What Makes Lagrange Points Special Locations In Space

[@SteveHodge]

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."

[@willemhaifetz-chen1588]

Good point

[@oldfrend]

was euler really that much of a genius? a wonder he's not spoken of with the same reverence as newton.

[@insanitysportal6692]

🤣

[@milkdrinker7]

@@oldfrend Euler was the greatest Mathematician to ever live

[@mathis8210]

That tells us just how bitchy and envious these people were. He figured that shit out, so he deserves the honor.

[@TusharGoyal1997]

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

[@danieldosen5260]

I came here to say the same thing. THESE pictures are worth a thousand words.

[@Allan_aka_RocKITEman]

I agree...👍👍

[@larryscott3982]

Ditto. Without reservation, Lagrange points have never been better described by graphics.

[@jeremystern1471]

Right, Scott is the man. Amazing video

[@petemurphy7164]

Was going to post the same.

[@l.mcmanus3983]

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.

[@r3dp9]

Even more wild, is that they discovered a rule of thumb that requires no math at all. L4 and L5 are located on two equilateral triangles with the long side centered on a line between both bodies. That's easy! (Though NASA points out that the distances involved are large enough that you have to take into account additional gravitational sources, such as the sun and nearby planets.

[@stephenbarrett8861]

Ole Romer was a boss. Calculating the speed of light in tar 17th century.

[@tiemen9095]

​@@r3dp9 Equilaterial triangles with a long side? They each form an equilateral triangle with the two bodies: E.g. Star-planet-L4 and Star-planet-L5 will form 2 equilateral triangles, and these triangles lie within the orbital plane. That perfectly defines the position of L4 and L5 for any system.

[@brendawilliams8062]

With you

[@eventhisidistaken]

They didn't have our tech, so they *had* to work it out on paper. ...practice makes perfect.

[@mjmonjure]

Finally, an explanation that is clear, concise, and visually communicative for us lay people. Thanks so much!

[@Sanquinity]

Exactly. I've had trouble understanding how the JWST could basically orbit "nothing" so far, but this video at least gave me a bit of an idea of how it works. Still can't fully wrap my head around it, but at least it doesn't just sound like math magic to me anymore. xD

[@sukuvar]

India's Aditya L1 Mission will reside at L1 for 5 years...L1 signifies Lagrange .

[@VeraTR909]

That 3d model representation was great!

[@danielmconnolly7]

Fantasy.

[@jamalalkaabi8]

Lagrange points getting a scott explanation is pretty awesome

[@apotheosis27]

Lagrange Points are incredibly complex concepts. Thank you Scott for helping me understand them a little bit more.

[@MikePaquette]

I'm pleased the youtube algorithm thinks I'm smart enough to appreciate this video

[@nicholasgold9021]

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

[@grantexploit5903]

I wonder if it'd have any use in an end-of-life eccentric Earth orbit or Heliocentric orbit...

[@erideimos1207]

@@grantexploit5903 Yes when it finishes the 12 year mission, if it can, it's supposed to stay in a heliocentric orbit and keeping reporting on any fly-bys.

[@StarkRG]

"We accidentally added a second fuel tank so we figured we might as well fill it."

[@sovo1212]

Let's hope Starship to make refueling easier.

[@Tudarc]

The fuel is planned for 11 years but the gossip is that they think they can get quite a few more years than than. The most significant factor is the Mid Course Correction (MCC) planned for 12.5 hours after launch. If it occurs on time it won't have to dip into the L2 station keeping fuel. If the MCC gets delayed for any reason it will eat into the fuel budgeted for the science mission causing the mission to be shorter.

[@chrisrandom7409]

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

[@stamfordly6463]

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.

[@Schyz]

What an amazing videogame.

[@AldorEricsson]

@@Schyz Yep. Space sims without that really stupid "space friction" can be counted on one hand, and two of them are I-War 1 & 2.

[@collinbarker]

@@AldorEricsson If you are looking for another space game with no space friction, you may be interested in Space Engineers. It is a building game though, rather than a sim. Think of it as mincraft in space with physics

[@watchm4ker]

The L1 point tends to crop up a lot in sci-fi because of a subtle misconception. Writers assume it's the point where the gravitational fields cancel out. It's not, but it is very close, astronomically speaking.

[@danilooliveira6580]

I think I first heard about lagrange points in Gundam, I was kinda surprised when I found out that the lagrange points were real and that the colonies design were inspired by a concept called O'Neill cylinders made by the physicist Gerard O'Neill.

[@ramji102]

Thanks, finally I understand why India Named Aditya L1 ( sun exposure mission), We are proud have say our Indian scientist made theoretical knowledge in practically applied and make the founder Proud...

[@cativillegas]

For a non-science person like myself, these graphics were super helpful to better understand this concept! Just witnessed the launch this morning so I had to look for more information to further clarify L2. Thank you!

[@nakfan]

Same here 😊 Webb is on its way (3rd day) to L2 so better understand it a bit better 😀 Hope Webb will last longer than the estimated 5 years...! Happy New Year from Denmark --- Per

[@techtheta2164]

You are not a non-science person if you're trying to understand it.

[@michaeldunlavey6015]

@Michael Jordan Rosalind Franklin

[@Samuel-hw6in]

@Michael Jordan Fishing I see

[@ddtus]

Does "non-science" mean low IQ?

[@1000dots]

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

[@idjles]

I learnt that L4 and L5 were wells- we didn’t get told about the Coriolis force.

[@1000dots]

@@idjles It makes so much more sense. I could never understand why those points didn't just slowly accumulate dust and debris until it made a big enough object to mess up the lagrange effect. An incorrect theory I'd had myself was maybe 'large' objects can form in lagrange points and then drift away but we'd just never seen it happen. I thought it could possibly be an important factor in planet formation or whatever. Now I know the better explanation: I had been misinformed in a sort of accurate way with the best of intentions. I love when you get to understand something in a new/better way. Anti-science people never understand that science is a self correcting method of understanding things, not a list of facts. Finding out I'm wrong is so damn exciting sometimes :)

[@jeffbenton6183]

Same.

[@Default012]

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

[@chrismusix5669]

Too.

[@maksphoto78]

I think Scott, Destin, Physics Girl, and Amy Teitel should collaborate to make one of a kind of a video!

[@mikefriend1514]

Methinks Scott and Destin track each other’s orbits!

[@DrUseful]

Brilliantly and clearly explained, and very interesting to watch. Thanks for finally managing to make this, Scott! The rotating potential well graphics were a complete revelation moment for me.

[@antoninbesse795]

Just watched for a second time; now I really get it thanks to Scott’s well paced authoritative narrative and great graphics. Thanks, and long live JWST!

[@EtzEchad]

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!

[@r3dp9]

Same here. It all makes sense now.

[@Dragrath1]

@Michael Bishop yeah though it is a matter of timescale even Jupiter's L4 & L5 aren't truly stable just stable enough to still have a bunch of captured bodies from the formation of the solar system over 4.5 billion years later. Though really given enough time no orbit is stable in our large complex universe where n approaches infinity and that is without considering gravitational waves which over vast amounts of time cause orbits to gradually radiate away energy

[@thomascharlton8545]

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.

[@dandan1364]

None of the other videos about Lagrange points make any sense … just guys retelling what they heard without understanding anything. I think you understand this stuff and explained it well. Thank you.

[@user-AdamSmith]

That time lapse of the Earth from the Sun's perspective as the year cycled was really fascinating.

[@austinbutts3000]

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

[@apotheosis27]

And add to that, EVERYTHING in the universe is attracted to everything else.

[@david94549]

Yeah and let me tell you, even if it was her idea in the first place, the third body still causes chaos

[@zloychechen5150]

@@apotheosis27 a friend of mine has a wife who is not very nice, and at one point was properly massive. I guess gravity is what kept them together during that time.

[@apotheosis27]

@@david94549 haha yeah man that story pretty much always ends the same way

[@walley2637]

well, if your going all the way to "that whore mound called LaGrange " you may as well pay for a 3rd body!

[@TusharGoyal1997]

Perfectly balanced, as all lagrange points should be!

[@kukulroukul4698]

spiffing brit

[@marvnuts]

I understood that reference.

[@cedriceric9730]

Just like my...

[@EclecticFruit]

Gravity is a perfectly balanced system with no exploits whatsoever

[@randycastleberry3194]

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

[@jeremynolan4681]

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.

[@scotthoover1568]

I'm no physicist, but I have played a lot of KSP. What baffles me about L1 and L2 is they match the rotational velocity of the smaller body while remaining stable. In my experience, closer to the larger body means a faster orbit, likewise farther away should be a slower orbit. But these points are balanced so perfectly that they're able to be farther away and closer to the large body while having the same orbital period as the small body. Truly amazing people figured this out

[@fritt_wastaken]

KSP only simulates single body orbit in a simplest fixed gravity field. You can't do any "cool" stuff in KSP

[@OnionCultist]

@@fritt_wastaken Im pretty sure there is a mod that implements multi-body physics into the game

[@shreeniwaz]

Thank you for this lucid explanation of a very interesting scientific fact. As India has sent it's first Solar mission 'Aditya' L1, the significance of the L1 helps to understand the purpose of the mission..👍🏻👍🏻

[@Yezpahr]

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

[@FabioCalissi]

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

[@cbst6w5]

Side3, if I’m not mistaken.

[@FabioCalissi]

FWIK L1 = Side 4 L2 = Side 3 + A Baoa Qu L3 = Side 7 + Luna two L4 = Side 2 + Side 5 L5 = Side 1 + Side 6 + Solomon

[@markmarco2880]

So much education in a single video. Thanks for teaching me how to chill in a group of orbital bodies.

[@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.

[@TusharGoyal1997]

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

[@UnshavenStatue]

There are dozens of spacecraft at SEL2, JWST will certainly be the most famous one. My personal favorite there is Gaia!

[@olmostgudinaf8100]

And SOHO is at L1. I thought Kepler was too, but could not find the reference. I must have misremembered it.

[@ivoivanov7407]

@@olmostgudinaf8100 Kepler telescope wasn't on L point, but on "trailing heliocentric" orbit. That is, it is a bit farther from the Sun than Earth, with orbital period of ~373 days.

[@kishordinkarsonar91]

And Aditya L1 of ISRO

[@magmaticly]

Interesting note: James Webb is going to orbit the Sun - Earth Lagrange point, not just park in the centre of it, because it needs to peek out of the Earth's shadow once in a while to get some Sun to power its stuff.

[@darrenmclellan6712]

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

[@trixer230]

I love how far science communication has came! Lagrange points used to be so uknown about to the common public I could use it as a password, and It was my go to "noone will be able to answer this" trivia question! I love how in just 30 or so years the adverage person now knows what these are!

[@bookingsessential]

Agree with the previous comment... I've seen the whole "big black trampoline with a heavyweight in the middle" explanation before... but this was the first time it made complete sense... Seriously.... Great Job!!

[@clearlyepic9958]

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

[@cstenzy9167]

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

[@georgelionon9050]

I got the idea of JWT going for L2 is also because it has earth's protective shadow shielding it from the sun, being in a position of permanent eclipse, because it needs to be cool for the infrared telescopy to work. Otherwise, L4/L5 would be better choices, no?

[@georgelionon9050]

@@bnightm okay, so now why is L2 chosen then for this? as L4 and L5 are much stabler wouldn't that mean a much longer period of operation? Or is it just than L4 and L5 are more difficult to reach making the additional fuel spent to stay stable in L2 not worth it?

[@markshumate78]

@@georgelionon9050 L2 was chosen so that the JWST can occlude both the sun AND earth (and moon?) with one heat shield. The infrared wavelengths that JWST will observe will be affected by the heat from the Sun of course, and even the earth (and moon for all I know). So having the JWST in an orbit such that a single heat shield can ALWAYS occlude the sun and earth is a great help

[@georgelionon9050]

@@markshumate78 I see makes sense, thank you

[@NotAyFox]

By far the most comprehensive description of Lagrange points I've seen so far.

[@positivelysteve]

I don't think I've had a better understanding of gravity wells than I did watching this video. Thank you, Scott, for all the science knowledge you impart so seemingly effortlessly.

[@ammobake]

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

[@_Mentat]

Possibly because the reason objects fall down the gravity wells is because of gravity. These "rubber sheet" explanations are effectively saying gravity works because of gravity.

[@xXCatalystic37Xx]

Always love a good Manley explainer

[@Briggsby]

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?

[@AldorEricsson]

@@gamerfortynine Not really a problem, just sync them all using the same set of quasars, then factor in gravitational time dilation. The tech is around since 1990s.

[@insanitysportal6692]

Short answer: yes Slightly longer answer: but it's not easy Slightly longer corollary: and it's prohibitively expensive

[@jamessheridan2142]

You could add in telescopes to this at the L1&2 points stabilized by solar sails and sharpen up your results.

[@jamessheridan2142]

@@gamerfortynine Sounds like a job for one of those new fangled computers they got in them there big city's.

[@DrDeuteron]

@@AldorEricsson I now quasars are fine for navigation, but are the fast enough to synch the phase of a radio wave?

[@mountainousterrain1704]

As a molecular biologist this is the best explanation of La Grange points I have seen. Great graphical representation. I understood (almost) everything. Looking forward to seeing JWST in action.

[@prodanman]

Thanks Scott Manley. Best Explanation Of Lagrange Points. Happy You Even Cover Coriolis Effect That Nobody Else Covers. Thanks For All You Do For Us Science & Space Geeks

[@Clyman974]

Wow I can't believe they named a point of space after a ZZ Top song

[@ArKritz84]

Damnit, I should go to bed, but now I *have* to listen to some ZZ Top! 😂

[@hodor3024]

beat me to it.

[@RCAvhstape]

RIP Dusty Hill, gone to the great Lagrange point in the sky...

[@jimleane7578]

I asked myself "how, how, how, how?" Now I know. Thanks Scott ☺️

[@hughbrackett343]

They got a lot of nice girls out there.

[@harrystuart7455]

I have to say, the visualisation here is absolutely superb. You've given great physical intuition for how Lagrange points and their (in)stability work without having to rely on any dense maths

[@ashokreddy2982]

It's where India is trying to set it's mission thing to observe sun

[@RijumanSen]

amazing graphic representation without overly oversimplifying. Awesome video.

[@larrylewis6771]

A picture is worth a thousand words. Thank you for making a difficult concept simple to an amateur mathematician.

[@conors4430]

Really neat, first came across this terminology when listening to the Apollo 13 flight controller tapes on KZbin, that’s when it actually clicked in my head that as a spacecraft rises further and further towards the moon it slows down like a tennis ball at the top of it ahrc before it falls, the aim is for it to have just enough Velocity that it crosses the LeGrange point and starts falling towards the moon. I never totally understood how it all worked until I realised that

[@RockChalk263]

There isn't a Earth-Moon LeGrange along the path Apollo 13 would have taken to get there. (Remember, the Apollo craft doesn't fly to the moon in a straight line, but rather a parabolic arc) The Sun-Earth L2 is several times further out from the moon's orbit. What you're referring to is the Apollo craft slowing down as it leaves the earth's sphere of influence and speeding up as it enters the Moon's and starts "falling" back down.

[@GregiiFlieger]

Play Kerbal Space Program and these things just fall into place :-)

[@conors4430]

@@RockChalk263 fair enough. I just assumed it was the halfway gravity point between two objects

[@ianthomas7139]

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.

[@walshrd]

Read up on your history of the original halo orbit mission, ISEE-3. After it completed its mission, it was sent out on another mission to the comet Giacobini-Zinner in 1985. That mission to the comet was very successful.

[@programmer1840]

You didn't really explain why the L2 Lagrange point has to orbit in a halo.

[@zachhouliston4508]

The way you explain complex concepts and make it so understandable and enjoyable is phenomenal thankyou scott

[@jeanqueudot6152]

Mille mercis Scott. Je ne parle pas anglais mais malgré des sous-titres approximatifs en français vos explications étant précises et abordables pour un nul en maths ainsi que vos animations parfaites j'ai tout compris aux points de Lagrange et pourquoi L2 avait été choisi pour Webb. Nous sommes le 20 janvier et Webb n'est plus qu'à 63000 km (environ 40 000 miles) de l'orbite L2. Vivement cet été que nous ayons les premières images ! Encore bravo pour votre vidéo

[@edstirling]

1:53, just casually witnessing the end of the world.

[@maksphoto78]

"Hello, it's Scott Manley here." - That's how you know you're gonna have a good day, watching an awesome video.

[@aaronjose6271]

Anybody watching this after JWST just got launched into the L2 Halo Orbit?

[@carlatteniese2]

Fascinating. The final graphic depicts the Lpoint scenario best.

[@Scripture-Man]

I just wanted to know what Lagrange points were and thought a 14-minute video would be going into too much detail. But I was captivated by the clear explanation and great graphics. Seems I got caught in a Lagrange point of my own.

[@soundjudgment2150]

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

[@friedhelmmunker7284]

Jupiter Trojaner are on T4 and T5. Stable position.

[@hak5129]

Here after Aditya L1 launched!

[@PaulCashman]

What a great look at LaGrange points! Informative and not too technical!

[@chethankumar9568]

That's a professional way to explain something which is complicate to understand. Thank you for enlightenment on this space atmosphere. I m stunned by the graphics used.

[@sudiptechnical368]

Finally Our ISRO🇮🇳❤️ has successfully put Aditya l1 probe to the Lagrange point 1❤️

[@georgeford6056]

Lagrange points are special locations, but not as special as that shack outside La Grange.

[@throwawayavclubber7269]

They've got a lot of nice girls.

[@D3emonic]

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

[@freefromreligion8090]

This is the best explanation of the Lagrange points that I've seen so far I still have to get a better understanding of the Coriolis effect

[@manaskumarhaldar2725]

I commented before hearing about position corrections needed for the Webb. You gave a good explanation of the stability of position at Lagrange points.

[@zainiikhwan9405]

First time I learn about Lagrange point is from Gundam series 😅

[@mjmabile22]

Me too! That’s where the space colonies are usually placed at

[@nightcat7741]

same! 😅😂

[@davidclark9469]

Finally a clear explanation of Halo orbits, including Coriollis, Thanks Scott, beautiful stuff.

[@triaxon3791]

Thanks, this helps me wrap my head around this a lot better, The motion graphics really help. Gr8 job man(ley).. 😀☮

[@Navneet_100]

waiting for ISRO Aditya L-1 launch .....letz go

[@swealf-nonofficial]

I've been waiting for an explanation of what exactly are Lagrange point for far too long, thank you for your video.

[@gardentimelapse]

This is the best video I have ever seen on Lagrange points. Thia is pure magic.

[@glenn_r_frank_author]

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.

[@user-si5fm8ql3c]

A relay out ar L4/5 that needs to relay all the way to mars would be a gigantic technological challenge. First of all, you need a huge, light weight radio dish, its very likely that a spysat operated by the US Airforce has a dish with a diameter of 100m, big enough for our purposes, but no one is sure if and how it works, state secrets and all. Secondly, you need a very powerfull amplifier to boost the signal, with large solar panels to power it all, further adding mass and complexity For now, and even for martian bases in the future it might be easier to just wait out

[@Demobot1]

@@user-si5fm8ql3c You would have a bigger problem of fuel. How would you refuel a relay station that far out?

[@user-si5fm8ql3c]

@@Demobot1 You would not need to, L4 and L5 are stable points, what little force is required could be easily generated by solar wind vanes, without needing any fuel

[@Demobot1]

@@user-si5fm8ql3c all the Lagrange points are stable. But fuel is still needed to reposition the antenna to point to Mars or wherever.

[@user-si5fm8ql3c]

@@Demobot1 no, any deviation from L1-3 is not countered by a sufficiant corrective force, staying at L1-3 costs fuel, at L4-5 the corrective force is big enough that you can stay there without spending fuel. Pointing to mars can be done with big panels that catch the solar wind to generate torque, its not much torque, but you can supplement it with reaction wheels for more accurate pointing.

[@canuckcorsa]

The BEST explanation I've ever seen. Great graphics!

[@frankdecrom6317]

This totally made sense with the 3D donut gravity well description. Thank you!

[@gutsm3k144]

Of course Euler discovered them first lmao.

[@shawnerz98]

This video confirms: math is hard.

[@dmzone64]

Nice, serious. No crazy, easy speculation... You, Sir, are a breath of fresh air and got yourself a subscriber.

[@srikkanthank]

Brilliant graphics rendition that makes it easy to understand.

[@Keavon]

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)?

[@RutvikMarathe327]

Well there's a L3, L4, L5 for each of the planet-sun pairs. Earth-sun will have its own Lagrange points, as will jupiter-sun, etc. Although you are correct in saying that even at something like the Earth-Sun Lagrange points, Jupiter and Saturn will still cause some gravitational perturbations to those orbits

[@dykam]

My uneducated guess is that it only works if you either adjust for them, or those influences are nearly negligible at those points.

[@thenasadude6878]

Because the distances are huge and each planet remains the dominant body well beyond the Lagrange points. Don't be fooled by the usual visualisations where planets are all amassed near the sun. This video makes a good job of showing actual proportions: kzbin.info/www/bejne/sIOWepqZaLebnMk

[@TrueThanny]

First is the fact that gravity varies by the inverse square of distance, so its effects go down very fast as distance increases. Second is that the dominant gravity in the relationship is from the Sun, which is more than 1000 times more massive than Jupiter, as well as closer to the L4/L5 points.

[@toriknorth3324]

Intuitively, I would think that an object placed at a lagrange point is most affected by planets that are in orbital resonance with the object. If we look at an asteroid in, say, the earth-sun L4 point, the earth and the sun would both pull on the asteroid with basically fixed force vectors (in a rotating reference frame with the sun and earth fixed). Each other planet would have a varying force vector that partially cancels out when you integrate it through time. The orbital resonance causes the earth to have a much larger effect on the asteroid than non-resonant planets would.

[@valaha]

Thank you for this very best of Lagrange point video. With that 3D graph at 6:00 finally i understood it

[@stephanieparker1250]

Ok this is amazing.. I finally understand! Thank you! The 3D graphic with the gravity wells was my light bulb moment!

[@cleon_teunissen]

There is a fundamental problem with the explanation as presented in this video. Many authors present this explanation, but there is a problem. Let me set up the context that will allow you to see the problem: Take a system with a primary much heavier than the secondary. Set the secondary in an orbit that is quite eccentric, for instance a ratio of 3 to 1 for distance at aphelion and perihelion. Now plot the motion of the secondary in a rotating coordinate system that is rotating with the same period as the orbit of the secondary. As we know, orbits loop back on themselves. The plot of the orbit loops back on itself in inertial space, and the plot for motion with respect to the rotating coordinate system also loops back on itself. (Crucially: this looping-back-on-itself occurs *only* when the motion is plotted in a rotating coordinate system that is rotating with the *same period* as the orbit of the secondary.) With the context as described above in place: According to the explanation presented in the video the fact that in the rotating coordinate system the orbit loops back on itself is to be attributed to the Coriolis Force. But when the orbit of the secondary is eccentric the motion with respect to the rotating coordinate system also has sections where the motion (wrt rotating coordinate system) curves *against* the coriolis force vector. Of course: the orbits of tertiaries in the vicinity of L4 and L5 of a secondary are always fairly circular orbits, never highly eccentric orbits. The point is: attributing bound system plots looping back on themselves to coriolis force is correct only in the case of planar motion subject to Hooke's law. When applied in the context of gravity you run into inconsistencies, as demonstrated for the case of eccentric orbits. My hope is that you will actually implement that in a simulation, as I have. I made that simulation, I watched the motion on the screen. I hope you will set up a demo in which an eccentric Kepler orbit is plotted with respect to a rotating coordinate system that is rotating with the same period as the orbit of the secondary. Plot the coriolis vector. Try a range of eccentricities. See if it matches your expectation. The Lagrange points L4 and L5 are in a sense points of repulsion. But the thing about orbital motion is that whatever your orbit is: after a full revolution the orbital mechanics returns you to the point where you were a period ago. You cannot not return. So even though L4 and L5 are points of repulsion, and objects are all the time experiencing a push *away* from their Lagrange point, that push away from the Lagrange point does not accumulate. In the case of L4 and L5 the push-away is in *all* directions: that is why there is no accumulation. In the case of L1, L2, and L3 the push away from the Lagrange point is not in all directions, and then you do get accumulation.

[@cslloyd1]

Incredible effort on this presentation.

[@rolfjacobson833]

"the three body problem" best book ever. will blow your mind. A must read!!!!!

[@jaknap1]

Best explanation on KZbin of the Lagrange points. Easy to follow and the graphics are amazing. Thanks!

[@ScottSlooper]

That is the best visual/graphical discussion of LaGrange Points I have ever seen. Thank you!

[@geoffreydowen5793]

being a luddite I had to watch this twice; I think I got the jist of this though so at the age of 64 I continue to be educated. love your channel your ability to simplify astrophysics , my bro is the physicist in oil though . thanks Scott top marks . fly safe yourself regards from the UK .

[@andrewwalker7276]

Loved this video, the Lagrange points can be difficult to understand and graphics/animations can make a huge difference. Was interesting hearing the bits on JWST near the end, now knowing it is up there and observing is amazing! You showed the Jupiter Trojans, quite a few of the other planets have also been discovered to have trojans from the large survey telescopes. Maybe a future video. This includes a temporary Saturn trojan I was involved in finding, 2019 UO14, a paper is appearing soon so stay tuned!

[@jujenho]

Congratulations, Scott Manley, for a clear explanation of a very complex celestial mechanics problem.

[@wiloux]

great video! this subject is so beautiful and always gets more complex when refining hypothesis on the system. It sits at the edge of newtonian dynamics and chaos theory!

[@severinopereiracarollofilh5933]

Thanks for the explanation and graphics that makes easy to understand how is a object's behavior on these Locations. Congratulations.

[@szkoclaw]

I think it's better explained by using orbital speeds. L points are on different distance from the main body so their orbital frequency should be different, but the second body adds a little bit of push or pull that allows them to stay in orbit that should not normally match their orbital speeds.

[@radhakrishnansivaramakrish9902]

Dear Scott This video is out of the world experience just enjoyed Big thanks

[@hangmann747tinmann8]

With out a Doubt your best video, thanks for taking something hard to understand, and made it very simple to understand

[@GuilhermeCarvalhoComposer]

Probably first time I really get an intuitive feel about Lagrange points. Many thanks, this was really great!