Why are space things the shape they are?
The earth is clearly a sphere and yet the Milky Way
is a disk.
The reason will get into some of the fundamental realities
of our universe.
Our universe really seems to be into two shapes in particular.
It loves building spheres like stars, planets, and moons,
and disks like spiral galaxies, solar systems,
and some crazy stuff like quasars.
All of these things obey the same laws of physics
and all of them are held together by gravity.
So how do they decide what shape to be?
Two key principles, equilibrium and symmetry.
Let's start with equilibrium.
Engineers are all about equilibrium.
Build a bridge and every brick, cable, and bolt
has to perfectly balance the tension, pressure, and torque
resulting from the downward gravitational pull
on all other parts of the bridge.
And even downward can be tricky.
Long bridges, like the Verrazano-Narrows Bridge
in New York, has to factor in the changing direction of down
due to the curvature of Earth's surface over its four mile
span.
Without this mechanical equilibrium,
unbalanced internal forces cause shapes to change.
That's bad for a bridge.
But when forces become balanced, they cancel each other out,
shape remains fixed.
And it's the symmetries of the forces
at work in creating that equilibrium that decide
what that final shape will be.
So let's talk about symmetry.
In terms of shape, things like planets and stars
have spherical symmetry, meaning you can rotate them
in three dimensions and the basic shape stays the same.
disk-shaped things like galaxies and solar systems
have circular symmetry.
They can be rotated around one axis
and keep their basic shape.
But how does a force have symmetry?
In the case of all the really big space stuff,
one of the important forces is always gravity.
So let's start with that.
Here it's fine to think about gravity Newtonianly as a force
rather than as an Einsteinian warping of space time.
Newton's Universal Law of Gravitation
tells us that the strength of gravity
drops off with the distance to the center of mass squared,
and it drops off at the same rate in all directions.
So gravity has spherical symmetry in the sense
that, if you're some distance from a space thing of any shape
and there's nothing else around, a surface
of constant gravitational field is a sphere.
Gravity exerts itself equally along the three
spatial dimensions.
And this type of dimensional egalitarianism
is also shared by another effect,
ultimately leading to the ball shapes of stars, planets,
and moons.
Before we talk about what that other effect is,
let's talk about planets.
In fact, let's talk about the Earth.
The Earth is definitely a sphere, or pretty close to.
It's held together by its own gravitational field,
which conveniently also keeps me stuck to the surface.
Just as conveniently, that chunk of rock just below me
keeps me from plummeting into the molten core.
And the chunk of rock below it holds it up, and holds me up,
too.
We can imagine this tower of Minecraft blocks of rock
extending all the way down to the center.
The downward crush of all that weight
is resisted because each of those blocks
is hard to compress beyond a certain point.
They're under a lot of pressure.
And the resulting pressure gradient force
balances gravity in the up-down direction.
See, pressure acts outwards.
A block around halfway to the center of the Earth
has to push up with the pressure needed
to support the weight of 3,000 blocks above it.
The one below it exerts more pressure.
It has to support 3,001 blocks.
We can sort of think of the planet
as a huge number of these block towers,
each one in perfect equilibrium in their up-down forces.
So each tower is responsible for only supporting itself
from downward collapse.
OK, cool.
But then, why do these towers need to form a sphere?
You can make, say, a flatter disky shape
by adding to the towers around the Equator.
Shouldn't those towers still be stable
if they're only responsible for their own up-down equilibrium?
Nope.
Because up and down aren't the only directions
that forces are working.
See, pressure shares that same symmetry as gravity.
Instead of pulling, it pushes in all directions equally.
And so any given block will push sideways
on the neighboring towers with the crushing weight
of all the blocks above it.
Now, in the case of a sphere, that's cool.
At any given depth blocks will be
pushing against their neighbors with equal force to each other
because they're all at the same depth and same pressure.
The forces cancel out and we have equilibrium.
But that is not the case with our flattened planet.
Any two neighboring blocks are actually at different depths
below the surface compared to each other, and so
are at different pressures.
Now, that doesn't affect their up-down equilibrium,
but the side-to-side forces won't cancel out.
A block closer to the Equator is further below the surface
and so will exert more pressure than its neighbor that's
closer to the pole.
There's a net positive sideways force squeezing away
from the Equator.
And unless there are other effects in place
to resist these forces, then everything
has to move until it finds an equilibrium.
That is, until it becomes a sphere.
This is all assuming a planet made of separate blocks.
But what about a planet made of completely solid rock?
Which the Earth isn't, but let's go with it.
See, rock is really, really good at not being
crushed by direct pressure.
It has very high compressive strength.
However, rock has a sheer strength.
That its resistance to sideways deformation.
That's 10 times lower than its compressive strength.
So a relatively solid, rocky planet
will fracture and reshape itself into a sphere
as long as its own gravitational field is strong enough.
It turns out that any body larger than several kilometers
in diameter will form a sphere.
For example, the 578-kilometer-diameter asteroid
Vesta is lumpy, but the 1,000-kilometer Ceres is
spherical.
And it's not just rocky things.
A very similar balance applies to stars.
Here the pressure comes from the upward flow of energy
from the nuclear fusion engine in the core.
And this hydrostatic equilibrium keeps stars like our sun
extremely spherical and happily burning away
for billions of years.
But wait, gravity and pressure are not the only things at work
here.
The Earth and the Sun, for that matter, rotate on their axes.
There's a centrifugal force that can counteract gravity
and should actually push a spherical object
towards exactly that flattened shape that we talked about.
It counteracts gravity so we can build higher block
towers towards the Equator while still maintaining equilibrium.
In the case of the Earth, how flat
does it get due to its spin?
At the Equator the upward acceleration
we feel due to the Earth's rotation
is 0.03 meters per second squared,
compared to 9.8 meters per second squared due to gravity.
That's a 0.3 percent difference.
And indeed, the Equator is around 20 kilometers further
from the center of the Earth than the pole,
0.3 percent of the total radius.
That's still pretty spherical.
This is not true of things like spiral galaxies, solar systems,
and the whirlpools of gas around quasars.
These things are even more massive
than single planets or stars.
So why don't they form spheres?
It's because the effect that prevents their collapse
has a very different symmetry.
Let's think about what happens when a vast interstellar
cloud of gas and dust collapses to form a star.
These things are so huge and spread out,
they barely fuel their own gravity,
and they collapse very, very slowly.
They also start out spinning very slowly,
but that spin speeds up as they collapse,
just like a spinning ice skater.
And all of the gas gets swept into the same swirling flow.
This global rotation makes it even harder for the cloud
to collapse.
The gas can't fall any closer to the axis of rotation
because it's orbiting that axis.
However, gravity is pulling both inward towards the axis
and down towards the center.
The cloud can still collapse in the down direction,
and it does so, ending up as a spinning disk when
it finds itself in equilibrium.
Now, these giant disks of stuff will clump off and form
the star in the center and the planets further out,
but the disk structure remains long after all the gas is gone.
Pretty much the same thing happens
with spiral galaxies like the Milky Way,
except on a much, much larger scale.
Short story.
Spheres happen when pressure is the dominant effect resisting
gravity.
Pressure is spherically symmetric.
Disks happen when orbital motion dominates the resistance
to gravity.
That's a circularly symmetric effect, and so you get,
well, a circle.
Now, these fundamental symmetries
don't just define the shapes of some of the largest
things in our universe.
They don't just give us our beautiful globe of the Earth,
our spiral Milky Way Galaxy.
They also give us things like the Laws of Conservation
of Energy and of Linear and Angular Momentum, topics
that we will get to.
Symmetries really do shape the universe
on all the scales of space time.
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In our recent episode, we talked about some
of the outstanding issues in the Big Bang Theory.
You guys had a lot of questions in the comments section.
Felix Ironfist asks, "why didn't the universe
collapse into a black hole, if it was so dense and massive?"
This is a classic question.
In order to make a black hole you don't just
need a high density, you need a high density
relative to the surrounding regions.
See, the Big Bang didn't happen as a sudden presence of energy
at some point.
Instead, the early universe is described
as a very high density over an extremely large, and possibly
infinite, volume.
Our observable universe was a tiny speck in that volume.
The region surrounding that speck
had very similar densities, and so there
was no net gravitational attraction towards our patch
of the greater universe.
Therefore, no universe-sized black hole.
Florent asks, "how can it be that we're still
continuously receiving the cosmic background
radiation today, given that it was all
emitted by a single point at the Big Bang?"
Well, the answer to this is related to the last.
The Big Bang happened everywhere,
not at a single point.
And at the moment of recombination,
when the CMB was emitted, it was emitted
by all of the observable universe and beyond
at the same time.
This patch of space, the Milky Way, the Earth,
has been bombarded with cosmic background radiation
for all of cosmic time.
That radiation originally came from regions nearby.
But as the universe got older, radiations from further
and further away had time to get to us.
It has always come from our cosmic horizon,
but that cosmic horizon expands.
Reuben Silva asks, "can we really 'science' anything?
Are there questions that are off limits to science?"
When I say we can science anything,
I mean that there's no question that is immune to,
or at least can't be benefited by, the scientific approach.
I don't mean that the scientific approach is
all powerful and the only way to address questions,
or even that it's necessarily the best
approach to many questions, just that there's
no realm that is fundamentally off-limits or unapproachable
by science.
For example, Stephen Jay Gould's non-overlapping magisteria
suggests that questions related to human values
are not the domain of science, they're the domain of religion.
However, our scientific understanding
of human psychology is massively helpful in understanding
human motives and values.
Science may not answer every question,
but scientific habits like reason, rigor,
evidence-based thinking, and active and repeated questioning
of your world view are powerful tools in any type of inquiry.
Dom Vasta asks, "why is science a verb now?"
Because I verbed it.
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