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Out-of-plane equilibrium points and invariant manifolds about an asteroid with gravitational orbit—attitude coupling perturbation

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Abstract

By considering the spacecraft as an extended, rigid body with a prior known attitude instead of a point mass, the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid, because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft (GOACP). The GOACP is defined as the difference between the gravity acting on a non-spherical, extended body (the real case of a spacecraft) and the gravity acting on a point mass (the approximation of a spacecraft in classical orbital dynamics). In-plane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies, including equatorial and in-plane non-equatorial equilibrium points. In this study, out-of-plane equilibrium points outside the principal planes of the asteroid were examined. Out-of-plane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP. The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP. Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP, respectively, while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges. Additionally, the invariant manifolds of out-of-plane equilibrium points were calculated, and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds. In practice, these equilibrium points can provide natural hovering positions for operations in proximity to asteroids, and their invariant manifolds can be used for transfers to or from the equilibrium points.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11602009, 11432001, and 11872007, as well as the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Astronautics, Beihang University, Beijing, 102206, China

    Yue Wang & Ruikang Zhang

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  1. Yue Wang
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  2. Ruikang Zhang
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Correspondence to Yue Wang.

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The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Yue Wang received his B.Eng. and Ph.D. degrees in aerospace engineering from Beihang University (formerly known as Beijing University of Aeronautics and Astronautics), Beijing, China, in 2009 and 2014, respectively. From 2014 to 2015, he worked as a postdoctoral fellow in the Distributed Space Systems Lab in the Faculty of Aerospace Engineering at Technion-Israel Institute of Technology, Haifa, Israel. In 2016, he joined the School of Astronautics at Beihang University as an associate professor of the “Zhuoyue” Recruitment Program. He was rewarded the Young Elite Scientist Sponsorship Program by China Association for Science and Technology. His current research interests center on orbital dynamics and control about asteroids and the Earth-Moon system, orbital evolution and reentry prediction of space debris, and NEO impact hazard assessment.

Ruikang Zhang received his B.Eng. degree in aerospace engineering from Beihang University (formerly known as Beijing University of Aeronautics and Astronautics), Beijing, China, in 2017. At present, he is a Ph.D. candidate in aerospace engineering at Beihang University. His research interests include orbital dynamics and control about asteroids and the Earth-Moon system.

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Wang, Y., Zhang, R. Out-of-plane equilibrium points and invariant manifolds about an asteroid with gravitational orbit—attitude coupling perturbation. Astrodyn 6, 269–283 (2022). https://doi.org/10.1007/s42064-021-0106-0

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  • DOI: https://doi.org/10.1007/s42064-021-0106-0

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