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Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

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Abstract

An alternative transfer strategy to send spacecraft to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around L1 is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecraft in elliptic orbits around L4 and L5 are analysed considering the restricted three-body problem Earth–Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth.

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References

  • Broucke, R.A.: Periodic orbits in the restricted three-body problem with Earth–Moon masses. Technical Report 32-1168, NASA–JPL, California (1968)

  • Broucke R.A.: Travelling between the Lagrange points and the Moon. J. Guid. Control Dyn. 2, 257–263 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • Broucke, R.A.: The Celestial Mechanics of the gravity assist. In: Astrodynamics Conference (AIAA paper 88-4220), Minneapolis (Aug. 1988)

  • Danby J.M.A.: Fundamentals of Celestial Mechanics. Willmann-Bell Inc, Virginia (1962)

    Google Scholar 

  • de Fillipi, G.: Station Keeping at the L4 Libration Point: A Three Dimensional Study. Master’s thesis, Dept. Aeronautics and Astronautics, Air Force Institute of Technology Wright-Patterson AFB, Ohio, USA (1978)

  • Melo C.F., Macau E.E.N., Winter O.C., Viera Neto E.: Alternative paths for the insertion of probes in to high inclination lunar orbits. Adv. Space Res. 40, 58–68 (2007)

    Article  ADS  Google Scholar 

  • Melo C.F., Macau E.E.N., Winter O.C.: Strategy for plane change of Earth orbits using lunar gravity and trajectories derived of family G. Celest. Mech. Dyn. Astron. 103, 281–299 (2009)

    Article  ADS  MATH  Google Scholar 

  • Euler, L.: De motu rectilineo trium corporum se mutuo attrahentium, Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, vol. 11 (1776)

  • Lagrange J.: Essasi sur le problème des trois corps. œuvre. 6, 229–324 (1772)

    Google Scholar 

  • McLaughlin W.I.: Walter Hohmann’s road in space. J. Space Mission Archit. 2, 1–14 (2000)

    Google Scholar 

  • NASA Safety Standard 1740.14.: Guidelines and Assessments Procedures for Limiting Orbital Debris. Office of Safety and Mission Assurance, 1 Aug. (1995)

  • O’Neill G.K.: The colonization of space. Phys. Today 27(9), 32–40 (1974)

    Article  Google Scholar 

  • Prado, A.F.B.A.: Optimal Transfer and Swing-by Orbits in the Two and Three-Body Problem. PhD Dissertation, University of Texas, Austin (1993)

  • Prado A.F.B.A.: Traveling between the Lagrangian points and the Earth. Acta Astronaut. 39(7), 483–486 (1996)

    Article  ADS  Google Scholar 

  • Prado A.F.B.A., Broucke R.A.: Transfer orbits in the Earth–Moon system using a regularized model. J. Guid. Control Dyn. 19, 929–933 (1996)

    Article  MATH  Google Scholar 

  • Schaub H., Junkins J.L.: Analytical Mechanics of Space Systems. AIAA, Virginia (2003)

    Book  Google Scholar 

  • Schutz, B.E.: Orbital mechanics of space colonies at L4 and L5 of the Earth–Moon system. In: AIAA Astrodynamics Specialist Conference, volume AIAA Paper No. 77–33 (1977)

  • Szebehely V.: Theory of Orbits The Restricted Problem of Three Bodies. Academic Press, N.Y. (1967)

    Google Scholar 

  • Woodcock G.R.: Missions and operations modes for lunar basing. In: Mendell, W.W. (ed.) Lunar Bases and Space Activities of the 21st Century, pp. 111–124. Lunar and Planetary Institute, Houston (1985)

    Google Scholar 

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Correspondence to F. J. T. Salazar.

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Salazar, F.J.T., de Melo, C.F., Macau, E.E.N. et al. Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5. Celest Mech Dyn Astr 114, 201–213 (2012). https://doi.org/10.1007/s10569-012-9426-y

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  • DOI: https://doi.org/10.1007/s10569-012-9426-y

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