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Euclid, Gaia and JWST are all orbiting Lagrange Point L2. Why is Euclid's orbit similar to JWST but not Gaia's, why is Gaia's orbit different than Euclid and JWST ?

Orbits are shown here for example:

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  • $\begingroup$ All 3 orbits look fairly similar to me, in a frame that's co-rotating with L2. I used my interactive 3D plot script at astronomy.stackexchange.com/a/49616/16685 Horizons has data for Euclid from 2023-Jul-02, see ssd.jpl.nasa.gov/api/… $\endgroup$
    – PM 2Ring
    Jul 29, 2023 at 16:00
  • $\begingroup$ @PM2Ring in the video the amplitude of the orbit (in the rotating frame) is much smaller (2x or 3x) for Gaia and much more Lissajous-like (i.e. in-plane and out-of-plane frequency ratio is further from 1:1) than the other two. In these two regards Gaia looks really different quantitatively as well as qualitatively than the other two. You can extract approximate in-plane and out-of-plane periods by fitting sine waves to excursions in each dimension separately, or just histogramming the times between successive appropriate zero-crossing (e.g. vertical plane crossings for horizontal period). $\endgroup$
    – uhoh
    Jul 29, 2023 at 22:17
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    $\begingroup$ @Mete Great question, and Welcome to Stack Exchange! If answers to your current question don't mention it, and if it's not covered in other Q&A here, I think a great follow-up question might be "Why is Gaia's halo orbit so small and so strongly Lissajous-like'?" $\endgroup$
    – uhoh
    Jul 29, 2023 at 22:20
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    $\begingroup$ @uhoh Oh, ok. I just watched the video. And made a plot of Gaia with a 7 year time span (in both the non-rotating & co-rotating frames). I see what you mean. $\endgroup$
    – PM 2Ring
    Jul 29, 2023 at 22:31
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    $\begingroup$ @uhoh sagecell.sagemath.org/… $\endgroup$
    – PM 2Ring
    Jul 29, 2023 at 22:44

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Here is my answer to my question for the future readers. More information regarding Halo and Lissajous orbits can be found in this answer including the references mentioned in this answer. I still did not check a reference text regarding astrodynamics, so I am still not sure if Halo is categorized under Lissajous or as a separate term, but it is not very important. What is meant at least in this question is small amplitude Lissajous orbit (Gaia's) vs. large amplitude Lissajous/Halo orbit (Euclid's and JWST's).

Regarding Gaia's orbit, the paper I mentioned in the comment: GAIA: TRAJECTORY DESIGN WITH TIGHTENING CONSTRAINTS is pretty good. As @asdfex also wrote in the comment above, Gaia is a spinning spacecraft, and has certain constraints which makes Halo orbit not possible for it.

I think, in general, Halo is a better one, there is no eclipse etc. Hence, Euclid and JWST is on a Halo orbit. (maybe also the transfer trajectory to Halo is preferred to one for small amplitude Lissajous, this is also mentioned in the paper referenced above)

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