Design of the Transfer Orbit for the Three-body Vertical Orbit in the Earth-Moon System

Toward solving the transfer design for vertical orbits at the Earth–Moon libration points under the constraints of Earth launch, the transfer orbit design of three-body vertical orbits in the Earth–Moon system was studied. First, a circular restricted three-body dynamic model was established, and the spatial characteristics and calculation method of vertical orbits were clarified. By introducing the concept of gravity-assist azimuth angle, a calculation method for B-plane parameters under the constraints of lunar gravity assist was proposed, which solved the problem of discontinuous calculation interval of the parameters. Considering constraints such as launch site inclination and perilune altitude, two transfer-orbit design strategies, namely, direct transfer and lunar gravity assist, were proposed for the vertical orbits in the Earth–Moon system. The design variables and objective quantities of each strategy were determined, and the transfer orbit design problem was transformed into a nonlinear programming problem. The numerical simulation results show that the velocity increment for orbit insertion of the spacecraft directly launched from the Earth to the vertical orbit is ~800 m/s with a transfer time of about 5 days. For the lunar gravity assist strategy, the velocity increment for orbit insertion is only ~300 m/s, ~500 m/s faster than the direct transfer, with a transfer time of 20~30 days.