Neil deGrasse Tyson Explains The Three-Body Problem | Universe

Added: 2026-05-23

[00:00:00]Let's Let's start simple. Okay. So, as we know, the moon orbits the Earth.

[00:00:05]>> Right. But, that's not the right way to say it. Okay.

[00:00:09]Okay? All right.

[00:00:10]>> The moon and the Earth orbit their common center of gravity.

[00:00:14]>> Ooh. So, Earth is not just sitting here >> Right. And the moon is going around >> it. They feel in their common center getting You know where it is? It's a thousand miles beneath Earth's surface.

[00:00:26]Along a line between the center of the Earth and the center of the moon. Got you.

[00:00:31]So, as the moon moves here, that center mass line shifts.

[00:00:35]>> Okay? Mhm.

[00:00:37]So, that means Earth is kind of jiggling Mhm.

[00:00:41]>> like this as the moon goes around. Got you.

[00:00:44]>> That's their center of mass. All right.

[00:00:45]This is the two-body problem. It is perfectly solved using equations of gravity Right.

[00:00:52]>> Makes sense. Perfectly solved. 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.

[00:01:03]>> Okay. Okay? That worked, too.

[00:01:06]So, in that system, let's ignore the moon for the moment. It's Earth going around the sun. Now, they're two-body system. All right?

[00:01:12]>> But, then he worried.

[00:01:14]He said, "Every time Earth comes around the back stretch and Jupiter's out there, Right. Jupiter will tug on it a little bit.

[00:01:23]>> of gravity.

[00:01:24]>> A little bit tug on it as we come around back the other side.

[00:01:28]>> What's up, Earth? All right. I didn't it comes around again, tugs on it again.

[00:01:31]>> 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. Okay. He looked at all these little tugs, and he says, "I'm worried that the solar system will go unstable." Right.

[00:01:49]Because it keeps tugging on it. It keeps pulling it away. The The previously stable orbit would just decay into chaos. Okay.

[00:01:57]>> Okay. He was worried about this.

[00:01:58]>> Okay. You know what he said? But I know my stuff works and it's been and it's looked 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.

[00:02:11]That's the answer.

[00:02:12]>> [laughter] >> Even Isaac Newton.

[00:02:15]Wow, look at that.

[00:02:16]>> Yeah. When in doubt >> When in doubt, just Just Just Let God figure it out.

[00:02:20]>> 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.

[00:02:28]>> So it's a God correction.

[00:02:29]>> God God correction. Okay.

[00:02:31]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. Mhm. Fast forward 100 and 13 years. All right. We get to uh Laplace.

[00:02:50]He studied this problem. Right. Okay?

[00:02:55]And he developed, I don't think he invented, but he developed a new branch of calculus Ooh. called perturbation theory. Aha. Okay?

[00:03:07]Unknown to Newton, even though Newton invented calculus.

[00:03:10]>> Right.

[00:03:11]He invented calculus. Right. All right?

[00:03:13]So he could have done it.

[00:03:15]He could have said, "In order to solve this problem, let me invent I need more calculus.

[00:03:19]>> I just need more calculus. I just need more calculus." Didn't do it. Mhm.

[00:03:21]Didn't do it.

[00:03:23]So Laplace 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. Mhm. It's not a big Jupiter's not sitting right here. It's way out there. 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.

[00:03:55]Got you. Okay? So, when it's out here, the tug is a little bit that way, but now it's over here and the the tug is less.

[00:04:03]>> 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. But Newton could not have known that without this new branch of calculus. Okay.

[00:04:15]>> Okay? Perturbation theory. So, that took care of that third body.

[00:04:18]Got you. Where so system is basically stable. Okay? For the foreseeable future in ways that Newton had not imagined, in ways that Newton required God. Right.

[00:04:28]>> Okay? Oh, by the way, just a quick aside, this is now we're up to the year 1800.

[00:04:33]Uh you know who summoned up these books to read them immediately? Cuz the there's a series of books called Celestial Mechanics.

[00:04:39]>> Okay.

[00:04:41]Napoleon. Ah.

[00:04:43]Not I'm Napoleon. Napoleon, who read all the books he could on physics and engineering and metallurgy. Look at that.

[00:04:52]>> wasn't just a tyrant. All right. He was like a >> It was a smart tyrant. smart tyrant.

[00:04:56]>> [laughter] >> All right. So, he summons up the book.

[00:04:59]Doesn't he doesn't have to be translated because they're both in French. Right.

[00:05:03]He reads it, goes to Laplace and says, "Monsieur, 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 Laplace replied, "Sir, I had no need for that hypothesis."

[00:05:18]>> Ooh, that's a mic drop. Ooh, that is tough. Man. Mhm.

[00:05:25]Ew.

[00:05:26]That's a dig on Napoleon and on Newton.

[00:05:29]>> 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 let's say we have a star and another star, double star system.

[00:05:45]Famously portrayed in what film?

[00:05:48]Uh Star Wars. Star Wars. Yeah. All right. Of course.

[00:05:51]>> So, those two suns and the planet is stable.

[00:05:55]And I'll tell you why in a minute. Mhm.

[00:05:57]>> But if you take a third sun and put it there, about approximately the same size, then what kind of orbits will they have? Now, give me two fists here, okay? So, I'm feeling this one, but Right.

[00:06:11]>> my gravitational allegiance?

[00:06:13]>> don't know where to go.

[00:06:14]>> going to come through? Right.

[00:06:16]>> 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? Yeah, but wait, and 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.

[00:06:35]I was about to say, that did not seem very stable. Something's got to give.

[00:06:40]Well, this is this is in the series what we're talking about. I don't I haven't seen the series. I'm just saying, something has to give.

[00:06:46]>> That's awesome. Two of these are going to collide. One is going to get ejected.

[00:06:50]Right.

[00:06:51]>> Okay? That is the classical three-body problem.

[00:06:55]Three objects of approximately similar mass trying to maintain a stable orbit.

[00:07:01]And it goes chaotic with just three objects. Look at that. It is an unsolvable.

[00:07:06]You can Let me say that differently. You can calculate incrementally what's happening and track it until the system dies. Or or or splits apart or whatever.

[00:07:17]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.

[00:07:30]>> a little bit, the solution diverges.

[00:07:33]>> Further down the line, it goes crazy.

[00:07:35]crazy. It's not just a little bit different later on down the line. It is exponentially >> exponentially different. Correct. Wow.

[00:07:41]>> With the with the smallest increment of distance. Right. So I'll say, I'll move you in this direction in this model and then in a slightly different direction in the other model, it goes chaotic.

[00:07:51]That's what we mean by chaos. Right.

[00:07:53]Okay. Okay. It's mathematically defined.

[00:07:55]Okay. So, now there's something called the restricted three-body problem.

[00:07:59]All right, okay.

[00:08:01]>> Okay. The restricted three-body problem?

[00:08:02]Never heard.

[00:08:03]>> You have Do you give me your two your two thing back? Okay. It's the two planets. You got that? Okay.

[00:08:07]>> Two bodies. You got your two bodies.

[00:08:09]Now, the third body is little. Aha. Now, you two will orbit each other.

[00:08:15]>> Right. Okay? And then And then this it's not messing with them. Right. So So this 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. Got you. 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.

[00:08:40]>> The little planet. There it is.

[00:08:41]>> And it's even better because the planet is so far away that it only really saw one merged gravity of the two stars.

[00:08:51]>> Right. Okay.

[00:08:53]>> You're far enough away that that difference is not really mattering to you. You maintain one stable orbit around them both.

[00:09:00]>> Around both stars.

[00:09:01]>> Both stars. Okay? Now, if it got really close, then you'll have issues.

[00:09:07]Because then it does Again, gravitational allegiance matters. Stars are not going to care, but you will cuz you're you'll get eaten. You don't know where to go.

[00:09:14]>> Yeah, you don't know where to go. I'm in love with two stars.

[00:09:16]>> [laughter] >> And I don't know what to do.

[00:09:18]Which way do I turn?

[00:09:20]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 unsolvable.

[00:09:32]>> into the system.

[00:09:32]>> The system is chaotic. Yeah. Okay?

[00:09:35]Unless you make certain assumptions about the system that you would then invoke so that you can solve it.

[00:09:44]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.

[00:09:53]>> out over a very long time scale this is chaotic.

[00:09:57]But much longer time scale 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.

[00:10:07]>> Right? So that's That's all it's not deeper than that.

[00:10:10]>> It's not that, yeah. Right? I could have said the four-body problem, but this problem begins at the three-body problem.

[00:10:15]>> Right, right. Cuz you're going to have the same thing in four bodies or five bodies. It's going to be the same.

[00:10:20]>> And we have star clusters with thousands of stars in them and they're all just orbiting.

[00:10:24]We have to We can model it, but we cannot predict with precision where everybody's going to be at any given time. Okay. Cuz it's chaotic.

[00:10:31]>> The chaotic So it's basically it's about the chaos.

[00:10:33]>> It's about the chaos.

[00:10:34]>> It's all about the chaos. Yeah, so what we do is we we model the chaos. Right.

[00:10:37]>> Right? We say this will be statistically looking like this over time. You're not going to track one object through the system Exactly.

[00:10:44]>> for eternity. That's not going to work.

[00:10:46]>> That's so cool. Yeah. All right.

[00:10:47]>> That is so cool. There it is. All right, another explainer slipped in from torn from the pages of science fiction.

[00:10:55]>> Yes.

[00:10:55]>> Just the Just a simple description of the three-body problem.

[00:11:00]Until next time.

[00:11:01]Keep looking up.

[00:11:09]>> [music]