So first we'll have to find a natural depression or we should create one. I understand you can only see a single portion of the sky since it can't be moved, so my money is on creating an artificial basin in an area where directly upwards it has the best view of the sky.
Imagine if we can build a 1000 m optical telescope like that. We'd be able to see exoplanets directly. We'd be able to see ancient galaxies. Even a 200 m one like this would do wonders. Are there any proposals?
The surfaces of telescopes need to be configured to a fraction of a wavelength. If one is working in the FAST wavelength range of 10 cm to metres, then that is a relatively straightforward engineering problem, even over a km diameter. However, the difficulty and expense ramp up enormously when the working wavelength is 500 nm. This would entail the construction of literally millions of precisely configured mirror segments to tile the inside of the structure and then some way of pulling them all into position and alignment (and keeping them that way) with a precision of 10 nm or so.
It helps that you aren't going to move the primary, and you can still track objects for 1-2 hours by having instrumentation at a movable focus. However, a second big problem is that the air above the mirror is turbulent and the size of the turbulent cells is much smaller than the size of the telescope. To take advantage of its large size, in terms of angular resolution, the individual parts of the telescope have to be individually controlled/deformed at a continuous rate of $\sim 100$ Hz. It is probable that to get the tenfold increase in resolution implied by the much larger diameter of this telescope would require higher frequency and more precise adjustment.
This sort of engineering is going on for effective mirror diameters as large as 39-m, but comes at a billion-Euro cost. Scaling up to something ten times bigger would almost certainly be a two order of magnitude increase in cost. So although there may be no show-stopping physics, it would cost about as much as all other astronomy research combined.
Large interferometers, with sparse arrays of telescopes, are a much more likely proposition but come with their own very difficult problems.
Why can't we build a huge stationary optical telescope inside a depression similar to the FAST?
Of course @ProfRob's answer is correct. If the crater were on Earth under Earth's atmosphere you'd have to probably build a zillion segments and use standard adaptive optics to both:
However, you could kill two birds with one stone by building in a giant crater on a low gravity body like the Moon at 0.16 g, or even Ceres at 0.03 g.
I don't know if you could get to even 200 meters right away, but the 2nd or 3rd iteration might do it if there was some reason to.
Inside the crater you would build a support for the mirror, but you'd really be supporting a race track to hold a concave basin in which a liquid compatible with vacuum would be added.
If you spin it fast enough, the liquid will climb the walls and assume a parabolic shape with a thickness of order a millimeter, and smooth out the imperfections in the support.
This is where low gravity comes in; the lower the gravitational acceleration, the lower angular rate at which you'd need to spin it.
The mirror technology described in Angel et al. 2008 is a spinning thin layer of an organic ionic liquid on to which is evaporated a thin silver surface. There is no spinning mercury in this proposed instrument, to be built on one of the poles of the Moon.
Texas Astronomers Revive Idea for ‘Ultimately Large Telescope’ on the Moon
ApJ: Angel et al. 2008: A Cryogenic Liquid-Mirror Telescope on the Moon to Study the Early Universe and arXiv
Abstract
We have studied the feasibility and scientific potential of zenith observing liquid-mirror telescopes having 20-100 m diameters located on the Moon. They would carry out deep infrared surveys to study the distant universe and follow up discoveries made with the 6 m James Webb Space Telescope (JWST), with more detailed images and spectroscopic studies. They could detect objects 100 times fainter than JWST, observing the first high-redshift stars in the early universe and their assembly into galaxies. We explored the scientific opportunities, key technologies, and optimum location of such telescopes. We have demonstrated critical technologies. For example, the primary mirror would necessitate a high-reflectivity liquid that does not evaporate in the lunar vacuum and remains liquid at less than 100 K. We have made a crucial demonstration by successfully coating an ionic liquid that has negligible vapor pressure. We also successfully experimented with a liquid mirror spinning on a superconducting bearing, as will be needed for the cryogenic, vacuum environment of the telescope. We have investigated issues related to lunar locations, concluding that locations within a few kilometers of a pole are ideal for deep sky cover and long integration times. We have located ridges and crater rims within 0.5° of the north pole that are illuminated for at least some sun angles during lunar winter, providing power and temperature control. We also have identified potential problems, like lunar dust. Issues raised by our preliminary study demand additional in-depth analyses. These issues must be fully examined as part of a scientific debate that we hope to start with the present article.
A telescope capable of reaching these limits has been proposed, for example, by Angel et al. (2008) in the form of a cryogenic liquid-mirror telescope on the surface of the moon. However, as the authors mention, a liquid mirror might face some challenges, as it is unclear what effect lunar dust would have on the instrument and the observations.
To avoid an articulating mount, the telescope would be placed at the lunar pole, constantly pointing at the zenith. To assure thermal isolation, it would be located in the permanent shadow in a lunar crater. The limit on exposure time is then given by the precession of the moon, and is of the order of several days. This can only be extended by the addition of some active tracking facility, for example a moving prime focus platform. However, to reach the sensitivities we require, a mirror diameter of 100 m is necessary. We note that Angel et al. (2008) do consider mirror sizes of 20 up to 100 m in their preliminary design studies. While 100 m is evidently challenging, it is within the realm of possibility for mid-century technology.
The proposed mirror uses an ionic liquid rather than a real liquid metal (e.g. mercury or some other eutectic). Nobody balks as using mercury because it might evaporate, because we have some sense that at low temperatures (e.g. room temperature) those of us who are old enough might have played with a bit in school presumably in a glass dish or at home from a broken thermometer, and remember that it just sits there; it doesn't boil away and nobody was worried about breathing vapor from it.
That's because the vapor pressure of mercury at room temperature is only of order $3 \times 10^{-7}$ atmospheres and the evaporation rate is low. We would not do such things today, but we have at least seen images if liquid mercury in air and don't think of it as evaporating quickly, and have heard of spinning mercury telescopes and mercury based barometers with one end exposed to atmosphere.
Going even somewhat below room temperature the vapor pressure and evaporation rates of mercury plummets.
It turns out that ionic liquids even those based on organic molecules can have similarly low vapor pressures in the regime below room temperature and above their freezing points.
An ionic liquid (IL) is a salt in the liquid state. In some contexts, the term has been restricted to salts whose melting point is below some arbitrary temperature, such as 100 °C (212 °F). While ordinary liquids such as water and gasoline are predominantly made of electrically neutral molecules, ionic liquids are largely made of ions and short-lived ion pairs. These substances are variously called liquid electrolytes, ionic melts, ionic fluids, fused salts, liquid salts, or ionic glasses.
So because their constituents hold each other due to strong ionic forces, many of these liquids can have very low vapor pressures and evaporation rates at room temperature and even lower at reduced temperatures still above their freezing points. These temperatures are readily available in space environments; as long as sunlight is appropriately shielded, radiative cooling to space allows access to cryogenic environments.
Angel et al. 2008 says:
Borrowing from techniques used to coat solid mirrors on Earth, we conducted a number of experiments coating a variety of liquids by vaporizing silver on their surfaces. A recent article (Borra et al. 2007) summarizes our recent efforts. We successfully coated an ionic liquid with silver. Coating an ionic liquid was a major breakthrough because ionic liquids have negligible vapour pressures and thus do not evaporate in vacuum. We experimented with a commercially available ionic liquid that solidifies at 175 K and we are actively pursuing ionic liquids with lower freezing temperatures. There is a realistic expectation of success because ionic liquids are organic compounds and there are at least 106 simple ionic liquids, and 1018 ternary ionic liquid systems (Borra et al. 2007), giving a phenomenally wide choice for optimizing the properties of the liquid substrate.
Borra et al. 2007 can be found in Nature: Deposition of metal films on an ionic liquid as a basis for a lunar telescope and also accessed in researchgate
click images for larger size
left: "Figure 1. Experimental vapor pressure data for mercury." Source: NIST Internal Report The Vapor Pressure of Mercury NISTIR 6643 (also here) and right: Source Don't do this!
See MIT's discussion of the dangers of mercury exposure in Mercury
There are various effects that mess up optical telescopes (for visible light). The primary effect is the atmosphere "wiggle" due to the motion and varying density of air. This is what makes stars twinkle. Assuming the telescope is state of the art and the mirror is a perfect parabola within 1/10th wavelength of light (not so hard to achieve actually). The next and lesser effect is the bending or sag of the mirror under gravity. The very large telescopes have computer controlled jacks under the mirror for tiny stress adjustments as the telescopes moves to point around the sky. Then big telescopes have adaptive optics and 100 times a second push on the mirror to bend it just "so" to compensate for atmospheric wiggle. Another effect is the mirror temperature. If the glass expands as it warms up it deforms the mirror. This is compensated my making the mirror of a very precise mix of glass and other things like quartz, so the expansion is zero. You still have to let the telescope "cool down" to night temperature before doing anything serious with it.
So lets just get around all those issues and put the telescope in space where there is no gravity (effectively) and is no air.
Then you have the problem of lifting the telescope to orbit and keeping the temperature stable. Which can be done. The current best is to launch the telescope with the mirror in hexagonal pieces and have motors bring the pieces together and then use little jacks to get it perfect. Difficult because you have to test every thing on the ground in gravity first, but it can and is about to be done.
Then you go bigger. For a while the limit is just what you can launch, assemble in orbit and pay for. When the mirror get very big the difference in gravity in orbit across the mirror adds stress. A solution is to put the telescope not in Earth orbit but out past the Moon's orbit or even in Solar orbit. As you get up to 1km in diameter and orbit the telescope out past Pluto the bending of light due to gravitational influence and relativity kicks in. So seeing oceans, continents and rivers on a planet ten lightyears away is still not possible, but you can get close.
The Universe simply is not that smooth over interstellar distances.
Put another way, stars are so far away the human mind has no intuition for such distances. The stars are not just "far away", they are so far you can't imagine it.
See this for a cool comparison of distances. https://blair.pha.jhu.edu/scale.html
Another reason that doesn't seem to have been mentioned is that many telescopic observations need long exposure times. For instance, the Hubble Ultra Deep Field took just under 1 million seconds (about 11 days) of cumulative observing time: https://en.wikipedia.org/wiki/Hubble_Ultra-Deep_Field. If your telescope basically rotates with the Earth, you can't keep it pointed in the same direction for any length of time.
