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Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole

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Abstract

The aim of this paper is to understand the common characteristics of the generalized flyby trajectory around natural elongated bodies. Such flyby trajectories provide a short-term mechanism to clear away vicinal objects or temporally capture ejecta into circling orbits. The gravitational potential of elongated bodies is described by a unified approximate model, i.e., the rotating mass dipole which is two point masses connected with a constant massless rod. The energy power is used to illustrate the flyby effect in terms of the instantaneous orbital energy. The essential of the single flyby trajectory is studied analytically, and the relationship between the flyby trajectory and its Jacobi integral is also illustrated. Sample trajectories are given to show the variational trend of the energy increment with respect to different orbital periapsides. The distribution of natural ejecting orbits is presented by varying the parameters of the approximate model.

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References

  1. Baoyin, H.X., Li, J.F.: A survey on orbital dynamics and navigation of asteroid missions. Acta Mech. Sin. 30, 282–293 (2014)

    Article  MathSciNet  Google Scholar 

  2. Scheeres, D.J., Ostra, S.J., Hudson, R.S., et al.: Orbits close to asteroid 4769 Castalia. ICARUS 121, 67–87 (1996)

    Article  Google Scholar 

  3. Jiang, F.H., Baoyin, H.X., Li, J.F.: Practical techniques for low-thrust trajectory optimization with homotopic approach. J. Guid. Control Dyn. 35, 245–258 (2012)

    Article  Google Scholar 

  4. Yu, Y., Baoyin, H.X.: Resonant orbits in the vicinity of asteroid 216 Kleopatra. Astrophys. Space Sci. 343, 75–82 (2013)

    Article  Google Scholar 

  5. Wang, X.Y., Gong, S.P., Li, J.F.: A method for classifying orbits near asteroids. Acta Mech. Sin. 30, 316–325 (2014)

    Article  Google Scholar 

  6. Xu, M., Xu, S.J.: Exploration of distant retrograde orbits around Moon. Acta Astronaut. 65, 853–860 (2009)

    Article  Google Scholar 

  7. Tricarico, P., Sykes, M.V.: The dynamical environment of dawn at Vesta. Planet. Space Sci. 58, 12–38 (2010)

    Article  Google Scholar 

  8. Scheeres, D.J., Williams, B.G., Miller, J.K.: Evaluation of the dynamic environment of an asteroid: applications to 433 Eros. J. Guid. Control Dyn. 23, 466–475 (2000)

    Article  Google Scholar 

  9. Scheeres, D.J.: Dynamics about uniformly rotating triaxial ellipsoids: applications to asteroids. Icarus 110, 225–238 (1994)

    Article  Google Scholar 

  10. Elipe, A., Lara, M.: A Simple model for the chaotic motion around (433) Eros. In: AAS 03-563. AAS/AIAA Astrodynamics Specialists Conference, Big Sky, Montana, 1–15 (2003)

  11. Bartczak, P., Breiter, S.: Double material segment as the model of irregular bodies. Celest. Mech. Dyn. Astron. 86, 131–141 (2003)

  12. Prieto-Llanos, T., Gómez-Tierno, M.A.: Stationkeeping at libration points of natural elongated bodies. J. Guid. Control Dyn. 17, 787–794 (1994)

    Article  Google Scholar 

  13. Liu, X.D., Baoyin, H.X., Ma, X.R.: Periodic orbits in the gravity field of a fixed homogenous cube. Astrophys. Space Sci. 334, 357–364 (2011)

    Article  MATH  Google Scholar 

  14. Blesa, F.: Periodic orbits around simple shaped bodies. In: Ninth international conference Zaragoza-Pau on applied mathematics and statistics: Jaca (Spain), September 19–21, 2005, 67–74. Seminario Matemático “García de Galdeano” (2006). (in Spanish)

  15. Li, X.Y., Qiao, D., Cui, P.Y.: The equilibria and periodic orbits around a dumbbell-shaped body. Astrophys. Space Sci. 348, 417–426 (2013)

    Article  Google Scholar 

  16. Zeng, X.Y., Jiang, F.H., Li, J.F., et al.: Study on the connection between the rotating mass dipole and natural elongated bodies. Astrophys. Space Sci. 356, 29–42 (2015)

    Article  Google Scholar 

  17. Yang, H.W., Zeng, X.Y., Baoyin, H.X.: Feasible region and stability analysis for hovering around elongated asteroids with low thrust. Research in Astronomy and Astrophysics (2015) (accepted)

  18. Zhang, J.R., Zhao, S.G., Yang, Y.Z.: Characteristics analysis for elliptical orbit hovering based on relative dynamics. IEEE Trans. Aerosp. Electron. Syst. 49, 2742–2750 (2013)

    Article  Google Scholar 

  19. Wang, X.Y., Jiang, Y., Gong, S.P.: Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies. Astrophys. Space Sci. 353, 105–121 (2014)

    Article  Google Scholar 

  20. Xu, M., Xu, S.J.: Study on stationkeeping for halo orbits at EL1: Dynamics modeling and controller designing. Trans. Jpn Soc. Aeronaut. Space Sci. 55, 274–285 (2012)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Basic Research Program of China (973 Program), (Grant 2012CB720000) and China Postdoctoral Science Foundation (Grant 2014M560076). Support from Shanghai Satellite Engineering Research Institute (Grant 13dz2260100) is also acknowledged.

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Authors and Affiliations

  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Xiangyuan Zeng & Junfeng Li

  2. Shanghai Satellite Engineering Research Institute, Shanghai, 200240, China

    Baodong Fang

  3. Observatoire de la Côte d’Azur, 06300, Nice, France

    Yang Yu

Authors
  1. Xiangyuan Zeng
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  2. Baodong Fang
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  3. Junfeng Li
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  4. Yang Yu
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Corresponding author

Correspondence to Xiangyuan Zeng.

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Zeng, X., Fang, B., Li, J. et al. Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole. Acta Mech. Sin. 32, 535–545 (2016). https://doi.org/10.1007/s10409-015-0487-5

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  • DOI: https://doi.org/10.1007/s10409-015-0487-5

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