# Talk:Lagrangian point

## How about an explanation for the common man?

I think that at least the first sentence should be changed. "The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be part of a constant-shape pattern with two larger objects." is horrible. The problem is the "be part of a constant-shape pattern with two larger objects" bit. This might be the best general description of the phenomenon but it's difficult to understand. It should either be replaced with something that doesn't include the term constant-shape pattern, or immediately afterword there should be a paragraph explaining it. I would suggest something like: "The speed at which an object orbits around another is related to how close it is. The closer the two objects get, the faster the orbiting object must be. This means that distance between two objects orbiting the same celestial body at different altitudes can not remain the same with the exception of five points provided one of the orbiting objects is of negligible mass. At these five Lagrange points the gravitational attraction of the larger orbiting object on the object of negligible mass either reduces or increases the speed required to orbit the celestial body at a certain altitude by exactly the amount needed so the smaller object can have the same orbital period as the larger orbiting object at a different altitude." Now I realize that of course all three objects are orbiting a common center but to include that would make it unclear. Also I might be a bit wrong because I'm not a physicist. Especially suspect is the use of equidistance as a goal, which is probably only valid for circular orbits (I don't know if that is the case). If it isn't valid for elliptical orbits, perhaps relative angles should be used or circular orbits should be specified. I came here hoping to understand the concept and then clicked back and went to the ESA webpage on the subject because this article starts too abstract and then just gets very technical. I haven't made the modifications directly, because I could be partially or totally wrong. I would kindly request that someone with more knowledge of orbital mechanics check my paragraph and include it or a modified version of it. Kaanatakan (talk) 16:13, 22 October 2013 (UTC)

## Add M1 M2 to diagram

The article discussed M1 M2 etc., but these symbols do not appear in the diagram. One would have to read the whole article to discover the definition of M1 and M2. This is quite frustrating. —Preceding unsigned comment added by 75.53.54.121 (talk) 18:32, 28 February 2011 (UTC)

## Exact position of L3, plus minor amendments

#### Beginning

The L-points are not necessarily in interplanetary space.

Corrected to "in orbital configuration".
> OK ("in an orbital ..." ??)

#### 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

#### Diagrams

Recreated contour plot with n=25

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)

The blue triangles (showing the gradient to be downhill going away from the points) indicate that L4 and L5 are unstable equilibria, whereas they are actually stable equilibria. —Preceding unsigned comment added by 208.71.200.91 (talk) 05:26, 24 February 2010 (UTC)

Yes L4 and L5 are the stable equilibria. But they really are the maxima of the pseudopotential; it takes the Coriolis force to keep objects from falling away from those points.
—WWoods (talk) 09:21, 24 February 2010 (UTC)
The triangles are equilateral and do not act effectively as arrows. It is therefore difficult if not impossible to be certain which direction they are intended to be pointing.
—thereaverofdarkness (talk) 20:47, 10 August 2015 (UTC)

#### 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)