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I'm looking for a comprehensive pros and cons of the two most commonly used station-keeping types of orbits used at libration points, Lissajous and halo orbits. When would one select one over the other and why? Do any of the criteria change depending on which Lagrange point (L1-L5) and libration points of which two bodies one would like to place an artificial satellite at? Or is this more mission specific, and depends more on what these satellites are doing there and how wide of an orbital box they require (say, to avoid transits through Earth's umbra or penumbra)?

Ideally, I'd like to see some mission design for which both types of station-keeping orbits were considered, and one chosen over the other based on some documented criteria. Perhaps ARTEMIS or ISEE-3 produced some detailed documentation about this? But if that isn't available, let's, for the sake of argument, pretend that I can't decide between the two for JWST. Why would I have picked a halo orbit for it, and not a Lissajous one?

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    $\begingroup$ I am quite glad you asked this question, as I was wondering myself the answer to this question... $\endgroup$
    – PearsonArtPhoto
    Jul 30, 2015 at 14:02
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    $\begingroup$ Good question. I am also curious if size of the halo makes a difference. If the halo is tiny, a small multi-layer-insulation shade would block heat from the sun and earth. The scope would have nearly 2 pi steradians of 4K sky in which to radiate heat. That would be great for an infrared scope. $\endgroup$
    – HopDavid
    Sep 24, 2015 at 1:16
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    $\begingroup$ Possible duplicate of What is the difference between halo orbits and Lissajous orbits? $\endgroup$
    – uhoh
    May 19, 2019 at 23:32
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    $\begingroup$ @uhoh: That question asks how to distinguish between the two; this one asks which of the two is better for spacecraft to actually use. $\endgroup$
    – Vikki
    May 20, 2019 at 1:00
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    $\begingroup$ In principle, closing an older question as duplicate of a younger question is not only possible, but also sensible if the younger question is better or has the better answers. $\endgroup$
    – Polygnome
    May 20, 2019 at 8:00

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The main difference between the two is that halo orbits tend to be much larger and are constricted to one plane. There's a NASA tech doc from 1993 comparing the station keeping costs between the two and finding none. The authors were quite clear that they did not know if this applied to all station keeping algorithms, but it was clear in the one they tested for both types of orbits.

As for the JWST, a halo orbit confines the telescope to motion in one plane. This should give it better ability to compensate for the motion and get higher resolution images. If it really makes a difference at all.

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    $\begingroup$ Pretty much everything in this answer is wrong. Halo orbits can be very small or very large. Lissajous orbits can be very small or very large. Have a look at JWST's orbit, it is not "in one plane", it's really 3D. "better ability to compensate for the motion and get higher resolution images." doesn't even make sense, attitude and position are completely decoupled. $\endgroup$
    – uhoh
    May 27, 2019 at 9:41
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    $\begingroup$ Thanks for the paper link! But the conclusion, back in 1993, notes that they only studied one station-keeping control algorithm, and two specific nominal trajectories. I suspect the question is still open, or depends on many other mission-specific considerations. And I agree with the points that @uhoh makes. $\endgroup$
    – nealmcb
    Dec 28, 2021 at 4:22

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