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Every orbit in space has its pros and cons. Low Earth Orbit has accessibility but frequent eclipses whereas a Solar Lagrange Point is clear and stable but distant. In the case of the Lunar Lagrange Points (for argument we'll specify L4, L5, and L2 in the Earth-Moon system) what pros and cons exist from a telescope's POV?

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LEO doesn't necessarily have to have frequent eclipses at all. In fact Sun Synchronous orbit never leaves the sunlight.

Contrasting to L2, L4, and L5 which all have eclipses. There's also the issue of stationkeeping. Lagrangian points are less stable then they appear; and keeping a spacecraft in one does require a good bit of fuel for stationkeeping. Lastly, there's an issue of data transmission. The spacecraft needs to be capable of returning high resolution photos back to the earth faster than it takes new ones; which requires increasingly large antennas and more power the farther from the earth you get.

By far the most fascinating orbit ever used for a space telescope has to be the one used for the Transiting Exoplanet Survey Satellite. It uses a highly elliptical 2:1 moon-synchronous orbit that goes pretty far out into space to make its observations, zips back close to the earth where it can achieve higher data rates, then back off to deep space it goes.

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  • $\begingroup$ The question is about halo orbits, which are out of plane and can be large and remain far from their associated Lagrange points. Is there any source that demonstrates that there can not be eclipse-free halo orbits about the Earth-Moon Lagrange points? $\endgroup$
    – uhoh
    Aug 4, 2018 at 0:40
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    $\begingroup$ @uhoh the question does not mention halo orbits; and halo orbits are most certainly NOT out of plane. They necessitate being in the same plane as the two primary bodies. $\endgroup$ Aug 6, 2018 at 18:32
  • $\begingroup$ Okay, then there are answers here that explain why one wouldn't put a spacecraft at L1 or L2, but instead in an orbit such as a halo orbit, though there are many kinds of orbits associated with L1 or L2. Planar Lyapunov orbits are in-plane, but halo orbits are absolutely out of plane. See the GIF in this question for example. See also this answer and this for some colorful orbitology. $\endgroup$
    – uhoh
    Aug 7, 2018 at 0:23
  • $\begingroup$ More about TESS' fascinating orbit space.stackexchange.com/a/26577/12102 $\endgroup$
    – uhoh
    Mar 6 at 17:28
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The Earth-Moon Lagrange points all have eclipses. Less frequently than Earth, but often enough to be a problem.

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In addition, L2 is behind the Moon. This shields the telescope from Earth radio transmissions which would be a benefit for a radio telescope, but you'd need a communications relay satellite in a polar orbit around the Moon.

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Pros and cons of space telescope in an Earth-Moon L2-associated libration orbit

Pros:

Some orbits will allow the possibility of spending some time behind the Moon which can completely eclipse Earth. That might be quite helpful for certain space-based radio telescopes. For frequencies above something like 20 to 50 MHz Earth's ionosphere is fairly transparent and terrestrial RF noise may be a problem. For frequencies below that Earth's surface is blocked but Earth's ionosphere is going to be noisy naturally.

For further reading about strange-looking libration orbits in the Earth-Moon system (especially those that spend time behind the Moon) refer to:

By the way, according to Wikipedia's Queqiao relay satellite:

Queqiao relay satellite... is a communications relay and radio astronomy satellite for the Chang'e 4 lunar farside mission. As part of the Chinese Lunar Exploration Program, the China National Space Administration (CNSA) launched the Queqiao relay satellite on 20 May 2018 to a halo orbit around the Earth–Moon L2 Lagrangian point. Queqiao is the first ever communication relay and radio astronomy satellite at this location.

See also:

Cons:

I don't see eclipses of the Sun as a particularly bad thing. Eclipses are a big problem for SAR satellites observing Earth in LEO because they are very power-hungry (near-continuous multi-kilowatt radar beams) but a radio telescope receiver doesn't eat much. I think the biggest payload-specific power drain might be in the digital signal processing and digital recording which could certainly run on dedicated batteries for that purpose.

The Earth-eclipsing parts of the orbit would prevent communications or data links with Earth (ground stations or those in LEO) but not all the relay satellites in GEO, so I don't think there's a big downlink penalty.

Just for example TESS (as mentioned in @JustinBraun's answer only downlinks its space telescope images once every two weeks every 13.7 days! See also:

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  • $\begingroup$ space.stackexchange.com/a/56053/6944 $\endgroup$ Mar 6 at 19:19
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    $\begingroup$ @OrganicMarble I'm discussing a radio telescope here; bus and payload power needs could be an order of magnitude smaller than those of JWST and a chicken-wire dish won't suffer anything like the same thermal expansion/excursion issues that a cryogenic optical telescope mirror would (wavelengths are centimeters rather than micrometers) $\endgroup$
    – uhoh
    Mar 6 at 19:39
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    $\begingroup$ @uhoh Astronomical RF receivers are routinely cryocooled to lower their noise. The VLA receivers (1-50 GHz), for example, are liquid He cooled. In fact, Planck's HFI instrument (100-857 GHz) was the coldest known object in space, at 100 mK. Planck consumed 1800 W of power, Herschel 1500 W, compared to JWST's 1000 W, and even that wasn't paying for the full cooling load, as both relied on non-reversible He cooling. $\endgroup$
    – user71659
    Mar 7 at 5:45
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    $\begingroup$ @user71659 Interesting! Yes indeed the receiver usually is, but not the entire telescope (cf. Why doesn't thermal radio emission from a DSN "hot dish" completely swamp the benefits of a cold LNA?) and a few degree drift does not deform the optics and dramatically degrade performance the way it would a vis/near-IR telescope like JWST ("centimeters rather than micrometers") The Those are certainly big numbers for the older telescopes. As I said, "could be an order of magnitude smaller" if it were necessary... $\endgroup$
    – uhoh
    Mar 7 at 5:55
  • $\begingroup$ @user71659 but if not and one needs to refrigerate the LNA and process/record a Gbit/sec data stream for offline interferometry, then one would need to bite the bullet and use some batteries. Still Since JWST has a zillion little actuators to calculate and control for continuous wavefront adjustment while a radio telescope is mostly just static chicken wire and it doesn't need to be pointed and stabilize to sub-arcsecond accuracy, I don't think that a future system built with modern tech would need as much power as the JWST, actuators and gyros and all. $\endgroup$
    – uhoh
    Mar 7 at 5:58

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