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Non-equatorial equilibrium points around an asteroid with gravitational orbit-attitude coupling perturbation

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A Correction to this article was published on 11 February 2022

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Abstract

A recently proposed orbital dynamics model in the close proximity of an asteroid, which is called “attitude-restricted orbital dynamics”, includes the perturbation caused by the spacecraft’s gravitational orbit–attitude coupling. This orbital model improves the precision of classical point-mass orbital model with only the non-spherical gravity. Equatorial equilibrium points have been investigated in the previous paper. In this paper, the in-plane non-equatorial equilibrium points, which are outside the asteroid’s equatorial plane but within its longitudinal principal plane, are further studied for a uniformly-rotating asteroid. These non-equatorial equilibrium points are more diverse than those in the classical point-mass orbital dynamics without gravitational orbit–attitude coupling perturbation (GOACP). Two families of them have been found. The equatorial equilibrium points studied before and the non-equatorial ones studied here give a complete map of equilibrium points in the asteroid’s principal planes. Compared with the classical point-mass orbital dynamics without GOACP, the equatorial equilibrium points have extended the longitude range of equilibrium points around an asteroid, while the non-equatorial ones studied here will extend the latitude range. These equatorial and non-equatorial equilibrium points provide natural hovering positions for the asteroid close-proximity operations.

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Acknowledgments

Yue Wang thanks the Editor-in-Chief Professor Bong Wie and two anonymous reviewers for their constructive comments and suggestions to improve this paper signifi-cantly. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11602009, 11432001, and 11872007, the Young Elite Scientist Sponsorship Program by China Association for Science and Technology under Grant No. 2017QNRC001, and 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 & Shijie Xu

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  1. Yue Wang
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  2. Shijie Xu
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Correspondence to Yue Wang.

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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. His research interests center on the astrodynamics, orbital dynamics, dynamics and control about asteroids, spacecraft proximity operations, and space debris mitigation. E-mail: ywang@buaa.edu.cn.

Shijie Xu (1951–2019) was not only a great researcher but also, more importantly, a great mentor and advisor in the field of astrodynamics and spacecraft control. He received his B.Eng. degree from the Department of Mechanical Engineering, Northeast Forestry University, Harbin, China, in 1976. His career in astrodynamics and spacecraft control started soon after he received his M.S. degree from the Laboratory of Flight Dynamics, Harbin Institute of Technology, Harbin, in 1983, as a teaching assistant at the same laboratory. He worked at Harbin Institute of Technology as a lecturer (1987), an associate professor (1989), and then as a professor (1993). During his tenure at Harbin Institute of Technology, he pursued his Ph.D. degree with a specialization in automatic controls from 1991 to 1995 at Henri Poincar´e University, Nancy, France. From 1995 to 2000, he was with Harbin Institute of Technology as a professor. In 2000, he joined the School of Astronautics, Beihang University, Beijing, China, as a professor. He carried out research spread out in the field of astrodynamics and spacecraft control, including the robust control theory and applications, the attitude control of flexible spacecraft, attitude control via momentum exchange devices, integrated attitude control and energy management, guidance and control of proximity operations, three-body problem, spacecraft dynamics about small bodies, and etc. He authored or coauthored over 300 papers in journals and conferences. He supervised more than 70 graduate students at Harbin Institute of Technology and Beihang University who are now active in China’s space industry and academia.

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Wang, Y., Xu, S. Non-equatorial equilibrium points around an asteroid with gravitational orbit-attitude coupling perturbation. Astrodyn 4, 1–16 (2020). https://doi.org/10.1007/s42064-019-0068-7

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