What are the Lagrange points?

By Phil Plait | July 25, 2008 9:00 am

In my live video chat session Saturday, I was asked about the Lagrange points, places of gravitational stability. I decided I needed props for this (yes, the return of the Squishy Brain of Science and the Mintie of Science!), and it works even better with pictures, so I created a video for it.

You can learn more details about the Lagrange points at the Montana University site. The Lagrange point images (and the WMAP picture) come from the WMAP website. The JWST picture is from the (duh) JWST site. The portrait of Lagrange is from Wikipedia. Everything else is pure me, baby.

CATEGORIZED UNDER: Astronomy, Science, Space, Video Blog

Comments (62)

  1. Protesilaus

    Phil, the video says no longer available.

  2. Protesilaus

    “This is a private video. If you have been sent this video, please make sure you accept the sender’s friend request”

    Looks like you made the video private.

  3. Bruce A

    Nothing to do with ZZ Top then? Huh.

  4. Dan Dangerously

    For me, it says the video just doesn’t exist at all.

  5. GodlessHeathen

    Oh, such a tease! I’ve been curious about what a Lagrange point really is since the term popped up in “2010”.

    Yes, I’ve been putting off looking it up since the early 80’s. Yes, I am a master procrastinator.

  6. Astronomy cast did a great job with Lagrange points in episode 76.


  7. Heinz Pierce

    I keep getting “Sorry video no longer available :(“

  8. Hugh

    The embedded video says “no longer available”, but the youtube page for it says that it’s private…

  9. Stoopid YooToob. I reset the permissions. Sorry.

    And yeah, maybe it’s not YouTube’s fault. :-)

  10. john.o.kerr

    Working fine now.

    Awesome video Phil, very informative. And always a nice little dose of optimism as well.

  11. Quiet Desperation

    *That’s* what the Lagrange points are? I thought they were… you know… Sheesh! No wonder my girlfriend won’t sleep with me anymore. :-(

    But seriously, I’ve always been partial to L5. Prime real estate there, and only a better class of folks, unlike those scruffy L4 types.

  12. rmbokliebn

    As a former alum, Montana STATE University, please.

    You gave a lecture there at one time. Are we so little in the infinite world of an international blogger that you forget us?

  13. R2K

    “July 25th, 2008 at 9:08 am

    Nothing to do with ZZ Top then? Huh.”

    You beat me to it!

    Damn you Bruce A,
    damn youuuuu!!!!!!!11111111111

  14. madge

    @ Quiet Desperation
    60 degrees above or below works for me 😉

  15. Thanks for the explanation, Phil. I’ve always been fascinated by Lagrange points.

    If you have two satellites in the L2 (Earth/Sun) Lagrange point, why don’t they crash into each other? Wouldn’t they fall toward the “bottom” (or “center”) of the Lagrange point (assuming there is a bottom)? Why don’t these points just fill up with dust, meteoroids, etc?


  16. A SOHO-like telescope at L3 with a communications relay at L4 or L5 would give some nice data on the sun. It would be most cool to be able to see both sides of the sun at the same time.

  17. AAEBoiler

    “Eric Goetz” – the satellites aren’t actually at the L2 Lagrange point. They are in an orbit that is tens of thousands to hundreds of thousands of kilometers away from L2. Small stationkeeping maneuvers are used to keep the satellites orbiting around L2. There little to no chance that they will ever come in contact with either. Once their primary mission is finished (or they run out of propellant) orbit perturbations will slowly push them away from L2 and they will either return towards Earth or leave the Earth-Moon system and enter a solar driftaway orbit (like STEREO or SPITZER).

  18. Shoeshine Boy

    Excellent explanation, Phil. It cleared-up a lot of confusion on my part.

    But what’s up with the little orbit-like circle around the L2 point in the diagram?

  19. Jon

    Eric, I believe that the satellites use some form of station keeping to keep them in orbit around the Lagrange point. They’re not right on top of it, in other words.

  20. Brent

    maybe the moon’s gravity spins the L2 point around?

  21. bigjohn756

    Phil, what do you think of The Planetary Society’s idea of assembling the manned Mars probe at the earth-moon L4 or L5 points instead of on the Moon? It sounded like a good idea to my uneducated mind.

  22. The page on Lagrange points has been actualized by the same author at:



  23. Navneeth

    Good one as usual. But I think this video has the most uh…uh…’s of them all! 😉

  24. Chip

    BTW – I like the sound of “centrifugal” – always reminds me of Bach. In fact there are, symbolically speaking, tonal equivalents of lagrange points in the formal structures of his fugues. That is to say, places where there is a balance point of related keys and counterpoint. (In the Bach universe, it is usually much closer to the end of the piece rather than 3/4 of the way through,) where the growing complexity and more remote harmonies from the main key give way to simplicity (or satisfying clarification to the ear,) and a return to the home key.

  25. ioresult

    Shoeshine Boy: that’s the Lissajous orbit of WMAP. JWST will have a similar orbit.

    Now, that’s a good question for Bad Astronomer: explain to us how the Lissajous orbits make the metastable Lagrange points more stable!

  26. ioresult

    Eric Goetz: the L1, L2 and L3 are metastable. Dust motes there will drift apart. And even if they accrete under their own (feeble) gravity, the bigger accreted mote will itself drift away eventually.

    The L4 and L5 are a minimum in potential gravitational energy. Stuff put around these two points will stay there and even orbit their point. The Trojan asteroids are in some kind of orbit around the L4 and L5 points of the Sun-Jupiter system. But as BA says, the L4 and L5 of the Earth-Moon system aren’t stable because of the gravity of the sun that interferes. Stuff there will take longer to drift away, but it’s going to eventually.

  27. Shoeshine Boy

    Is the L6 point where they keep the secret space station?
    (just kidding) 😉

  28. AAEBoiler

    ioresult – Satellites don’t just hang out at the Lagrange points. In fact, a satellite at the L2 point would need an RTG (i.e. plutonium) to generate power as it would be in the Earth’s shadow. So, satellites need to orbit around the Lagrange points in Lissajous Orbits (like WMAP), Halo Orbits (like SoHO), or Toroidal Orbits (bounded Lissajous Orbits).

  29. Lagrange is in Ohio, don’t know what you’re all yammering on about 😉

  30. I learned about these with my ex wife when we went to Lagrange classes when she was pregnant.

  31. QD, you seem to be missing the point… at least that’s what your girlfriends says :)

    Madge, wow! :)

  32. CanadianLeigh

    @ Michael L.
    The organizers of the Fort Langley event have made it into a two night star party. They are worried about the weather for Saturday night. Below is a link to more info. Maybe you can make it. I will be going tonight for sure. Hope to be there by 9:00 so to set up in the light and park outside the gate before it locks.
    QD would probably done better if he was a stamp collector.

  33. Charles

    “Lagrange is in Ohio, don’t know what you’re all yammering on about ;)”

    * LaGrange, Arkansas
    * La Grange, California
    * LaGrange, Georgia
    * La Grange, Illinois, village in Cook County
    * LaGrange, Indiana
    * La Grange, Kentucky
    * Lagrange, Maine
    * La Grange, Missouri
    * LaGrange, New York
    * La Grange, North Carolina
    * LaGrange, Ohio
    * La Grange, Tennessee
    * La Grange, Texas
    * Lagrange, Virginia
    * La Grange, Monroe County, Wisconsin
    * La Grange, Walworth County, Wisconsin
    * La Grange, Wyoming
    * Lagrange County, Indiana
    * Lagrange Township, Bond County, Illinois
    * LaGrange Township, Michigan
    * LaGrange Township, Lorain County, Ohio

    Haw haw haw can there be so many Lagrange’s in the US? I bet they’re fine, if you got the time, but then again, I might be mistaken…

  34. Don’t forget SOHO. Its near L1. L2 is also metastable. Spacecraft there need tweaking burns to stay there, or they will quickly drift away.

    “so these regions are big enough that you can put lots of stuff there”, referring to telescopes in L2. The more fuel you’re willing to use to make your tweaking burns, the larger these “regions” become. They’re actually a sizeless point. The way we crowd so many into the area is to use Lissijous orbits or Halo orbits. Objects on L1, L2, or L3 are only unstable along the primary-secondary line. If you push such an object up or down, it will oscillate about the L point. Or if you push it forwards or backwards in its orbit, it will also oscillate. It you push it in both these directions, you can get it to orbit the L point in a halo orbit. Correction burns are still necessary along the primary-secondary line to prevent the spacecraft from drifting, slowly at first, but rapidly accelerating, away from the L point.

    As far as the Sun messing up the Earth / Moon’s L4 and L5 points, that’s been my experience when I try to simulate objects placed there. With some luck, I can get an object to stay as long as about 20 years, but usually its much shorter-lived. Take away the Sun, and they’re stable indefinately. But a recent paper, “Solar and planetary destabilization of the Earth-Moon triangular Lagrangian points”, by Jack J. Lissauer and John E. Chambers, suggests its the planets that destabalize Earth/Moon’s L4 and L5 points. Take away the planets, but leave the Sun, and they claim that objects can stay in the vicinity of L4 and L5 for billions of years, but throw the planets back in, and they’re only stable for millions of years. I’d love to simulate their claims, but their graphs are confusing to interpret. So I’ve never been able to create their starting conditions. Maybe this discussion will motivate me to try again.

    Here’s a link to a calculator I made that computes for you the distance to the 5 L points, including the velocity your spacecraft would need to stay there: http://www.orbitsimulator.com/formulas/LagrangePointFinder.html

  35. CanadianLeigh

    @ Michael L.
    I forgot the link, as well as a few words in my post. Stupid English!


  36. huma

    don’t forget about a great cast on lagrange points at the astronomy cast, too


  37. Thanks Canadian. Unfortunately this weekend is out for me. My mother just had knee replacement surgery, and I’ll be looking after her for the next while til she recovers.

  38. CanadianLeigh

    Family comes first. Hope your mother has a speedy recovery. I hope your health is improving as well. By the look of the clouds right now you might not be missing anything. Who’s bright idea was it to have a hobby that relies on clear skys here at the wet coast. If it rains as predicted for this weekend it will be the first rain this month. Talk about crocodile luck.

  39. bjn

    Rumour spreadin’ a-’round in that texas town
    ‘Bout that shack outside La Grange
    And you know what I’m talkin’ about.

    Just let me know if you wanna go
    To that home out on the range.
    They gotta lotta nice (metastable) girls.

    Have mercy.
    A haw, haw, haw, haw, a haw.
    A haw, haw, haw.

    Well, I hear it’s fine if you got the time
    And the ten to get yourself in.
    A hmm, hmm.
    And I hear it’s tight most ev’ry night,
    But now I might be mistaken.
    Hmm, hmm, hmm, hmm.

    Have mercy.

    (Zed Zed Top)

  40. It would be interesting to check back in a couple hundred years to see if the Lagrange points become valuable ‘real estate’ where you could own a piece of a gravity well, instead of just owning regular old dirt.

    Id love to fly by some L2 spot and see a FSBO sign just drifting.

  41. Quiet Desperation

    60 degrees above or below works for me

    Above or below the clitoris or the ecliptic?

    Now there’s a line you see every day. :-)

  42. Quiet Desperation

    Or rather *don’t* see.

    Please… for the love of the Flying Spaghetti Monster, give us previews!

  43. Kurt

    you say “centrigual – it is a real force”
    but it’s not a real force. its a fictitious force. it only presents itself when a situation is viewed from a rotating frame of reference.
    is this some kind of inside joke you were making??

  44. JonMcSkeptic

    Being an alum as well, I must stick up for my fellow Bobcats and implore the esteemed BA to show some love and credit Montana STATE University. Otherwise them good for nothing liberal arts Grizzlies get the credit they don’t deserve.

  45. drewski

    [url=http://xkcd.com/123/]One of my favourite XKCD’s on centrifugal force[/url]

  46. Autumn

    As no reference frame is special, both centripedal and centrifugal forces are real, they merely depend upon which frame one chooses.

    Since the BA mentioned Jupiter, I have to announce that I have just seen, with my little ol’ telescope, the Galileian satellites. My first time, and it left me sweaty, squinting, and with a sore back.

  47. Shouldn’t that be “centripeTal”, Autumn?

    These issues bewilder me. I did a thought experiment once where I set something rotating so that there was a perceived centrifugal force, and then I removed the rest of the universe. I then couldn’t work out whether that force would still be perceived. I mean, how would the object “know” it was still rotating without any other matter to refer to as a framework? My search for the answer led me to some pretty bizarre places, and I’m still not entirely sure of the answer…

  48. AAEBoiler

    Phil. the region where you can maintain an orbit about the L2 point is ginormous. Imagine a volume centered at L2 that is 500,000 km (along the Earth-Sun line) by 3,000,000 km (perpendicular to the Earth-Sun line) in the plane of the ecliptic and 2,000,000 million km out of the ecliptic plane. There would be no chance for satellites to bump into each other.

  49. DaveS

    Hmm. In engineering, they refer to it as centripetal acceleration in a rotating frame. In a non-rotating frame, it’s simply acceleration.

    Phil, according to my own Midwestern accent and every dictionary I can find, “centrifugal” is pronounced with the accent on the second syllable, whether you say “cen-TRIH-fuh-gul” or “cen-TRIH-fyuh-gul”.

    Also, it’s funny, but in engineering there’s statically stable, dynamically stable, and static and dynamically unstable. There’s no meta-stable. That would be statically stable by dynamically unstable. But in most of science there seems to be the distinction of “meta-stable”. Interesting.

    How does one calculate the outer reaches of the stable Lagrange points? In other words, how high an orbit around one could you do without falling out?

  50. Uh oh – this “Cen-TRIH-fuh-gul” thing smacks of “Kil-LO-me-ter”. Let’s not start that debate again! :)

    In Britain, I’ve never heard anyone stress the second syllable, only the first and third equally.

  51. DaveS

    Mike, perhaps it’s a cross-Atlantic thing, then. Phil’s in the US.

    Dictionaries are generally a good indication of common pronunciation,
    even in the UK. As far as Kilometer, a good dictionary will clearly state that
    it is commonly pronounced either way, so claiming one is more right than
    the other is primarily a religious argument. Same with “nuclear”.

    But if you’re pronouncing a word differently than anything listed in the
    dictionary, but can’t explain it by accent or dialect (Phil has a very
    neutral American accent, just like I do), you’re most likely, well, saying
    it wrong. Even if it turns out Phil was raised in Whales, but has managed
    to expunge every bit of the accent except that one in favor of American,
    well, he’s wrong.

    To claim otherwise is to claim that you kank pruntonuo a worknd enenky
    war you wank tow.

  52. Shoeshine Boy

    @ DaveS: In electronic engineering, there is most certainly something called metastable. When a flip-flop is clocked, its output should go to a “0” or “1” within some specified time period based on the inputs to the flop when it was clocked. If the inputs change too close to the clock edge (a setup or hold violation) the flop can go metastable. Essentially, it gets confused and does not know what to do. In this case, the output is neither “1” nor “0”. It can hang in this state for a long period of time before finally deciding whether the output should be a “0” or a “1”. This behavior can wreak havoc on digital systems, and is a common problem that must be dealt with in asynchronous interfaces.

  53. DaveS

    You’re right, of course, Shoe. I was thinking of classical dynamics.

  54. You got the link wrong for the James Webb Space Telescope. the correct link is http://www.jwst.nasa.gov/ – you didn’t have the www at the beginning.

  55. And it looks like I messed up my linking, too! http://www.jwst.nasa.gov

  56. Tom Marking

    As no reference frame is special, both centripedal and centrifugal forces are real, they merely depend upon which frame one chooses.”

    The equivalence of all reference frames (special theory of relativity) only applies to non-accelerating reference frames.

  57. AHHH!!!!! My EARS!!!!! I can’t believe you said centrifugal force was real. When I think of forces, I think of fundamental forces (gravity, electromagnetic, strong nuclear, weak nuclear). These are forces. Which of these fundamental forces (if it is indeed real) is centrifugal force? You may counter – but what about friction??? Is friction a fundamental force? I say yes. Friction is a macroscopic phenomena caused by the electromagnetic interaction between atoms in the two materials.

    It is fine to TREAT the centrifugal force as real in your calculations, that works depending on your frame of reference, but as one commenter pointed out: not all frames are equal (non-inertial frames are different than inertial).

    A much better way to deal with “this centrifugal stuff” is to go back to Newton’s 2nd law, when written like this: F_net = dp/dt (left off the vector signs) then the “centrifugal” part would fall on the right side as a change in momentum due to circular motion. Just because you can algebraically move it to the left side of the equation does not make it a real force.

    I feel better now. (maybe I will talk about this more on my blog)

  58. It’s me again. I thought about this some more and it seems that this centrifugal force thing is common enough that I put a post on my blog about it – http://dotphys.net/files/bad_physics.html

    I think the best point against centrifugal force being real is the example of a person sitting in a car that is accelerating forward. What is the force that pushes that person back into his/her seat? Yes, there is no such force. It is exactly the same for circular motion and the centrifugal force.

    Alas, this blog post is too old. No one will even see these comments anyway. So why am I still talking? I don’t know.


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