Lagrange Points and other Trojan Ramblings
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- Опубліковано 31 сер 2014
- In which I discuss the Lagrangian points. What they are, where they are and how to apply them to a fictional setting.
Artifexian on the Interweb:
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Lagrangian points:
en.wikipedia.org/wiki/Lagrangi...
Lagrange Point Calculator:
orbitsimulator.com/formulas/La...
Standing on the Shoulders of Giants:
arxiv.org/abs/0810.3192
Building the Ultimate solar system (PlanetPlanet):
planetplanet.net/2014/05/13/bu...
Just to be clear Nibiru is 100% not a thing!!! - Розваги
I was just looking for the band "Lagrange Point", but this is interesting.
I guess it is quite off topic but do anybody know a good site to stream newly released tv shows online?
You could put parking garages for starships at L1 and L2
Probably L2. I don't wanna have to live in the shade of a giant space station that's constantly in the sun
You know, normally I'm not a fan of the name Edgar but I actually like it on you. I think your voice and accent fits well with it.
Accent? Dialect!
@@-arche-7926 eh
@@MohammedAli-hl4mr ?
The most likely theory for the creation of the moon is a mars sized planet in the L4 or L5 point of the earth sun system, which later collided with the earth due to gravitational disturbances from venus.
After watching the video, I've been curious. The Lagrange points shed light on why Jupiter has two groups of asteroids in its orbit, but it's also apparent that their accumulative mass would have almost no influence on the gas giant.
Are trojan planets possible? And how many could there possibly be?
Is it feasible to have a binary planet system that orbits a star? Or even a planet system above binary?
Are trojan planets possible?
Yes
How many could there possibly be?
Perhaps 2, one at L4 and the other at L4. But the more planets you stick in an orbit the more contrived the system becomes and the less likely it is to crop up in nature.
Is it feasible to have a binary planet system that orbits a star?
Yes. Pluto and Charon are effectively a double planet system.
Or even a planet system above binary?
Not really but at a huge stretch you could perhaps have a double planet system with a double planet system at L4 and another double at L5. This is super super contrived but "technically" plausible.
Artifexian Those are surprising thoughts.
Though the reason I ask is because I want to create an intriguing solar system; one that is almost identical to ours, but where Theia, the theorized rouge protoplanet that collided with Earth to create the moon, instead entered a double planet system with our home.
Would that be extremely contrived as well? Would either planet be inhabitable?
I know that the planets would have to orbit a significant distance away from each other to avoid collision, radical warping, and life-ending tsunamis, but I'm lacking the research to calculate all that.
So if it's alright, I'd like to nominate a "Worldbuilding | Double planet system" video.
+Artifexian Would a planet located in a L4/L5 point also have its own collection of Lagrange points?
+D.C. Williams I think that such a planet would have the L1 and L2 Lagrange points and the Langrange point in which its companion planet is. I think that L3 and L4/L5 won't be Lagrange points, but that there will be new ones for the combined system of the two planets.
@@Artifexian Pluto**
Not entirely sure why, but I love Lagrange Points. Great video!
Yes! Lagrange points are awesome. Been brain-cracking this one for a quiet awhile. Glad you enjoy. Thanks for watching!
Artifexian Good vid man keep up the good work
RoboKing77 It's always very gratifying when a 77th generation cyborg monarch likes your videos :)
Thanks for watching. Means a lot.
+Artifexian could you explain what the capital m means in v=sqrt GM/r
I think that given the vastness of space and the sheer amount of stuff out there, there is probably at least one system with legrange 4 and 5 planets
3:22 oh no, debt rays... :P
SuperLlama53 my dad gets hit by them a lot!
I've seen a video once that tried to explains how in minecraft, sun and moon are always oposite, if it was a solar system with a sun, wnd earth and a moon, nothing else, so what if the moon in minecraft is at L two?
It pretty much has to be at L2 in order to remain antipodal to the sun in the sky.
Lapis Septo Flufftail even then there would be variability, as objects do no sit still at Lagrange points. They orbit them
@@blackoak4978 but this doesn't change anything in this case does it?
I didn't realize you did a video on Lagrangian points.
There's a reddit page based around a futurist tech and every now and than they talk about Lagrangian points and that stuff just went over my head.
Great video, as always!
Cheers, sir. Glad you enjoy and thanks for sharing.
Small correction: you displayed the gravitational force equation as G=m1m2/r^2. Where G is the universal gravitational constant m is a mass value and r is the radius between the two bodies. The equation should be Fg=Gm1m2/r^2 where Fg is the force of gravity. Still a great video! Keep up the great work!
Nice work!
Love your videos Edgar! I have a question though, isn't a planet offset by any distance but in the same orbit co-orbital? And if so, what's special about the L4 and L5?
Why are there no points between L1 and L4/L5? Surely there are points where the gravitational pull for the earth and the sun are the same besides those three... It appears to me is would form an arc and even extend round to meet L2 like a kidney bean shape.
I am wondering just how the L4 and L5 would be situated in eccentric orbits?
As excellent as this is in explaining the use of Lagrange points in worldbuilding, it's a bit short on the clarification of exactly how the gravitational forces create the relevant effects.
I have yet to find a video that does a good job of that for the nonspecialist.
Anyone have any suggestions for any that you've found, here at YT or (heresy, I know) elsewhere?
You said "geologically" stable, it's more accurate to either "gravitationally" or "physically"
By geologically he means "for geological times"
It would be delightful if you would explain the Barycenter is a center of mass and that It is a “circle”.
Two linked questions here:
1. Can you have objects of similar mass to the main body at L4 and L5?
2. If so, what's to prevent a recursion where these things of roughly equal mass to the earth at L4 and L5 from having their own Lagrangian systems, with earth at their L5 and L4 respectively, and something wrist in their other Lagrange points? Other than a degree of implausibility for the amount of mass needed to build such a system, is there anything stopping a solar system from having several rings of roughly equally massed objects sharing interlocking Lagrangian orbits?
I don't think I explained that second one well...
1. No, you cannot. When the objects at L5 start to become close in mass to the main planet (the threshold is at about 50 to 100 times less massive, so about the ratio between the Moon and Earth), the system becomes unstable and is at risk of breaking down. That means in practice, you cannot have anything larger than the Moon in a long term lagrange point around a planet like Earth.
wow this is amazing
Could you stack those Lagrange co-planets to have a ring of planets around a star, each in the L4 and L5 points of their neighbors?
L4, the planet and L5 form one third of a perfect hexagon, so with six objects, it could work out. These planets would even match up with L3
don't get your hopes up with Pluto, the IAU specifically made an exception for bodies at L4 and L5.
Amazing work, Artifexian! I really wish I'd had all this to hand years ago when I started my own little project. I just had a question. I'm trying to develop an S-type system in which a habitable planet orbits the secondary star. I was wondering - with binary systems orbiting a barycentre, what's the likelihood of those two stars - which cross each other's orbit - coming so close that that they disrupt each other's planetary system?
+Subodhana Wijeyeratne That depends on how close the stars get to one another. It also has to do with the Roche sphere or Hill sphere and the Roche lobe. Essentially the farther they are out the better off your planets will be, I think he gave a good estimate in a previous video, I think building Anti-Tatooine.
Interesting video, pretty sure someone would take advantage of it to have a Pandora (or using the Star Wars analogy, Yavin) style world but without the whole radiation and planetary rotation i.e. day and night as per a gas giant moon.
Though it would be useful to note that for a stable world to inhabit a lagrangian/liberation point long enough to house life, let alone sapient life, the total mass cannot exceed a certain limit or else get a Giant Impact ala Thera and Earth. I can't exactly remember, but on the GURPS/Steve Jackson forum when I posed the inquiry it was like the total mass cannot exceed 1% of the secondary body, I can't really recall clearly.
I don't think that 1% figure is exactly correct. In "Worldbuilding - A writers guide to constructing star systems and life supporting planets", Stephen L Gillet puts that figure at about 4%. But the book is old, published ca 1995, so those figures may be out of date and I'm more than open to being corrected here.
Thanks for watching btw glad you found it interesting :)
Artifexian Just looked back at the thread that I started on the Steve Jackson forum and it WAS 4% but for the primary mass but with the addendum in which for stable Lagrangian Points 4 and 5 the ratio between the two bodies is 25:1.
The details of said discussion is here (pray for my fingers, I'm doing this on an Android Smartphone) forums.sjgames.com/showthread.php?s=962c604c395a043c3d38996d15f6a853&t=67196
But I think, personally, aiming for the low end of that particular spectrum would be more prudent unless corrected otherwise with more up to date calculations, data, and whatnots.
Though now I can't help but wonder if it wouldn't be impossible for that Trojan/Greek Earth of said gas giant to have a moon or even a Co-orbital world via barycenter as well. Though more than likely not possible due to Orbital disruption, but it's an entertaining thought none the less.
As for what to call "planets" with co-orbitals? *shrugs* I don't know, Lagrangian Bodies/Planets?
Sabersonic I think, in any world governed by logic, we would have to call them planets. It seems a no brainer to me. But somethings "definition by committees" can become messy.
Thats really interesting about the 25:1 mass ratio. Haven't come across that before and I'm really glad you filled me in :)
Also that thread you linked is very interesting too. I hope others read your post and check it out. Very helpful stuff.
And yes, I think giving yourself a margin of error with regards to selecting values when worldbuilding is always a good idea.
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Plausibility aside would it be possible for 6 planets to form a circle in eachothers L4 and L5 points?
4:46 - Sad face :p
“trojan ramblings”
as a notre dame fighting irish fan, i approve of the name of the video
Can the gas giants still have terrestrial moons if they have lagrange planets?
Given the right conditions could a double binary star system hold 16 habitable planets? 2 on the edges of the habitable zone per star. Then 2 planets at Lagrange 4+5 per planet?
Idea: but a high albedo moon at the L2 point and you'll get an everlasting blood moon.
At 3:22, that object at L3 looks like Centerpoint Station.
So...hypothetically, could the planets at the Lagrange points also have their own Lagrange points that could be filled in with planets or satellites?
For those here who don't know Star citizen uses Lagrange points for stations its cool
If only worldbuilding was a multiplayer game. It would be soo fun!
In the calculator, why is there three results for Lagrange Points 4 and 5 respectively?
4:37 And so would Ceres. Remember Ceres. #CeresIsAPlanetToo
I think you got the universal gravitation equation a bit messed up, it should be F = GM1M2/r^2. In order for G to be on the left hand side it would have to be a ratio of F/G. In order to isolate G you would have to express the equation as F(r^2)/M1M2 = G
Is it possible for multiple L4 and L5 to be created via multi planet being in the right place? So the string worlds system be real?
In short, no.
Lagrange points are by their very definition entities that exist in a 2-body system, preferably where one body is negligibly light in comparison to the other.
If there are more significantly heavy bodies in the vicinity, then we have a 3-or-more body problem, which in the world of astronomy is nothing short of infamous for being notoriously difficult to solve, especially if we're looking for stable solutions.
Talking about stability, in a 3-4-and so on body systems, stable points (like L4 and L5 in *2 body problem*) certainly exist, but usually only temporarily or in specific conditions and they are fundamentally not the same thing as Lagrange points.
so, in theory a ring of planets can orbit at the same distance from a star, and stabilise each other, but it would be convoluted as hell and could be easily collapsed?
Are there points where the gravitational forces of 3 bodies are all balanced? So for the Earth Moon Sun system, are there any points where you would have equal gravity from the earth, the moon, and the sun? And are any of these points stable?
Caters Carrots the earth-moon system has lagrange points that aren't influenced by the sun. The james web space teliscope is going to sit on the moon's L2 point
Just to clarify, L1/2/3 have nothing inherently unstable about them. We reside in a system with several large bodies (like Jupiter) that severely mess with those Lagrange points. These also interfere with L4/5, but to a much smaller degree. In simple system with just one star and one planet, and no other significant amounts of mass, L1/2/3 should be just as stable as 4 or 5.
At least, this is my understanding of the mechanics. If I am wrong, somebody please tell me why such a system would still result in unstable L1/2/3.
Also, you say that anything at a Lagrange point will orbit at the same speed as the Earth (or whatever given body). While true for 3/4/5, this isn't technically the case for 1 and 2. I believe you meant to say that they have the same orbital PERIOD as the Earth. And since they all have the same period then L1 actually travels slower because it has a shorter distance to cover, and L2 faster because it has a longer distance to cover.
Could a sun have 6 planets in the same orbit, sitting in each others lagrane points
Ok, so small Earthlike worlds, outposts, satellites, stations... these are great and all, but I'm thinking a bit more out of the box here... What about a massive Lagrangian point large enough to contain a stable gas cloud, this Lagrangian point may also contain several captured asteroids with perhaps ice, or amino acids. This Trojan world is entirely made of an expansive atmosphere and does not contain any planetlike objects larger than a small moon. The goal is to allow stable life is possible and cultivated in this Lagrangian space within a gas cloud.
What I'm seeking is a visual image of such a world. Would it be a place containing multiple asteroids covered in plant-like life, seeming to appear like floating islands? How about a spiral of rotating gasses orbiting a moon? A nebula of life? What would a Trojan world look like?
would it be possible for there to be Dwarf planets at the L4 and L5 points of an earth like planet?
+NeilSonOfNorbert Maybe 1 at L4 or L5, it's more unlikely for there to be one at L4 and L5 as the points assume the bodies at them are of a negligible mass and so the larger the body, the less true that holds. However if you separate them by 120 degrees, and only have 1 at L4 or L5 then its much more likely according to this paper. adsabs.harvard.edu/abs/2010CeMDA.107..487S
How do you draw so fast?
Lmao!
Could the Earth-Sun-Moon system have a Luna-Sized object at L4/L5?
For that matter, how does the presence of the gravitational impact of our Moon effect the stability of the various Lagrange points?
+D.C. Williams If you want to consider the Earth-Sun-Moon system, reduce the Earth and Moon to the Earth-Moon system which would be a theoretical body with all the mass of the Earth and Moon orbiting the sun at the barycenter of the Earth and Moon (which is at around 3/4 of the distance from the center of Earth to the crust if I remember correctly). That might be able to sustain a Moon-sized object at L4 or L5 without becoming unstable, but it is more unlikely, but most certainly not if you want one at L4 or L5. It might be better to separate the two bodies by 120 degrees rather than 60 degrees according to this adsabs.harvard.edu/abs/2010CeMDA.107..487S. Also any body that is a moon instead of a double-planet system would have little effect on the Lagrangian points and certainly near none on the stability other than increasing the mass of any theoretical stable object at L4 and L5.
Lagrangian brachistochrone course set
Is this the wrong time to point out that the idiom is "for all intents and purposes"?
1. Would the Lagrange Points work with a p type system?
2. Can L4 and L5 both be filled with planets of similar mass to the secondary?
3. Since L4 and L5 are at a 60 degree angle, could there be up to six bodies in one stable orbit?
+Clayton Krumm 1. I think so if you use use the barycenter as the center of mass for the stars, though its a bit more tricky as the Lagrangian points more or less assume a near-perfect circular orbit like most of our solar system and a p-type system would probably have more elliptical orbits.
2.The Lagrangian points assume that anything stationed at them has a mass that is negligible to compared to the two bodies. So for the Earth-Sun system you can only have objects up to large asteroids or maybe small moons occupy those points. Though a small moon could potentially be habitable, but it'd be a stretch.
3. If you look at the last link you can find out that because of the previous reason that this really isn't possible with similar mass objects, but if you don't have anything occupying the secondary position and instead have two similar mass objects in the same orbit about 120 degrees from each other, that actually is fairly stable.
Thank you very much
Lagrange points are a specific case of the three body problem, based upon the assumption that the third body has negligible mass compared to the second-most massive body. If the mass of it is substantial, then you're in the as-yet-unsolved portion of the three body problem.
For (3), see en.wikipedia.org/wiki/Klemperer_rosette
3:00 Readin taxicab number in wikipedia ? , why 5 times ?
Lagrangian Positioning System, to detect where a spacecraft had been on a solar system
Origin aside, could a system with six planets in the same orbit, each at each-others' Lagrange points, be stable? Assume each planet is earth-like. Would this affect the planets' L1 and L2 points? What other affects would this have on the star or planets? how would these planets appear to each other?
*****
How would it be unstable? I'm not asking why, I get gravity, but in what way? As far as I know gravity is fairly uniform and legrange points seem to be a way to work with gravity instead of against it. Would it be because of the movement of six planets on the same orbit affecting the stars? Or do legrange points require objects to be smaller than each other?
Remember, origin aside, we can have whatever celestial engineers we need as long as its the planets and their gravity that maintain stability, not some leftover technology.
Thomas Jenkins It would only be stable if it was just the star andthose 6 planets. Any other bodies, even if they where as far as neptune would eventualy collapse the orbits. This would only happen if was engineered tbh, also the planets would need to all have the same mass and rotational speed, and no moons. It's not an ideal setting.
So, you have a terrestrial planet. At that planet’s L4, there’s another terrestrial planet. The first planet is at the second’s L5, right? Could you then continue this all the way around an orbit with six(?, guessing that because 60° from planet to star to L4) planets in a single orbit?
Each iteration the moon has to be at least 50 to 100 times less massive than its parent planet otherwise it is too massive to be stable, and you can't have that much of a mass difference between two habitable planets, so no. However you could imagine a habitable planet that's in a gas giant's lagrange point, and that gas giant could then have one or more habitable moons, for example.
I have a question: does the barycentre orbits around the sun too?
Neveind i understand now
Did you buy Bitcoin around the time you made this clip? How'd that work out for you mate?
For orbit simulator, I need masses of the planets, but I only have the distances, bcs he didn't say anything about the weight of the planet.
At what degrees would the L4 and L5 planets appear in the sky? I imagen that they would appear to sit on both sides of the sun.
More like barely above the horizon
Well, they form equilateral triangles so they would be almost exactly 60° east and west of the Sun.
And also the habitable planet has one big moon and a smaller one further out
Kordylewski Dust Satellites?
An important thing to point out is that objects do not sit still at Lagrange points, they orbit around them
Wouldn’t gravity cause light from behind the sun to become visible on Earth? How come some stars are only visible during solar eclipses?
The lensing effect of the sun's gravity on light is measurable, but absolutely tiny, and it only has a noticeable effect on stars that are very near the sun, so stars that couldn't otherwise be visible outside of a solar eclipse.
Anyone notice the war face at 4:44?
I'm sorry what?
Wow
Wait, how are objects at L1 orbiting at the same speed as Earth? In the drawing you show, Earth covers more distance than objects at L1 in the same time frame. More distance in the same time frame = higher speed. So L1 is orbiting slower than Earth?
Maul009 Their orbital *period* sync up, not their orbital speed.
But if a planet orbits via another's Lagrange point, surely A) that new planet has its own Lagrange points, but more importantly B) it would have it to be so that it orbited at the same speed? I mean, for a real-world example, look at Theia; that didn't turn out well.. Although assuming that would never happen, I suppose it would be one way to have a planetary system with more than one planet in the Habitable Zone.
Probably why you recommended having space-stations and the like there instead?
When I mentioned keeping station with the earth, I was essentially referring to a Lagrangian object orbiting at the same speed as earth.
Lagrange points are a gravitational by product of a two body system. So its unlikely a lagrangian/trojan object will have stable L points 'cause its no longer a three body system.
Yup, habitable worlds at L4 and L5, and for extra life in the habitable zone stick space habitats at L1, L2 and L3
Artifexian Just so I understand this, lagrange point bodies are lagrange points in their nature and not just in relation to the whatever they are the lagrange point of? So, you couldn't have 6 bodies orbiting every 60 degrees as an l4/l5/actuallyaplanet all in the same orbit?
***** So what's actually going on here is a thing called the restricted three body problem. Wiki it for info. But in short, as the name implies you need 3 bodies (sun, planet + L-point object) anymore and gravity becomes messy and things probably wont be stable.
+empty If you had 6 bodies in the same orbit, the only way I could see that working would be if they were going much faster than what one would normally expect from their orbit. Since they would all receive the same amount of gravitational attraction to the sides as well as to towards the other planets it might be feasible. Any other number besides maybe 2 under special conditions, and it's not even remotely plausible. They'd mess up each other's orbits too much.
+Trevyn Case However, it'd be nigh impossible for a six-body orbit to develop naturally.
You know, this vesio is ekstremele helping
Naughty Greeks get sent to Jupiter's L4 lagrange point
"A planet is any object in orbit around the Sun that is dominant in its immediate neighbourhood."
That is the third criterion for the IAU definition of a planet. A planet has not cleared out its orbit, rather it dominates its orbit. Being that Lagrange points depend on a two body system it follows that the two important objects are (in this case) the Earth and Sun. And any Earth Trojan asteroids would not be cleared out from the Earth's orbit, but they WOULD be dominated by the Earth's orbit. Not Earth Trojans and the Earth happily sharing an orbit symbiotically together. Rather the Earth deigning to allow Earth Trojans to call Earth's orbit their home at the whim of the Earth.
Pluto does not dominate its orbital path. It is in fact dominated by the orbit of Neptune. Not in a Lagrange point, but in a 2:3 resonance. A resonance that is shared by MANY Kuiper Belt objects because Neptune dominates the outer solar system. And in addition we've found many other Kuiper Belt objects that are nearly the same size as Pluto, and AT LEAST one that is bigger, Eris. And we're finding more and more. The only difference between Ceres and Pluto is that the other asteroids were discovered mere months after Ceres was discovered. And the other Kuiper Belt objects were discovered decades after Pluto. Pluto has found a home that suits it better than hanging out with the rest of the terrestrial planets. Leave it be!
Aaaaaaand I just saw the video where you say all that. Hahaha.
why should L3 be unstable? because if, earths (erts :D) orbit would be unstable aswell as for l3's vison the earth is l3 aswell, and thus Unstable.
L1, L2, and L3 are saddle points in the effective potential field, which means a body placed there could wander off without gaining or losing energy.
en.wikipedia.org/wiki/Lagrangian_point#Mathematical_details
zenon space station or space stay maybe ?
Yup! May well happen
Artifexian, when you drew the street signs, you wrote these:
Jupiter
Saturn
Mercury
Venus
Nibiru
WHY DID YOU WRITE "Nibiru"???? THAT'S THE MYSTICAL "Planet X"!!!!! AAAAAAAAAAAAAAAAA- err420: planetX.exe has stopped working
ERROR ERROR ERROR
ERROR 69
The explanation of L3, L4, L5 did go a bit too fast for me. I still don't understand those Lagrange points.
L2 seems useful for a hubble telescope 2.0
+-Double Negative- Yes. That is why they are putting the James Webb Space Telescope there. It is not quite a Hubble II, but it is close. Look it up, it is cool.
And in the same system there's a super Mercury a Venus the planet Mars like planet two dwarf planets one like cerer and another one like Pluto
Little bit of news here, the ESA launched a satellite X-ray telescope destined for L2
I'm the 1700 person exactly to like this video. Signature look of superiority
So Side 3 in Gundam would be just fantasy? ooh...
this is Asap's job.
2:31 You speak of vertices, but the singular of vertices is one VERTEX. Not vertice.
How much make a habitable planet the distance of Earth and it's habitable put a gas giant at one of the L4 points put a habitable Moon around that gas giant
We should get the IAU to account for Lagrangian planets so we can get this over with so either (a) we rule out the possibility of it making Pluto a planet (and nobody hopes it does) or (b) it somehow makes Pluto a planet again (...cyclocentri-gravito... I don't know) and everyone is happy (the idiots because they got their arbitrary name back, the smart people because it makes the definition better and doesn't classify it as a planet arbitrarily).
An object of sufficient mass at a Lagrange point will already be classified as a dwarf planet due to the fact that it has not cleared it's orbit
If you were to put an Earth-size planet at L4, would that mean that Earth is at this planet's L5?
yes
Josh Maleszewski Ok, thanks!
1:32
equidistance so grown up
Taxi!
Yup. :)
I will call you spaceman because you know a lot about space
Lagrangion space stations > colonizing mars
Unnerving at best
NCC 1749... USS Langley, not USS Enterprise. Still, both are constitution class, so still valid. Nice Easter egg.
L1, L2, L3 are unstable! Just like the Ringworld.
C-C-C-CHECK YOUR PARADIGM!!!
it's called earth... earttthhhhhhh... wtf is "ert"