Skip to main content
SpringerLink
Log in

Long term evolution of distant retrograde orbits in the Earth-Moon system

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

This work studies the evolution of several Distant Retrograde Orbits (DROs) of varying size in the Earth-Moon system over durations up to tens of millennia. This analysis is relevant for missions requiring a completely hands off, long duration quarantine orbit, such as a Mars Sample Return mission or the Asteroid Redirect Mission. Four DROs are selected from four stable size regions and are propagated for up to 30,000 years with an integrator that uses extended precision arithmetic techniques and a high fidelity dynamical model. The evolution of the orbit’s size, shape, orientation, period, out-of-plane amplitude, and Jacobi constant are tracked. It has been found that small DROs, with minor axis amplitudes of approximately 45,000 km or less decay in size and period largely due to the Moon’s solid tides. Larger DROs (62,000 km and up) are more influenced by the gravity of bodies external to the Earth-Moon system, and remain bound to the Moon for significantly less time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Notes

  1. Obtained December 2014 from https://boutell.com/fracster-src/doubledouble/doubledouble.html.

References

  • Benest, D.: Astron. Astrophys. 32, 39 (1974)

    ADS  Google Scholar 

  • Benest, D.: Astron. Astrophys. 45, 353 (1975)

    ADS  Google Scholar 

  • Benest, D.: Astron. Astrophys. 54, 563 (1977)

    ADS  Google Scholar 

  • Bezrouk, C., Parker, J.S.: AIAA/AAS Astrodynamics Specialist Conference (14-4424) (2014)

  • Bezrouk, C., Parker, J.S.: AAS/AIAA Space Flight Mechanics Meeting (AAS 15-302) (2015)

  • Broucke, R.A.: Periodic orbits in the restricted three-body problem with earth-moon masses. Technical report 32-1168, Jet Propulsion Laoratory (1968)

  • Dekker, T.J.: Numer. Math. 18, 224–242 (1971)

    Article  MathSciNet  Google Scholar 

  • Folkner, W.M., Williams, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: The planetary and lunar ephemerides de430 and de431. IPN Progress Report 42-196 (2014)

  • Gottlieb, R.G.: Fast gravity, gravity partials, normalized gravity, gravity gradient torque and magnetic field: derivation, code and data. Technical Report NASA Contractor Report 188243, NASA Lyndon B. Johnson Space Center (February 1993)

  • Hénon, M.: Astron. Astrophys. 1, 223 (1969)

    ADS  Google Scholar 

  • Hénon, M.: Astron. Astrophys. 9, 24 (1970)

    ADS  Google Scholar 

  • Howell, K.C.: Celest. Mech. 32(1), 53 (1984)

    Article  ADS  Google Scholar 

  • Knuth, D.E.: The Art of Computer Programming: Seminumerical Algorithms, 2nd edn. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  • Lam, T., Whiffen, G.J.: Adv. Astronaut. Sci. 05(110), 5 (2005)

    Google Scholar 

  • Lara, M., Russell, R., Villac, B.: 15th AAS/AIAA Spaceflight Mechanics Meeting AAS 05-2189 (2005)

  • Lara, M., Russell, R., Villac, B.F.: Acta Astronaut. 69, 186–199 (2011)

    Article  ADS  Google Scholar 

  • Lundberg, J.B., Schutz, B.E.: J. Guid. 11(1), 31 (1988)

    Article  Google Scholar 

  • Ming, X., Shijie, X.: Acta Astronaut. 65, 27–39 (2009)

    Article  Google Scholar 

  • Murray, C.D., Dermott, S.F.: Solar System Dynamics, 1st edn. Cambridge University Press, New York (1999)

    MATH  Google Scholar 

  • Parker, J.S., Bezrouk, C.: AAS/AIAA Space Flight Mechanics Meeting (AAS 15-331) (2015)

  • Petit, G., Luzum, B.: Iers conventions (2010). IERS Technical note 36, International Earth Rotation Service (2010). http://www.iers.org/TN36/

  • Priest, D.M.: On properties of floating point arithmetics: numerical stability and the cost of accurate computations. PhD thesis, University of California, Berkeley (November 1992)

  • Scott, C., Spencer, D.: Astrodynamics Specialist Conference and Exhibit (6431) (2008)

  • Shewchuk, J.R.: Discrete Comput. Geom. 18(3), 305 (1997)

    Article  MathSciNet  Google Scholar 

  • Strange, N., Landau, D., McElrath, T., Lantoine, G., Lam, T.: International Electric Propulsion Conference (2013-321) (2013)

  • Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 3rd edn. Microcosm Press, Hawthorne (2007)

    MATH  Google Scholar 

  • Villac, B.F., Aiello, J.J.: 15th AAS-AIAA Spaceflight Mechanics Meeting AAS 05-0150 (2005)

Download references

Acknowledgements

We thank Joshua Hopkins, William Pratt, and their team at the Lockheed Martin Space Systems Company for their valuable insights and probing questions. This work has been partially funded by the Lockheed Martin Space Systems Company. Research for this paper was conducted with Government support under contact FA9550-11-C-0028 and awarded by the Department of Defense, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a.

Author information

Authors and Affiliations

  1. Colorado Center for Astrodynamics Research, ECNT 320, 431 UCB, University of Colorado, Boulder, CO, 80309-0431, USA

    Collin Bezrouk & Jeffrey S. Parker

Authors
  1. Collin Bezrouk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey S. Parker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Collin Bezrouk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bezrouk, C., Parker, J.S. Long term evolution of distant retrograde orbits in the Earth-Moon system. Astrophys Space Sci 362, 176 (2017). https://doi.org/10.1007/s10509-017-3158-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-017-3158-0

Keywords

Search

Navigation