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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