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Are L1 and L2 libration point orbital periods always half the orbital period of the massive bodies?

The halo orbital period of JWST is a half a year. https://webb.nasa.gov/content/about/orbit.html

The halo orbital period of Artemis-P1 around either Earth/Moon L1 or L2 is a half a lunar month. https://www.nasa.gov/mission_pages/themis/news/artemis-orbit.html

Is this a coincidence or an inherent property of halo orbits?

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  • $\begingroup$ Not exactly, but roughly see this answer and my comment $\endgroup$
    – uhoh
    Jan 22, 2022 at 16:52
  • $\begingroup$ I think problem is that the Lagrange points are for circular orbits. From elliptic orbits, things become problematic and probably a periodic 3-body solution is what everybody wants to have. $\endgroup$
    – peterh
    Jan 22, 2022 at 21:31
  • $\begingroup$ Did you mean "Lagrange" point rather than libration? $\endgroup$
    – Greg Miller
    Nov 29, 2022 at 13:15
  • $\begingroup$ @GregMiller ... The terms can be used interchangeably, although they have different origins. Cambridge Dictionary defines Libration as "a slight backwards and forwards movement of something, especially of planets etc. in the sky". In this case, the points at the center of the libration movements are Lagrange points. $\endgroup$
    – Woody
    Nov 29, 2022 at 16:09

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