Talk:Lagrangian point/Archive 1
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Arbitrary section header
Perhaps someone could generate a diagram of the various points?
While I was staring at the lagrange points diagram, I realized that the diagram resembles a large "peace sign". Has anyone noticed this? I wonder if the concept of "balance" (of gravity) that the lagrange points represent was borrowed to also represent peace.
Does anyone have any knowledge in this area? What do you think about adding a short sentence or two on this resemblance?
- Jamie E (USA)
- Jamie, your question is a common one but the resemblance between the Lagrange point diagram and the peace symbol is only coincidental. The peace symbol is a superposition of the flag semaphore symbols for 'N' and 'D' and form the acronym "ND" for *N*uclear *D*isarmament. That these two semaphore symbols for N and D were encircled is no mystery either as many sigils exploit the symbolism of the circle, and the peace symbol was certainly an embodiment of the peace movement as such. Cheers, Astrobayes 04:54, 15 July 2006 (UTC)
That would be lovely, but I'm restricted to ASCII here and I'm not about to start fiddling with slashes and backslashes and capital letter O's all afternoon :P -- Paul Drye
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- Not exactly what you had in mind, I know - but I wondered if this would be any good for the page (it's NASA so presumably public domain, I havent seen anything contradicting that posted anywhere) - http://map.gsfc.nasa.gov/m_ig/990529/990529b.jpg --Si42 01:10, 31 January 2006 (UTC)
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- Template:PD-USGov-NASA says it is okay, and I think it'd be a useful picture to have, for instance in the Stability section. -- Jitse Niesen (talk) 15:42, 31 January 2006 (UTC)
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The paragraph
- The Earth's companion object Cruithne is in a somewhat Trojan-like orbit around the Earth, but not in the same manner as a true Trojan. It has a regular solar orbit that is bumped at times by Earth. When the asteroid approaches Earth, the asteroid takes orbital energy from Earth and moves into a larger, higher energy orbit. When the asteroid (in a larger and slower orbit) is caught up by Earth, Earth takes the energy back and so the asteroid falls into a smaller, faster orbit and eventually catches Earth to begin the cycle anew. Epimetheus and Janus, satellites of Saturn, have a similar relationship, though they are of similar masses and so actually exchange orbits periodically.
is fascinating information, but has nothing to do with Lagrangian points or Trojan objects. Whither should it be moved?
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- Which class of asteroids is Cruithne in and do we have a page for it?
- Put back in the "but differing" that Xaonon took out. It's a critical part of the definition!
Are you sure? I'm fairly certain that two equal masses orbiting each other would result in libration points as well -- a binary star system, for example. -- Xaonon
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- Well, technically you get them, but without the mass difference you lose the fundamental quality of an L-point: stability. Unless...
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- Mass A is "substantially" larger than mass B -- by about a factor of 30.
- Mass C, at the libration point, has essentially no mass in comparison to both A and B.
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- ...the points aren't linearly stable and can't hold anything. Basically, the centre of gravity of the system must be pretty close to A or it doesn't work. See J.M.A. Danby's "Fundamentals of Celestial Mechanics" (I think) where the ratio is discussed. -- Paul Drye
Take "differing" out! Even if the above is true (which I doubt, at least for L1, L2, & L3), the intro makes no sense with "differing" when you consider the two "slightly differing" cases. It would have you believe the L points vanish at the point mass equality is passed. It's just nonsense.
And the idea in the intro that two masses combine to form L points is just lousy English, which amounts to more nonsense if you don't read between the lines.
And the intro fails to mention the important point that bodies at the L points are not at all in equilibrium, unless they have a certain velocity. Such bodies must be inserted into their L orbits as any orbital body must be.
This is my first and last contribution to the Wikipedia, as I see below that contributions must be licensed under the GNU FDL, which has proprietary features that require me to be less liberal than I normally care to be.
---
Very good article, but I think the explanation as to why L1 L2 and L3 are unstable compared to L4 and L5 needs to be clearer. If you map the gradient fields for these points you'll notice that L1 L2 and L3 are at the top of hills but L4 and L5 are at the bottom of a depression, im not sure why that is but I think it is an expanation as to why objects would stay in their holes.--ShaunMacPherson 07:11, 10 Mar 2004 (UTC)
- No, L1-3 are at saddle points in the pseudopotential field, while L4, L5 are at the tops of hills. (follow the external link to a pretty picture of the field.) Objects at 1-3 can just wander off, while staying at the same level. Objects at 4 and 5 fall down the hills, but then the Coriolis force kicks in, and keeps them in orbit around the Trojan points. –– wwoods 09:34, 25 Mar 2004 (UTC)
- In Lagrangian mechanics, a Lagrangian point is…
I changed this opening sentence to In celestial mechanics…, basically because:
- The old definition suggested that Lagrange points emerge uniquely in Lagrangian mechanics. But Lagrange points are a physical phenomenon, independent from the theories or formalisms you use. They exist in Newtonian mechanics and in general relativity just as well.
- While not actually a tautology to the insider, it may look confusingly so to an outsider. The old definition might have been true, but didn't really explain anything.
- It makes sense to define a concept in the context of a wider, more generally known concept. Celestial mechanics meets that criterion better than Lagrangian mechanics does.
—Herbee 00:15, 2004 Mar 20 (UTC)
An asteroid was discovered to be in Neptune's L4 point. I was wondering if someone could work it into the part talking about similar systems? The asteroid's name is 2001 QR322, and I just created a page for it. --Patteroast 16:50, 15 Jun 2004 (UTC)
Can anyone answer a hypothetical question for me? If one had two super massive bodies of precisely equal mass orbiting about each other, would they generate Lagrange points as described here? I suspect that the positions of L1, L2 and L3 will be similar, but will L4 and L5 still be at the 60Deg Trojan points?
Thanks in advance, PBA
- Yes, a system of two equal masses (they don't have to be "super massive") orbiting around their common center of mass will have all five Lagrange points. However the L4 and L5 points will be unstable. They will also be in a much higher orbit than the masses. If the masses are at a distance r from the CM, then the L4/5 points will be from the CM.
--wwoods 19:07, 23 Jun 2004 (UTC)
So how does the rest of the solar system fit in? I mean it's all very well to speak of a 3 body system, but for all practical purposes, the other planetary bodies are going to interact with as well. How does that affect the relative stability of, for examaple, the Terra-Sol Lagrange points, or the Luna-Terra L-points? Is this possible effect the reason why one hears L5 advanced as a site for a sizable space habitat? Or is that due to some literary influence of which I am ignorant?
- Yes, the presence of other masses in the real Solar System perturbs bodies at the L4 and L5 points, but obviously not too much, as evidenced by the presence of objects at various L4&5 points around the system.
- L5 was proposed as a habitat site because the stability reduces the need for station-keeping, and because it was close to the Moon in terms of delta v (~0.7 km/s).
- —wwoods 17:44, 21 Aug 2004 (UTC)
Coriolis effect
I'm unhappy with invoking the Coriolis effect for explaining why a point is stable. The Coriolis effect is merely a device to explain the apparent deviation of a free moving object when viewed from a rotating frame of reference. It cannot really explain the stability of a Lagrange point. What says anyone? Paul Beardsell 23:46, 23 August 2005 (UTC)
Nuthin'. Paul Beardsell 00:53, 5 September 2005 (UTC)
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- I realize that this point is a bit belated, but classifying L4 and L5 as "unstable" is done by looking at an effective potential for the two body system in a rotating reference frame. However, this effective potential doesn't take into account the existance of the Coriolis forces in this reference frame. Thus, the Coriolis forces effectively cause these points to be stable, when we are looking at it in a rotating reference frame. Unfortunately, to look at this problem in an inertial reference frame would be technically quite difficult, although perhaps conceptually clearer, since you don't need to invoke centrifugal or Coriolis forces. If you did do the problem in the inertial frame, you would see that the Lagrange points (Lagrange orbits, if you will) would be stable, in the sense that a small perturbation from the Lagrange orbit would effectively cause epicyclic motion about the circular Lagrange orbit. Grokmoo 04:24, 1 March 2006 (UTC)
needs pronounciation
This article needs a sentence about how to pronounce it. Is the g hard or soft (for both of them)?
- Thanks for your comment. The first g is pronounced as in go, the second as in judge. I added the pronunciation in IPA. -- Jitse Niesen (talk) 12:45, 4 September 2005 (UTC)
Wrong in L2 Examples?
I got another value for the example values on the L2 point. Sun-earth OK: 1.5*10^6km from earth Moon-earath : 65348 km
Maybe due to measuring from surface and center. Nor my source, nor wiki specifices. However centre would make more sense, don't you think.
I also get (distance from earth): L1 sun-earth: 1.49*10^6km L3 sun earth: 2.992*10^8km
I also get (distance from moon): L1 sun-earth: 57660km L3 sun earth: 764956km
wrong example?
"Earth–Moon L2 would be a good location for a communications satellite covering the Moon's far side."
no it wouldn't. how would you send information to it? isn't the moon in the way? I did not remove the sentence yet. —The preceding unsigned comment was added by 212.120.85.242 (talk • contribs) .
- Satellites operating "at" collinear libration points (such as L2) are generally not actually located at the point, but rather in a halo or lissajous orbit around the point. If the amplitude of this periodic orbit is sufficiently large then the spacecraft will always have line-of-sight to the Earth. --Allan McInnes (talk) 05:22, 1 March 2006 (UTC)
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- Especially line-of-sight to a comms array in geostationary orbit around the earth.--Si42 19:45, 15 April 2006 (UTC)
Deleted false sentence
I deleted this sentence from the first picture's caption since it's nonsense to me:
- An object in free-fall would trace out a contour (such as the Moon, shown).
Just look at the sharpness of the contours near L1: an object in free-fall could never do those movements, since the centre of the (fictional) centrifugal force isn't at L1, but at the centre of masses of the Sun and the Earth. In addition, free-falling objects can perfectly have elliptical orbits, thus crossing several contours. So the sentence is false in every posible way it could be. --euyyn 00:43, 13 May 2006 (UTC)
L4/L5 explanation using only gravity and 'centrifugal' force?
The examples given under L1/2/3 nicely explain, imho, the existence of these points from the simple addition (cancellation) of the gravitational fields and the centrifugal force. But I notice there is no such explanation under the L4/5 points. Can someone who understands these points add in a similar example/explanation? If it were possible for a body to sit at exactly the top of the potential hill at L4/5 , then it seems to me that one could remove the Earth and that body would stay in exacly the same position and same orbit. This implies that the presence of the Earth for a body at these points of irrelevent..but I don't understand how that can be as adding the additional force of the Earth would surely drag the body out of its circular orbit about the Sun. Anyway, I'm just looking for a clearer physical picture using only gravity/centrifugal force to explain the L4/5 points. Thanks!
- You need the coriolis force to explain them.... This link http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html has some good info (most of this page seems to be sourced from it) & if you know some maths you could download the pdf & have a look at it. 203.97.255.167 00:14, 3 September 2006 (UTC)
Third pronunciation
I pronounce "Lagrangian" as [ləˈgɹe(ɪ)n.dʒiˌʊn]. Does anyone else? Denelson83 00:28, 12 June 2006 (UTC)
- Yeah. do that too. Is that a "mispronunciation"? AEuSoes1 06:39, 24 August 2006 (UTC)
Fictional References
I was delighted to finally read a clear explanation of the L4 and L5 points as they are extensively used in the Transhuman Space roleplaying game. This includes the Trojans and the L4 and L5 points around Earth. I suppose this goes under the mention made of hard science, but I thought I might as well mention it. - Philippe J (FR)
Just noticed that the Peter F. Hamilton, Nights Dawn, refernce is incorrect. This occurs in the first book, The Reality Dysfunction, as part of the battle for Lalonde. p 1172-73 and 1189-94 in the 1997 Pan Books paperback edition. The episode in the second book involves making a gas giant go nova to create a debris front that the Lady Mac would be in front of, and the pursuing starship would be caught by.
stability of L4/L5
Aren't L4 and L5 stable points in the Earth-Sun model? The blue arrows in de picture show them as instable, which I think is incorrect. --Mushlack 17:32, 2 August 2006 (UTC)
- They are potential peaks, hence the blue downwards-slope arrows. They are, as you say, stable, even though the potential diagram does not show it. It requires slightly more sophisticated maths... 203.97.255.167 00:15, 3 September 2006 (UTC)
Kordylewski cloud at Earth-Moon L4/L5
There are supposed to be coulds of dust at both of this points. Does anybody have any specific details how much dust there is (or if there even is dust there) in stable halo orbit? Since this orbit is the size of the earth this could have large combined mass (enough to collect and use?) or could pose a problem to any object in it's halo orbit. --Taho s 18:49, 24 February 2007 (UTC)
Lagrange points over time
Over a period of time, do Lagrange points change as the objects, such as earth, continue in their orbits?
And also, the equations and the points seem to be based on a circular orbit, wouldnt the Lagrangian points be different using the elliptical orbits that planets truly move in? Xlegiofalco 06:34, 22 November 2006 (UTC)
- The Lagrange points would only change if the orbits themselves change. And as long as the eccentricity is low enough (I'm not sure what the cutoff point would be, I suspect it varies depending on mass and other factors), the same principle holds, although it would create somewhat more complex orbits, I believe Nik42 01:31, 26 May 2007 (UTC)
Please, re-check info on the page
This page and the one on the Advanced Composition Explorer contradict each other about the satellite's orbit. This page informs that ACE is kept on Lissajous orbit and ACE's page tells about an Halo orbit.
Can someone correct either?
--Dr. Pnz 04:11, 21 January 2007 (UTC)
"In orbit around" L2?
Is it correct to describe the satellite as being "in orbit around" the L2 point here:
"The Wilkinson Microwave Anisotropy Probe is already in orbit around the Sun–Earth L2."
- Maybe they're two separate statements: "The probe is already in orbit" and "The probe is around (near) L2".--Nonpareility 22:43, 30 January 2007 (UTC)
- It certainly is correct; see Lagrangian point#Stability. –EdC 23:17, 30 January 2007 (UTC)
What is M? It suddenly apears in the L2 description. --5telios 12:38, 25 April 2007 (UTC)
Lagrangian points and spacecraft
The article speaks of multiple existing and planned spacecraft operating at a single Lagrangian point. Of course, it's impossible for multiple objects to occupy the same point in space, so I'm assuming that the spacecraft are/will be within a certain radius that's "close enough". Could some text be added to explain this?--Nonpareility 22:43, 30 January 2007 (UTC)
- Again, Lagrangian point#Stability explains how quasi-stable, quasi-periodic orbits around the L-points can exist. Where relevant, "at" should be amended to "in orbit around". –EdC 23:19, 30 January 2007 (UTC)
Science Fiction Counter-Earth Lagrangian?
Is a science fiction "counter-Earth" actually a Lagrangian concept when it's not an object of "negligible" mass -- and the two Earths would seem to be just counter-balancing each other? (Well I mean "Earth's Evil Twin" -- same mass.)
Asteroid(s) orbiting Earth at L4/5?
Wasn't there a discovery in the last few years of one or two asteroids at/orbiting the Earth-Sun L4 and/or L5 points? —The preceding unsigned comment was added by 67.121.242.84 (talk) 23:53, 30 January 2007 (UTC).
Exact position of L4 and L5, plus minor amendment to figure
In subsection L4 and L5 :
Para 1 has "The L4 and L5 points lie at the third point of an equilateral triangle whose base is the line " no, "The L4 and L5 points lie at the third corners of two equilateral triangles whose common base is the line " or " ... whose bases are ...".
- Well, it could be "The L4 and L5 points each lie at the third point...". Your wording is better, though. EdC 17:39, 23 February 2007 (UTC)
Para 1 has "whose base is the line between the two masses" - suggest '... between the centres of the two ...'. That does not change the natural meaning, but it does stress 'centres'.
- Yes. EdC 17:39, 23 February 2007 (UTC)
Para 1 has "the smaller mass in its orbit around the larger mass". But both masses orbit the barycentre, and L4/L5 are outside the orbit of the secondary. Omit "in ... mass"?
- I don't think "in its orbit" is intended to convey that they share the orbit; rather it is intended to qualify "ahead"/"behind". It could be misleading, though; I've changed "in" to "with regard to". EdC 17:39, 23 February 2007 (UTC)
Result could be "The L4 and L5 points lie at the third corners of two equilateral triangles whose common base is the line between the centres of the two masses, such that the point is ahead of (L4), or behind (L5), the smaller mass."
- Changed, modulo the above. EdC 17:39, 23 February 2007 (UTC)
By the way, L4 is ahead of the secondary but behind the primary, in angle frem the barycentre. If mass were steadily transferred from primary to secondary, then as the secondary became the primary and vice versa, so would L4 and L5 exchange names.
- True, but rather irrelevant, as L4 and L5 are only stable when there is a large disparity in mass between primary and secondary; binary star systems don't have trojan points. EdC 17:39, 23 February 2007 (UTC)
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- Well, we're dealing with Lagrange points, not Trojans. Pluto-Chiron, mass ratio about 10, still has five L-points but no T-points. The property is necessary for an exact solution. It should have a place in more mathematical pages.
- 82.163.24.100 22:41, 26 February 2007 (UTC)
Last para ends ", and asteroids there are named after characters from the respective sides of the war". Nowadays they are; but the convention was not established in the early days. See entries for 'Trojan asteroid', 'Trojan camp', 'Greek camp'. Given the detail elsewhere, I think the quoted bit can be omitted, or replaced by something like "; but there is a spy in each camp".
- A little too humourous for an encyclopaedia, I think. A "mostly" qualifier will suffice; the reader can anyway follow the links to the detail, as you point out. EdC 17:39, 23 February 2007 (UTC)
In subsubsection Examples the page has "The Sun–Earth L4 and L5 points lie 60° ahead of and 60° behind the Earth in its orbit around the Sun." No, just outside its orbit. Maybe better to put it from another aspect - something like "As measured from the centre of the Sun, L4 and L5 are 60° ahead of and behind the Moon in the line of its orbit."
- Again, I think "in its orbit" has a different intended meaning from how you're reading it. I've changed "in its orbit around the Sun" to "as it orbits the Sun". EdC 17:39, 23 February 2007 (UTC)
Figure
If the top-of-page diagram can again be edited, I suggest moving the blue triangles at L3 outwards a modicum, so that the grey circle of the Earth's orbit can be seen as it passes L3.
82.163.24.100 12:11, 23 February 2007 (UTC)
- Doable, yes; unfortunately every time that image gets edited it loses quality (it's in JPEG). I'd prefer to develop Image:Lagrange points.svg to the degree that it can replace the NASA image.
- By the way, Wikipedia is the encyclopedia that anyone can edit; your suggested edits would have been fine had you made them yourself. Be bold, I think the saying is. EdC 17:39, 23 February 2007 (UTC)
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- (1) not until I'm more familiar with page-editing convention, (2) A second opinion is valuable.
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- 82.163.24.100 22:41, 26 February 2007 (UTC)
Correction to first diagram?
Shouldn't the L4/L5 arrows in the first diagram face inward and be red?--Michalchik 00:51, 10 March 2007 (UTC)Michalchik
- Nope. Sorry. AFAIK the diagram is correct. I never did get my head around why it's the other way than you would expect, but I think it's something to do with coriolis effects closing the orbit.WolfKeeper 08:30, 10 March 2007 (UTC)
Euler and collinear libration points
In a lecture at CalTech in 2004, Shane Ross asserted that Euler first "discovered" the collinear libration points in the 3-body problem. Is there any written source to cite for this? Sdsds 21:39, 25 March 2007 (UTC)
L1 intuitively (mis) understood
The article currently makes the assertion regarding L1: "It is the most intuitively understood of the Lagrangian points: the one where the gravitational attractions of the two other objects effectively cancel each other out." Is this a good first-order understanding of stability at L1? It seems to work like that when viewed in a rotating frame of reference. But isn't a rotating frame of reference non-inertial? Aren't there are psuedo-forces that need to be considered? Considering L1 in a non-rotating frame centered at the barycenter of the system, would one in general expect the period of rotation of an object at the L1 point to match the period of rotation of of the smaller mass? Wouldn't it move out of alignment? What's really "intuitive" in the L1 case? Sdsds 22:19, 11 April 2007 (UTC)
- Hmm, these are good questions. Basically, the L1 point is the only one that you expect to see in a non-rotating reference frame. i.e., if just had two solid masses sitting still, you would expect to find an equilibrium between them. Of course, this equilibrium is not at the same place as you find L1, due to the centrifugal 'force' you mention. So maybe this isn't really all that intuitive. Grokmoo 15:18, 13 April 2007 (UTC)
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- If you just had two solid masses sitting still, you would expect gravity to draw them together! What you describe would only make sense if you somehow pinned the locations of those two masses. In that totally weird and uncreatable situation, then it would be possible to "balance" a third object at a point somewhere near L1.
But this is a fundamentally flawed approximation of the true situation: there are "obviously" no orbits around that balance point as there are around L1.Sdsds 14:30, 25 April 2007 (UTC)
- If you just had two solid masses sitting still, you would expect gravity to draw them together! What you describe would only make sense if you somehow pinned the locations of those two masses. In that totally weird and uncreatable situation, then it would be possible to "balance" a third object at a point somewhere near L1.
Diagram caption
This currently says,
- "... The blue arrows indicate the boundaries of the stable areas, beyond which an object would fall away from a Lagrange point; the red arrows indicate the planes along which an object will fall back towards a Lagrange point."
No they don't. The blue arrows around L4/5 aren't at the largest orbits, and there are no stable areas around L1/2/3. The red arrows don't indicate planes; they indicate directions within the orbital plane. What the arrows actually indicate is the slope of the pseudopotential surface: downhill away from local highpoints L4/5 (blue), downhill from the saddlepoints L1/2/3 along the line connecting the masses (blue), and downhill toward the saddlepoints in the perpendicular direction (red).
—wwoods 02:08, 24 May 2007 (UTC)
Mass of Lagrangian object?
What is the maximum mass, relative to the two main bodies, that an object in a Lagrangian point can have? For example, how large could an object be in the Sun-Earth L4 or L5 point? Nik42 01:35, 26 May 2007 (UTC)
Gundam Wing
Each of the pilots comes from a different lagrange point. Heero from L1, Duo from L2, and so on. It's where they get the numbers that the characters are originally reffered to by the Order of the Zodiak before they obtain their names. It's also that same practice used in fanfiction when reffering to relationships. NemFX 00:53, 4 June 2007 (UTC)
Footnote 3
Footnote 3, referring to the "24.96" which is the minimum ratio between M1 and M2 to have stable L4 and L5 points, says:
Actually
Isn't that rather a complicated formula which can be expressed more simply? If I've done my math right,
and the latter is not only a simpler, but also a more conventional way to express the number. Would someone double-check my math and verify that? Chuck 23:04, 11 June 2007 (UTC)
- Yes, you're right. I've changed the article to use the simpler expression. --Zundark 10:09, 12 June 2007 (UTC)
merge with L1 orbit
I cant see any reason there should be a second page for L1 orbit. Chris H 13:12, 29 July 2007 (UTC)
- Support. I have reworked the merge suggestion tags to indicate where discussion of L1 fits into this article. (And this article is not yet too long to include what's in the L1 Orbit article! ;-) (sdsds - talk) 21:56, 29 July 2007 (UTC)
/History and Concepts/
"In 1772, the Italian-French mathematician Joseph-Louis Lagrange was working on the famous three-body problem when he discovered an interesting quirk in the results."
What quirk is that exactly? I don't know, although I'd presume it's the hypothesis referred to later. In any case, it's unclear. Can someone look at this? --60.230.200.219 11:19, 23 September 2007 (UTC)
Source of L4/L5 claim
The section on natural objects claims bodies in Sun/Saturn and Jupiter/Jovian satellite Lagrange points. AFAICT, there's no other mention of such things elsewhere in Wikipedia, and no source cited here. Do they really exist? ~Lynn M —Preceding unsigned comment added by 131.212.212.174 (talk) 18:50, 26 September 2007 (UTC)
Pop culture
Pop culture list is long and detracts from the main article. Should be moved to a seperate article list of lagrangian points in fiction or so. For now, marking it as trivia, for want of a better tag. Brianski 04:37, 30 October 2007 (UTC)
Other Co-orbitals
Technical point behind edit. The higher, slower orbit represents a greater orbital energy rather than lower. Wording adjusted to reflect that. roger.ritenour, 28 November 2007 —Preceding unsigned comment added by Roger.ritenour (talk • contribs) 14:56, 28 November 2007 (UTC)
- PS - See Wikipedia:What_Wikipedia_is_not
Pitch Black scenario
The Pitch Black (film) article does not currently address the use of Lagrange points in the movie. To tell you the truth, I don't know how much they've been discussed at all, but the movie clearly shows a scenario with a planet at the middle of an orrery with a star and a double star revolving on opposite sides, which presumably makes it an L1 point. To add to the complexity a pair of gas giant planets orbit the L1 point (with different periods, I think). The question is... is it conceivably possible? I know the L1 point normally would be an unstable spot for a planet, but I won't even pretend I know what happens to a five body system. 70.15.116.59 (talk) 02:08, 31 December 2007 (UTC)