Talk:Lagrangian point

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Contents 1 Exact position of L3, plus minor amendments 1.1 Beginning 1.2 History and concepts 1.3 Diagrams 1.4 Section "L3" 1.5 External Links 1.6 See ... 2 Contradiction 3 Changes made to the Intuitive Explanation

[edit] Exact position of L3, plus minor amendments

[edit] Beginning

The L-points are not necessarily in interplanetary space.

Corrected to "in orbital configuration".

> OK ("in an orbital ..." ??)

[edit] History and concepts

His name was hyphenated : Joseph-Louis Lagrange.

Good catch.

It has "It took hundreds of years before his mathematical theory was observed". His theory was published around 1772; Trojans were observed around 1905. Thet's not "hundreds of years" later.

"Over a hundred years"?

> OK

[edit] Diagrams

The first, "... contour plot ...", diagram shows Earth, L3, L4 & L5 on a Sun-centred circle, and L1 & L2 reasonably close to Earth. That's satisfactory.

Actually, it shows L3 just outside the circle. It may not be all that clear.

> Agreed, agreed.

The problem is that the contour plot clearly shows a system where the ratio of masses primary:secondary is of the order of 10:1-50:1. In that case L3, L4 and L5 will be visibly off the secondary's orbit. I recreated the diagram here. –EdC 00:36, 5 February 2007 (UTC)

The second, "... far more massive ...", diagram shows L3 outside the circle. But if Earth, L4 & L5 all lie (as far as can be seen) on a primary-centred circle, then L3 should be similarly on that circle; not outside it.

The circle should be the orbital path of the secondary (centred on the barycentre), in which case L3 lies outside it. The diagrams should be fixed by moving the primary away from the barycentre, and L4 and L5 outside the circle.

> Doubt. Could be better to have "very much more massive" with Moon L3 L4 L5 on a circle centred on Earth, and L1 L2 very near Moon, AND also "considerably more massive" with everything properly shown. If the latter is a bit bigger, it will serve also for the L4 L5 geometrical srgument.

Yes, that could work. In that case the "very much more massive" diagram should have L1 and L2 pulled in as far as practicable. –EdC 00:36, 5 February 2007 (UTC)

Done, now we need to decide how to fix the contour plot. –EdC 02:16, 5 February 2007 (UTC)

[edit] Section "L₃"

The page says : "L₃ in the Sun-Earth system exists on the opposite side of the Sun, a little farther away from the Sun than the Earth is" - my italics. That wording will naturally be taken as saying that L3 is further from the centre of the Sun than the centre of the Earth is.

The better calculations measure distances from the barycentre, and show that L3 is a little further from the barycentre than the centre of the Earth is. But it seems that L3 is a little nearer to the centre of the Sun than the centre of the Earth is.

Hm. Yes, it is, isn't it?

> Not a lot of people know that, though.

Fixed - I hope. –EdC 01:05, 5 February 2007 (UTC)

New point: the article says "Example: L3 in the Sun–Earth system exists on the opposite side of the Sun, a little outside the Earth's orbit but slightly closer to the Sun than the Earth is." But how can it be OUTSIDE the Earth's orbit but CLOSER to the sun??

Because the Sun also orbits the barycenter – hence the Sun is closer to the far side of the Earth's orbit (if we ignore eccentricity, perturbation from other planets, and possibly a bunch of other things I forgot).  :) — the Sidhekin (talk) 21:48, 24 May 2008 (UTC)

[edit] External Links

Should include the paper itself, via Gallica.

Which paper?

> the one for which the reference in the main page is missing ...

> Lagrange, Joseph-Louis, ESSAI SUR LE PROBLÈME DES TROIS CORPS

> via <a href="http://www.merlyn.demon.co.uk/gravity4.htm#Refs">.

> It's written in Maths, slightly diluted with French.

Added as a reference. –EdC 02:15, 5 February 2007 (UTC)

[edit] See ...

<a href="http://www.merlyn.demon.co.uk/gravity4.htm#GLP">The Geometry of the Lagrange Points</a>.

Looks useful.

Added as an external link. –EdC 02:16, 5 February 2007 (UTC)

82.163.24.100 23:05, 2 February 2007 (UTC)

Thanks for your comments. –EdC 04:49, 3 February 2007 (UTC)

> 82.163.24.100 15:52, 3 February 2007 (UTC)

[edit] Contradiction

The issue of whether L4 and L5 are stable has been raised several times above. Could this be sorted out please. At the moment there's a straight contradiction between the contour plot, showing blue arrows leading "downhill" from L4 and L5, and the statement "the triangular points (L4 and L5) are stable equilibria ...". I can't fix it myself because I don't know which one is right. Occultations (talk) 11:37, 24 February 2008 (UTC)

The points are dynamically unstable (an object perturbed from L4 will continue to move away) but form stable equilibria (Coriolis force will curve an object's path back to L4). EdC (talk) 15:46, 24 February 2008 (UTC)

The plot's caption used to say, "Counterintuitively, the L₄ and L₅ points are the high points of the potential." Maybe something about the stability of L4 and L5 should be added to the introduction?

—WWoods (talk) 17:23, 24 February 2008 (UTC)

[edit] Changes made to the Intuitive Explanation

The Intuitive Explanation as presented was simply wrong. The outward force sensed by the hand twirling the string is a real physical force, namely the tension. It is not the centrifugal force. Further, the fact that when released the revolving mass travels on a straight tangential trajectory has nothing to do with the centrifugal force being 'fictitious'. When the string is cut, there is no longer any centrifugal nor centripetal force, so we are in an entirely new dynamical situation which is unrelated to the previous state. In addition to fixing these problems I have made the section less verbose and replaced the word 'weight' (which actually means 'gravity force') by a specific item, the stone. PlantTrees (talk) 20:26, 12 March 2008 (UTC)