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A Lagrange Point is something that occurs in a system of multiple gravitational pulls, like that of the Earth and the Moon. These points occur in any two-body gravitational system. This of course means that Lagrange points exist in the Earth-Moon system, as well as in the Sun-Earth system. These points in the system are gravitationally neutral, the force of gravity is the same in all directions such that there is no net force exerted in that part of space.
There are always five Lagrange Points in any of the systems described above, and they are all designated L1-L5. If an object were to be placed at a Lagrange Point it would (in theory) remain there indefinitely. However, out of the five points, L1-L3 are unstable, and require adjustments in order for an object to remain in place. And in 1956, large amounts of dust were found by the Polish astronomer Kordylewski at the L4 and L5 Lagrange points of the Earth-Moon system. In relation to the two bodies in the system in our case, the Earth and the Moon, an object at a Lagrange point would either have to continually adjust its position, or find a way to deal with the dust that would constantly be pounding it.
Because of this stability, Lagrange points are usually used as the locations for Space Colonies in the Gundam universes.