimization techniques, that results in significant reduction in computational time compared to existing methods that require boundary value problem solution and numerical integration of differential equations. The proposed approach to design a spacecraft flight scheme utilizes spheres of influence method, which involves segmenting the trajectory into several sections. Each section is represented as an orbit defined by a conic section. The first segment of the trajectory is a geocentric orbit of the spacecraft flight to the Moon. The second segment of the trajectory is a lunar orbit of spacecraft flight within the Moon sphere of influence. The last segment represents is the trajectory of the spacecraft leaving the Moon and returning to Earth along a geocentric orbit. To ensure a passive lunar flyby and subsequent return to Earth without using additional impulsive maneuvers, the parameters of each trajectory must be determined by the initial conditions. To do this the optimization problem was formulated aimed at determining the trajectory initial parameters. The cost function is the criteria for minimizing the spacecraft’s closest approach distance to the Moon and the total flight time. By varying the weight coefficients in the cost function, various trajectory configurations can be formulated. The result of the optimization problem solutions is the initial parameters of the flight trajectory to the Moon from Earth orbit were selected, ensuring the spacecraft’s entry into the Moon sphere of influence and enabling its return to Earth without impulsive maneuvers. The results show the fundamental applicability of the proposed approach to designing lunar missions using a genetic algorithm.