2717: L6 Lagrange Point

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L6 Lagrange Point
It's difficult to orbit L6 stably due to gravitational perturbation from Akron and Toledo.
Title text: It's difficult to orbit L6 stably due to gravitational perturbation from Akron and Toledo.


In celestial mechanics, the Lagrange points are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Or in simpler terms, positions in space where objects can float motionless relative to the defining bodies.

There are five traditional Lagrange points. Two form equilateral triangles with the two massive objects (in this case the Earth and the Sun), and three more are collinear with the massive objects. The L1, L2, and L3 points are unstable, as any drifting off the point (e.g. due to the gravity of other bodies) might quickly increase the tendency to depart the area. However, there are quasi-stable Halo orbits around these points, like the one used by the James Webb Space Telescope. The L4 and L5 points can actually retain objects stably over long periods, resulting in the Sun-Jupiter L4 and L5 points capturing the Trojan Asteroids.

Randall claims that a sixth Lagrange point has been discovered outside of Cleveland, Ohio. This is pretty obviously farcical,[citation needed] as this would be part of the Earth and thus not gravitationally balanced between Earth and the Sun, though it is balanced by the countering forces that hold anything stable on the surface of any body: gravity and electromagnetism. The joke here is that there actually is a small village named LaGrange, OH (population 2,595 in 2020) just outside Cleveland (map). However, the village name is spelled with a capital G, unlike Joseph-Louis Lagrange after which the Lagrange points were named.

There is, however, a Lagrange in Maine, a Lagrange in Virginia and a Lagrange Township in Illinois which all use the lower case g in their spelling like Joseph-Louis Lagrange. There are also twenty-six other communities in the United states with a spelling of LaGrange or La Grange, as well as four in France and two in Australia with one of the three spellings. This includes La Grange, Texas which became famous as the title of a ZZ Top song.

The title text mentions Akron and Toledo, two other large cities in Ohio. It says that their gravitational influence is the reason why orbits around the LaGrange L6 are unstable. The Lagrange points are solutions for a simplified three-body system, and orbits around them may be disrupted if additional bodies such as moons or planets are close enough or massive enough to cumulatively exert significant gravitational forces over time (the Moon does factor into the Earth-Sun L1 and L2 Lagrange points, especially, but that can be accounted for in the station-keeping measures already required). Trying to orbit around a point on the ground would, of course, run into much more serious problems, such as the ground.


Grey on white diagram of the Earth orbiting the Sun, not to scale. Earth is depicted as a circle with pale grey continents on darker grey seas, and shows a view from above the North Pole without any Arctic ice. The sun is drawn surrounded by radially symmetrical exaggerated wave pattern.
Also in grey, approximate locations of Lagrange points 1 to 5 are marked with dots and labels: "L1" "L2" "L3" "L4" "L5".
In black, a point on the Earth's surface within the boundary of a continent that could be North America. Also in black, an arrow pointing towards the point, and the label "L6".
[Caption below the panel:]
Huge space news: Astronomers have discovered a new Lagrange point just outside Cleveland.

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Daily comics. —While False (museum | talk | contributions | logs | rights | printable version | page information | what links there | related changes | a late contribution | current time: 18:24) 19:05, 27 December 2022 (UTC)

This came out about a year after JWST was launched, and it's stationed at a Lagrange point of the Sun and Earth. It might be related to the anniversary, although it would make more sense if it came out in a month, on the anniversary of the telescope reaching L2. Barmar (talk) 20:49, 27 December 2022 (UTC)

Missed opportunity to reference La Grange, Texas, the basis of the song by ZZ Top. RandalSchwartz (talk) 21:13, 27 December 2022 (UTC)

Well I hear it's fine, if you got the time 13:55, 28 December 2022 (UTC)

Not probable but maybe a reference to the recent "Ohio" meme? 22:14, 27 December 2022 (UTC)Bumpf

Probably not on purpose but it definitely fits in with the rest of the “Ohio” memes 22:38 27 December 2022 (ETC) Comi123
Can I use a subscript notation in the transcript?

Any clues where to find the code? Comic seems to have the numeral portions of "L1" to "L6" as subscripts. Is that a standard notation for Lagrange points, if so should we also use it in the main article? 06:14, 28 December 2022 (UTC)

Sure. Use HTML <sub> tags. 07:41, 28 December 2022 (UTC)

Why Cleveland? Well, Yakov Smirnoff said, "In every country, they make fun of city. In U.S. you make fun of Cleveland. In Russia, we make fun of Cleveland." 12:14, 28 December 2022 (UTC)

The center of the Earth is also a Lagrange point (I think I'll call it L0). So Lagrange, OH is only 4,000 miles off, which should be close enough for many astronomers. 16:12, 28 December 2022 (UTC)

Well, LaGrange, OH is in a stable orbit around L0, so would this also be a Halo orbit? 09:26, 29 December 2022 (UTC)
Not really. It rotates around a point 4800km north of L0, but I don't think this is technically an orbit since it experiences a lot of non-gravitational forces. Quantum7 (talk) 07:28, 1 January 2023 (UTC)

And I thought La Grange was in Texas I should not listen to three wise men with beards, even at this time of year. Wikipedia tells m there are over 25 across the US. 10:38, 29 December 2022 (UTC)

Two men with beards, one man named Beard. 11:35, 29 December 2022 (UTC)
Thus three men, each with a beard. (Actually the phrase "three wise men with beards" isn't explicit about how many beards they have between them.)

Normally cartoons come out MWF, but this came out on a Tuesday. Any known (or hypothesized) reason. Should the unusual timing get a mention. No comic in the normal Wed slot. MAP (talk) 02:36, 30 December 2022 (UTC)

In the light of there being "no Wednesday", in the obvious manner, we can make the presumption that this was supposed to be the Wednesday but (for some reason; ...other tween-holiday commitents? ...had the usual "what actual day is this of the season? ...distracted by family gatherings?) was released super-early. As in even Tuesday in more advanced timezones. Either that, or he was visiting a GMT+6 (or greater) place and posted it merely 'early Wednesday', but I don't think he would be visiting China (GMT+8) - for any number of reasons. Aus/NZ/etc? (Forgive me, just musing. Still no reason to think so.) 23:32, 30 December 2022 (UTC)

There are several places called Lagrange in France (with correct spelling), there are also Lagrange Bay on Western Australia and Lagrange, Virginia and Lagrange, Maine. There are many places with names spelled as LaGrange or La Grange in the U.S.A.. Arifsaha (talk) 19:35, 31 December 2022 (UTC)

I don't think this joke is about the town of LaGrange (especially since there's so many of them), but rather a reference to the "Wait, it's all Ohio?" meme [1]. Soralen (talk) 09:03, 2 January 2023 (UTC)

Interesting conjecture, but I would be very surprised if the "joke" in this was based on that meme. That doesn't seem like the kind of humor xkcd normally plays on. Map makers and census takers may see LaGrange, OH as an insignificant town, much smaller than other locations with the same name, but it is more commonly known as being part of [Greater Cleveland https://en.wikipedia.org/wiki/Greater_Cleveland]. Because of that connection, LaGrange, OH is well-known enough in the United States that Randall Munroe could expect his readers to understand the reference. Hackerb9 (talk) 22:08, 23 January 2023 (UTC)
Side-note to Hackerb9 and other editors: External URL links of that kind are [<url><space><text to use as link>] (the above 'works' only because the lack of opening URL prevents it from linkifying in the way intended, it is taken as literal, and the literal URL is (by its own terms) linkified as itself).
For Wikipedia links, however, there's the {{w}}-template which allows {{w<pipe><wikipage title>}} or {{w<pipe><wikipage title><pipe><text to use as link>}} forms, as necessary, which are much 'nicer' to read.
Just an FYI, to remember for next time. 06:53, 24 January 2023 (UTC)

Google map view of the major pathways of gravitational perturbation around L6