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Conquering the LaGrange Points?
3laws_safe writes "For decades, people have dreamed about building colonies at the five LaGrange points, intersections in space where gravitational and centrifugal forces balance out to provide orbital stability. But now, the official magazine of the U.S. Space Command advocates seizing control of the LaGrange points before other nations do it. From the article: 'We face the need to control the chokepoints of the solar system.' Arthur C. Clarke, who depicted a LaGrange colony in his classic 1961 novel A Fall of Moondust, is not very happy about this. He argues we should not 'export national rivalries beyond the atmosphere.' Is he right? Or should we prepare for the fact that such rivalries are inevitable, even in space?"
L1 and L2 are unstable on the timescale of 23 days.
L3 is unstable on a timescale of 150 years. That is, it's pretty stable for satellites, just not for planetary bodies. Of course, it also happens to be a friggin' useless orbit, as it never has line of sight visibility with Earth.
L4 and L5 are stable, so long as the mass of the larger object is greater than 24.96 times the mass of the smaller object. (Yes, it's really that odd number: it's actually 25*((1+sqrt(1-4/625))/2) ).
L4 and L5 are actually strange. They don't act like classical stability points, like most people think. If you push something away from L4/L5, it doesn't come back to L4/L5. It does, however, begin to orbit L4/L5, and those orbits are stable.