How precisely you need to ‘park’ on a Lagrange point?

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.

Seems to be quite roomy, at least at 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.

https://jwst.nasa.gov/content/about/orbit.html

If L2 is unstable, how can you orbit around it? Is it a point of attraction? If so, how is it not stable?

It's a point of equilibrium, a point of equilibrium can be stable or unstable

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

You just basically restated the problem, and given no explanation for L2 specifics.

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.

Wikipedia for the help:

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.

L1, L2, and L3 have 3 "modes" associated with them, where "mode" refers to what happens to a satellite placed near those points with just the right initial conditions (position and velocity relative to the point). Since you can't place a satellite perfectly in practice, its motion will always be a combination of the modes, but in theory the 3 modes are: stable, unstable, and oscillatory.

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.

IIRC JWST is not actually at the Lagrange point, but it drifts a bit, and occasionally fixes itself.

A sibling comment to yours points out that it actually orbits the L2 at the same distance the moon orbits the Earth and takes 6 months to complete a revolution.

Yes, the orbit isn't exact / perfect/ stable either [1].

> 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

L2 is unstable, so you need some amount of active thrust to stay in the orbit. The point is relatively close to the moon, and changes enough to not collect natural bodies. Same with L1 and L3. Once the James Webb runs out of fuel it will leave the point quickly, probably within 30 days.

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.

> L2 is unstable, so you need some amount of active thrust to stay in the orbit

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

My understanding is that earth-sun L4/5 also collect; not asteroids but dust

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...

I was confusing points using the Earth and Moon and those using the Sun and Earth. You are right in a given system the points draw an equilateral triangle.

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.

Does this mean that you don't need to occupy the centers of L4 and L5, but could instead orbit them at a smallish distance?

Seems clear from references in other comments that the usable sphere is large enough that Lagrange points can be "shared" by many parties (within most conceptions of current equipment size and interference).

What about the opposite - how feasible is it to "control" a Lagrange point even if you wanted to exclude other equipment?

At best, wildly impractical.

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.

Wouldn't a randomly moving platform with 4 gatling guns on there give full-sphere coverage and defense against passive weapons by the random movement? You have fuel issues, but that can be solved by rotating shifts, or (vulnerable) in-place refueling.

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.

I believe you can even orbit a Lagrange point.

There's no military value to the Lagrange Points. This is posturing, and a pointless waste of public resources.

- "ensuring the United States is the first country to permanently station assets at all Lagrange Points"

(I did look into the report to see if what reasoning they offered, but the whole thing's juts three lines of the 53-page document. I'm convinced this is some throwaway joke—I believe zero intelligent thought went into this).

It’s not a scientific document but a political one. By mentioning china and military threat the House can build support for funding defense contractor space spend.

Always two there are, no more, no less. One to fill parking orbits at the Lagrange points and the other to crave them.

Five rings he made for the Lagrange points, in their halls ever above Arda

Perfectly balanced, as all things should be.

still looking forward to the Call of Duty objective:

"Hold the Lagrange Point until reinforcements arrive"

Is there a Burger Town there?

"Ramirez! Get me an Orbital Shake! And keep your head down!"

>I'm convinced this is some throwaway joke—I believe zero intelligent thought went into this

"Briefly stated, the Gell-Mann Amnesia effect is as follows. You open the newspaper to an article on some subject you know well. In Murray's case, physics. In mine, show business. You read the article and see the journalist has absolutely no understanding of either the facts or the issues. Often, the article is so wrong it actually presents the story backward—reversing cause and effect. I call these the "wet streets cause rain" stories. Paper's full of them. In any case, you read with exasperation or amusement the multiple errors in a story, and then turn the page to national or international affairs, and read as if the rest of the newspaper was somehow more accurate about Palestine than the baloney you just read. You turn the page, and forget what you know."

-Michael Crichton

there's still strong points and week points in journalism and journalists.

science and tech journalism are definitely less likely to tell a compelling story with the existing facts and coherently.

what's more likely happening is dumbing down certain expert information to the perceived idiots.

> * science and tech journalism are definitely less likely to tell a compelling story with the existing facts and coherently.*

Why do you believe this is limited to these two areas?

Because science and tech journalism requires a certain knowledge of science and technology, but people who want to go into journalism generally don't study those topics and aren't interested in them.

Science journalists often do have a scientific background, like Ed Yong for example (MPhil Biochemistry).

There are some great ones out there, particularly at ArsTechnica, but there are also journalists working at mainstream newspapers who are sent/told to cover some tech/science thing and presumably they do their best but they end up out of their depth and just put something together to meet the deadline.

^ This.

My wife was a high level reporter in DC covering the White House and even traveling with POTUS at times (locally via motorcade, never on Air Force One). I can't count the number of times she'd call and say "I have a 3pm deadline.. what do you know about X?"

The number of reporters who have special training or specific background within a beat are exceptionally small. They're there but they are NOT the norm.

I have seen some political journalism first hand (in a micro cosm, not the big world stage) and I saw how wrong journalists can get details sometimes. That was even without assuming a bias of the journalists involved, which is more often present than not.

Anyone who’s played Civ 6 already knew this…

Thank you for this important remark; we will be deleting this redundant article shortly.

Oh, I've seen this anime. Didn't end well for Sydney.

Lol. They aren't really points. They are regions, massive areas. Most sats don't even park at the mathematical point but slowly "orbit" it. Literally millions of sats could live out there without ever seeing each other. Just like geostationary slots, this isn't about real estate rather radio spectrum. And even that problem will start going away as laser connections become the norm.

If you want hardcore, no-hand-waving math explaining the Lagrange points, see here: https://www.youtube.com/watch?v=8q9in-VfpUM

OR, this is a psyop against our enemies to get them to spend money and waste resources on something useless.

That was done frequently against the Soviet Union.