WEBVTT

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you're going to get an astrophysicist

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explanation of the literal three-body

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problem without reference to anything

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that's shown up on streaming services

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and that means he's not gonna ruin the

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show for you I don't know anything about

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I don't know anything about the show but

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I do know enough to describe the three

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body problem to you coming up

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[Music]

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let's let's start simple okay okay okay

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so as we know the moon orbits the earth

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right but that's not the right way to

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say it okay okay all right the Moon and

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the Earth orbit their common center of

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gravity oo so Earth is not just sitting

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here right and the moon is going around

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going around it they feel in their

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Common Center you know where it is it's

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a thousand miles beneath earth's surface

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along line between the center of the

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earth and the center of the Moon gotcha

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so as the moon moves here that Center

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Mass line shifts

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okay so that means Earth is kind of

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jiggling like this as the moon goes

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around gotta that's their Center of mass

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all right this is the two- body problem

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it is perfectly solved using equations

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of gravity right and mechanics makes

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sense perfectly solved yeah Isaac Newton

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solved it okay my boy that's your man so

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that worked then Isaac applied the

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equations to the Earth Moon system going

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around the Sun okay okay that worked too

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so in that system Let's ignore the moon

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for the moment it's earth going around

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it's another two- body system two system

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all right but then he worried he said

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every time Earth comes around the

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backstretch and Jupiter's out there

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right Jupiter about tug on it a little

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bit a lot of gravity a little bit tug on

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it as we com around back to the other

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side what's up Earth all right and then

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it comes around again tugs on it again

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what's up earth right and of course

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everybody's moving in the same direction

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around the Sun so the Earth would have

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to go a little farther in its orbit to

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be aligned again with Jupiter but it's

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going to tug on it right okay he looked

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at all these little tugs and he says I'm

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worried that the solar system will go

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unstable right because it keeps tugging

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on it it keeps pulling it away and the

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previously stable orbit would just Decay

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into chaos okay okay he was worried

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about this you know what he said but I

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know my stuff works and it's been and

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it's looks stable to me right so clearly

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it is stable even though it looks like

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maybe it wouldn't be stable you know

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what he says he said every now and then

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God fixes things well there you go

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that's the answer even Isaac

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Newton wow look at that when in doubt

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went in doubt just just let God figure

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it out right I can't figure it out God

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Did It clearly we're all still here and

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we haven't been yanked out of orbit by

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Jupiter right but Jupiter is pulling on

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us so it's a god correction God God

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correction okay this this is the first

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hint that a third

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body is messing with you right okay in

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some way that maybe is harder to

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understand fast forward

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113 years oh right we get to uh

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llas he studied this problem right okay

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and he developed I don't think he

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invented but he

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developed a new branch of calculus oo

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called perturbation Theory aha okay

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unknown to Newton even though Newton

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invented calculus right he invented

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calculus right all right so he could

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have done it he could have said in order

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to solve this problem let me invent more

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calcul more calcul just need more calcul

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I just need more do do it didn't do it

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so LL develops perturbation Theory and

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it comes down to we have two bodies the

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Sun and the Earth in this case and the

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third one the tug is small but it's

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repeating it's not a big Jupiter's not

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sitting right here it's way way out

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there it's just a little tug and so you

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can run the equations in such a way and

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realize that a two body system that is

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tugged Often by something small that it

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all cancels out in the end gotcha okay

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okay so when it's out here the tug is a

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little bit that way but now it's over

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here and the tug is less right all right

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and then sometimes it's tugging you in

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this direction when that's the

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configuration you add it all up it all

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cancels out Newton could not have known

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that without this new branch of calculus

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okay okay pertubation Theory so that

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took care of that third body gotcha

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where solar system is basically stable

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okay for the foreseeable future in ways

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that Newton had not imagined in ways

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that Newton required God right okay oh

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by the way just a quick aside this is

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now we're up to the year 1800 uh you

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know who summoned up these books to read

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them immediately because the there a

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series of books called Celestial

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mechanics okay Napoleon ah na am

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Napoleon Napoleon who read all the books

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he could on physics and engineering and

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metalurgy look at that okay it wasn't

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just a tyrant right he was like he was a

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smart Tyrant smart Tyrant was all right

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so he summons up the book doesn't need

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doesn't have to be translated because

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they're both in French right he reads it

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goes to llas and says Monier this is a

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beautiful piece of work brilliant but

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you make no mention of the architect of

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the system he's referring to God and

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llas replied sir I had no need for that

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hypothesis oo that's a mic drop oh that

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is tough

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man you that's a dig on Napoleon and on

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new Newton yeah and on Newton I have oh

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man look at that yeah all right so let's

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keep going go ahead so now let's say we

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have not just the planet and one of its

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moons but let's say we have a star and

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another star double star system famously

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portrayed in what film uh Star Wars Star

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Wars yeah all right of course so those

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two suns and the planet is stable and

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I'll tell you why in a minute mhm but if

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you take a third sun and put it there

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about approximately the same size then

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what kind of orbits will they have give

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me two fists here okay so I'm feeling

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this one but now I feel that where's my

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gravitational allegiance to go am I

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going to come through but then am I

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going to go that that way or this way so

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I'm coming into the system and do I go

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to you in orbit but wait you're still

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coming around here now I feel this

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and so it turns out the orbits of a

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three-body problem are mathematically

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chaotic yes I was about to say that did

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not seem very stable SS has to give well

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this is this is in the series what talk

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something I don't I haven't seen the

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series I'm just saying something has to

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give that's all two of these are going

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to collide one is going to get ejected

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right okay that is the classical three

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body problem three objects of a

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approximately similar mass trying to

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maintain a stable orbit and it goes

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chaotic with just three objects look at

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that it is an unsolvable you can let me

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say that differently you can calculate

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incrementally what's happening and track

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it until the system dies right or splits

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apart or whatever but you cannot

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analytically predict the future of the

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three-body system because what chaos

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will do for you in your mathematical

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model is if you change the initial

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conditions by a little bit right a

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little bit the solution diverges further

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down the line that goes crazy it's not

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just a little bit different later on

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down line it is exponentially

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exponentially different correct with the

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with the smallest increment of distance

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so I'll say I'll move you in this

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direction in this model and then in a

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slightly different direction than the

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other model it goes chaotic that's what

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we mean by chaos right okay it's

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mathematically defined Okay so now

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there's something called the restricted

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three body problem all right okay okay

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the restricted three body problem never

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heard you have give me your two your two

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things back two plan you got that okay

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two bodies you got your two bodies now

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the third body is little ah now you two

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will orbit each other right okay and

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then and then this it's not messing with

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them right so so there restricted three

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body problem we have two masses of

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approximately equal and one that's much

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less than the other two that is solvable

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right it's called the restricted three

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body problem gotcha in the Star Wars

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case that's the restricted three body

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problem right because you have the two

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stars and you have the little planet the

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little planet deal and it's even better

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because the planet is so far away that

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it only really saw one merged gravity of

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the two stars right okay you're far

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enough away that that difference is not

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really mattering to you you maintain one

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stable orbit around them both around

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both stars both Stars okay now if it got

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really close then you'll have issues

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because then ites again gravitational

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Allegiance matters the stars are not

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going to care but you will cuz you

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you'll get eat you don't know where to

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go you don't know where to go I'm in

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love with two stars and I don't know

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what to do which way do I

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turn so anyhow I so so the three body

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problem the takeaway here is it's

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unsolvable yes not just because we don't

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know how to do it yet because it's

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mathematically UNS bu into the system

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the system is chaotic yeah okay unless

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you make certain assumptions about the

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system that you would then invoke so

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that you can solve it and so one of them

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is a small object around bigger ones

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another one oh by the way in this

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solution with Jupiter out there slightly

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tugging right yes it turns out over a

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very long time scale this is chaotic

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but much longer time skill than Newton

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ever imagined okay okay because yes we

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are small compared to the Sun but

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Jupiter isn't all right and we're trying

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to orbit between them right right so

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that's that's all it's not deeper than

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that it's not yeah right I could have

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said the four body problem but this

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problem begins at the three body problem

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right right because you're going to have

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the same thing in four bodies or five

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bodies it's going to be the same we have

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star clusters with thousands of stars in

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them and they're all just orbiting we

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have to we can model it but cannot

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predict with Precision where everybody's

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going to be at any given time okay CU

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it's chaotic the're chaotic so it's

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basically it's about the chaos it's

00:11:06.958 --> 00:11:10.479
about the chaos it's all about the chaos

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yeah so what we do is we model the chaos

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right right we say this will be

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statistically looking like this over

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time you're not going to track one

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object through the system exactly for

00:11:17.679 --> 00:11:21.638
eternity that's not going to work that's

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so cool yeah all right that is so cool

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there it is all right another explainer

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slipped in from torn from the pages of

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Science Fiction yes just the just a

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simple description of the three body

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problem until next time keep looking up

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[Music]