L4 and L5 are stable; if an object there is perturbed, a restoring force will keep it in the vicinity of the point. This is different from L1-3, which are saddlepoints; if perturbed, an object will just keep on going away from the point.Vince wrote:To Kizarvexis
The L4 and L5 Lagrange points of the Earth-Moon system are not quite fully stable. When the Sun is included in the calculations, it takes very little disturbance for an object at the L4 or L5 Lagrange points to begin moving away from it. This makes sense since the Lagrange points can be thought of as 'higher' in terms of how much energy is required to reach them, with the nearby space being 'lower'.
With the Sun in the calculations, instead of an object being right at the L4 or L5 point, it is more stable to have the object in an orbit around the Earth so that from the point of view of an observer at the Lagrange point, the object would appear to be orbiting the point.
Vince wrote: An even better orbit would be a 2:1 resonance orbit around the Earth, with an apogee is ~200,000 miles and a perigee of ~100,000 miles. This orbit is completely stable, with an orbital period of slightly less than 2 weeks.
An orbit that sweeps out so much of the space around a planet is going to be inconvenient if you want to build a lot of other facilities there. I think most large objects are going to be in low-eccentricity orbits.