Celestial Mechanics and Dynamical Astronomy

, Volume 127, Issue 2, pp 185–210 | Cite as

Trajectory exploration within asynchronous binary asteroid systems using refined Lagrangian coherent structures

  • Haibin Shang
  • Xiaoyu Wu
  • Pingyuan Cui
Original Article


Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid’s spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected.


Binary asteroids Asynchronous binary systems Lagrangian coherent structure Dynamical behavior Trajectory categories Escape Impact Flyby 



This work was supported by the National Basic Research Program of China (“973” Program) (Grant No. 2012CB720000), The National Natural Science Foundation of China (Grant No. 11102021). Especially, Our deepest gratitude goes to reviewers’ careful works and thoughtful suggestions for improving the readability of our paper word for word, which improves this paper substantially.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Key Laboratory of Dynamics and Control of Flight VehicleBeijing Institute of TechnologyBeijingChina

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