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Open AccessArticle
Divergence Evaluation Criteria for Lunar Departure Trajectories Under Bi-Circular Restricted Four-Body Problem
by
Kohei Takeda
Kohei Takeda 1,*
and
Toshinori Kuwahara
Toshinori Kuwahara 1,2,*
1
Department of Aerospace Engineering, Tohoku University, Sendai 980-8579, Japan
2
Research Center for Green X-Tech, Tohoku University, Sendai 980-8579, Japan
*
Authors to whom correspondence should be addressed.
Aerospace 2025, 12(10), 918; https://doi.org/10.3390/aerospace12100918 (registering DOI)
Submission received: 30 April 2025
/
Revised: 29 September 2025
/
Accepted: 30 September 2025
/
Published: 12 October 2025
Abstract
This study focuses on the nonlinear departure dynamics of spacecraft from the Near Rectilinear Halo Orbit (NRHO) to the outer regions of Selenocentric Space. By carefully selecting the combination of orbital parameters and the order of the evaluation process, it becomes possible to precisely identify the divergence moment and to reliably classify the subsequent dynamical space. An empirical divergence detection algorithm is proposed by integrating multiple parameters derived from multi-body dynamical models, including gravitational potentials and related quantities. In an applied analysis using this method, it is found that the majority of perturbed trajectories diverge into the outer Earth–Moon Vicinity, while transfers into the inner Earth–Moon Vicinity are relatively limited. Furthermore, transfers to Heliocentric Space are found to be dependent not on the magnitude of the initial perturbation but on the geometric configuration of the Sun, Earth, and Moon during the transfer phase. The investigation of the Sun’s initial phase reveals a rotationally symmetric structure in the perturbation distribution within the Sun–Earth–Moon system, as well as localized conditions under which the destination space varies significantly depending on the initial state. Identifying the divergence moment allows for comparative evaluation of the spacecraft’s nonlinear dynamical state, providing valuable insights for the development of safe and efficient transfer strategies from selenocentric orbits, including those originating from the NRHO.
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MDPI and ACS Style
Takeda, K.; Kuwahara, T.
Divergence Evaluation Criteria for Lunar Departure Trajectories Under Bi-Circular Restricted Four-Body Problem. Aerospace 2025, 12, 918.
https://doi.org/10.3390/aerospace12100918
AMA Style
Takeda K, Kuwahara T.
Divergence Evaluation Criteria for Lunar Departure Trajectories Under Bi-Circular Restricted Four-Body Problem. Aerospace. 2025; 12(10):918.
https://doi.org/10.3390/aerospace12100918
Chicago/Turabian Style
Takeda, Kohei, and Toshinori Kuwahara.
2025. "Divergence Evaluation Criteria for Lunar Departure Trajectories Under Bi-Circular Restricted Four-Body Problem" Aerospace 12, no. 10: 918.
https://doi.org/10.3390/aerospace12100918
APA Style
Takeda, K., & Kuwahara, T.
(2025). Divergence Evaluation Criteria for Lunar Departure Trajectories Under Bi-Circular Restricted Four-Body Problem. Aerospace, 12(10), 918.
https://doi.org/10.3390/aerospace12100918
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