Neil deGrasse Tyson Explains The Three-Body Problem

you're going to get an astrophysicist explanation of the literal three-body problem without reference to anything that's shown up on streaming services and that means he's not gonna ruin the show for you I don't know anything about I don't know anything about the show but I do know enough to describe the three body problem to you coming up [Music] let's let's start simple okay okay okay so as we know the moon orbits the earth right but that's not the right way to say it okay okay all right the Moon and the Earth orbit their common center of gravity oo so Earth is not just sitting here right and the moon is going around going around it they feel in their Common Center you know where it is it's a thousand miles beneath earth's surface along line between the center of the earth and the center of the Moon gotcha so as the moon moves here that Center Mass line shifts okay so that means Earth is kind of jiggling like this as the moon goes around gotta that's their Center of mass all right this is the two- body problem it is perfectly solved using equations of gravity right and mechanics makes sense perfectly solved yeah Isaac Newton solved it okay my boy that's your man so that worked then Isaac applied the equations to the Earth Moon system going around the Sun okay okay that worked too so in that system Let's ignore the moon for the moment it's earth going around it's another two- body system two system all right but then he worried he said every time Earth comes around the backstretch and Jupiter's out there right Jupiter about tug on it a little bit a lot of gravity a little bit tug on it as we com around back to the other side what's up Earth all right and then it comes around again tugs on it again what's up earth right and of course everybody's moving in the same direction around the Sun so the Earth would have to go a little farther in its orbit to be aligned again with Jupiter but it's going to tug on it right okay he looked at all these little tugs and he says I'm worried that the solar system will go unstable right because it keeps tugging on it it keeps pulling it away and the previously stable orbit would just Decay into chaos okay okay he was worried about this you know what he said but I know my stuff works and it's been and it's looks stable to me right so clearly it is stable even though it looks like maybe it wouldn't be stable you know what he says he said every now and then God fixes things well there you go that's the answer even Isaac Newton wow look at that when in doubt went in doubt just just let God figure it out right I can't figure it out God Did It clearly we're all still here and we haven't been yanked out of orbit by Jupiter right but Jupiter is pulling on us so it's a god correction God God correction okay this this is the first hint that a third body is messing with you right okay in some way that maybe is harder to understand fast forward 113 years oh right we get to uh llas he studied this problem right okay and he developed I don't think he invented but he developed a new branch of calculus oo called perturbation Theory aha okay unknown to Newton even though Newton invented calculus right he invented calculus right all right so he could have done it he could have said in order to solve this problem let me invent more calcul more calcul just need more calcul I just need more do do it didn't do it so LL develops perturbation Theory and it comes down to we have two bodies the Sun and the Earth in this case and the third one the tug is small but it's repeating it's not a big Jupiter's not sitting right here it's way way out there it's just a little tug and so you can run the equations in such a way and realize that a two body system that is tugged Often by something small that it all cancels out in the end gotcha okay okay so when it's out here the tug is a little bit that way but now it's over here and the tug is less right all right and then sometimes it's tugging you in this direction when that's the configuration you add it all up it all cancels out Newton could not have known that without this new branch of calculus okay okay pertubation Theory so that took care of that third body gotcha where solar system is basically stable okay for the foreseeable future in ways that Newton had not imagined in ways that Newton required God right okay oh by the way just a quick aside this is now we're up to the year 1800 uh you know who summoned up these books to read them immediately because the there a series of books called Celestial mechanics okay Napoleon ah na am Napoleon Napoleon who read all the books he could on physics and engineering and metalurgy look at that okay it wasn't just a tyrant right he was like he was a smart Tyrant smart Tyrant was all right so he summons up the book doesn't need doesn't have to be translated because they're both in French right he reads it goes to llas and says Monier this is a beautiful piece of work brilliant but you make no mention of the architect of the system he's referring to God and llas replied sir I had no need for that hypothesis oo that's a mic drop oh that is tough man you that's a dig on Napoleon and on new Newton yeah and on Newton I have oh man look at that yeah all right so let's keep going go ahead so now let's say we have not just the planet and one of its moons but let's say we have a star and another star double star system famously portrayed in what film uh Star Wars Star Wars yeah all right of course so those two suns and the planet is stable and I'll tell you why in a minute mhm but if you take a third sun and put it there about approximately the same size then what kind of orbits will they have give me two fists here okay so I'm feeling this one but now I feel that where's my gravitational allegiance to go am I going to come through but then am I going to go that that way or this way so I'm coming into the system and do I go to you in orbit but wait you're still coming around here now I feel this and so it turns out the orbits of a three-body problem are mathematically chaotic yes I was about to say that did not seem very stable SS has to give well this is this is in the series what talk something I don't I haven't seen the series I'm just saying something has to give that's all two of these are going to collide one is going to get ejected right okay that is the classical three body problem three objects of a approximately similar mass trying to maintain a stable orbit and it goes chaotic with just three objects look at that it is an unsolvable you can let me say that differently you can calculate incrementally what's happening and track it until the system dies right or splits apart or whatever but you cannot analytically predict the future of the three-body system because what chaos will do for you in your mathematical model is if you change the initial conditions by a little bit right a little bit the solution diverges further down the line that goes crazy it's not just a little bit different later on down line it is exponentially exponentially different correct with the with the smallest increment of distance so I'll say I'll move you in this direction in this model and then in a slightly different direction than the other model it goes chaotic that's what we mean by chaos right okay it's mathematically defined Okay so now there's something called the restricted three body problem all right okay okay the restricted three body problem never heard you have give me your two your two things back two plan you got that okay two bodies you got your two bodies now the third body is little ah now you two will orbit each other right okay and then and then this it's not messing with them right so so there restricted three body problem we have two masses of approximately equal and one that's much less than the other two that is solvable right it's called the restricted three body problem gotcha in the Star Wars case that's the restricted three body problem right because you have the two stars and you have the little planet the little planet deal and it's even better because the planet is so far away that it only really saw one merged gravity of the two stars right okay you're far enough away that that difference is not really mattering to you you maintain one stable orbit around them both around both stars both Stars okay now if it got really close then you'll have issues because then ites again gravitational Allegiance matters the stars are not going to care but you will cuz you you'll get eat you don't know where to go you don't know where to go I'm in love with two stars and I don't know what to do which way do I turn so anyhow I so so the three body problem the takeaway here is it's unsolvable yes not just because we don't know how to do it yet because it's mathematically UNS bu into the system the system is chaotic yeah okay unless you make certain assumptions about the system that you would then invoke so that you can solve it and so one of them is a small object around bigger ones another one oh by the way in this solution with Jupiter out there slightly tugging right yes it turns out over a very long time scale this is chaotic but much longer time skill than Newton ever imagined okay okay because yes we are small compared to the Sun but Jupiter isn't all right and we're trying to orbit between them right right so that's that's all it's not deeper than that it's not yeah right I could have said the four body problem but this problem begins at the three body problem right right because you're going to have the same thing in four bodies or five bodies it's going to be the same we have star clusters with thousands of stars in them and they're all just orbiting we have to we can model it but cannot predict with Precision where everybody's going to be at any given time okay CU it's chaotic the're chaotic so it's basically it's about the chaos it's about the chaos it's all about the chaos yeah so what we do is we model the chaos right right we say this will be statistically looking like this over time you're not going to track one object through the system exactly for eternity that's not going to work that's so cool yeah all right that is so cool there it is all right another explainer slipped in from torn from the pages of Science Fiction yes just the just a simple description of the three body problem until next time keep looking up [Music]

Channel: StarTalk

Views: 2,314,557

Keywords: startalk, star talk, startalk radio, neil degrasse tyson, neil tyson, science, space, astrophysics, astronomy, podcast, space podcast, science podcast, astronomy podcast, niel degrasse tyson, physics, three body problem, Isaac newton

Id: 6GfIDwwxfsM

Length: 11min 44sec (704 seconds)

Published: Tue Apr 16 2024