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. Quick announcement. PBS Digital Studios has
put together a survey to find out what types
of digital series you are most
interested in seeing. If you'd like your
voice heard, PBS would love to hear from you. You'll find the link to the
survey in the description, and 25 participants
will be chosen at random to win PBS
Digital Studios t-shirts. Just click on the link
and take a few minutes to fill out the survey. 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. [MUSIC PLAYING]
I love pbs space-time but....I can't tell if I found this one dumbed down too much because i was already familiar with these concepts or if it was actually dumbed down.
I posted this in the other thread about this video, but since this seems to be the surviving once, I'll repost here.
Unfortunately I feel like this video ultimately fails at explaining what's going on. This answer and this one at the Physics Stack Exchange do a better job, I think.
All this talk about centrifugal force leaves me scratching my head; people are going to come away thinking that there is something different about rotating objects such that they have a force pushing outward as they rotate. But, of course there isn't any such force.
The video also leaves out any mention of elliptical galaxies, which are pretty close to spherical. And of course the difference is important, because it turns out that stars basically never collide directly, so the mechanism by which galaxies 'flatten' is provided by interstellar gas, which tends to be much more dense in spiral galaxies than elliptical ones.
As far as we can tell, galaxies DO start out basically spherical (and the dark matter, which basically has no collisions, stays spherical). Then, if there is enough gas around, the areas of higher density, like the beginnings of nebulas and such, experience drag caused by collision with all this gas. Those collisions continue until most of the stars and other high density objects are moving with the same average velocity as the gas around them. If the gas started out spinning, then the average velocity at different points in the gas has a preferred plane; it isn't random. And so everything large and dense enough to feel significant drag tends to collapse down into that plane until it roughly matches the average velocity of the remaining gas at every point along its orbit.
Once you have a disk, it doesn't collapse to form a sphere even though gravity is pulling it for exactly the same reason that the moon doesn't crash into the Earth. Gravity is pulling everything toward the center, but stars are always moving perpendicular to the line connecting them and the center of the galaxy a little. Because gravity pulls ONLY along the line connecting the two objects, there's always some part of the velocity perpendicular to that, and gravity can never get rid of it because it doesn't act in that direction. Of course, if there's a big clump of stuff at the center of the galaxy, gravity doesn't have to make you move directly toward the center of the galaxy; it only has to get you close enough to crash into the stuff. And this happens to objects that started out moving slowly enough perpendicular to the gravitational force, and forms the central bulge of spiral galaxies. The faster stars, though, are going so fast perpendicular to the line connecting them to the center of the universe that they never get close enough to hit anything, and so they stay in the outer disk. There doesn't have to be and isn't any magical centrifugal force that's opposing gravity (and I noticed they were careful to say 'orbital motion' later in the video rather than 'centrifugal force').