Skip to main content
SpringerLink
Log in

Revisit of the Theorem of Image Trajectories in the Earth-Moon Space

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

On the occasion of the 50th anniversary of the theorem of the image trajectories in the Earth-Moon space, the author revisits the theorem and clarifies the relation between the class of image trajectories and the class of symmetric free-return trajectories, which were employed in the Apollo program. In a nutshell, the symmetric free-return trajectories are those image trajectories that intersect the Earth-Moon axis orthogonally at some point above the far side of the Moon. Optimization implications are pointed out.

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

Similar content being viewed by others

References

  1. Miele, A.: Theorem of image trajectories in Earth-Moon space. Acta Astronaut. 6(5), 225–232 (1960)

    Google Scholar 

  2. Schwaniger, A.J.: Trajectories in the Earth-Moon Space with Symmetric Free-Return Properties. NASA Technical Note D-1833 (1963)

  3. Weber, R., Pauson, W., Burley, R.: Lunar Trajectories. NASA Technical Note D-866 (1961)

  4. Egorov, V.A.: Three-Dimensional Lunar Trajectories. NASA Technical Translation F-504 (1969)

  5. Almeida Prado, A.F.B.: Orbital maneuvers between the Lagrangian points and the primaries in the Earth-Moon system. J. Braz. Soc. Mech. Sci. Eng. 28(2), 131–139 (2006)

    Google Scholar 

  6. Miele, A., Mancuso, S.: Optimal trajectories for Earth-Moon-Earth flight. Acta Astronaut. 49(2), 59–71 (2001)

    Article  Google Scholar 

  7. Miele, A., Mancuso, S.: Design of Moon missions. In: Miele, A. (ed.) Advanced Design Problems in Aerospace Engineering, vol. 1, pp. 31–64. Kluwer Academic/Plenum, New York (2003), Chap. 3

    Google Scholar 

  8. NASA Website, Apollo Section, located at http://www.nasa.gov/mission_pages/apollo/index.html

Download references

Author information

Authors and Affiliations

  1. Rice University, Houston, TX, USA

    Angelo Miele

Authors
  1. Angelo Miele
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Angelo Miele.

Additional information

The author acknowledges the comments of Professor David G. Hull (University of Texas, Austin, Texas), C. David Eagle (a.i. solutions, Kennedy Space Center, Florida), Dr. Marco Ciarcià (US Naval Postgraduate School, Monterey, California), Dr. Salvatore Mancuso (European Space Agency, Paris, France).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miele, A. Revisit of the Theorem of Image Trajectories in the Earth-Moon Space. J Optim Theory Appl 147, 483–490 (2010). https://doi.org/10.1007/s10957-010-9734-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-010-9734-x

Keywords

Search

Navigation