The American Museum of Natural History is planning an exhibit on the future of space exploration. We are promised authentic old equipment, models, a walk-through diorama of the Martian surface, and information on current space probes.

So far, so good.

They are also offering a "full-size recreation of a lunar habitat" (can you recreate things that don't yet exist?) and a model of a space elevator.

That much is on the web page. The museum newsletter, Rotunda, specifies that this hypothetical space elevator would run from the surface of the moon to about 100 miles above Earth's surface. Passengers or cargo would travel that last 100 miles by spaceplane (which presumably could be launched to connect to wherever the cable is hanging at a given time).

The lunar end of the cable is supposed to be at the South Pole, because there's likely to be water there. That a south pole base makes sense doesn't make it a good anchor point for a space elevator. Yes, there's a lot to be said for a base near the most likely source of water, but that doesn't mean it's a good place to anchor a space elevator.

Furthermore, one of the arguments for building this thing is that it would be a way to get Helium-3 to Earth. Yes, space elevators in the service of nuclear fusion.

The article is by the exhibit curator, Michael Shara, who is described as an astrophysicist. A quick google tells me that his work is on things like the dynamics of dwarf stars. Also, the most recent of the "recent publications" that the museum lists for him is from 2000. He may have been studying engineering and materials science in the decade since, and it's possible that the exhibit will talk about the strains that the elevator cables would need to take, but I am not optimistic. That said, I may go, just for the space hardware.
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