I never did take the geosync rope seriously. Hence Paul Birch and his orbital ring, with Kevlar (or Zylon). Tonight I've been alerted to the selenosync rope. Unlike the cables to the Galapagos or Nairobi lifts, Elon promises to talk with us about Sinus Medii's cable.
Luna doesn't exactly have a "LEO" like our GEO but she does share with us a (t)LL1. (And L2, darkside.) Also see Jeremy Hsu from 2019.
First problem: 'tis halo. One could stationkeep it with aluminum/oxygen thrusters, but that seems likely to dust up the region. "Gamma Factor" notes a better idea: that this Luna-focused rope will need a counterweight, as we're pulling toward the Moon whenever we use it. That's another rope dangling toward Earth - the Spaceline.
GEO is uninhabited by space-stations today. Only unmanned sats float there. So shall GEO ever be.
The spaceline does not dip into our GEO unless GEO hosts an orbital ring, which it probably won't ever. The idea is that the Earthside point of the counterbalancing tether get its own little station, mostly just a hook for the (long) pull up to L1. From GEO to this hook requires a little boost through vacuum. Which shouldn't be that bad compared to getting from Earth to GEO in the first place. In fact small cargo might be possible by railgun or spinlaunch rather than rocket.
REWRITE 7/20/23 - ugh this poast "GEO space-stations won't happen" was baaad. I've redone it.
ABOUT L2 5/18/24 - This poast left alone what to do with the far side of the Moon and, three years later, I'm still stumped. Its tangential delta-V against the ecliptic is too powerful for anything out to Vesta. It can lob parts of a longterm-transport at (say) Ceres, to be assembled en-route. So... maybe that?
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