Rotating Mercury Lunar Observatory
Fraser Cain writes "Universe Today is reporting on a proposal under consideration by NASA from Dr. Robert Angel at the University of Arizona. He wants to build a 100-meter liquid mirror telescope into a crater on the Moon. It would only be able to look at a specific spot in the sky, but the view would bury Hubble's Deep Field Survey." The challenges of off-Earth construction are left as an exercise for the reader.
You mean something like this?
Sure, the LZT can only look straight up, but liquid mirror telescopes are being done, and done fairly well.
Part of the idea with a polar crater is to protect the instrument from temperature variations, something you would get a lot of on a monthly basis with a mirror anywhere else on the Moon. Tycho sits in sunlight for two weeks, then in darkness for two weeks. That's not a stable environment.
Also, a telescope made with a liquid mirror can be aimed in one direction only, towards zenith. Even the slow, monthly rotation of the Moon wouldn't allow for significant exposure times without motion blur, something you don't want when photographing distant galaxies spanning less than an arc second in the sky. The celestial poles are the only two spots in the sky that don't move around (they merely rotate), allowing for arbitrarily long exposures (the article suggests a year) using a camera synchronized with the sky.
If Celestia has the correct orientation of the Moon, the lunar axis points at constellation Draco in the northern hemisphere and at constellation Dorado in the south, the latter including the Large Magellanic Cloud. However, I don't know what particular deep sky objects would be visible using a telescope such as the proposed one at either pole.
If it changes density on 'freezing' that will cause distortions, probably bad enough that the surface is no longer very reflective. I tried it with wax once, and the main problem was that the edges froze first, which caused ripples in the rest of the surface.
u id_metal/liquid_metal.html
There's also a not-very-toxic alternative to mercury for anyone who wants to try building a small LMT; Gallium/Indium/Tin alloys which are liquid at room temp.
http://www.scitoys.com/scitoys/scitoys/thermo/liq
Cthulhu loves you.