EDIT: I guess the assumption about basketball played on the moon is that most of us would watch that on television. But how much would a team have to make in TV advertising revenues to recover the cost of sending athletes to the moon and keeping them alive there? (A similar question applies to the costs of running the Olympics on the moon.) Ladies and gentlemen, those are fun jokes, but is this kind of joking response going to prompt anyone to invest their own money in a moon mission?
For one we could set up a lunar observatory.
Both of the space telescopes I mentioned are targeted for L2, which is well beyond the Moon's orbit, so there's no chance they'll de-orbit. I believe they use reaction wheels for pointing, not propellant, but as L2 is not stable, you're right that it needs some fuel for station keeping.
On the other hand, the Moon has quakes, and large temperature swings. Wouldn't that be much easier to set up an effectively stationary sunshield for the stillness of L2 instead? Plus, the Moon blocks out about 1/2 the sky, which seems like it might limit what you can do.
Sure :) But it's attaching something to a satellite rather than launching a satellite. After all, the moon is a satellite of the earth, but a natural one rather than an artificial one.
There has been talk of very large liquid based mirrors (limited in size on earth), the far side of the moon is free from radio interference from the earth and a bunch of other proposals. All of them were shot down based on a very simple observation: we don't have people on the moon, nor do we have a power plant or a way to install this stuff or assemble it out of pieces after landing it there.
But that might change.
"Really long term" on the Moon means dealing with moonquakes, which can last for more than 10 minutes. That's going to affect any baseline distances.
We can get a much longer baseline in space than on the Moon. LISA and DECIGO give some idea of how accurate we can expect to measure a baseline that is over 1 million km long. There's no way the Moon can match that baseline, if that's what you're looking for.
Labeyrie has proposed a 100-kilometer space-based 'Hypertelescope' that might be able to directly see continents on planets up to 10 light years away. I strongly suspect this is harder to pull off on the Moon, which has gravity, vibrations, and every-changing thermal stresses messing up the interferometry.
I think you are confusing two different telescope projects. Liquid-based mirrors are for optical telescopes, which aren't affected by radio interference. While there are proposals for 20m-100m liquid mirrors on the Moon, they have the big problem that they can't be pointed; it seems to be more cool than useful, as the lack of research for projects on Earth like the Large Zenith Telescope suggests.
While there's some advantage to using the Moon as a radio shield, the WP page at http://en.wikipedia.org/wiki/Far_side_of_the_Moon points out other difficulties in addition to the simple difficulties you pointed out:
> Before deploying radio telescopes to the far side, several problems must be overcome. The fine lunar dust can contaminate equipment, vehicles, and space suits. The conducting materials used for the radio dishes must also be carefully shielded against the effects of solar flares. Finally the area around the telescopes must be protected against contamination by other radio sources.
As an alternative, the radio telescope can be built in lunar orbit, as, for example, the OLFAR proposal at http://doc.utwente.nl/75270/1/Smallsat_final.pdf . This seems cheaper and easier than building a farside telescope and support infrastructure with the same capabilities.
Two questions: first, in a zero-sum model, why is human exploration of the moon more worthy than other similar unfunded projects? In an non zero-sum model, why is it worthy enough to justify growing the funding pie for science projects?
How many billions of dollars are there in "a little more effort", in your estimation?
It's not in either case in my opinion, and I would argue is it significantly less worth than those other projects.
Even if I can expand available resources because of the promise of these alternatives, or through reinvestment of gains, I still must choose what to do at any time, until I have enough resources to pursue all promising avenues simultaneously.