kengr

Given the amount of construction (and maintenance) likely required, a lunar base is probably easier.

Hmmm. I know treaties say that Luna can't be claimed by a nation. I wonder what they say about claiming *part* of it? Much less a lunar base or colony declaring itself an independent state?

Then again, if it's an alternate timeline, they may have been there *before* the treaty. :-)

An "educational" channel giving info about various parts of the moon might be popular. Especially if there's an observatory at Farside base.

A large mirror array would be fairly easy to build (assuming you have the people and tech to build things on the moon in the first place). And a multi kilometer radio dish in a crater ought to be doable as well.