# Neil deGrasse Tyson Explains The Three-Body Problem

Apr 24, 2024You'll get an astrophysical explanation of the literal

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without reference to anything shown on streaming services, and that means it won't ruin the show for you. I know nothing. I know nothing. about the program, but I know enough to describe the#### three

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to you. Let's start simple, okay, okay, just like we know that the Moon orbits the Earth correctly, but that's not the right way to say it, okay, okay, okay, the Moon. and the Earth orbits their common center of gravity, oo so the Earth isn't just sitting here and the Moon revolves around it, they feel like it's at their Common Center, you know where it is, it's a thousand miles below the surface of the Earth along the line between the center. of the Earth and the center of the Moon, I have it, so as the Moon moves here, the center of mass line shifts well, that means the Earth moves like this as the Moon rotates, that It's your center of mass, okay, these are the two.The body problem is perfectly solved using gravity equations, right, and the mechanics make sense, perfectly solved, yeah, Isaac Newton solved it, okay boy, that's your man, so it worked, then Isaac applied the equations to Earth-Moon system that revolves around the Sun, okay, that worked too. So in that system, let's ignore the Moon for the moment, it's the Earth going around, it's another two-body system, two systems, okay, but then he got worried and said that every time the Earth comes down the home stretch and Jupiter is out there, Jupiter is about to pull her a little. A little bit of a lot of gravity, a little bit of tugging as we go back to the other side of the Earth, okay and then it spins again, pulls it again, what's on the Earth and of course they all move in the same direction around the Sun, so the Earth would have to go a little further in its orbit to align itself with Jupiter again, but it will pull it in just fine.

Well, he looked at all these little tugs and says: I'm worried about the solar system becoming unstable. right, because keep pulling on it, keep pulling it away and the previously stable orbit would just disintegrate into chaos, okay, he's worried about this, you know what he said, but I know my stuff works and it has and it seems stable to me, TRUE? It's clearly stable although it seems like maybe it wouldn't be stable, you know what he says, he said from time to time, God makes things right, there you go, that's the answer, even Isaac Newton, look at that when in doubt.

Doubt, just let God work it out for you. I can not understand it. God did it. Clearly, we're all still here and Jupiter hasn't pulled us out of his orbit, right, but Jupiter is pulling us, so it's a divine correction. God, God, correction, okay, this is the first indication that a third body is bothering you, right, okay, in some way that's maybe harder to understand, let's fast forward 113 years, oh right, we get to uh, he studied this problem, okay, and developed I. I don't think he invented, but he developed a new branch of calculus called perturbation theory, uh-huh, okay, Newton didn't know about it, although Newton invented calculus. problem let me make up more calculations more calculations I just need more calculations I just need more do it he didn't do it then LL develops the perturbation theory and it all boils down to we have two bodies, the Sun and the Earth in this case and the third the pull is small but it repeats it is not a big Jupiter is not sitting here it is very far away it is just a small tug and then you can run the equations in such a way and realize that a two body system that is often pulled by something small that at the same time In the end it all cancels out, I got you good, okay, so when it's here the pull is a little like that, but now it's here and the pull is less good, and sometimes it pulls you in this direction when that's the configuration, you add it all up, everything cancels out Newton couldn't have known without this new branch of calculus, okay, okay, perturbation theory, so that took care of that third body, where the solar system is basically stable, okay, in the foreseeable future, in the way that Newton I had not in any way imagined that Newton required God, okay, oh, by the way, just a quick comment, now we are in the year 1800, you know who summoned these books to read them from immediate because there is a series of books called Celestial Mechanics, okay Napoleon, ah na, I'm Napoleon, Napoleon, who read all the books he could on physics, engineering and metallurgy, look at that, okay, he wasn't just a tyrant, True, it was as if he were an intelligent tyrant.

The intelligent tyrant was fine, so he calls to upload the book, it doesn't need to be translated because they are both in French, right, he reads it, goes to them and tells Monier, this is a beautiful, brilliant work, but you don't mention the architect of the system. referring to God and them he responded sir, I had no need for that hypothesis oo that's a mic drop oh, that's tough, man, that's a dig at Napoleon and the new Newton, yeah, and on Newton, I have, oh man , look at that, yeah, okay. Let's move on, so now let's say that not only do we have the planet and one of its moons, but we have a star and another famous double star system portrayed in what movie, uh, Star Wars, Star Wars, yeah, okay, 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 the same size, then what kind of orbits will they have, give me two fists here, okay?

I'm feeling this, but now I feel like where my gravitational loyalty is going. I'm going to get through it, but then I'm going to go this way or this way. So I'm going to log into the system and I'm going to you. orbit but wait you're still coming this way now I feel this and it turns out that the orbits of a three body problem are mathematically chaotic yes I was about to say it didn't seem very stable SS has to give in well this is this is in the series, what is being said about something that I don't know, I haven't seen the series, I'm just saying that something has to give, the two are going to collide, one is going to be expelled, okay?

That's the classic three-parter. problem three objects of approximately similar mass trying to maintain a stable orbit and it becomes chaotic with only three objects look it's unsolvable can you let me tell you that in a different way you can incrementally calculate what is happening and track it until the system dies correctly or crashes divide or whatever, but you can't analytically predict the future of the three-body system because what chaos will do for you in your mathematical model is that if you change the initial conditions a little bit, the solution diverges further downward. The line that goes crazy isn't just a little bit different further down the line, it's exponentially exponentially different, right with the smallest increment of distance, so I'm going to say I'm going to move you in this direction in this model and then in one direction. slightly different direction than the other model, it becomes chaotic, that's what we mean by chaos, right, it's mathematically defined.

Well, now there's something called the restricted three-body problem, okay, okay, the restricted three-body problem, I never heard of, you've given me your two, your two. things back, two plans, you have it right, two bodies, you have your two bodies, now the third body is small, ah, now you two will orbit each other, good, and then, and then, this is not bothering you, like this that there is a restricted three-body problem. you have two approximately equal masses and one that is much smaller than the other two that can be solved, right, it's called the restricted three-body problem.

In the case of Star Wars, that's the restricted three-body problem, because you have the two stars and you have the little one. Planet, the little planet deal and it's even better because the planet is so far away that it actually only saw a merged gravity of the two stars. Okay, you're far enough away that that difference doesn't really matter to you. You maintain a stable orbit. around both around both stars both stars are fine now, if it gets too close then you will have problems because then it becomes gravitational again. Loyalty matters, the stars won't care, but you will care because they will eat you, 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 I turn so anyway so the three body problem the conclusion here is that it has no solution, yes, not just because we don't know how to do it yet because it's mathematically UNS but in the system, the system is chaotic, yeah, okay, unless you make certain assumptions about the system that you would then invoke in order to solve it, and so one of them. is a small object around larger ones, another, by the way, in this solution with Jupiter pulling slightly to the right, yes, it turns out that on a very long time scale, this is chaotic, but a much longer time skill than Newton ever imagined, okay, okay, because yeah, we.

They are small compared to the Sun, but Jupiter is not doing well and we are trying to orbit between them, so that's it, it's not deeper than that, it's not, yeah, right. I could have said the four-body problem, but this problem starts with the three-body problem, of course, because you are going to have the same thing in four or five bodies, it will be the same, we have star clusters with thousands of stars in them and they're all just orbiting, we have to be able to model it but I can't accurately predict where everyone will be at any given time, okay, CU is chaotic, they're chaotic, so basically it's about chaos, it's about chaos, yeah, so what we do is model chaos. right, we say statistically it's going to look like this over time, you're not going to track an object through the system exactly for eternity, that's not going to work, that's cool, yeah, okay, that's cool, there it is, it's there okay, another explanation.

Slid from the pages of science fiction, yes, just a simple description of the three-body problem, until next time, keep looking.

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