On optimal three-impulse Earth-Moon transfers in a four-body model
- Paper number
IAC-22,C1,IP,22,x73449
- Author
Ms. Shanshan Pan, China, Nanjing University
- Coauthor
Dr. Francesco Topputo, Italy, Politecnico di Milano
- Coauthor
Prof. Xiyun Hou, China, Nanjing University
- Coauthor
Mr. Yang Wang, Italy, Politecnico di Milano
- Year
2022
- Abstract
The Earth-Moon transfer trajectory based on impulsive maneuvers has been extensively studied. The traditional method to construct such a transfer trajectory is the Hohmann transfer, which usually requires a high fuel cost and hardly meets the always-increasing demand of science-to-investment ratios in future space missions. Most investigations focus on the two-impulse Earth-Moon transfers using the simplified dynamical models, such as the patched two-body problem and the circular restricted three-body problem. To enhance the effectiveness of preliminary orbit design, it is essential to study the fuel cost for multi-impulse transfers in high-fidelity models. This work investigates the optimal three-impulse Earth-Moon transfers in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. Unlike the two-impulse transfers, the three-impulse trajectory optimisation is inherently an optimal control problem with interior-point constraints, and the problem becomes more challenging due to the high sensitivity introduced by the time-dependent four-body model. To address this issue, an efficient methodology for constructing optimal three-impulse Earth-Moon transfers in the four-body model is proposed by using the primer vector theory. First, based on the existing two-impulse Earth-Moon transfer, a feasible three-impulse Earth-Moon transfer as the initial guess solution is constructed by using the calculus of variations. Second, the optimal three-impulse transfer is further achieved by developing a robust continuation method and verified by the primer magnitude time history. Finally, thousands of optimal solutions for different transfer times are successfully obtained. A more general picture encompassing known solutions in literature as special points is allowed to frame, which enables the complete trade-off study between fuel cost and transfer time. It is shown that three-impulse solutions can effectively reduce the fuel cost than the two-impulse solutions. Families of these three-impulse solutions are further defined and characterised, and their features are discussed.
- Abstract document
- Manuscript document
IAC-22,C1,IP,22,x73449.pdf (🔒 authorized access only).
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