Will there be a space elevator before 2060? Earth or Lunar
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Will there be a space elevator attached to either the Earth or the Moon by 2060? It doesn’t need to support a heavy payload, but it needs to be a continuous structure from the surface of the Earth to beyond geostationary orbit. In the case of a lunar space elevator it needs to attach to the lunar surface and extend beyond the L1 Lagrange point between the Moon and the Earth.

Note the tensile strength requirements for a lunar space elevator are less than a terrestrial space elevator.

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I did some rough math. The Earth space elevator needs something like carbon nanotubes while the lunar space elevator is at the limits of what carbon fiber can do. This is with slim to no factor of safety.