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

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## Abstract

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.

## Keywords

Celestial mechanics: restricted three-body problem Periodic orbits## Notes

### Acknowledgements

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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