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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:

Mete
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  • 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 https://astronomy.stackexchange.com/a/49616/16685 Horizons has data for Euclid from 2023-Jul-02, see https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=Euclid – PM 2Ring Jul 29 '23 at 16:00
  • @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). – uhoh Jul 29 '23 at 22:17
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    @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'?" – uhoh Jul 29 '23 at 22:20
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    @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. – PM 2Ring Jul 29 '23 at 22:31
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    @uhoh https://sagecell.sagemath.org/?z=eJxNUcFKxDAQvRf6D0MFN13DWlvcgxDwIJ4UFvEmS8mmaZu1m4QkXcGvN2miLoFhZpj33szLFTRP8CKspUc1W2CzOXO4Bq2EdHYDu1eo34QcoK7qu41_VZ6dqUErtyrz7NEPcUOZy7OO99AiShoMB1JjYOQeJxayrTBY8c1DaxEg72bmOM8AekNPqYSOms-Uam6s5syJ31mgs1PtrDvqOHmmk-XlQ8B7BiBw9qPKoA-mLKJrVwY5iQ5_GfPZvozz2lmP-OiRI3MJvTIwg5BgDZUDR37Teq1FjLdx_3IfkTuPWzpNhzxLuikEf5aalCGF4V2RdEQfb01rRoIbz0DDyc4I1upJBa4eA3IYkrRfOfTb5F2zrTxh5HAjP3G_RBGcKoJCSIB7N6CYxDC6It1o1DG4p2SYvjBzAV3UCauMG9VgqB4FSxS7jR3VF4r_s0Qc9ckS8YUG-U8xKDkJGT-t_AFjmbpT&lang=sage – PM 2Ring Jul 29 '23 at 22:44
  • can you replot it in 1970's green oscilloscope phosphor streaks - slightly out of focus :-) (humor!) – uhoh Jul 29 '23 at 23:44
  • Thanks for the comments. I know only a little bit about the topic, so I guess I cannot add more than maybe to further clarify why I am asking this. First, I am confused about the use of terms Lissajous and Halo on internet when describing the Euclid's orbit, because some says it is Halo (ESA, as in the video), some says it is Lissajous (wikipedia), some says both (Lissajous Halo) (CNES). I have an impression all L2 orbits are Lissajous (probably I am wrong?), but large amplitude ones are (also) called Halo? – Mete Jul 30 '23 at 09:44
  • and the particular point I would like to know is, since, I think, all these space telescopes have the same reasons for being in L2, why Gaia's orbit is different, at least why it is not large amplitude. Does Gaia's orbit and Euclid's orbit have different pros and cons, and they are selected accordingly or was there a different limitation so Gaia has this particular orbit (i.e. otherwise it would have a Halo/large amplitude orbit like Euclid's) ? – Mete Jul 30 '23 at 09:51
  • @Mete See What is the difference between halo orbits and Lissajous orbits? – PM 2Ring Jul 30 '23 at 09:52
  • @PM2Ring thanks, from the pages linked from this one, I found this paper GAIA: TRAJECTORY DESIGN WITH TIGHTENING CONSTRAINTS. I dont fully understand it but it seems to explain why Gaia's orbit is as such. I dont know about JWST, but Gaia seems to have particular differences comparing to Euclid. So my answer to my question at the moment is that Halo orbit is actually better, but for different reasons regarding the spacecraft it may not be a valid one as is the case with Gaia. – Mete Jul 30 '23 at 10:26
  • @Mete It seems the central point is that Gaia needed a small amplitude to keep the direction of earth fairly constant. They can't slew the space craft around like JWST because it is spinning and has sensors with large opening angles. – asdfex Jul 30 '23 at 18:21
  • @asdfex that is also my understanding from the paper mentioned. – Mete Jul 31 '23 at 10:37

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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)

Mete
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