There’s obviously a singular, ideal Lagrange point, but I would assume there’s something like a practically viable sphere around it where you would benefit from the advantages.
Given the vast distances, I would assume that this viable sphere is sufficiently large to accommodate more than enough man-made space infrastructure.
L4 and L5 are way out from the Earth Moon system and are very stable. They collect natural satellites, and once parked there you would remain indefinitely.
The actual math is pretty complex, and has to do with mass ratios of bodies involved, but all the major bodies in our solar system have their own Lagrange points.
True
> The point is relatively close to the moon, and changes enough to not collect natural bodies.
This is awkwardly written. Let's get some background first: the Lagrange points are derived by assuming the Moon's orbit around the Earth is circular. In actual fact it's elliptical, so the distance from the Earth to the Moon changes and consequently the distance from the Moon to L2 changes. The distance from the Earth to the Moon averages 384,400km and at that point L2 is 64,000km away from the Moon.
But the reason no natural bodies (like asteroids) collect around L2 is because it's unstable, not because it moves.
> L4 and L5 are way out from the Earth Moon system
L4 and L5 form an equilateral triangle with the Earth and the Moon, meaning they are (on average) 384,400km away from both the Earth and the Moon at any given time.
> and are very stable.
No, they are "meta-stable." If you drift away from L4/5 you will not be drawn back to the Lagrange point itself, but you can orbit those points without extra fuel. We see asteroids gathering at Sun-Jupiter L4/5, so that suggests they are weakly stable, but when you do the linearized stability analysis of those points you find that they are neither stable nor unstable.
> The actual math is pretty complex
It is. I made an effort to create some educational videos on the topic: https://www.youtube.com/watch?v=8q9in-VfpUM
https://en.wikipedia.org/wiki/Kordylewski_cloud
I believe you’d have to avoid the point itself and orbit around it.
Edit: apparently, there are two Earth Trojans:
https://en.wikipedia.org/wiki/List_of_objects_at_Lagrange_po...
But JWST orbits the Sun Earth L2 point, so the moon is not directly involved. Of course it influences, but it’s different than the Earth Moon L2.
> Webb orbits around L2; it does not sit stationary precisely at L2. Webb's orbit is represented in this screenshot from our deployment video (below), roughly to scale; it is actually similar in size to the Moon's orbit around the Earth! This orbit (which takes Webb about 6 months to complete once) keeps the telescope out of the shadows of both the Earth and Moon.
A glass bead at the bottom of a bowl is in a stable equilibrium, if you shake the bowl side to side it'll come back at the bottom. A basketball spinning on your index finger is in an unstable equilibrium, it stays there while the conditions are met and any small deviation will make it fall
L2 is called unstable above. So orbiting around it instead of hovering immediately at it should be like trying to spin a ball slightly off the tip of your finger. E.g. you wouldn't want to do it.
Sibling replies have proper explanations.
https://en.wikipedia.org/wiki/File:Lagrange_points2.svg
The idea of plainly stable and unstable points only happen if you have rotational symmetry, and doesn't really apply to most of the points. Leading the discussion on those terms isn't productive.
It orbites in a plane where it's always subject to attraction, but that doesn't mean the point always attracts the satellite.
Like I said, since you can't place a satellite perfectly in practice, its motion will always be a combination of the 3 modes, and eventually the unstable mode will dominate and the satellite will move away from L1/2/3. BUT, if you get the math right you can position the satellite so that most of its motion is in the oscillatory mode (i.e. orbiting the point), and then as it drifts into the unstable mode you nudge it back to the oscillatory mode with a thruster firing.
For context, the amount of thruster firings necessary to keep the ARTEMIS probes around Earth-Moon L1/2 was about 5m/s per year.
What about the opposite - how feasible is it to "control" a Lagrange point even if you wanted to exclude other equipment?
At minimum, you need weapons coverage over a complete sphere about the point you want to protect. If your claim is larger than your spacecraft, you need multiple in a 3D perimeter.
But even supposing you had enough weapons, it would take much more effort to destroy all the shrapnel before it hits you.
And even then, if someone decides to throw something very heavy at you very fast, there's sweet FA you can do about it. If I throw a big satellite or a ship into a kamikaze vector at you, your one and only option is to move out of the way as fast as you can. Even if you hit it with all your weapons at once, you still have almost as much mass flying at you almost as fast, but now it's buckshot instead of a cannon ball.
It really isn't practical to defend any amount of space, not even a planet.
Controlling a Lagrange point would have to be a political mechanism. You can't really physically enforce it in space. You'd end up fighting wars on the ground over a point in space.
If the Lagrange point is indeed unstable the random movement should be rather efficient to achieve. And kinetic weapons would need luck to hit you. For explosive weapons you might be able to rely on the gatling guns.
It seems to me like the Lagrange points might be one of the few things in space you could occupy and deny an enemy. Perhaps LEO should added to that because it can be hit from the ground.
> An L2 orbit is unstable, so JWST needs to use propellant to maintain its halo orbit around L2 (known as station-keeping) to prevent the telescope from drifting away from its orbital position.[186] It was designed to carry enough propellant for 10 years,[187] but the precision of the Ariane 5 launch and the first midcourse correction were credited with saving enough onboard fuel that JWST may be able to maintain its orbit for around 20 years instead.[188][189][190]
[1] https://en.wikipedia.org/wiki/James_Webb_Space_Telescope