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11:44
Transcript
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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
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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
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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]
— end of transcript —
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