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Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies

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Abstract

Research on the stabilities of periodic orbits is useful for selection of parking orbits in asteroid and comet missions. In this paper, retrograde near-circular periodic orbits near equatorial planes (RNPOEP) of small irregular bodies are discussed, especially for their bifurcations and stabilities. RNPOEPs of six bodies are calculated based on a polyhedral method. The results reflect that two Period-Doubling Bifurcations (PDBs) cause the annular unstable regions, where RNPOEPs are all unstable, in the gravitational fields of some bodies. The unstable annular regions in the gravitational field of some bodies such as 243 Ida are wide, while those of some other bodies such as 216 Kleopatra are narrow. Based on the bodies’ shapes, they are classified as two categories. Bodies of the first category have straight shapes which are approximately symmetric about the x-axis, such as 216 Kleopatra. Bodies of the second category have arched shapes which are approximately symmetric about the y-axis, such as 243 Ida. In order to provide insight of the dominating factors for the range of unstable annular regions, simplified models are proposed in the analysis. Specifically, a double-particle-linkage model is used for the first category while a triple-particle-linkage model is used for the second category. It is found that the distribution of the unstable annular regions in the gravitational field of simplified models is similar to those of the polyhedral models. Numerical results validate that the mass distribution dominates the range of the annular regions for both types of small bodies.

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References

  • Barucci, M.A.: MarcoPolo-R: near Earth asteroid sample return mission. Candidate as ESA-M3 class mission. In: Proceedings of the 39th COSPAR Scientific Assembly, Mysore, India, vol. 105 (2012). Abstract F3.2-24-12

    Google Scholar 

  • Barucci, M.A., Cheng, A.F., Michel, P., et al.: MarcoPolo-R: near Earth asteroid sample return mission. Exp. Astron. 33(2–3), 645–684 (2012a)

    Article  ADS  Google Scholar 

  • Barucci, M.A., Michel, P., Böhnhardt, H., et al.: MarcoPolo-R mission: tracing the origins. In: Proceedings of the European Planetary Science Congress, Madrid, Spain (2012b). EPSC2012-157

    Google Scholar 

  • Blesa, F.: Periodic orbits around simple shaped bodies. Monogr. Semin. Mat. García Galdeano 33, 67–74 (2006)

    MathSciNet  MATH  Google Scholar 

  • Boynton, W.V., Lauretta, D.S., Beshore, E., et al.: The OSIRIS-REx mission to RQ36: nature of the remote sensing observations. In: Proceedings of the European Planetary Science Congress, Madrid, Spain (2012). EPSC2012-875

    Google Scholar 

  • Brucato, J.R.: MarcoPolo-R: asteroid sample return mission. In: Proceedings of the 39th COSPAR Scientific Assembly, Mysore, India, vol. 251 (2012). Abstract B0.5-4-12

    Google Scholar 

  • Chanut, T.G.G., Winter, O.C., Tsuchida, M.: 3D stability orbits close to 433 Eros using an effective polyhedral model method. Mon. Not. R. Astron. Soc. 438(3), 2672–2682 (2014)

    Article  ADS  Google Scholar 

  • Chanut, T.G.G., Winter, C.O., Amarante, A., et al.: 3D plausible orbital stability close to asteroid (216) Kleopatra. Mon. Not. R. Astron. Soc. 452(2), 1316–1327 (2015)

    Article  ADS  Google Scholar 

  • Duffard, R., Kumar, K., Pirrotta, S., et al.: A multiple-rendezvous, sample-return mission to two near-Earth asteroids. Adv. Space Res. 48(1), 120–132 (2011)

    Article  ADS  Google Scholar 

  • Elipe, A., Riaguas, A.: Nonlinear stability under a logarithmic gravity field. Int. Math. J. 3, 435–453 (2003)

    MathSciNet  MATH  Google Scholar 

  • Gabern, F., Koon, W.S., Marsden, J.E., et al.: Binary asteroid observation orbits from a global dynamical perspective. SIAM J. Appl. Dyn. Syst. 5(2), 252–279 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Glassmeier, K.H., Boehnhardt, H., Koschny, D., et al.: The Rosetta Mission: flying towards the origin of the solar system. Space Sci. Rev. 128(1), 1–21 (2007)

    Article  ADS  Google Scholar 

  • Jiang, Y.: Equilibrium points and periodic orbits in the vicinity of asteroids with an application to 216 Kleopatra. Earth Moon Planets 115(1–4), 31–44 (2015)

    Article  ADS  MATH  Google Scholar 

  • Jiang, Y., Baoyin, H.: Orbital mechanics near a rotating asteroid. J. Astrophys. Astron. 35(1), 17–38 (2014)

    Article  ADS  Google Scholar 

  • Jiang, Y., Baoyin, H., Li, J., et al.: Orbits and manifolds near the equilibrium points around a rotating asteroid. Astrophys. Space Sci. 349(1), 83–106 (2014)

    Article  ADS  Google Scholar 

  • Jiang, Y., Baoyin, H., Li, H.: Collision and annihilation of relative equilibrium points around asteroids with a changing parameter. Mon. Not. R. Astron. Soc. 452(4), 3924–3931 (2015a)

    Article  ADS  Google Scholar 

  • Jiang, Y., Yu, Y., Baoyin, H.: Topological classifications and bifurcations of periodic orbits in the potential field of highly irregular-shaped celestial bodies. Nonlinear Dyn. 81(1–2), 119–140 (2015b)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Liu, X., Baoyin, H., Ma, X.: Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube. Astrophys. Space Sci. 333, 409–418 (2011)

    Article  ADS  MATH  Google Scholar 

  • Muñoz-Almaraz, F.J., Freire, E., Galán, J., et al.: Continuation of periodic orbits in conservative and Hamiltonian systems. Physica D 181(1–2), 1–38 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ni, Y., Jiang, Y., Baoyin, H.: Multiple bifurcations in the periodic orbit around Eros. Astrophys. Space Sci. 361(5), 1–15 (2016)

    Article  MathSciNet  Google Scholar 

  • Ozimek, M.T., Atchison, J.A.: NASA double asteroid redirection test (DART) low-thrust trajectory concept. In: 27th AAS/AIAA Space Flight Mechanics Meeting, San Antonio, USA, vol. 221 (2017)

    Google Scholar 

  • Perna, D., Barucci, M.A., Ishiguro, M., et al.: Spectral and rotational properties of near-Earth asteroid (162173) Ryugu, target of the Hayabusa2 sample return mission. Astron. Astrophys. 599, L1 (2017)

    Article  ADS  Google Scholar 

  • Romanov, V.A., Doedel, E.J.: Periodic orbits associated with the libration points of the homogeneous rotating gravitating triaxial ellipsoid. Int. J. Bifurc. Chaos 22(10), 514–519 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • Romanov, V.A., Doedel, E.J.: Periodic orbits associated with the libration points of the massive rotating straight segment. Int. J. Bifurc. Chaos 24(24), 1430012 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Scheeres, D.J.: Orbital mechanics about small bodies. Acta Astronaut. 72, 1–14 (2012)

    Article  ADS  Google Scholar 

  • Scheeres, D.J., Ostro, S.J., Hudson, R.S., et al.: Orbits close to asteroid 4769 Castalia. Icarus 121(1), 67–87 (1996)

    Article  ADS  Google Scholar 

  • Wang, X., Jiang, Y., Gong, S.: Analysis of the potential field and equilibrium points of irregular-shaped small celestial bodies. Astrophys. Space Sci. 353(1), 105–121 (2015)

    Article  ADS  Google Scholar 

  • Wang, X., Li, J., Gong, S.: Bifurcation of equilibrium points in the potential field of asteroid 101955 Bennu. Mon. Not. R. Astron. Soc. 455(4), 3724–3734 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  • Werner, R.A., Scheeres, D.J.: Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celest. Mech. Dyn. Astron. 65(3), 313–344 (1997)

    Article  ADS  MATH  Google Scholar 

  • Yang, H.W., Zeng, X.Y., Baoyin, H.: Feasible region and stability analysis for hovering around elongated asteroids with low thrust. Res. Astron. Astrophys. 15(9), 1571–1586 (2015)

    Article  ADS  Google Scholar 

  • Yu, Y., Baoyin, H.: Orbital dynamics in the vicinity of asteroid 216 Kleopatra. Astron. J. 143(3), 160–161 (2012)

    Article  Google Scholar 

  • Zeng, X., Jiang, F., Li, J., Baoyin, H.: Study on the connection between the rotating mass dipole and natural elongated bodies. Astrophys. Space Sci. 356(1), 29–42 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (11572166).

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Authors and Affiliations

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

    Lei Lan, Hexi Baoyin & Junfeng Li

  2. College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hongwei Yang

  3. Laboratory of Space New Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hongwei Yang

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  1. Lei Lan
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  2. Hongwei Yang
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  3. Hexi Baoyin
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  4. Junfeng Li
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Correspondence to Lei Lan.

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Lan, L., Yang, H., Baoyin, H. et al. Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies. Astrophys Space Sci 362, 169 (2017). https://doi.org/10.1007/s10509-017-3148-2

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  • DOI: https://doi.org/10.1007/s10509-017-3148-2

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