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==Earth–Moon==
[[Image:Lagrange points Earth vs Moon.jpg|thumb|right|300px|A diagram showing the five [[Lagrangian point]]s in a two-body system, with one body far more massive than the other (e.g. Earth and Moon). In this system {{L3}}–{{L5}} will appear to share the secondary's orbit, although they are situated slightly outside it.]]The only two stable Lagrange points are {{L4}} and {{L5}}. They are stable provided that the mass of the primary body (e.g. the Earth) is at least 24.9599 times the mass of the secondary body (e.g. the Moon)<ref>{{cite web|last1=Fitzpatrick|first1=Richard|title=Stability of Lagrange Points|url=http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node126.html|website=Newtonian Dynamics|publisher=
An {{L1}} station would have a number of important functions due to its stationary position between the [[Earth]] and [[Moon]]. It is in an excellent ___location to monitor and coordinate communications among various missions on the nearside of the Moon. A vessel launched from L1 could reach any place on the Moon within a few hours to a day. This would make it ideal for crisis management if an emergency occurred on the Moon. Furthermore, it could serve as a way station, especially once built up, and would probably be used to handle tourists and casual visitors to the Moon. A station like this could also serve as a repair center for ships moving throughout the [[Solar System]].
The {{L2}} point, on the [[far side of the Moon]], is completely shielded from Earth by the Moon so [[radio telescope]]s placed there would receive much less interference than existing telescopes. Of course, since the Moon is [[tidally locked]], any colony on the [[far side of the Moon]] has this same benefit; a lunar facility, however, would suffer from [[Moonquake]]s.
Both L1 and L2 require active [[stationkeeping]] since neither is fully stable (they are [[saddle point]]s on the energy landscape). Colonies at the {{L4}} and {{L5}} positions would have the advantage of being stable without any need for stationkeeping, and could be used as a waypoint for travel to and from [[cislunar space]].
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