Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape

Abstract

We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape. The gravitational potential and effective potential of asteroid 1333 Cevenola are calculated. The zero-velocity curves for a massless particle orbiting in the gravitational environment have been discussed. The linearized dynamic equation, the characteristic equation, and the conserved quantity of the equilibria for the large-size-ratio binary asteroid system have been derived. It is found that there are totally five equilibrium points close to 1333 Cevenola. The topological cases of the outside equilibrium points have a staggered distribution. The simulation of orbits in the full gravitational potential caused by the 3D irregular shape of 1333 Cevenola shows that the moonlet’s orbit is more likely to be stable if the orbit inclination is small.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    Hirabayashi, M., Morimoto, M. Y., Yano, H., Kawaguchi, J., Bellerose, J. Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: application to fast rotating asteroid 2000EB14. Icarus, 2010, 206(2): 780–782.

    Article  Google Scholar 

  2. [2]

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

    Article  Google Scholar 

  3. [3]

    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, 15(9): 1571–1586.

    Article  Google Scholar 

  4. [4]

    Yang, H. W., Tang, G., Jiang, F. H. Optimization of observing sequence based on nominal trajectories of symmetric observing configuration. Astrodynamics, 2018, 2(1): 25–37.

    Article  Google Scholar 

  5. [5]

    Venditti, F. C. F., Rocco, E. M., Prado, A. F. B. A. Trajectory control around non-spherical bodies modelled by parallelepipeds. Journal of Physics: Conference Series, 2013, 465(1): 012008.

    Google Scholar 

  6. [6]

    Feng, J. L., Noomen, R., Yuan, J. P. Orbital motion in the vicinity of the non-collinear equilibrium points of a contact binary asteroid. Planetary and Space Science, 2015, 117: 1–14.

    Article  Google Scholar 

  7. [7]

    Bartczak, P., Breiter, S., Jusiel, P. Ellipsoids, material points and material segments. Celestial Mechanics and Dynamical Astronomy, 2006, 96(1): 31–48.

    MathSciNet  Article  MATH  Google Scholar 

  8. [8]

    Jiang, Y., Baoyin, H. X., Li, J. F., Li, H. N. Orbits and manifolds near the equilibrium points around a rotating asteroid. Astrophysics and Space Science, 2014, 349(1): 83–106.

    Article  Google Scholar 

  9. [9]

    Wang, X. Y., Jiang, Y., Gong, S. P. Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies. Astrophysics and Space Science, 2014, 353(1): 105–121.

    Article  Google Scholar 

  10. [10]

    Aljbaae, S., Chanut, T. G. G., Carruba, V., Souchay, J., Prado, A. F. B. A., Amarante, A. The dynamical environment of asteroid 21 Lutetia according to different internal models. Monthly Notices of the Royal Astronomical Society, 2017, 464(3): 3552–3560.

    Article  Google Scholar 

  11. [11]

    Yu, Y., Baoyin, H. X. Orbital dynamics in the vicinity of asteroid 216 Kleopatra. The Astronomical Journal, 2012, 143(3): 62.

    Article  Google Scholar 

  12. [12]

    Chanut, T. G. G., Winter, O. C., Tsuchida, M. 3D stability orbits close to 43. Eros using an effective polyhedral model method. Monthly Notices of the Royal Astronomical Society, 2014, 438(3): 2672–2682.

    Article  Google Scholar 

  13. [13]

    Chanut, T. G. G., Winter, O. C., Amarante, A., Arajo, N. C. S. 3D plausible orbital stability close to asteroid (216. Kleopatra. Monthly Notices of the Royal Astronomical Society, 2015, 452(2): 1316–1327.

    Article  Google Scholar 

  14. [14]

    Yu, Y., Baoyin, H. X. Generating families of 3D periodic orbits about asteroids. Monthly Notices of the Royal Astronomical Society, 2012, 427(1): 872–881.

    Article  Google Scholar 

  15. [15]

    Jiang, Y., Baoyin, H. X. Periodic orbit families in the gravitational field of irregular-shaped bodies. The Astronomical Journal, 2016, 152(5): 137.

    Article  Google Scholar 

  16. [16]

    Tardivel, S., Scheeres, D. J., Michel, P.. Van Wal, S., Sanchez, P. Contact motion on surface of asteroid. Journal of Spacecraft and Rockets, 2014, 51(6): 1857–1871.

    Article  Google Scholar 

  17. [17]

    Yu, Y., Baoyin, H. X. Modeling of migrating grains on asteroids surface. Astrophysics and Space Science, 2015, 355(1): 43–56.

    Article  Google Scholar 

  18. [18]

    Jiang, Y., Zhang, Y., Baoyin, H. X. Surface motion relative to the irregular celestial bodies. Planetary and Space Science, 2016, 127: 33–43.

    Article  Google Scholar 

  19. [19]

    Va.Wal, S., Scheeres, D. J. The lift-off velocity on the surface of an arbitrary body. Celestial Mechanics and Dynamical Astronomy, 2016, 125(1): 1–31.

    Google Scholar 

  20. [20]

    Hanuš, J., Durech, J., Brož, M., Warner, B. D., Pilcher, F., Stephens, R., Oey, J., Bernasconi, L., Casulli, S., Behrend, R. et al. A study of asteroid pole-latitude distribution based on an extended set of shape models derived by the lightcurve inversion method. Astronomy & Astrophysics, 2011, 530: A134.

    Google Scholar 

  21. [21]

    Johnston, W. R. (1333) Cevenola, 2014. https://doi.org/www.johnstonsarchive.net/astro/astmoons/am-01333.html.

    Google Scholar 

  22. [22]

    Warner, B. D. Asteroid photometry at the palmer divide observatory: results for 1333 Cevenola and 2460 Mitlincoln. Minor Planet Bulletin, 2002, 29: 74–75.

    Google Scholar 

  23. [23]

    Ni, Y. S., Baoyin, H. X., Li, J. F. Orbit dynamics in the vicinity of asteroids with solar pertubation. The 65th International Astronautical Congress, 2014, 7: 4610–4620.

    Google Scholar 

  24. [24]

    Jiang, Y., Baoyin, H. X. Orbital mechanics near a rotating asteroid. Journal of Astrophysics and Astronomy, 2014, 35(1): 17–38.

    Article  Google Scholar 

  25. [25]

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

    Article  Google Scholar 

  26. [26]

    Dullin, H. R., Worthington, J. The vanishing twist in the restricted three-body problem. Physica D: Nonlinear Phenomena, 2014, 276: 12–20.

    MathSciNet  Article  MATH  Google Scholar 

  27. [27]

    Werner, R. A., Scheeres, D. J. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celestial Mechanics and Dynamical Astronomy, 1996, 65(3): 313–344.

    MATH  Google Scholar 

  28. [28]

    Scheeres, D. J., Bellerose, J. The restricted hill full 4-body problem: application to spacecraft motion about binary asteroids. Dynamical Systems, 2005, 20(1): 23–44.

    MathSciNet  Article  MATH  Google Scholar 

  29. [29]

    Jiang, Y., Baoyin, H. X., Li, H. N. Collision and annihilation of relative equilibrium points around asteroids with a changing parameter. Monthly Notices of the Royal Astronomical Society, 2015, 452(4): 3924–3931.

    Article  Google Scholar 

  30. [30]

    Jiang, Y., Baoyin, H. X., Wang, X. Y., Yu, Y., Li, H. N., Peng, C., Zhang, Z. B. Order and chaos near equilibrium points in the potential of rotating highly irregular-shaped celestial bodies. Nonlinear Dynamics, 2016, 83(1–2): 231–252.

    Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 11772356) and China Postdoctoral Science Foundation{General Program (No. 2017M610875).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yu Jiang.

Additional information

Yu Jiang received his B.S. degree from Peking University, and M.S. degree as well as Ph.D. degree from Tsinghua University. He is now a researcher at State Key Laboratory of Astronautic Dynamics and Tsinghua University. His research interests mainly focus on dynamics and control around multiple asteroid systems, surface motion and soft-landing on minor bodies, space debris, as well as dust dynamics.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jiang, Y. Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape. Astrodyn 2, 361–373 (2018). https://doi.org/10.1007/s42064-018-0029-6

Download citation

Keywords

  • equilibrium points
  • orbits
  • polyhedral model
  • asteroids
  • 1333 Cevenola