The Gravity of the Situation: Crash Course Astronomy #7

By | December 6, 2019


We live — and stop me if I’m going too
fast — on a planet. I mean, sure, duh. But this isn’t the natural
state of the Universe; or, at least, it’s not the way things usually are. Most of the
Universe is pretty empty — that’s why we call it “space” — and if I were to
magically transport you someplace randomly in the cosmos, the chances are you’d be a million
light years from the nearest substantial object. Evolving on a planet has warped our sense
of physics. If I throw an object away from me, it comes back. That’s bizarre! It should
just keep going, moving away from me at a constant speed. Instead though it goes up,
slows, stops, then falls back down toward me. The difference between living on a planet
and being in deep space is gravity. Gravity from an object goes on forever, but it gets
weaker rapidly with distance. A zillion light years away, the Earth’s gravity is fantastically
weak, but here on Earth it’s literally a force to be reckoned with. And in some places it can be a lot
stronger than what we experience right here. For most of history, gravity was just a fact
of life, neither understood nor examined terribly closely. In the mid 1600s, scientists like
Robert Hooke and Isaac Newton started investigating it using math — in fact, the two men got
into a bitter feud over who thought of what first. But whoever it was who first got it
right, now we have a much better understanding of how gravity works. One thing before we get to gravity. An important
concept that comes up a lot is mass. It’s a bit tricky to define, but you can think
of it as how much stuff makes up an object. I know, that’s not very scientific sounding,
but it’s not a bad way to think about it. Something with more mass has more stuff in it. Size doesn’t really play into this; two
objects can have the same mass but one can be much larger than the other. In that case,
the bigger object’s mass is more spread out, so we say it has lower density, where density
is how much mass is inside a given volume. In science terms, mass tells us how much an
object resists having its motion changed. An object with more mass is harder to get
moving than an object with less mass, which is pretty obvious if you’ve ever tried pushing
on a toy car versus a real truck. But mass is also defined using gravity. Everything that has mass also has gravity
and can inflict this force on another object. The amount of force you feel from the gravity
of an object like a planet depends on three things: How much mass it has, how much mass
you have, and how far away you are from it. In fact, distance dominates here; the force
of gravity weakens with the square of the distance. Double your distance from an object
and the force of gravity drops by 2 x 2=4 times. Go 10 times farther away and the force
drops by 10 x 10=100 times. Gravity is also attractive: It can only draw
things in, not repel them. But how it attracts things is where it gets fun. If I hold up a rock and let go of it, it falls
to the ground. What might be hard to see is that it gets faster the longer it drops. Forces
accelerate objects, so the longer the force acts, the more the object’s velocity changes
– in this case getting faster. If I drop a rock from higher up, it’ll move faster
when it hits the ground. Other forces act on moving objects, as well, like friction
and air resistance, counteracting gravity, making this acceleration hard to see. But in
space, the force of gravity becomes very clear. Two objects that have mass will attract each
other. If there are no other forces acting on them, they’ll accelerate toward each
other until they meet. Remember, though, that the force of gravity depends on those masses.
If one is really massive, and the other not so much, then in more practical terms the
massive one will pull in the less massive one. The more massive one does move, but much
less than the other one. When objects are free to move under the effects
of gravity, we say they are in orbit. The simplest kind of orbit may not be what you
think: It’s actually just a line! When you drop a rock, it’s very briefly in orbit.
Ignoring things like the Earth’s rotation (which adds a bit of sideways motion) it’s
close enough to say the rock just falls straight down, and is stopped because the Earth itself
gets in the way. That’s not a terribly interesting orbit!
So what if, instead of dropping the rock, we throw it? That gives it a little bit of
sideways motion, so instead of hitting the ground at my feet, it hits a bit farther away.
If I throw it harder, it moves horizontally even more before it hits. What if I throw it really hard? This is where Newton’s genius comes in.
He realized that if you throw the ball hard enough sideways, it will fall at the exact
same rate the Earth would curve away underneath it. As Douglas Adams said in “Hitchhiker’s
Guide to the Galaxy,” flying is just falling and missing the ground. It turns out, that’s
exactly what orbiting is, too. A rock thrown hard enough sideways will fall
toward the Earth, but always miss it, going instead into a circular path around it, guided
only by gravity. It will orbit the Earth in a circle, taking about 90 minutes to go around
the planet once. Circles are simple orbits. The speed at which
the orbiting satellite travels depends on the mass of the object it’s orbiting, and
its distance from it. The farther it is, the weaker gravity is, so it doesn’t have to
travel as quickly to maintain the orbit. Roughly 400 years ago, the astronomer Johannes
Kepler realized that there can be other shapes of orbits as well. He discovered the planets
orbit the Sun on ellipses, when previously it was thought they orbited in perfect circles.
An elliptical orbit happens when you throw the rock sideways even harder than it takes
for a circular orbit; it goes up higher on one end of the orbit than on the other. In fact, the harder you throw the rock, the
more elongated the orbit gets. An orbit like this is still closed; that is, the orbit repeats
itself and the rock is still bound to the Earth by gravity. At some point, though if
you throw the rock hard enough, an amazing thing happens: It can escape. Remember, gravity gets weaker with distance.
If you throw a rock hard enough, while gravity can slow it down, the gravity gets weaker
the farther away the rock is. If the rock has enough velocity, gravity weakens too quickly
to stop it. The rock can escape, moving away forever, so we call this the escape velocity. The escape velocity of an object like a planet
or star depends on how much mass it has and how big it is. For the Earth, that turns out
to be about 11 kilometers per second — for Jupiter, it’s about 58 kilometers per second,
and for the Sun it’s a whopping 600 kilometers per second. Whatever the particular escape
velocity for your cosmic location is, if you fling a rock away from it faster than that,
I hope you kissed it goodbye first, ‘cause it ain’t coming back. One way to think of
it is that the rock is always slowing, getting ever closer to stopping, but it never actually
stops. If it could travel infinitely far away, it would stop, but that’s kind of a long
trip. This works in reverse, too. If I go way far
away from the Earth and drop a rock, it’ll accelerate. When it hits the planet it’ll
be moving at escape velocity, that same 11 kilometers per second. And if I give it a
little sideways kick, it’ll miss the Earth but still pass us at escape velocity. An escape
orbit is open — it doesn’t come back — and is shaped like a parabola. What if you throw the rock even harder than
that? The rock doesn’t come back, and moves away even faster. The orbit is now a hyperbola,
which is similar to a parabola, but is even more open. The rock never stops, even at infinity.
It just keeps movin’ on. Like all forces, gravity gets weaker with
distance. But its force never quite drops to zero; it just gets smaller and smaller
as you get farther and farther away. So why then are astronauts on the space station
“weightless”? Gravity is still pulling on the astronauts!
In fact, at the height of the station, Earth’s gravity has only decreased by a little bit;
it’s still about 90% as strong as it is on the Earth’s surface. If they were in
a tower 320 kilometers high they’d weigh 90% of what they do on the Earth’s surface.
But the big difference is that the astronauts are in orbit, falling around the Earth. Weight
is actually not just the force of gravity on a mass, but how hard a surface pushes back
on that mass. For example, when you stand on the ground, the ground pushes back. Otherwise
you’d fall through! The force of the ground back on you is what causes you to have weight. In free fall, there’s nothing pushing back.
You’re falling freely, and so you have no weight. NASA likes to call this condition
“microgravity,” since there are subtle forces acting on you. This actually highlights the difference between
mass and weight. In space you have the same mass as you do on Earth, but no weight. If
another astronaut pushed on you they’d have to exert a force, but if you stood on a scale
in space it wouldn’t register anything. Space is weird. Well, compared to Earth. One more thing, and this is truly weird: Photons,
particles of light, have no mass, yet they can be affected by gravity, too, bending their
direction of flight as they pass a massive object! It turns out gravity can actually
warp space! Light travels along the fabric of space like a truck on the road, and if
the road curves, so does the truck. I know this is an odd concept, and we’ll be dealing
with it later in more detail when we push escape velocity to its limits… with black
holes. Today you learned that gravity is a force,
and everything with mass has gravity. Gravity accelerates object, changing their speed and/or
direction. An object moving along a path controlled by gravity is said to be in orbit, and there
are many different kinds: straight lines, circles, ellipses, parabolae, and hyperbolae.
You can’t ever escape gravity, but if you travel faster than escape velocity for an
object you’ll get away from it without falling back. And if you’re in orbit, in freefall,
you have no weight, but you still have mass. This episode is brought to you by Squarespace.
The latest version of their platform, Squarespace Seven, has a completely redesigned interface,
integrations with Getty Images and Google Apps, new templates, and a new feature called
Cover Pages. Try Squarespace at Squarespace.com, and enter the code Crash Course at
checkout for a special offer. Squarespace. Start Here. Go Anywhere. Crash Course Astronomy is produced in association
with PBS Digital Studios, and you can head over to their channel and find more awesome
videos. This episode was written by me, Phil Plait. The script was edited by Blake de Pastino,
and our consultant is Dr. Michelle Thaller. It was co-directed by Nicholas Jenkins, and
Michael Aranda, edited by Nicole Sweeney, and the graphics team is Thought Café.

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