Lunar space elevator
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The lunar space elevator (also called a moonstalk) is an analog to the better known space elevator idea (a cable suspended above the Earth, with its center of gravity in geostationary orbit). It would instead be constructed with its center of gravity in a stationary position above the surface of the Moon, providing a controlled means to transport people and/or materials between the surface and lunar orbit.
A lunar elevator could massively reduce the costs for reliably and cheaply soft-landing equipment on the lunar surface. For example, it permits the use of mass-efficient high impulse/low thrust drives such as Ion drives which otherwise cannot land on the Moon. Since the cable would possess a microgravity point, these and other drives can reach the cable from low Earth orbit (LEO) with very minimal launched fuel from the Earth. With conventional rockets, the fuel needed to reach the lunar surface from LEO is many times the landed mass, thus the elevator can slash launch costs by a similar factor.
Location
There are two lunar-synchronous points where the elevator could be placed that would be stable: the Lagrange points L1 and L2. L1 on the Earth side of the Moon is 56,000 km up from the surface, and L2 on the far side is 67,000 km up. In these positions, the forces of gravity and centrifugal force equalize, and as long as the system remained balanced, it would remain stationary.
Both of these positions are substantially farther up than the 36,000 km from Earth to geostationary orbit. Furthermore, the limb of the cable system extending down to the Moon would have to be balanced by the cable extending further up, and the Moon's slow rotation means the upper limb would have to be much longer than for an Earth-based system. To suspend a kilogram of cable or payload just above the surface of the Moon would require 1000 kg of counterweight, 26,000 km beyond L1. (A smaller counterweight on a longer cable, e.g. 100 kg at a distance of 230,000 km – more than halfway to Earth – would have the same balancing effect.) Without the Earth's gravity to attract it, a cable anchored at L2 would require 1000 kg of counterweight at a distance of 120,000 km from the Moon.
Fabrication
Because of the Moon's lower gravity and lack of atmosphere, a lunar elevator would have less stringent requirements for the tensile strength of the material making up its cable than an Earth-tethered cable. An Earth-based elevator would require materials at the edge of what is theoretically possible (e.g. carbon nanotubes), whereas a lunar elevator could be constructed using high-strength commercially available materials such as Kevlar or Spectra.
Compared to the Earth, there would be few geographic and no political restrictions on the location of the surface connection. Due to the lower gravity, the connection point of a lunar elevator would not necessarily have to be directly under its center of gravity, and could even be near the poles, where (some controversial evidence suggests) there might be frozen water in deep craters that never see sunlight; if so, this might be collected and converted into rocket fuel.
Jerome Pearson has proposed a cable design using M5 fiber that would weigh only 6,800 kilograms (not including climbers and other equipment) that would be capable of lifting or depositing 200 kilograms at the lunar surface; such an elevator could be sent to the Moon in a single shot using the largest existing launcher designs. It would be an extremely minimalist cable; the design is intended to be strengthened and expanded over time using materials taken from the lunar surface.