[00:00] you're going to get an astrophysicist
[00:02] explanation of the literal three-body
[00:05] problem without reference to anything
[00:07] that's shown up on streaming services
[00:09] and that means he's not gonna ruin the
[00:11] show for you I don't know anything about
[00:13] I don't know anything about the show but
[00:15] I do know enough to describe the three
[00:17] body problem to you coming up
[00:21] [Music]
[00:33] let's let's start simple okay okay okay
[00:35] so as we know the moon orbits the earth
[00:38] right but that's not the right way to
[00:40] say it okay okay all right the Moon and
[00:43] the Earth orbit their common center of
[00:46] gravity oo so Earth is not just sitting
[00:49] here right and the moon is going around
[00:51] going around it they feel in their
[00:53] Common Center you know where it is it's
[00:55] a thousand miles beneath earth's surface
[00:59] along line between the center of the
[01:01] earth and the center of the Moon gotcha
[01:04] so as the moon moves here that Center
[01:06] Mass line shifts
[01:09] okay so that means Earth is kind of
[01:13] jiggling like this as the moon goes
[01:15] around gotta that's their Center of mass
[01:18] all right this is the two- body problem
[01:20] it is perfectly solved using equations
[01:23] of gravity right and mechanics makes
[01:25] sense perfectly solved yeah Isaac Newton
[01:27] solved it okay my boy that's your man so
[01:30] that worked then Isaac applied the
[01:32] equations to the Earth Moon system going
[01:35] around the Sun okay okay that worked too
[01:39] so in that system Let's ignore the moon
[01:41] for the moment it's earth going around
[01:42] it's another two- body system two system
[01:44] all right but then he worried he said
[01:47] every time Earth comes around the
[01:51] backstretch and Jupiter's out there
[01:54] right Jupiter about tug on it a little
[01:56] bit a lot of gravity a little bit tug on
[01:58] it as we com around back to the other
[02:00] side what's up Earth all right and then
[02:02] it comes around again tugs on it again
[02:04] what's up earth right and of course
[02:06] everybody's moving in the same direction
[02:08] around the Sun so the Earth would have
[02:09] to go a little farther in its orbit to
[02:11] be aligned again with Jupiter but it's
[02:13] going to tug on it right okay he looked
[02:15] at all these little tugs and he says I'm
[02:17] worried that the solar system will go
[02:20] unstable right because it keeps tugging
[02:23] on it it keeps pulling it away and the
[02:25] previously stable orbit would just Decay
[02:28] into chaos okay okay he was worried
[02:30] about this you know what he said but I
[02:32] know my stuff works and it's been and
[02:34] it's looks stable to me right so clearly
[02:37] it is stable even though it looks like
[02:39] maybe it wouldn't be stable you know
[02:40] what he says he said every now and then
[02:42] God fixes things well there you go
[02:44] that's the answer even Isaac
[02:47] Newton wow look at that when in doubt
[02:50] went in doubt just just let God figure
[02:53] it out right I can't figure it out God
[02:55] Did It clearly we're all still here and
[02:57] we haven't been yanked out of orbit by
[02:59] Jupiter right but Jupiter is pulling on
[03:01] us so it's a god correction God God
[03:03] correction okay this this is the first
[03:06] hint that a third
[03:09] body is messing with you right okay in
[03:12] some way that maybe is harder to
[03:14] understand fast forward
[03:17] 113 years oh right we get to uh
[03:22] llas he studied this problem right okay
[03:28] and he developed I don't think he
[03:30] invented but he
[03:32] developed a new branch of calculus oo
[03:35] called perturbation Theory aha okay
[03:40] unknown to Newton even though Newton
[03:42] invented calculus right he invented
[03:44] calculus right all right so he could
[03:46] have done it he could have said in order
[03:49] to solve this problem let me invent more
[03:51] calcul more calcul just need more calcul
[03:53] I just need more do do it didn't do it
[03:56] so LL develops perturbation Theory and
[04:00] it comes down to we have two bodies the
[04:02] Sun and the Earth in this case and the
[04:04] third one the tug is small but it's
[04:07] repeating it's not a big Jupiter's not
[04:10] sitting right here it's way way out
[04:12] there it's just a little tug and so you
[04:14] can run the equations in such a way and
[04:17] realize that a two body system that is
[04:22] tugged Often by something small that it
[04:26] all cancels out in the end gotcha okay
[04:29] okay so when it's out here the tug is a
[04:31] little bit that way but now it's over
[04:33] here and the tug is less right all right
[04:37] and then sometimes it's tugging you in
[04:39] this direction when that's the
[04:41] configuration you add it all up it all
[04:43] cancels out Newton could not have known
[04:45] that without this new branch of calculus
[04:47] okay okay pertubation Theory so that
[04:49] took care of that third body gotcha
[04:52] where solar system is basically stable
[04:55] okay for the foreseeable future in ways
[04:57] that Newton had not imagined in ways
[04:59] that Newton required God right okay oh
[05:02] by the way just a quick aside this is
[05:04] now we're up to the year 1800 uh you
[05:07] know who summoned up these books to read
[05:09] them immediately because the there a
[05:11] series of books called Celestial
[05:12] mechanics okay Napoleon ah na am
[05:17] Napoleon Napoleon who read all the books
[05:20] he could on physics and engineering and
[05:23] metalurgy look at that okay it wasn't
[05:25] just a tyrant right he was like he was a
[05:27] smart Tyrant smart Tyrant was all right
[05:30] so he summons up the book doesn't need
[05:32] doesn't have to be translated because
[05:34] they're both in French right he reads it
[05:36] goes to llas and says Monier this is a
[05:39] beautiful piece of work brilliant but
[05:41] you make no mention of the architect of
[05:45] the system he's referring to God and
[05:46] llas replied sir I had no need for that
[05:50] hypothesis oo that's a mic drop oh that
[05:54] is tough
[05:57] man you that's a dig on Napoleon and on
[06:01] new Newton yeah and on Newton I have oh
[06:05] man look at that yeah all right so let's
[06:08] keep going go ahead so now let's say we
[06:11] have not just the planet and one of its
[06:14] moons but let's say we have a star and
[06:17] another star double star system famously
[06:19] portrayed in what film uh Star Wars Star
[06:22] Wars yeah all right of course so those
[06:25] two suns and the planet is stable and
[06:28] I'll tell you why in a minute mhm but if
[06:30] you take a third sun and put it there
[06:33] about approximately the same size then
[06:35] what kind of orbits will they have give
[06:39] me two fists here okay so I'm feeling
[06:42] this one but now I feel that where's my
[06:44] gravitational allegiance to go am I
[06:47] going to come through but then am I
[06:49] going to go that that way or this way so
[06:52] I'm coming into the system and do I go
[06:55] to you in orbit but wait you're still
[06:57] coming around here now I feel this
[07:00] and so it turns out the orbits of a
[07:04] three-body problem are mathematically
[07:07] chaotic yes I was about to say that did
[07:09] not seem very stable SS has to give well
[07:13] this is this is in the series what talk
[07:16] something I don't I haven't seen the
[07:17] series I'm just saying something has to
[07:19] give that's all two of these are going
[07:20] to collide one is going to get ejected
[07:23] right okay that is the classical three
[07:27] body problem three objects of a
[07:29] approximately similar mass trying to
[07:32] maintain a stable orbit and it goes
[07:34] chaotic with just three objects look at
[07:37] that it is an unsolvable you can let me
[07:40] say that differently you can calculate
[07:43] incrementally what's happening and track
[07:45] it until the system dies right or splits
[07:49] apart or whatever but you cannot
[07:52] analytically predict the future of the
[07:54] three-body system because what chaos
[07:57] will do for you in your mathematical
[07:59] model is if you change the initial
[08:01] conditions by a little bit right a
[08:03] little bit the solution diverges further
[08:06] down the line that goes crazy it's not
[08:09] just a little bit different later on
[08:10] down line it is exponentially
[08:13] exponentially different correct with the
[08:14] with the smallest increment of distance
[08:17] so I'll say I'll move you in this
[08:19] direction in this model and then in a
[08:22] slightly different direction than the
[08:23] other model it goes chaotic that's what
[08:25] we mean by chaos right okay it's
[08:27] mathematically defined Okay so now
[08:30] there's something called the restricted
[08:31] three body problem all right okay okay
[08:34] the restricted three body problem never
[08:35] heard you have give me your two your two
[08:38] things back two plan you got that okay
[08:40] two bodies you got your two bodies now
[08:43] the third body is little ah now you two
[08:46] will orbit each other right okay and
[08:49] then and then this it's not messing with
[08:52] them right so so there restricted three
[08:55] body problem we have two masses of
[08:57] approximately equal and one that's much
[08:59] less than the other two that is solvable
[09:02] right it's called the restricted three
[09:03] body problem gotcha in the Star Wars
[09:07] case that's the restricted three body
[09:09] problem right because you have the two
[09:11] stars and you have the little planet the
[09:13] little planet deal and it's even better
[09:16] because the planet is so far away that
[09:18] it only really saw one merged gravity of
[09:22] the two stars right okay you're far
[09:26] enough away that that difference is not
[09:28] really mattering to you you maintain one
[09:31] stable orbit around them both around
[09:33] both stars both Stars okay now if it got
[09:37] really close then you'll have issues
[09:40] because then ites again gravitational
[09:42] Allegiance matters the stars are not
[09:44] going to care but you will cuz you
[09:46] you'll get eat you don't know where to
[09:47] go you don't know where to go I'm in
[09:48] love with two stars and I don't know
[09:50] what to do which way do I
[09:52] turn so anyhow I so so the three body
[09:56] problem the takeaway here is it's
[09:59] unsolvable yes not just because we don't
[10:02] know how to do it yet because it's
[10:03] mathematically UNS bu into the system
[10:05] the system is chaotic yeah okay unless
[10:09] you make certain assumptions about the
[10:12] system that you would then invoke so
[10:15] that you can solve it and so one of them
[10:18] is a small object around bigger ones
[10:20] another one oh by the way in this
[10:22] solution with Jupiter out there slightly
[10:24] tugging right yes it turns out over a
[10:27] very long time scale this is chaotic
[10:30] but much longer time skill than Newton
[10:32] ever imagined okay okay because yes we
[10:34] are small compared to the Sun but
[10:36] Jupiter isn't all right and we're trying
[10:38] to orbit between them right right so
[10:41] that's that's all it's not deeper than
[10:42] that it's not yeah right I could have
[10:44] said the four body problem but this
[10:47] problem begins at the three body problem
[10:48] right right because you're going to have
[10:50] the same thing in four bodies or five
[10:51] bodies it's going to be the same we have
[10:53] star clusters with thousands of stars in
[10:55] them and they're all just orbiting we
[10:57] have to we can model it but cannot
[11:00] predict with Precision where everybody's
[11:01] going to be at any given time okay CU
[11:03] it's chaotic the're chaotic so it's
[11:05] basically it's about the chaos it's
[11:06] about the chaos it's all about the chaos
[11:08] yeah so what we do is we model the chaos
[11:10] right right we say this will be
[11:11] statistically looking like this over
[11:14] time you're not going to track one
[11:15] object through the system exactly for
[11:17] eternity that's not going to work that's
[11:19] so cool yeah all right that is so cool
[11:21] there it is all right another explainer
[11:23] slipped in from torn from the pages of
[11:27] Science Fiction yes just the just a
[11:29] simple description of the three body
[11:31] problem until next time keep looking up
[11:37] [Music]