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Stable periodic orbits for spacecraft around minor celestial bodies

A Correction to this article was published on 11 February 2022

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Abstract

We are interested in stable periodic orbits for spacecraft in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration, but also for studying the long-time stability of small satellites in the large-size-ratio binary asteroids. The irregular shapes and gravitational fields of the minor celestial bodies are modeled by the polyhedral model. Using the topological classifications of periodic orbits and the grid search method, the stable periodic orbits can be calculated and the topological cases can be determined. Furthermore, we find five different types of stable periodic orbits around minor celestial bodies: (1) stable periodic orbits generated from the stable equilibrium points outside the minor celestial body; (2) stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points; (3) retrograde and nearly circular periodic orbits with zero-inclination around minor celestial bodies; (4) resonance periodic orbits; (5) near-surface inclined periodic orbits. We take asteroids 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley for examples.

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Acknowledgements

This research was supported by the State Key Laboratory of Astronautic Dynamics Foundation (No. 2016ADL0202).

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Correspondence to Yu Jiang.

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Yu Jiang received his bachelor degree from Peking University, and master degree as well as Ph.D. degree from Tsinghua University. He is now a researcher in State Key Laboratory of Astronautic Dynamics and Tsinghua University. His research interests are in the dynamics and control around multiple asteroid systems, surface motion and soft-landing on minor bodies, space debris, as well as cometary dust dynamics.

Jürgen Arno Schmidt received his diploma degree in theoretical physics from the University of Saarbrcken, Germany, and his Ph.D. degree in theoretical physics from the University of Potsdam, Germany. He is now professor in the Astronomy Research Unit of the University of Oulu, Finland. His research interests in the field of celestial mechanics focus on the dynamics of circumplanetary dust and dense planetary rings. He is co-investigator in the science teams of the Cassini Cosmic Dust Analyzer, the Surface Dust Mass Analyzer of the Europa Clipper Mission, and the JANUS camera onboard the Jupiter Icy Moons Explorer.

Hengnian Li received his bachelor degree in mathematical computation from Lanzhou University, and master degree in computer science from National University of Defence Technology as well as Ph.D. degree in system science and engineering from Xi’an Jiaotong University. He is now the director as well as a researcher in State Key Laboratory of Astronautic Dynamics, China. His research interests cover many fields in spacecraft dynamics and control, including to orbital perturbation models, orbital tracking and precision determination, artificial intelligent machine learning, etc.

Xiaodong Liu received his B.S. degree in engineering mechanics from Shandong University in 2008, and Ph.D. degree in aeronautical and astronautical science and technology from Tsinghua University in 2013. He received the grand prize for graduate students at Tsinghua University, and national excellent doctor thesis in the field of aeronautical and astronautical science and technology. Currently he is a postdoctoral researcher in the Astronomy Research Unit at University of Oulu, Finland. His research interest focuses on circumplanetary and interplanetary dust dynamics, tenuous planetary rings, estimate of dust hazard to spacecraft, and orbital dynamics around non-spherical bodies.

Yue Yang received her bachelor degree from Sichuan University. She is now a graduate student in Xi’an Jiaotong University, majoring in software engineering. Her research interests are in data mining and performance abnormality diagnosis.

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Jiang, Y., Schmidt, J.A., Li, H. et al. Stable periodic orbits for spacecraft around minor celestial bodies. Astrodyn 2, 69–86 (2018). https://doi.org/10.1007/s42064-017-0014-5

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  • DOI: https://doi.org/10.1007/s42064-017-0014-5

Keywords

  • asteroid
  • comet
  • deep space exploration
  • periodic orbits
  • stability
  • orbit design