Lagrange Points

Mathematically they are points, by definition: you solve a system of equations and you find the equilibrium solutions, which will have all three coordinates constant, hence they are 0-dimensional solutions. You can put a three dimensional body in there (with small mass, definitely not a space station) and make sure its center of mass coincides with the Lagrange pt, then the body will be stationary.

You got me wondering. While they are solutions to equations, they extend over an area that varies with the size of the orbitting masses. Then I found this: "But that doesn't mean these places are completely boring. In fact, there are dust clouds at L4 and L5. They're about four times as big as the Moon. They're very wispy and insubstantial, but they've been photographed a couple of times. In 1990 the Polish astronomer Winiarski found that they are a few degrees in apparent diameter, that they drift up to ten degrees away from the Lagrange points, and that they're somewhat redder than the usual "zodiacal light" - the light reflecting off dust in the solar system." http://math.ucr.edu/home/baez/lagrange.html

So there something larger than the point. I would suggest that you do a search for more information.

Well, mine was a purely mathematical POV...

I understand, but LaGrange points also have physical aspects.

Kenny said:

I've done a brief amount of research into the L-points around Earth however I cannot seem to find answers to a couple of questions.

1st how big are L4 and L5
2nd can multiple space stations be housed there without bumping into each other (I guess yes (depending on the size) as they would orbit the outside of the Lagrange points).
3rd are the L-points 3d or 2d (this could be answered by Q1 I guess).

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You mean if something at the point is disturbed in any dimension, will it tend to back to the point? Yes, I would certainly think so. There would be a distance or perhaps more correctly an 'escape velocity" at which an object won't come back. I'm speculating that velocity might be different in different directions, but it would take a lot of research, or math, to find out. The escape velocity would of course be determined by the other two masses involved.

Kenny said:

4th any other information about L-points that might be interesting or useful for a semi-hard Sci-Fi.

Thanks in advance,
Kenny

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One point already mentioned is that there's already 'stuff' there, as it's a small gravitational well in space and random things will get caught in it. There have also been asteroids/rocks observed in Jupiter's orbit at the L points ahead and behind Jupiter's location. And of course the other planets (the ones not part of the L points) perturb the locations, just as they perturb one another's orbits.

ETA: Yes, with several space stations at a point, they would probably be "orbiting" one another very slowly so they don't hit. And even so, they would have small jet engines to occasionally adjust their orbits, much like satellites in geostationary orbit do. Unless they go zombie.

benbradley said:

One point already mentioned is that there's already 'stuff' there, as it's a small gravitational well in space and random things will get caught in it.

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The stable ones would, yes. It appears though that three are unstable and hence if you put a mass in there it would indeed stay put but escape at the smallest perturbation. Those would not be attractive wells.

ETA: This is a nice website:

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/lagpt.html

The figure shows which ones are the stable points and how a mass would orbit around them, in which case I suppose it would be feasible to have two different stations on different orbits around the two pts. So, what you mean to ask, is not how big these points are, but rather the radius of the limiting orbit, ie the largest orbit you can find around the equilibrium point. The unstable ones, I wouldn't recommend for that!!!

Your space stations would still have to be very small with respect to the Moon, or else you end up with an additional gravitational mass in there...