Normally liquid mirror telescopes depend on having some amount of gravity to work correctly (the liquid needs to pool in a certain way). There's workarounds to

Normally liquid mirror telescopes depend on having some amount of gravity to work correctly (the liquid needs to pool in a certain way). There's workarounds to do this in space but it gets really complicated. Other issues with space based telescopes: They need fuel + thrusters to go where you want them to be (or just to maintain their orbit!) Heat dissipation is a big problem. Being able to use the whole moon as a thermal flywheel could help out a lot. In space you can use things like cryocoolers to regulate temps, but they cause vibrations which can be problematic if you need your telescope to remain steady. If this requires refrigeration, you can put the vibrating parts far enough away from the telescope that they don't move it. Putting the thing in a crater probably helps regulate temps too (less direct sun) Humanity in general is better at building and maintaining things on solid ground. If you drop a bolt on the moon, you lean over and pick it up. If you drop a bolt in orbit, you have to worry about it damaging your spacecraft at the next conjunction.