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Lagrange points solved one of physics' biggest problems
- Traubenfuchs 5y agoIsn‘t it more of a lagrange... „membrane“? A complex, three dimensional bubble with zero thickness and very complex topology, formed by the infinite amount of lagrange points whereas there is exactly one lagrange point for the earth to each globe 2D coordinate?
- rich_sasha 5y agoIn the restricted three-body problem, where two massive bodies orbit each other in a circle, the Lagrange points are literally points - anywhere but the five exact 3d coordinates and there is a net acceleration away from your location. Not sure if that's what you mean, but if you're happy to assume that the massive bodies (e.g. Earth and Sun) are spherical, then you can exactly replace them with point masses, without approximation, so there's no multiplicity in Lagrange points coming from that. Of course, orbits are not circular, and there are external forces too - other planets' gravity, (tiny) orbital drag, solar wind pressure etc. so in practice it's all a bit different anyway.
- Traubenfuchs 5y agoI more viewed it as an all body problem, with the question always being: How far above my head is the lagrange point at some specific coordinates on earth? I mean, every earth coordinate (e.g. New York, Tokyo, etc.) has it‘s lagrange point, right?
- mperham 5y agoThis YouTube video about the Webb telescope’s orbital mechanics is fascinating, recommended. https://youtu.be/ybn8-_QV8Tg https://youtu.be/ybn8-_QV8Tg
- xtiansimon 5y agoGreat vidy. Total pop-science neophyte here. I found it very very interesting to hear about the work required of the “flight dynamics” team to keep the telescope in its orbit. Wondering how this project stacks up against other man-made orbiting bodies in this regard. Is there a set-it-and-forget it to Webb range of complexity story here?
- 8bitsrule 5y agoWow. The 6-month-long orbit around L2 is twice the size of the Moon-Earth orbit. Sure it's 4 times as far away. But still, with the Earth rotating, the comms calculations for these guys must be messy: [https://eyes.nasa.gov/dsn/dsn.html https://eyes.nasa.gov/dsn/dsn.html Deep Space Network]
- ncmncm 5y agoI thought I knew all about the Lagrange points, but then JWST took up an orbit around what was supposed to be an unstable one, and all I thought I knew went out the window.
- jakear 5y agoDo you place your telescope at the top of the mountain with boulders falling away from it in all directions or at the bottom of a crater with boulders falling towards it from all directions?
- burnished 5y agoThe latter. Adversity encourages strength.
- tux3 5y agoOne statement often applied to others, seldom for oneself. People don't choose adversity, they only like to dispense it.
- SideburnsOfDoom 5y agoPositioning of telescopes is about "how good is the view from here?" it favours hills, but that is not driven by the hazards. However the hazards up on hills are more typically those of exposure, altitude and isolation, not incoming gravitationally-propelled objects.
- robertlagrant 5y agoGiven Euler's insane genius, I'm amazed anyone bothered to even look to try and extend his work. Good for Lagrange.
- goldenkey 5y agoWell Lagrange was the OG of differential equations. A lagrange point is basically an area where the vector field of the DE is 0. You can see it better in this contour plot: https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Lagrange_points2.svg/1920px-Lagrange_points2.svg.png https://upload.wikimedia.org/wikipedia/commons/thumb/e/ee/La...
- Narishma 5y agoCan multiple spacecraft stay at the same Lagrange point? If not, what happens if two space agencies want to put something at the same point?
- caymanjim 5y agoSpace is big and you don't need to be at the literal "point". There are already plenty of things sharing them.
- nwiswell 5y agoSure. Being close to a Lagrange point doesn't mean you need _zero_ fuel, just a small amount. There's still the influence of the solar wind -- station keeping is inevitably necessary. As a result it doesn't really matter if a spacecraft is exactly at the Lagrange point or 100 km away from it, so there's no shortage of space. Also, this might be obvious, but it usually wouldn't make sense to park a spacecraft exactly at a Lagrange point because the spacecraft had to be moving in the first place in order to reach the Lagrange point. It would be a waste of fuel to slow down, so an orbit would typically be used instead.
- kryptiskt 5y agoBoth Gaia and Webb are at the same Lagrange point, but in completely different orbits around it (Here is a visualization: https://www.universetoday.com/155022/esas-gaia-just-took-a-picture-of-l2-neighbor-jwst/ https://www.universetoday.com/155022/esas-gaia-just-took-a-p...). There is a smattering of solar observatories at L1 too.
- jmyeet 5y agoObligatory XKCD [1]. Does anyone else find it fascinating how quickly things get complicated? As the article mentions, the three body problem is the classic example. For two bodies it's easy. Add just one more and there's now no general solution and you get a bunch of edge cases like Lagrange points. I too thought I understood the general principle of Lagrange points (including stability) but then JWST comes along and starts orbiting Earth's L2. [1]: https://xkcd.com/1356/ https://xkcd.com/1356/
- matheusmoreira 5y agoMaybe students should be playing kerbal space program in school...
- ngcc_hk 5y agoIt is Lagrange Mechanics that is great. L - V that means something and that is odd, unlike L + V the Hamiltonian which is conservation of energy. It is used also in quantum field theory due to its treatment of time, unlike Hamilton. That is very strange. But it works. Also, the principle of action is so odd (sort of Feynman Diagram but in classical world) you really just have to believe it instead of thinking too hard on it.
- codeflo 5y agoThe formulation that the forces “cancel out” at the Lagrange points bothers me, even though it’s not technically wrong. At each of the five points, there’s a net gravitational force towards the sun (to be more precise: towards the common barycenter). This is easiest to see at L2 and L3 where the gravitational forces pull in the same direction. There are now two ways to look at this combined gravitational force: 1. In an inertial reference frame (the one we imagine when we say the Earth revolves around the Sun), this combined gravitational force acts as a centripetal force. At the Lagrange points, it has precisely the correct value to keep the object in an orbit with period 1 year. 2. In the reference frame where Sun and Earth don’t move (that is, the reference frame that rotates at 1/year around the barycenter), every point experiences an apparent centrifugal force. At the Lagrange point, this centrifugal force cancels with the gravitational forces to keep the object stationary in this reference frame. The math is completely the same (x=y vs. x-y=0). I personally just find the first view to be more intuitive.
- sreevisakh 5y agoI occasionally come across this argument that there is no gravity on anything in space (orbit). Their reasoning is that the gravitational force is canceled out by centrifugal force. You could say that the forces cancel out, if you consider pseudo-forces like centrifugal force or Coriolis force as real forces. However, that view sometimes lead to very misleading notions like 'there is no gravity in space'. It also makes explanation of other phenomena like tidal forces needlessly complicated. For this reason alone, I discourage people from analyzing in non-inertial frames. Inertial frames make life simpler and clearer by removing caveats on Newton's second law. You no longer need to invent imaginary forces.
- stouset 5y agoI apologize for my ignorance, but how does one consider gravity a "force" from within an inertial reference frame? As I understand it, from the perspective of an observer floating in space inside the gravity well of a nearby object, that observer experiences no net forces. They experience acceleration from the perspective of an outside observer, but not from their own reference frame. A classic example is a person inside a falling elevator. From their own perspective, they're floating with no external forces acting upon them (until, of course, the elevator crashes into the ground). Only when the elevator is held stationary (from the POV of an external reference frame) does the occupant feel an acceleration force upward pushing back against the gravitational well they're standing in.
- musgravepeter 5y agoL4 and L5 are stable when the smaller mass is less than about 0.0385 times the larger mass [1]. This means e.g. a typical binary star system would not have stable L4/L5 points. The reference [1] works through this in careful detail and is an excellent reference on this topic. [1] Solar System Dynamics, Murray and Dermott, Cambridge University Press.
- throwra620 5y ago
- egberts1 5y agoI can’t help but wonder if the principle of Lagrange Points can also apply toward atomic orbitals.
- aw1621107 5y agoAs I understand it, atomic orbitals share only their name with the orbits of objects in space. The underlying mechanics are completely different, so the concept of Lagrange points would not transfer to the atomic realm. For example, look at the shape of the electron orbitals in a hydrogen atom [0]. These are not shapes one could reproduce using just gravity. [0]: https://upload.wikimedia.org/wikipedia/commons/e/e7/Hydrogen_Density_Plots.png https://upload.wikimedia.org/wikipedia/commons/e/e7/Hydrogen...
- egberts1 5y agoBut the principle of Lagrange Points (interaction of 3-body) could be expanded and then delve into n-body, and that too could apply to anything orbital, atomic including?
- aw1621107 5y ago> But the principle of Lagrange Points (interaction of 3-body) could be expanded and then delve into n-body Given that there's no known analytical closed-form solution to the unrestricted 3-body problem, let alone the arbitrary n-body problem, I think there are good reasons to be skeptical that such a generalization is possible. Not to mention the idea of a Lagrange Point arguably becomes iffy in such situations. For example, what might a Lagrange Point be for the figure-8 3-body orbit [0]? And how would you define Lagrange points for a chaotic system? > and that too could apply to anything orbital, atomic including? Not really. As I said, the name is pretty much the only common thing between atomic orbitals and orbits in space. The equations used to describe the motions of celestial bodies are completely inapplicable to the motions of subatomic particles. [0]: https://i.stack.imgur.com/xlWIh.gif https://i.stack.imgur.com/xlWIh.gif