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            Video Content Summary:
            An astrophysicist introduces the three-body problem without revealing any spoilers from the show. The explanation of the two-body problem is presented, emphasizing the common center of gravity between Earth and the Moon. Isaac Newton's concerns about the stability of the solar system due to gravitational tugs from Jupiter are discussed. Laplace develops perturbation theory, explaining how small gravitational influences can be mathematically managed. A historical dialogue reveals Napoleon's interaction with Laplace regarding the absence of a divine hypothesis in celestial mechanics. The complexities and chaotic nature of the three-body problem are illustrated through gravitational interactions in a double star system. The unsolvable nature of the three-body problem is emphasized, highlighting the chaos inherent in such systems.

            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 life.

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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.

158
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You add it all up, it all cancels out.

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And it just cancels out.

160
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But Newton could not have known that without this new branch of calculus.

161
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Okay.

162
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Okay?

163
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Perturbation theory.

164
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So that took care of that third body.

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Gotcha.

166
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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.

197
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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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Mm.

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You.

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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, look at that.

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Yeah.

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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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Star Wars.

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Star Wars.

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Yeah.

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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.

230
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Okay.

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

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Right.

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00:06:46,320 --> 00:06:47,020
You don't know where to go.

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Am I going to come through?

235
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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?

239
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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.

242
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And so, it turns out the orbits of a three-body problem are mathematically chaotic.

243
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Yes.

244
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I was about to say, that did not seem very stable.

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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.

251
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Something has to give.

252
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That's odd.

253
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Two of these are going to collide.

254
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Right.

255
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One is going to get ejected.

256
00:07:23,480 --> 00:07:23,920
Right.

257
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Okay.

258
00:07:25,540 --> 00:07:28,080
That is the classical three-body problem.

259
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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.

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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.

269
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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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Exactly.

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It is exponentially different.

277
00:08:12,820 --> 00:08:13,720
Exponentially different.

278
00:08:13,860 --> 00:08:14,000
Correct.

279
00:08:14,160 --> 00:08:14,460
Wow.

280
00:08:14,580 --> 00:08:16,980
With the smallest increment of distance.

281
00:08:17,080 --> 00:08:17,260
Right.

282
00:08:17,260 --> 00:08:24,520
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.

283
00:08:24,780 --> 00:08:26,020
That's what we mean by chaos.

284
00:08:26,100 --> 00:08:26,320
Right.

285
00:08:26,320 --> 00:08:26,560
Okay.

286
00:08:26,760 --> 00:08:27,040
Okay.

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

288
00:08:28,260 --> 00:08:28,460
Okay.

289
00:08:28,460 --> 00:08:28,640
Okay.

290
00:08:29,100 --> 00:08:32,160
So now there's something called the restricted three-body problem.

291
00:08:32,800 --> 00:08:33,400
All right.

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

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

294
00:08:34,240 --> 00:08:34,580
All right.

295
00:08:34,580 --> 00:08:35,600
The restricted three-body problem.

296
00:08:35,680 --> 00:08:36,200
Never heard.

297
00:08:36,260 --> 00:08:38,620
You have, give me your two, your two thing back.

298
00:08:38,620 --> 00:08:38,860
Okay.

299
00:08:38,860 --> 00:08:39,220
It's the two planets.

300
00:08:39,220 --> 00:08:39,700
You got that.

301
00:08:40,060 --> 00:08:40,300
Okay.

302
00:08:40,500 --> 00:08:41,000
Two bodies.

303
00:08:41,140 --> 00:08:41,920
You got your two bodies.

304
00:08:42,260 --> 00:08:45,060
Now, the third body is little.

305
00:08:45,240 --> 00:08:45,800
Uh-huh.

306
00:08:46,100 --> 00:08:48,020
Now, you two will orbit each other.

307
00:08:48,080 --> 00:08:48,400
Right.

308
00:08:48,560 --> 00:08:48,960
Okay.

309
00:08:49,180 --> 00:08:52,860
And then this, it's not messing with them.

310
00:08:53,100 --> 00:08:53,420
Right.

311
00:08:53,420 --> 00:08:56,380
So there's restricted three-body problem.

312
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.

313
00:09:00,460 --> 00:09:01,320
That is solvable.

314
00:09:01,780 --> 00:09:02,260
Right.

315
00:09:02,420 --> 00:09:04,000
It's called the restricted three-body problem.

316
00:09:04,360 --> 00:09:04,700
Gotcha.

317
00:09:05,280 --> 00:09:09,560
In the Star Wars case, that's the restricted three-body problem.

318
00:09:09,680 --> 00:09:09,980
Right.

319
00:09:10,100 --> 00:09:12,900
Because you have the two stars, and you have the little planet.

320
00:09:13,060 --> 00:09:13,480
The little planet.

321
00:09:13,480 --> 00:09:14,540
So it's no big deal.

322
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

323
00:09:21,740 --> 00:09:24,620
gravity of the two stars.

324
00:09:24,800 --> 00:09:25,040
Right.

325
00:09:25,400 --> 00:09:25,720
Okay.

326
00:09:25,880 --> 00:09:26,540
You're far enough away.

327
00:09:26,660 --> 00:09:29,680
That difference is not really mattering to you.

328
00:09:29,960 --> 00:09:33,140
You maintain one stable orbit around them both.

329
00:09:33,200 --> 00:09:34,140
Around both stars.

330
00:09:34,240 --> 00:09:34,840
Both stars.

331
00:09:35,020 --> 00:09:35,560
Okay.

332
00:09:35,560 --> 00:09:39,680
Now, if it got really close, then you'll have issues.

333
00:09:40,740 --> 00:09:43,620
Because then, again, gravitational allegiance matters.

334
00:09:43,700 --> 00:09:45,420
The stars are not going to care, but you will.

335
00:09:45,480 --> 00:09:46,720
Because you'll get eaten.

336
00:09:46,720 --> 00:09:47,380
You don't know where to go.

337
00:09:47,420 --> 00:09:48,160
You don't know where to go.

338
00:09:48,220 --> 00:09:49,280
I'm in love with two stars.

339
00:09:49,740 --> 00:09:51,020
And I don't know what to do.

340
00:09:51,520 --> 00:09:52,620
Which way do I turn?

341
00:09:52,620 --> 00:10:00,560
So, anyhow, so the three-body problem, the takeaway here is it's unsolvable.

342
00:10:00,820 --> 00:10:01,140
Yes.

343
00:10:01,220 --> 00:10:04,940
Not just because we don't know how to do it yet, because it's mathematically unsolvable.

344
00:10:04,960 --> 00:10:05,800
It's built into the system.

345
00:10:05,900 --> 00:10:07,460
The system is chaotic.

346
00:10:07,680 --> 00:10:08,060
Yeah.

347
00:10:08,180 --> 00:10:08,360
Okay?

348
00:10:08,360 --> 00:10:16,220
Unless you make certain assumptions about the system that you would then invoke so that you

349
00:10:16,220 --> 00:10:16,960
can solve it.

350
00:10:17,620 --> 00:10:20,460
And so one of them is a small object around bigger ones.

351
00:10:20,460 --> 00:10:25,440
Another one, oh, by the way, in this solution with Jupiter out there, slightly tugging.

352
00:10:25,600 --> 00:10:25,820
Right.

353
00:10:26,300 --> 00:10:26,480
Yes.

354
00:10:26,480 --> 00:10:29,320
It turns out over a very long timescale, this is chaotic.

355
00:10:29,880 --> 00:10:32,800
But much longer timescale than Newton ever imagined.

356
00:10:32,980 --> 00:10:33,280
Okay.

357
00:10:33,500 --> 00:10:33,780
Okay?

358
00:10:34,080 --> 00:10:37,420
Because, yes, we are small compared to the sun, but Jupiter isn't.

359
00:10:37,420 --> 00:10:37,900
All right?

360
00:10:37,960 --> 00:10:39,660
And we're trying to orbit between them.

361
00:10:39,860 --> 00:10:40,240
Right.

362
00:10:40,300 --> 00:10:40,540
Right?

363
00:10:40,740 --> 00:10:41,920
So that's all.

364
00:10:41,980 --> 00:10:43,100
It's not deeper than that.

365
00:10:43,140 --> 00:10:43,820
It's not, yeah.

366
00:10:44,220 --> 00:10:44,460
Right?

367
00:10:44,600 --> 00:10:48,660
I could have said the four-body problem, but this problem begins at the three-body problem.

368
00:10:48,660 --> 00:10:48,840
Right.

369
00:10:48,840 --> 00:10:48,900
Right.

370
00:10:48,900 --> 00:10:51,960
Because you're going to have the same thing in the four bodies or five bodies.

371
00:10:52,200 --> 00:10:53,160
It's going to be the same.

372
00:10:53,220 --> 00:10:55,540
And we have star clusters with thousands of stars in them.

373
00:10:55,660 --> 00:10:56,700
And they're all just orbiting.

374
00:10:57,520 --> 00:11:02,060
We have to, we can model it, but we cannot predict with precision where everybody's going

375
00:11:02,060 --> 00:11:03,040
to be at any given time.

376
00:11:03,080 --> 00:11:03,420
Okay.

377
00:11:03,700 --> 00:11:04,320
Because it's chaotic.

378
00:11:04,460 --> 00:11:04,900
The chaotic.

379
00:11:05,060 --> 00:11:06,820
So it's, basically, it's about the chaos.

380
00:11:06,900 --> 00:11:07,360
It's about the chaos.

381
00:11:07,360 --> 00:11:08,100
It's all about the chaos.

382
00:11:08,360 --> 00:11:08,540
Yeah.

383
00:11:08,600 --> 00:11:10,260
So what we do is we model the chaos.

384
00:11:10,400 --> 00:11:10,620
Right.

385
00:11:10,720 --> 00:11:10,920
Right?

386
00:11:10,980 --> 00:11:14,480
We say this will be statistically looking like this over time.

387
00:11:14,620 --> 00:11:16,940
You're not going to track one object through the system.

388
00:11:17,040 --> 00:11:17,440
Exactly.

389
00:11:17,440 --> 00:11:18,040
For eternity.

390
00:11:18,040 --> 00:11:18,880
That's not going to work.

391
00:11:18,940 --> 00:11:19,620
That's so cool.

392
00:11:19,760 --> 00:11:19,960
Yeah.

393
00:11:20,100 --> 00:11:20,480
All right.

394
00:11:20,520 --> 00:11:21,520
That is so cool.

395
00:11:21,600 --> 00:11:22,120
There it is.

396
00:11:22,240 --> 00:11:22,400
All right.

397
00:11:22,440 --> 00:11:27,980
Another explainer slipped in from, torn from the pages of science fiction.

398
00:11:28,100 --> 00:11:28,460
Yes.

399
00:11:28,560 --> 00:11:31,860
Just a simple description of the three-body problem.

400
00:11:32,920 --> 00:11:33,660
Until next time.

401
00:11:34,500 --> 00:11:35,100
Keep looking up.

402
00:11:35,100 --> 00:11:35,240
...

403
00:11:35,640 --> 00:11:37,360
...

404
00:11:37,380 --> 00:11:40,600
...

405
00:11:40,600 --> 00:11:41,200
...



            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.