Periodic orbits in the Chermnykh problem


Periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as the engineering aspect for deep space explorations. The rotating mass dipole, referred to as the Chermnykh problem, is a good alternative model to study qualitative dynamical environments near elongated asteroids, like the asteroid 1620 Geographos, 216 Kleopatra, or 25143 Itokawa. In this paper a global searching method is adopted to search for periodic orbits around the dipole model based on the concept of Poincaré section of surface. Representative families of periodic orbits are illustrated with respect to all three topological cases of the dipole model. Topological transitions of orbits during iso-energetic continuations are also presented as well as identification of new types of periodic orbits.

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Thanks for the thoughtful discussions and suggestions of Yanshuo Ni and Prof. Junfeng Li from Tsinghua University, Beijing, China. This work was supported by the National Natural Science Foundation of China (No. 11602019). The Excellent Young Teachers Program of Beijing Institute of Technology (No. 2015YG0605) and Beijing Institute of Technology Research Fund Program for Young Scholars were also acknowledged.

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Correspondence to Xiangyuan Zeng.

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Xiangyuan Zeng received his Ph.D. degree in mechanics from Tsinghua University, China, in 2013, and was a visiting scholar of Texas A&M University in 2011 and 2012. After two years as a research assistant in Tsinghua University, he joined Beijing Institute of Technology as an assistant professor in 2015. Currently, he is an AIAA member, a winner of the “Excellent Young Teachers Program of BIT” and “Young Elite Scientist Sponsorship Program by CAST (YESS)”. His area of expertise is in interplanetary trajectory design and optimization. His current research interests are astrodynamics and orbit control near asteroids. E-mail:

Kyle T. Alfriend is the TEES Distinguished Professor of aerospace engineering at Texas A&M University. He is a University Distinguished Professor. He is a member of the National Academy of Engineering and an Honorary Fellow of the AIAA. He has received the AIAA Guidance, Navigation and Control Award, the AIAA Mechanics and Control of Flight Award, and the AAS Dirk Brouwer Award. For more than 40 years, he has been making key contributions to the understanding of the flight mechanics and control of space vehicles. His career includes an unusually mix of experience in academia, industry, and government. His current research interests are primarily astrodynamics and space situational awareness.

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Zeng, X., Alfriend, K.T. Periodic orbits in the Chermnykh problem. Astrodyn 1, 41–55 (2017).

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  • periodic orbits
  • the Chermnykh problem
  • topological transition
  • iso-energetic continuation