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Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape

Abstract

This paper investigates the equilibria and their stabilities in the doubly synchronous binary asteroid systems, which are modelled as the two tri-axial ellipsoids with various shape and system parameters. Particularly, the in uences of shape and system parameters on equilibria are discussed analytically. Firstly, the geometrical models of doubly synchronous binary asteroid systems are established. The dual second degree and order gravity field is employed to approximate the gravitational potential of the system. Six shape and system parameters are defined. Then, based on the linearized perturbation equations, the explicit expressions of the offsets of equilibria in doubly synchronous systems are derived, which clearly illustrate the relationship between the distribution of equilibria and the variations of shape parameters. Further, the approximate expressions are applied to estimate the offsets of equilibria due to parameter errors, respectively. Finally, in order to have a better insight into the equilibriaum structure, the stabilities of equilibria under different system parameters are investigated. In particular, critical regions of triangular equilibria are calculated and the role of the relative distance on the stability is discussed in detail. This study could provide a preliminary analysis of equilibria for the mission design in doubly synchronous binary asteroid systems.

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Acknowledgements

This work was supported by the Chang Jiang Scholars Program and the National Natural Science Foundation of China (Grant No. 11572038).

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Correspondence to Dong Qiao.

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Xiangyu Li is a Ph.D. candidate in Beijing Institute of Technology. His major is the orbit dynamics in the vicinity of small bodies.

Dong Qiao is a professor in Beijing Institute of Technology. He was a visiting scholar in University of Strathclyde in 2014 and was selected as the Young Chang Jiang Scholar in 2016. He is mainly engaged in the research of orbit dynamics and control in deep space.

M. A. Barucci is the senior astronomer of LESIA, the Paris Observatory. She mainly works on celestial mechanics, astrophysics, and space science. She is credited by the Minor Planet Center with a total of 3 minor planet discoveries in 1984 and 1985. She currently focuses on ESA Asteroid Sample Return Mission and engages in the Cosmic Vision M5 Program.

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Li, X., Qiao, D. & Barucci, M.A. Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape. Astrodyn 2, 133–146 (2018). https://doi.org/10.1007/s42064-017-0016-3

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  • DOI: https://doi.org/10.1007/s42064-017-0016-3

Keywords

  • doubly synchronous
  • binary asteroid
  • equilibria
  • non-spherical shape
  • stability