Y’know, if Shakespeare had been an astronomer, he’d have said that “there is a tide in
the affairs of the Universe, and on such a full sea are we now afloat.”
He would’ve been right. You might just think of tides as the ocean going in and out every
day, but in fact what astronomers call tides are a subtle but inexorable force that have
literally shaped most objects in the Universe.
And to understand tides, we start with gravity.
Gravity is a force, and it weakens with distance. An important thing to note is that we measure
gravity from the center of mass of an object, not its surface. One way to think of the center
of mass of an object is the average position in an object of all its mass. For an evenly
distributed sphere, that’s it’s center.
Right now, unless you’re an astronaut, you’re about 6400 kilometers from the center of the
Earth. If you stand up, your head is a couple of meters farther away from the Earth’s
center than your feet. Since gravity weakens with distance, the force of Earth’s gravity
on your head is an eensy weensy bit less than it is on your feet. How much less? A mere
0.00005%. And that’s way too small for you to ever notice.
But what if you were taller? Well, the taller you are, the farther your head is from the
Earth’s center, and the weaker force it will feel. If you were, say, about 300 kilometers
tall, the force of gravity would drop by about 10% at your head. That probably would be enough
to notice, if you weren’t dying from asphyxiation and, y’know, being 300 kilometers tall.
This change in the force of gravity over distance is what astronomers call the tidal force.
When you have a massive object affecting another object with its gravity, its tidal force depends
on several factors. For one thing, it depends on how strong the gravity is from the first
object; the stronger the force of gravity, the stronger stronger the tidal force will be on the affected object.
It also depends on how wide the affected object is. The wider it is, the more the force of
gravity from the first object changes across it, and the bigger the tidal force.
Finally, it depends on how far the affected object is from the first object. The farther
away the affected object is, the lower the tidal force will be. Tides depend on gravity,
and if gravity is weaker, so is the tidal force.
The overall effect of the tidal force is to stretch an object. You’re applying a stronger
force on one end than you are on the other, so you’re pulling harder on one end. That’ll
stretch it! And this is where tidal forces become very important.
Look at the Moon. It has gravity, but much less than the Earth because it’s less massive.
It’s 380,000 kilometers away, so the gravitational force it has on you is pretty small. And you’re
pretty small compared to that distance, just a couple of meters long from head to feet.
But the Earth is big! It’s nearly 13,000 kilometers across. That means the side of
the Earth facing the Moon is about 13,000 kilometers closer to the Moon than the other
side of the Earth. This is a pretty big distance, enough for tides to become important. The
side of the Earth facing the Moon is pulled harder by the Moon than the other side of
the Earth, so the Earth stretches. It becomes ever so slightly football-shaped, like a sphere
with two bulges, one pointing toward the Moon, and one pointing away.
This is probably the weirdest thing about tidal forces. You might expect only one bulge,
on the side of the Earth facing the Moon. But remember, we measure gravity from the
centers of objects. The side of the Earth facing the Moon feels a stronger pull toward
the Moon than the Earth’s center, so it’s pulled away from the center.
But the side facing away from the Moon feels a weaker force toward the Moon than the Earth’s
center. This means the center of the Earth is being pulled away from the far side. This
is exactly the same as if the far side is being pulled away from the center, and that’s
why you get two bulges on opposite sides of the Earth.
The tidal force is therefore strongest on the sides of the Earth facing toward and away
from the Moon, and weakest halfway in between them on each side.
A lot of the Earth is covered in water, and water responds to this changing force, this
stretching. The water bulges up where the tidal force is strongest, on opposite sides
of the Earth. If there’s a beach on one of those spots, the water will cover it, and
we say it’s high tide. If a beach is where the tidal force is low, the water’s been
pulled away from it, and it’s low tide.
But wait a second: The Earth is spinning! If you’re on the part of the Earth facing
the Moon, you’re at high tide. Six hours later, a quarter of a day, the Earth’s rotation
has swept you around to the spot where it’s low tide. Six hours after that you’re at
high tide again, and then another six hours later you’re at low tide for the second
time that day. Finally, a day after you started, you’re back at high tide once more.
And that’s why we have two high tides and two low tides every day. Very generally speaking,
the ocean tide causes the sea level to rise and fall by a meter or two, every day.
Incidentally, the solid Earth can bulge as well. It’s not as fluid as water, but it
can move. The tidal force stretches the solid Earth by about 30 centimeters. If you just
sit in your house all day, you move up and down by about that much...twice!
Like the saying goes, a rising tide lifts all… surfaces.
The Earth’s spin has another effect. Lag in the water flow means the water can’t
respond instantly to the tidal force from the Moon. The Earth’s spin actually sweeps
the bulges forward a bit along the Earth. So picture this: the bulge nearest the Moon
is actually a bit ahead of the Earth-Moon line.
That bulge has mass; not a lot, but some. Since it has mass, it has gravity, and that
pulls on the Moon. It pulls the Moon forward in its orbit a bit, like pulling on a dog’s
leash, accelerating it. The Moon responds to this tug by going into a higher orbit:
The Moon is actually moving away from the Earth! The rate of recession of the moon has
been measured and it’s something like a few centimeters per year, roughly the same
speed your fingernails grow.
Now get this: the Moon has gravity. Just as the bulge is pulling the Moon ahead, the Moon
is pulling the bulge back, slowing it down. Because of friction with the rest of the Earth,
this slowing of the bulge is actually slowing the rotation of the Earth itself, making the
day longer. The effect is small, but again it’s measurable.
OK, let’s get a little change of perspective. Everything I’ve said about the Moon’s
tidal effect on the Earth works the other way, too. The Moon feels tides from the Earth,
and they’re pretty strong because the Earth is more massive and has more gravity than
the Moon. Just like Earth, there are two tidal bulges on the Moon; one facing the Earth and one facing away.
Long ago, the Moon was closer to the Earth, and spinning rapidly. The Moon’s tidal bulges
didn’t align with the Earth, and the Earth’s gravity tugged on them, slowing the Moon’s
spin and moving it farther away. As it moved farther away, the time it took to orbit once
around the Earth increased: Its orbital period got longer. Eventually, the lengthening rotation
of the Moon matched how long it took to go around the Earth. When that happened, the
axis of the bulges pointed right at the Earth.
That’s why the Moon only shows one face to us! It spins once per month, and goes around
us once per month. If it didn’t spin at all, over that month we’d see the entire
lunar surface. But since it does spin once per orbit, we only ever see one face.
This is called tidal locking, and it’s worked on nearly every big moon in the solar system;
tides from their home planet have matched their spin and orbital period. These moons
all show the same face toward their planet!
Now wait a second. If the Moon has gravity, which causes tides, and is the root cause
behind all these shenanigans, what about the Sun? It’s even bigger than the Moon!
Tides depends on the gravity from an object, and your distance from it. The Sun is far
more massive than the Moon, but much farther away. These two effects largely cancel each
other out, and when you do the math, you find the Sun’s tidal force on the Earth is just
about half that of the Moon’s. The way the Sun’s tidal force and the Moon’s tidal
force interact on Earth depends on their geometry, which changes as the Moon orbits us.
At new Moon, the Earth, Moon, and Sun are in a line. The Moon’s tidal force aligns
with the Sun’s, reinforcing it. This means we get an extra high high tide and an extra
low low tide on Earth. We call this the spring tide.
When the Moon is at first quarter, the tidal bulge from the Moon is 90° around from the
Sun’s; high tide from the Moon overlaps low tide from the Sun. We get a slightly lower
high tide, and a slightly higher low tide. We call those neap tides.
The pattern repeats when the Moon is full; the Moon, Earth, and Sun fall along a line
again, and we get spring tides. A week later the Moon has moved around, and we get neap tides again.
Not only that, the Moon orbits the Earth on an ellipse. When it’s closest to us we feel
a stronger effect. If that also happens at New or Full Moon, we get an added kick to
the spring tides. This is called the proxigean tide, and can lead to flooding in low-lying areas.
Unless you live on the coast, I bet you had no idea tides were so complex!
Tides are universal; they work wherever there’s gravity. If two stars orbit each other, each
raises a tide in the other. Just like the Earth and Moon, that can slow their spin and
increase their separation. Many planets orbiting other stars may be tidally locked to those
stars. Near a black hole, where the gravity is incredibly intense, the tides are so strong
they would pull you like taffy into a long, thin string. Astronomers call this effect…
spaghettification. No, seriously, that’s what we call it!
Today you learned that tides are due to the changing force of gravity over distance. The
strength of the tidal force from an object depends on the gravity of the object, and
the size of and distance to the second object. Tides raise two bulges in an object, creating
two high tides and two low tides per day on Earth. Tides have slowed the Earth’s rotation,
moved the Moon away from the Earth, and locked the Moon’s rotation and orbit so that the
Moon always has one side facing us.
So. Tide goes in. Tide goes out. It turns out, I can explain that. Now you can too.
Crash Course is produced in association with PBS Digital Studios. 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 Nicole Sweeney, and the graphics
team is Thought Café.