Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example
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The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.
KeywordsBinary asteroids Restricted full three-body problem Equilibrium points Periodic orbit families Homotopy method
This work has been supported by the National Natural Science Foundation of China under Grants 11432001 and 11602009, the Young Elite Scientist Sponsorship Program by China Association for Science and Technology, and the Fundamental Research Funds for the Central Universities.
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Conflict of interest
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the paper submitted.
- Bellerose, J.: The restricted full three body problem: applications to binary asteroid exploration. PhD thesis, University of Michigan (2008)Google Scholar
- Bellerose, J., Scheeres, D.J.: Periodic orbits in the vicinity of the equilateral points of the restricted full three-body problem. In: AAS/AIAA Conference, Lake Tahoe, California, AAS-05-295, vol. 711 (2005)Google Scholar
- Chappaz, L., Howell, K.: Trajectory exploration within binary systems comprised of small irregular bodies. In: 23rd AAS/AIAA Space Flight Mechanics Meeting, Kauai, Hawaii (2013)Google Scholar
- Dichmann, D., Doedel, E., Paffenroth, R.: The computation of periodic solutions of the 3-body problem using the numerical continuation software auto. Libration Point Orbits and Applications, pp. 429–488 (2003)Google Scholar
- Fahnestock, E.G.: The full two-body-problem: simulation, analysis, and application to the dynamics, characteristics, and evolution of binary asteroid systems. PhD thesis, University of Michigan (2009)Google Scholar
- Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory, vol. 112. Springer, Berlin (2013)Google Scholar
- Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments: Applications to Asteroid, Comet and Planetary Satellite Orbiters. Springer, Berlin (2016)Google Scholar
- Scheeres, D., Van Wal, S., Olikara, Z., Baresi, N.: The dynamical environment for the exploration of Phobos, ists-2017-d-007. International Symposium on Space Technology and Science. Ehime, Japan, pp. 3–9 (2017)Google Scholar