>>9860587Produce it on the Moon, and it doesn't have to weigh a lot to begin with. We obviously wouldn't start off colonizing the Moon by building a space elevator, it'd be overkill and a waste of resources better spent building habitats. However once the Moon is populated enough and there's enough back and forth travel between the two worlds to justify a space elevator, we'd explore building one at that point.
L1 is 56,000 km above the near side of the Moon. If we want to do the extended cable design for making Earth transport easier, then we'll round that up to 75,000 km.
Steel is an acceptably strong material to make a space elevator cable on the Moon. To make the calculations easier I'm going to assume a starter cable diameter of 1.12 mm, because a section of this cable 1 mm long has exactly one cubic millimeter of volume. 75,000 km is 75,000,000,000 mm. Conveniently, that means there's also 75 billion cubic millimeters of steel in this cable. That works out to 75 cubic meters of steel, which would weigh 588,750 kg or 588.75 metric tons.
So, if BFR can deliver up to 150 tons of cargo to the Moon per flight, that means four BFR flights can deliver the entire mass of steel needed for the cable to the surface of the Moon. Alternatively, and perhaps more effectively, a single BFR could deliver a 150 ton spool of cable with 1/4 the cross sectional area but the full 75,000 km length directly to the L1 point, which could then be lowered via unspooling from a purpose-built satellite with the help of a plumbob down to the Moon's surface. We would then have a very thin but functional space elevator in place.
The second step would be to produce additional steel cables on the surface of the Moon and lift them via the original cable, and build up the combined thickness of each steel thread until significantly large masses could climb the cable into orbit. Each additional thread could be thicker than the individual ones preceding it.