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            Video Content Summary:
            An introduction to the three-body problem is given without spoilers for any related media adaptations. The discussion begins with the simple two-body problem of the Earth and Moon orbiting their common center of gravity. Isaac Newton's exploration of the Earth-Moon system and the potential destabilizing effect of Jupiter is shared. Newton's resolution about potential instability relies on divine intervention. Laplace advances perturbation theory to address the three-body problem, omitting God from scientific solutions. Laplace responds to Napoleon about the omission of divine intervention in celestial mechanics. The chaotic nature of the classical three-body problem with examples of orbits under gravitational influence is explained. The restricted three-body problem involving smaller third bodies is described as more predictable and stable. Chaos theory's implications for modeling systems with multiple bodies, as learned from the three-body problem, are summarized.

            Full Transcript Excerpt:
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You're gonna get an astrophysicist explanation of the literal three-body problem

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without reference to anything that's shown up on streaming services.

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And that means he's not gonna ruin the show for you.

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I don't know anything about the show,

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but I do know enough to describe the three-body problem to you.

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Coming up.

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Let's start simple.

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Okay.

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So as we know, the moon orbits the earth.

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Right.

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But that's not the right way to say it.

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Okay.

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Okay?

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All right.

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The moon and the earth orbit their common center of gravity.

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Ooh.

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So earth is not just sitting here.

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Right.

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And the moon is going around.

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Going around it.

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They're feeling their common center.

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You know where it is?

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It's a thousand miles beneath earth's surface.

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Along a line between the center of the earth and the center of the moon.

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Got you.

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So as the moon moves here, that center mass line shifts.

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Okay?

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Mm.

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So that means earth is kind of jiggling like this as the moon goes around.

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Got you.

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That's their center of mass.

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All right.

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This is the two-body problem.

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It is perfectly solved using equations of gravity.

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Right.

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And mechanics.

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Makes sense.

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Perfectly solved.

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Yeah.

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Isaac Newton solved it.

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Okay.

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My boy.

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That's your man.

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So that worked.

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Then Isaac applied the equations to the earth-moon system going around the sun.

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Okay.

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Okay?

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That worked too.

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So in that system, let's ignore the moon for the moment.

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It's earth going around the sun.

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Another two-body system.

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Another two-body system.

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All right?

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But then he worried.

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He said, every time earth comes around the back stretch and Jupiter's out there.

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Right.

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Jupiter, but tug on it a little bit.

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Yeah, that's a lot of gravity.

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A little bit.

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Tug on it.

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Yeah.

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As we come around back the other side.

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What's up, earth?

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All right.

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And then it comes around again.

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Tugs on it again.

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What's up, earth?

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Right?

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And of course, everybody's moving in the same direction around the sun.

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So the earth would have to go a little farther in its orbit to be aligned again with Jupiter.

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Right.

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But it's going to tug on it.

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Right.

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Okay.

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He looked at all these little tugs and he says, I'm worried that the solar system will go unstable.

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Right.

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Because if it keeps tugging on it, it keeps pulling it away.

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Yeah, it's just keep pulling away.

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And the previously stable orbit would just decay into chaos.

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Okay.

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Okay.

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He was worried about this.

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Okay.

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You know what he said?

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But I know my stuff works and it looks stable to me.

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Right.

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So clearly it is stable, even though it looks like maybe it wouldn't be stable.

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You know what he says?

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He said, every now and then God fixes things.

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Wow.

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There you go.

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That's the answer.

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Even Isaac Newton.

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Wow.

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Look at that.

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Yeah.

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When in doubt.

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When in doubt.

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Just let God figure it out.

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Right.

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I can't figure it out.

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God did it.

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Clearly, we're all still here and we haven't been yanked out of orbit by Jupiter.

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Right.

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But Jupiter is pulling on us.

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So it's a God correction.

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God correction.

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Okay.

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Okay.

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This is the first hint that a third body is messing with you.

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Right.

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Okay.

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In some way that maybe is harder to understand.

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Mm-hmm.

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Fast forward 113 years.

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All right.

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We get to Laplace.

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He studied this problem.

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Right.

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Okay.

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And he developed, I don't think he invented, but he developed a new branch of the world.

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calculus.

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Ooh.

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Called perturbation theory.

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Aha.

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Okay.

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Unknown to Newton, even though Newton invented calculus.

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Right.

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He invented calculus.

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Right.

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All right.

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So he could have done it.

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He could have said, in order to solve this problem, let me invent.

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I need more calculus.

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More calculus.

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I just need more calculus.

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I just need more calculus.

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He didn't do it.

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Didn't do it.

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So Laplace develops perturbation theory.

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And it comes down to, we have two bodies, the sun and the earth in this case.

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And the third one, the tug is small, but it's repeating.

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Mm-hmm.

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It's not a big, Jupiter's not sitting right here.

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Right.

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It's way out there.

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Way out there.

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It's just a little tug.

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And so you can run the equations in such a way and realize that a two-body system that

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is tugged often by something small, that it all cancels out in the end.

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Gotcha.

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Okay.

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So when it's out here, the tug is a little bit that way, but now it's over here and the

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tug is less.

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Right.

156
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All right?

157
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And then sometimes it's tugging you in this direction when that's the configuration.

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You add it all up, it all cancels out.

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And it just cancels out.

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But Newton could not have known that without this new branch of calculus.

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Okay.

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Okay?

163
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Perturbation theory.

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So that took care of that third body.

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Gotcha.

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Where solar system is basically stable, okay, for the foreseeable future in ways that Newton

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had not imagined in ways that Newton required God.

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Right.

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Okay?

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Oh, by the way, just a quick aside.

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This is now, we're up to the year 1800.

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Do you know who summoned up these books to read them immediately?

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Because there's a series of books called Celestial Mechanics.

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Okay.

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Napoleon.

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Oh!

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I am Napoleon!

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Napoleon, who read all the books he could on physics and engineering and metallurgy.

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Look at that.

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Okay, he wasn't just a tyrant.

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Right.

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He was like a-

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It was a smart tyrant.

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Smart tyrant.

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All right.

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So he summons up the book.

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Doesn't have to be translated because they're both in French.

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Right.

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He reads it, goes to Laplace and says, Monsieur, this is a beautiful piece of work.

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Brilliant.

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But you make no mention of the architect of the system.

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He's referring to God.

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And Laplace replied, Sir, I had no need for that hypothesis.

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Ooh.

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That's a mic drop.

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Ooh.

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That is tough.

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Man.

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Ooh.

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Ooh.

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That's a dig on Napoleon and on Newton.

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And on Newton.

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Yeah.

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And on Newton.

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I have- Oh, man.

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Look at that.

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All right.

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So, let's keep going.

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Go ahead.

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So now, let's say we have not just the planet and one of its moons, but let's say we have

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a star and another star, double star system.

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Right.

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Famously portrayed in what film?

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Star Wars.

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Star Wars.

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Yeah.

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All right.

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All right.

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Of course.

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So, those two suns and the planet is stable.

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And I'll tell you why in a minute.

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Mm-hmm.

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But if you take a third sun and put it there, about approximately the same size, then what

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kind of orbits will they have?

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Give me two fists here.

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Okay.

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Okay.

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So, I'm feeling this one, but now I feel that where is my gravitational allegiance?

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Right.

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You don't know where to go.

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Am I going to come through?

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Right.

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But then am I going to go that way or this way?

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So, I'm coming into the system.

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Do I go to you in orbit?

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But wait, you're still coming around here?

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Right.

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Now I feel this.

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And so, it turns out the orbits of a three-body problem are mathematically chaotic.

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Yes.

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I was about to say, that did not seem very stable.

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No.

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Something has to give.

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Well, this is in the series.

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What we're talking about.

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I haven't seen the series.

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I know.

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I'm just saying.

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Something has to give.

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That's odd.

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Two of these are going to collide.

252
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Right.

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One is going to get ejected.

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Right.

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Okay.

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That is the classical three-body problem.

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Three objects of approximately similar mass trying to maintain a stable orbit.

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And it goes chaotic with just three objects.

259
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Look at that.

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It is unsolvable.

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You can, let me say that differently.

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You can calculate incrementally what's happening and track it until the system dies.

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Right.

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Or splits apart or whatever.

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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.

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Right.

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A little bit.

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The solution diverges.

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Further down the line.

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It goes crazy.

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It goes crazy.

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It's not just a little bit different later on down the line.

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Right.

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Exactly.

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It is exponentially different.

276
00:08:13,060 --> 00:08:13,720
Exponentially different.

277
00:08:13,880 --> 00:08:14,000
Correct.

278
00:08:14,160 --> 00:08:14,460
Wow.

279
00:08:14,580 --> 00:08:16,980
With the smallest increment of distance.

280
00:08:17,080 --> 00:08:17,240
Right.

281
00:08:17,240 --> 00:08:23,660
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.

282
00:08:23,820 --> 00:08:24,540
It goes chaotic.

283
00:08:24,840 --> 00:08:26,020
That's what we mean by chaos.

284
00:08:26,120 --> 00:08:26,320
Right.

285
00:08:26,380 --> 00:08:26,580
Okay.

286
00:08:26,780 --> 00:08:27,040
Okay.

287
00:08:27,040 --> 00:08:28,180
It's mathematically defined.

288
00:08:28,280 --> 00:08:28,480
Okay.

289
00:08:28,480 --> 00:08:28,660
Okay.

290
00:08:29,120 --> 00:08:32,160
So now there's something called the restricted three-body problem.

291
00:08:32,160 --> 00:08:33,340
Oh, right.

292
00:08:33,500 --> 00:08:33,800
Okay.

293
00:08:33,920 --> 00:08:34,120
Okay.

294
00:08:34,260 --> 00:08:35,620
The restricted three-body problem.

295
00:08:35,700 --> 00:08:36,200
Never heard.

296
00:08:36,260 --> 00:08:38,620
You have, give me your two thing back.

297
00:08:38,820 --> 00:08:38,840
Okay.

298
00:08:38,840 --> 00:08:39,220
Two planets.

299
00:08:39,220 --> 00:08:39,700
You got that.

300
00:08:40,100 --> 00:08:40,300
Okay.

301
00:08:40,500 --> 00:08:41,000
Two bodies.

302
00:08:41,160 --> 00:08:41,920
You got your two bodies.

303
00:08:42,260 --> 00:08:45,060
Now the third body is little.

304
00:08:45,240 --> 00:08:45,800
Uh-huh.

305
00:08:46,100 --> 00:08:48,020
Now you two will orbit each other.

306
00:08:48,080 --> 00:08:48,400
Right.

307
00:08:48,580 --> 00:08:48,980
Okay.

308
00:08:48,980 --> 00:08:52,860
And then this, it's not messing with them.

309
00:08:53,100 --> 00:08:53,420
Right.

310
00:08:54,000 --> 00:08:56,380
So there's restricted three-body problem.

311
00:08:56,460 --> 00:09:00,340
We have two masses of approximately equal and one that's much less than the other two.

312
00:09:00,460 --> 00:09:01,320
That is solvable.

313
00:09:01,320 --> 00:09:02,240
Right.

314
00:09:02,440 --> 00:09:04,000
It's called the restricted three-body problem.

315
00:09:04,360 --> 00:09:04,700
Gotcha.

316
00:09:05,280 --> 00:09:09,580
In the Star Wars case, that's the restricted three-body problem.

317
00:09:09,680 --> 00:09:09,980
Right.

318
00:09:10,120 --> 00:09:12,920
Because you have the two stars and you have the little planet.

319
00:09:13,080 --> 00:09:13,840
The little planet.

320
00:09:14,020 --> 00:09:14,540
So it's no big deal.

321
00:09:14,540 --> 00:09:21,740
And it's even better because the planet is so far away that it only really saw one merged

322
00:09:21,740 --> 00:09:24,700
gravity of the two stars.

323
00:09:24,800 --> 00:09:25,040
Right.

324
00:09:25,400 --> 00:09:25,740
Okay.

325
00:09:25,900 --> 00:09:26,540
You're far enough away.

326
00:09:26,680 --> 00:09:29,680
That difference is not really mattering to you.

327
00:09:29,680 --> 00:09:33,140
You maintain one stable orbit around them both.

328
00:09:33,180 --> 00:09:34,140
Around both stars.

329
00:09:34,240 --> 00:09:34,840
Both stars.

330
00:09:35,140 --> 00:09:35,540
Okay.

331
00:09:35,660 --> 00:09:35,820
Okay.

332
00:09:35,820 --> 00:09:39,680
Now, if it got really close, then you'll have issues.

333
00:09:40,640 --> 00:09:43,620
Because then, again, gravitational allegiance matters.

334
00:09:43,680 --> 00:09:44,640
The stars are not going to care.

335
00:09:44,800 --> 00:09:45,400
But you will.

336
00:09:45,460 --> 00:09:45,600
Yeah.

337
00:09:45,600 --> 00:09:46,720
Because you'll get eaten.

338
00:09:46,720 --> 00:09:47,380
You don't know where to go.

339
00:09:47,420 --> 00:09:48,160
You don't know where to go.

340
00:09:48,220 --> 00:09:49,280
I'm in love with two stars.

341
00:09:49,740 --> 00:09:51,020
And I don't know what to do.

342
00:09:51,540 --> 00:09:52,620
Which way do I turn?

343
00:09:52,620 --> 00:09:56,960
So, anyhow, so the three-body problem.

344
00:09:57,400 --> 00:10:00,540
The takeaway here is it's unsolvable.

345
00:10:00,820 --> 00:10:01,140
Yes.

346
00:10:01,220 --> 00:10:03,060
Not just because we don't know how to do it yet.

347
00:10:03,220 --> 00:10:04,940
Because it's mathematically unsolvable.

348
00:10:04,960 --> 00:10:05,800
It's built into the system.

349
00:10:05,900 --> 00:10:07,460
The system is chaotic.

350
00:10:07,680 --> 00:10:08,060
Yeah.

351
00:10:08,180 --> 00:10:08,360
Okay.

352
00:10:08,360 --> 00:10:16,960
Unless you make certain assumptions about the system that you would then invoke so that you can solve it.

353
00:10:16,960 --> 00:10:20,460
And so one of them is a small object around bigger ones.

354
00:10:20,800 --> 00:10:21,220
Another one.

355
00:10:21,280 --> 00:10:25,440
Oh, by the way, in this solution with Jupiter out there, slightly tugging.

356
00:10:25,580 --> 00:10:25,840
Right.

357
00:10:26,300 --> 00:10:26,540
Yes.

358
00:10:26,540 --> 00:10:29,320
It turns out over a very long timescale, this is chaotic.

359
00:10:29,880 --> 00:10:32,800
But much longer timescale than Newton ever imagined.

360
00:10:32,980 --> 00:10:33,280
Okay.

361
00:10:33,500 --> 00:10:33,780
Okay.

362
00:10:34,080 --> 00:10:36,220
Because, yes, we are small compared to the sun.

363
00:10:36,280 --> 00:10:37,420
But Jupiter isn't.

364
00:10:37,420 --> 00:10:37,900
All right.

365
00:10:37,960 --> 00:10:39,660
And we're trying to orbit between them.

366
00:10:39,860 --> 00:10:40,240
Right.

367
00:10:40,300 --> 00:10:40,560
Right.

368
00:10:40,680 --> 00:10:41,920
So that's all.

369
00:10:41,980 --> 00:10:43,100
It's not deeper than that.

370
00:10:43,140 --> 00:10:43,500
It's not.

371
00:10:43,680 --> 00:10:43,860
Yeah.

372
00:10:44,240 --> 00:10:44,480
Right.

373
00:10:44,480 --> 00:10:48,660
I could have said the four-body problem, but this problem begins at the three-body problem.

374
00:10:48,840 --> 00:10:48,860
Right.

375
00:10:49,020 --> 00:10:49,160
Right.

376
00:10:49,480 --> 00:10:51,980
Because you're going to have the same thing in the four bodies or five bodies.

377
00:10:52,200 --> 00:10:53,160
It's going to be the same.

378
00:10:53,220 --> 00:10:55,520
And we have star clusters with thousands of stars in them.

379
00:10:55,660 --> 00:10:56,700
And they're all just orbiting.

380
00:10:57,520 --> 00:10:58,120
We have to.

381
00:10:58,200 --> 00:11:03,040
We can model it, but we cannot predict with precision where everybody's going to be at any given time.

382
00:11:03,100 --> 00:11:03,420
Okay.

383
00:11:03,700 --> 00:11:04,320
Because it's chaotic.

384
00:11:04,480 --> 00:11:04,900
The chaotic.

385
00:11:05,060 --> 00:11:06,800
So basically, it's about the chaos.

386
00:11:06,900 --> 00:11:07,340
It's about the chaos.

387
00:11:07,340 --> 00:11:08,100
It's all about the chaos.

388
00:11:08,360 --> 00:11:08,540
Yeah.

389
00:11:08,600 --> 00:11:10,260
So what we do is we model the chaos.

390
00:11:10,420 --> 00:11:10,620
Right.

391
00:11:10,720 --> 00:11:10,920
Right.

392
00:11:10,920 --> 00:11:14,480
We say this will be statistically looking like this over time.

393
00:11:14,620 --> 00:11:16,960
You're not going to track one object through the system.

394
00:11:17,040 --> 00:11:17,440
Exactly.

395
00:11:17,540 --> 00:11:18,080
For eternity.

396
00:11:18,200 --> 00:11:18,880
That's not going to work.

397
00:11:18,940 --> 00:11:19,620
That's so cool.

398
00:11:19,760 --> 00:11:19,960
Yeah.

399
00:11:20,100 --> 00:11:20,480
All right.

400
00:11:20,520 --> 00:11:21,520
That is so cool.

401
00:11:21,600 --> 00:11:22,120
There it is.

402
00:11:22,240 --> 00:11:22,400
All right.

403
00:11:22,440 --> 00:11:27,980
Another explainer slipped in from torn from the pages of science fiction.

404
00:11:28,120 --> 00:11:28,460
Yes.

405
00:11:28,840 --> 00:11:31,860
Just a simple description of the three-body problem.

406
00:11:32,760 --> 00:11:33,660
Until next time.

407
00:11:34,520 --> 00:11:35,100
Keep looking up.

408
00:11:35,100 --> 00:11:35,140
Keep looking up.

409
00:11:35,140 --> 00:11:36,140
Keep looking up.

410
00:11:36,140 --> 00:11:37,140
Keep looking up.

411
00:11:37,140 --> 00:11:37,180
Keep looking up.

412
00:11:37,180 --> 00:11:38,140
Keep looking up.

413
00:11:38,140 --> 00:11:39,140
Keep looking up.

414
00:11:39,140 --> 00:11:39,180
Keep looking up.

415
00:11:39,180 --> 00:11:39,260
Keep looking up.

416
00:11:39,260 --> 00:11:39,640
Keep looking up.

417
00:11:39,640 --> 00:11:40,900
Keep looking up.

418
00:11:40,900 --> 00:11:41,900
Keep looking up.



            Please analyze the content and generate:
            1. 10 specific advertisement keywords or phrases
            2. For each keyword, provide:
            - The target audience demographic
            - Relevance score (1-10)
            - Category (e.g., Sports Equipment, Fashion, Technology, etc.)
            - Predict the country or area of the person watching
            - Predict personality trait of the person watching
            - Predict mood of the person watching
            - Predict the age of the person watching(a numerical value)


            Format the response as a JSON array with the following structure for each keyword:
            {
                "keyword": "<specific keyword or phrase>",
                "target_demographic": "<target audience description>",
                "relevance_score": <number between 1 and 10>,
                "category": "<category name>"
                "area":"<country>"
                "personality":"<Extraversion, Introversion, Friendliness, Responsibility, Calmness, Curiosity, Leadership, Follower, Risk-Taking, Carefulness, Understanding, Kindness, Positive Thinking, Negative Thinking, Flexibility, Stubbornness>"
                "mood":"<fear, contempt, disgust, sadness, anger, happiness,surprise>"
                "age":<age number between 1 and 100>
            }

            Ensure the keywords are highly relevant to the video content and would interest the target audience.