A family of periodic orbits in the three-dimensional lunar problem

  • Edward BelbrunoEmail author
  • Urs Frauenfelder
  • Otto van Koert
Original Article


A family of periodic orbits is proven to exist in the spatial lunar problem that are continuations of a family of consecutive collision orbits, perpendicular to the primary orbit plane. This family emanates from all but two energy values. The orbits are numerically explored. The global properties and geometry of the family are studied.


Celestial mechanics: restricted three-body problem Periodic orbits 



Edward Belbruno would like to acknowledge the support of Humboldt Stiftung of the Federal Republic of Germany that made this research possible and the support of the University of Augsburg for his visit from 2018-19. Research by E.B. was partially supported by NSF grant DMS-1814543. Urs Frauenfelder was supported by DFG grant FR 2637/2-1, of the German government. Otto van Koert was supported by NRF grant NRF-2016R1C1B2007662, funded by the Korean Government.

Compliance with ethical standards

Conflicts of interest

The authors state that they have no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Astrophysical SciencesPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsYeshiva UniversityNew YorkUSA
  3. 3.Institute für MathematikAugsburg UniversityAugsburgGermany
  4. 4.Department of Mathematical SciencesSeoul National UniversitySeoulSouth Korea

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