What Makes Lagrange Points Special Locations In Space

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Lagrange Points are special locations in planetary systems where gravitational and rotational forces cancel out. Sometimes we find asteroids or dust clouds lingering near these places. Space missions may use some of these locations for spacecraft as they offer many advantages over orbiting in the Earth directly.

Universe Sandbox is used for some of the 3 body problem animations

Other graphics are created with GMAT and POV Ray

For a more mathematical derivation of these check out this series:

  1. Marc-Antoine

    “But I think it’s a lot easier to look at this in terms of *force*.” It’s ironic, considering we are talking about Lagrange.

  2. Ryan R

    4:44 as with physical objects with approximately uniform density, the gravitational pull becomes linear (x instead of 1/x^2) with distance once you enter the object, meaning the potential well becomes quadratic (x^2 instead of presumably 1/x or 1/x^3) inside the bounds of the object.

  3. Isaac Plays Bass

    Beautifully presented and illustrated Scott, Thank you. I have always had problems visualizing Lagrange points and comprehending a “rectilinear halo orbit” until now, it makes so much more sense now.

    Have you considered “Thesis by publication” a la Steve Nerlich of Cheap Astronomy Podcast?

  4. Ryan

    I’ve been looking at lagrange points for a while and this video gets me as close as ever to understanding them.
    That L3 on the other side of the sun continues to baffle me though 🤣

  5. Ian Thomas

    These get a role in the Neal Stephenson book “Seveneves” where some characters use Lagrange points to head out of the gravity well and go after a comet without burning insane amounts of propellant. Great book, be awesome to have Scott review it and some of the orbital mechanics used within it.

  6. oraz

    When equations have no analytic solution it’s fascinating. I’ve never seen anyone show the expressions for the 2 vs 3 body problem and why you get something with no antiderivative. I don’t even know what book to find that in.

  7. M E

    This is exactly the nuanced explanation I’ve been looking for every time I look up Lagrange points, thank you!!

  8. Angarsk100

    Oh boy! Of all of your vids that I’ve watched and enjoyed, this is by far the most comprehensive, yet simple enough to be a huge learning point for this subject. Thanks!

  9. JulianShagworthy

    0:35 It’s refreshing to hear a science communicator YouTuber say ‘orbiting each other’ instead of ‘(smaller mass) orbiting (larger mass)’. It’s little things like this that help people to understand :)

  10. ScotsmaninUtah

    As an aerospace engineer this is a wonderful introduction to Lagrange points and the graphics are very impressive . Thank you for posting.

  11. CrushOfSiel

    I remember having to solve and show that all these lagrange points exist in my graduate mechanics class. Man… those were some icky problem sets. It wasn’t uncommon to see 30-40 pages of scribble being turned in per student. I always felt awful for the TA.

  12. Austin Butts

    “But adding a third body just leads to chaos.”
    I love how that statement is both technically and colloquially accurate.

  13. Don W

    Thank you Scott, I’ve never fully understood how L2 and L3 were stable. They seemed to me that they would drift toward the main body. Your explanation makes sense to me

  14. Michael Grundler

    That 3D graphic at 5:36 is easily the most elegant and most descriptive visualization of all five Lagrange Points I have ever seen!

    I knew the amount and position of the Lagrange Points before and I also knew that they exist because all the forces cancel out but one glance at this graphic intuitively showed me how and why the forces cancel out at these points.

  15. Pastor Dan Muller

    Best “lay person’s” explanation of La Grange points I’ve had yet. I should know, I am one. Thank Scott!

  16. Gary Holmes

    I’ve known about Lagrange points for years, but never quite ‘got it’ with L4/L5 until this video. Nice work, Scott. I shall now commence flying even safer than before. Cheers.

  17. Rmaia3d

    People already said it, but I’ll say it again: those well graphic visualizations were just next level! I understood the concept of the Lagrange points, but not fully grasped it until seeing those graphics. Wow, instant “aha” moment! Makes perfect sense. Thanks a bunch Scott for putting this together! 👍🏻👍🏻

  18. Snacksy

    So Lagrange points are just those three gravetational functions combined where the derivative equals zero?

  19. René Schmitz

    This was the best demonstration of lagrange points that I have seen. Awesome!

  20. Matthew B

    The nunber of “aHA!” moments of me realizing what you were saying because of the animations was quite high. Really good stuff, Scott.

  21. Tim Robinson

    I always wondered how big the L-points were in relation to their respective bodies. This was a super helpful explanation and the 3D model really made things clear. Thanks!

  22. TheYear2525

    Oooh! That’s the best explanation of Lagrange points I’ve seen so far. Now even I get all the points. Usig a gravity well map and introducing centrifugal force to it made it all clear.

  23. Kirk Wagner

    That 3D image is a really good illustration. L-points are flat spots in the space/time curvature. Thanks!

  24. Daniel Robertson

    This is great, I’ve never understood how L4 and L5 could be Lagrange points until I saw your visualization, thanks Scott Manly!

  25. Xenosplitter

    I’ve known about Lagrange points and had a basic understanding of what was going on, but the visualizations at 5:35 really made it click! I think it helps I’ve been recommended that one video on flipping a sphere inside out, but with the combined gravity wells diagramed as deformities on the object’s surface having the “bowls” (although bowls in this diagram aren’t Lagrange points themselves), “saddles”, and “domes” I finally pieced it together! While I’m not using the proper terminology each time the surface “inverts” a point exists where a theoretical marble would fail to fall out of it’s place.

  26. Sound Judgment

    Well that’s the most interesting thing I’ll see today. Thanks Scott. Great animations also. Makes me want to run a simulation with two “tethered” particles orbiting on opposite side of the L4 or L5 to see if it cancels out orbit instability at all

  27. Nominal So Far

    This is a great video in respect of explaining some pretty complex Orbital mechanics in an understandable, intuitive way to those of us not blessed with the math skills to understand the formulae alone 😆 Thanks Scott, top class as always!

  28. Etienne B

    It makes so much more sense to me now, thanks to these amazing graphics. Thank you Scott!

  29. David

    Thank you! I’m a casual space fan and I finally understood Lagrange points.

  30. Rebs RedOne

    Thinking about scientists like Leonard Euler or Joseph-Louis Lagrange for me has the same effect as looking at pictures taken by the Hubble telescope (and hopefully soon JWT). I feel like a tiny, insignificant speck of dust in an infinitely vast universe.

  31. Glenn R. Frank

    I was wondering… as the Mars Rovers all had to take some time off from activity because of the Solar conjunction… Has anyone ever proposed putting relay communications satellites at L4 and/or L5? so we could send a signal AROUND the Sun to Mars? or is that just not worth the expense and time? Better just to wait out the conjunction? Seems like if we ever put settlements or manned missions on Mars we would need this though.

  32. Antonio Soffici

    FINALLY I have a real grasp of the whys of Lagrange points!
    Thank you, Mr Manley. I owe you one

  33. Fabio Calissi

    the most dangerous is Lagrange Point 5 where Solomon, Zeon’s stronghold, is located

  34. epincion

    Very good informative talk Scott, my brain hurts at the thought of Euler and Lagrange doing the math with quill and parchment.

  35. Jeff Cox

    Scotty; Honestly, “The” coolest video you have produced! As an ex SSBN submariner. Launching bad things into space if not necessary I learned a bit about physics and orbital mechanics. Thank you for being a nerd and a DJ like myself. BTW I miss the “Night a DJ saved my life.” Off of your bookshelf!

  36. Dave Pin

    This 3d explaination is magnificent. I understood the lagrange points but this visualisation is better than any other that I have seen.
    Top marks as usual.

  37. Prich038

    Would be cool to put space habitation centers out there, like giant rings like in Halo so they’d move very little

  38. maksphoto78

    “Hello, it’s Scott Manley here.” – That’s how you know you’re gonna have a good day, watching an awesome video.

  39. simonas rotkinas

    I was astonished when I was not able to find your video about Legrange points, last week. Thank you for this video!

  40. james sheridan

    This will go down as a “Classic Explanation” along with the lectures of Richard Feynman.

  41. What The Function

    My greatest fear is the earth being suddenly ejected from its orbit.

  42. Kevin Morford

    Thank you Scott for the clearest explanation I have seen to date regarding La Grange points, and why some are more stable than others. Keep up the good work.

  43. Skukkix23

    I mean you can watch a whole lecture about it or literally see 1 render from Scott for 1 minute. I am glad youre not a teacher/prof cause you have a great paying job and teach for fun for millions of people.

  44. etherealessence

    Wait…. they’re actually gonna launch it? O.o

    I… I wasn’t prepared for this.

  45. Masterplan Oaks

    Great video. Full illustrates the concept of Lagrange points and halo-orbits. Thanks Scott.!

  46. Trooper 6190

    Thaaaank you for going into depth explaining this! Destin’s last video about the James Webb telescope touched on this and I’ve been hungry for more info since!

  47. Yezpahr

    I’ve seen a hundred of these explanations, but now I finally understand it.

  48. Randy Castleberry

    That weird shadow on the Sun sphere almost convinced me I had dead pixels on my display.

  49. chris random

    I literally just learned about Lagrange multipliers today, with an exam on multivariable critical points/ extrema on Monday and now its connected to my favorite subject, space, and my day is made

  50. PH-G

    Just learned about Lagrange points in classical mechanics. How convenient!

  51. Steve Hodge

    As wikipedia says, “In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler.”

  52. master shooter64

    Why is euler everywhere??? okay I’m convinced that euler’s a time travelling math wizard

  53. Anders Juel Jensen

    That was a bloody epic visual representation! :D

  54. PsychoLucario

    always amazes me what 18th century polymaths accomplished given how little practical application a lot of it had in their age

  55. cstenzy

    First learned about Lagrange points through one of the cards in Terraforming Mars, great to have an in-depth explanation!

  56. Shoot 2 Splatter

    Been watching your videos for years and was hoping you would break this topic down into simple terms. L1-3 make intuitive sense but I never bothered to read enough about L4&5. Thanks

  57. mike miller

    it’s been awhile, looks like you have stepped up your game. now just make a video that explains the basics of Calculus.

  58. Patrick's Music

    Love the good visualizations! Really helps me understand the concept. Also, is this logic practical in kerbal?

  59. L. Mcmanus

    It always blows me away what math people were able to work out centuries ago. So much of where we are today and what we are able to accomplish is based on hundreds and even thousands of years of technology and mathematical understanding.

  60. john frink

    What a great channel based in physics! And eager to explore the unusual. Thanks

  61. Jack Taylor

    Hey Scott, you should do a video or two on the board game High Frontier. It’s a very real projection of the solar system on a fixed board, and makes heavy use of Lagranges.

  62. shawnerz98

    This video confirms: math is hard.

  63. Witchdoctor

    I thought I know what Lagrange points are, but these visualizations were great and showed me that I know nothing :D thanks Scott for another informative video

  64. ammobake

    For some reason I’ve always disliked the idea of gravity being depicted in a flat 2D context. But neat graphic!

  65. Steaksaucer

    My mind is being blown right now! 🤯🤯🤯 I’ve never understood L4 and L5 before!

  66. Darren McLellan

    Thank you for a well-done explanation Scott. It’s not easy to wrap one’s head around this but you have helped immensely.

  67. Demonic

    The moment when you wish Scott would release a new video… to realise an hour later, he did. Thanks!!

  68. sj sharksfan

    That was an excellent explanation for this Scott, thanks for sharing! Fly safe brother 👊

  69. Cole Smith

    I remember writing simulations of this after taking multivariable calculus… Such an awesome problem to work on as a challenge!

  70. Nerb1

    Awesome. Your contour explanation was clear as a bell. Im not sure how many people asked how an object can orbit nothing on the previous video, but I was definitely one.
    Thanks Scott.

  71. Clearly Epic

    This video so simplified the concept of LeGrange Points! Thank you Scott!

  72. Marked Ashamed

    I need to see more L4 and La2 in space opera ship combat.

    The Battle of L4 has a nice ring to it.

  73. De boa na Lagoa

    I’m a physics student and I’ve done the math. But those graphics were really next level. Thanks, Scott!

  74. Thomas Charlton

    Thanks Scott!
    Now I have a much better understanding of the stability of the Lagrange Points. Likely not capable of a complete understanding but I do now have a “better” understanding. Orbital mechanics is basically simple yet mind numbingly complex.

  75. 1000dots

    I thought I already had a good understanding of lagrange points but I learned lots here <3

  76. Zach Manburg

    Best explanation/representation of Lagrange points I’ve seen. Thanks.

  77. J E R E M Y N O L A N

    Thank you so much for this. My layman mind has been struggling with this for 2 years while reading about and watching videos on the James Webb telescope. This is simplest and most easily understood explanation of the Lagrange points I’ve found.

  78. Richard Maier

    I’ve always wondered just how much is hiding in the Sargasso Seas of Jupiters Lagrange points 3+4?

  79. Stam Fordly

    First heard of L-points in the ’90s game “I-War” where they were used as start and end points for interstellar jumps but I never quite “got” why all of them existed. So thanks for this Mr Manly, you’ve dissipated a bit of twenty-odd year old incomprehension.

  80. Andrew Mills

    Fascinating Scott – plus the added bonus of a weird edit at 12:08

  81. David Messer

    Wonderful explanation of the LaGrange points! I knew what they were from the equations, but I never saw the rotating reference from potential wells before. That really makes it clear what’s going on.
    I also didn’t know why L4 and L5 were stable. It’s pretty obvious that the others wouldn’t be stable though.
    You are a wonderful teacher Scott!

  82. Keavon Chambers

    I’ve still always been confused: how does L3, L4, and L5 work in the real solar system, which isn’t just three bodies? At the distance to L4/L5 and especially L3, the gravitational pull of the Earth must be extremely small. How come other bodies, like Jupiter and Saturn, don’t play a much larger influence than Earth does on the entire opposite side of the solar system (L3) or as far away as the sun is (L4/L5)?

  83. Nicholas Gold

    I cannot wait for the James Webb. I hope the fuel it has on board miraculously lasts much longer than it is supposed to.

  84. Tushar Goyal

    Those were some of the most intuitive graphics I’ve seen when explaining Lagrange points. Well done, Scott!

  85. D

    Just watched SmarterEveryday’s videos on JWST and was very interested in learning more about all the Lagrange points. Thanks for the video scott

  86. dracula3811

    Great visuals and explanation of lagrange points. I understood what they were before but the graphics helps me with the comprehension considerably.

  87. Mark Harlan

    SM is a national treasure

  88. Mike Counsell

    Brilliant! Wanted to learn about the nitty gritty if the Lagrange points since first heard about them.

  89. Tushar Goyal

    Interesting to see both Lucy and JWST having their missions/orbits focuced on Lagrange Points!

  90. Tushar Goyal

    Perfectly balanced, as all lagrange points should be!

  91. Jason

    Does earths elliptical orbit affect this in anyway? And the fact that our elliptical orbit changes over time around the sun?

  92. Vera de Wolf

    That 3d model representation was great!

  93. Michael Henson

    Could you put a pair of radio telescopes at Earth’s L4 and L5 points and use interferometry to get an effective dish size of only slightly smaller than Earth’s orbit?

  94. Gutsm3k

    Of course Euler discovered them first lmao.

  95. subliminalvibes

    La Grange means “barn” in France.

    Quite poetic really, to place your satellites in a nice safe barn in space. 👍😎

  96. Jonathan Janzen

    Instant thumbs up! I’ve been waiting for this video!

  97. YooZherName

    “Adding a third body just leads to chaos…” Anyone who’s ever been cheated on knows that one ;)

  98. Jamal AL

    Lagrange points getting a scott explanation is pretty awesome

  99. Adam Kerman

    Right when I think to myself about a subject Scott uploads a video about that very subject without fail

  100. xXCatalystic37Xx

    Always love a good Manley explainer

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