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