Editing Lunar space elevator (section)

==Location==
There are two points in space where an elevator's docking port could maintain a stable, lunar-synchronous position: the Earth-Moon [[Lagrange points]] {{L1}} and {{L2}}.  The 0.055 eccentricity of the lunar orbit means that these points are not fixed relative to the lunar surface : the {{L1}} is 56,315&nbsp;km +/- 3,183&nbsp;km away from the Earth-facing side of the Moon (at the lunar equator) and {{L2}} is 62,851&nbsp;km +/- 3,539&nbsp;km from the center of the Moon's [[Far side (Moon)|far side]], in the opposite direction.  At these points, the effect of the Moon's [[gravity]] and the effect of the [[centrifugal force]] resulting from the elevator system's synchronous, [[rigid body]] rotation cancel each other out.  The Lagrangian points {{L1}} and {{L2}} are points of unstable gravitational equilibrium, meaning that small inertial adjustments will be needed to ensure any object positioned there can remain stationary relative to the lunar surface.

Both of these positions are substantially farther up (from the Moon) compared to the 36,000&nbsp;km from Earth to [[geostationary orbit]].
Furthermore, the weight of 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, or be topped by a much more massive counterweight.
Suspending a kilogram of cable or payload just above the surface of the Moon in the direction of the {{L1}} point  would require 1,000&nbsp;kg of mass as counterweight in an orbit 26,000&nbsp;km closer to Earth as {{L1}} is.
(A smaller mass on a longer cable, e.g., 100&nbsp;kg at a distance of 230,000&nbsp;km — more than halfway to Earth — would have the same balancing effect.)
Suspending a kilogram of cable or payload just above the surface of the Moon in the direction of the {{L2}} point would require 1,000&nbsp;kg at a distance of approximately 120,000&nbsp;km from the Moon as counterbalance (more than 51 thousand kilometer further away from the Moon as the {{L2}} point, almost 59 thousand&nbsp;km when the {{L2}} point is closest to the Moon).
These 1,000&nbsp;kg would be in an [[orbit]] around Earth with the same [[orbital period]] as [[Orbit of the Moon|the Moon]], yet its mean orbital radius would be almost one third larger as that of the Moon and the [[centripetal force]] to keep it in such an orbit would equal the [[Gravitation of the Moon|weight of 1&nbsp;kg at Moon's surface]].

The anchor point of a space elevator is normally considered to be at the equator. However, there are several possible cases to be made for locating a [[lunar base]] at one of the Moon's poles; a base on a [[peak of eternal light]] could take advantage of near-continuous solar power, for example, or small quantities of water and other volatiles may be trapped in permanently shaded crater bottoms. A space elevator could be anchored near a lunar pole, though not directly at it. A tramway could be used to bring the cable the rest of the way to the pole, with the Moon's low gravity allowing much taller support towers and wider spans between them than would be possible on Earth.