Thanks to Surfshark for helping support this episode.
Hey Crazies.
You know how we always see the same side of the Moon,
the side with the face on it?
Well, that can happen with planets too, if there's enough time.
The same side of a planet could always be facing the star it's orbiting,
continuous sunlight on one side and continuous darkness on the other.
It would make the planet kind of look like an eyeball.
But will that ever happen to Earth?!
If you give a system enough time, it'll settle into the most stable configuration it can find.
You could randomize the motion of particles in a room all you want,
but if they're bumping into each other a bunch of times,
they'll settle into something fairly predictable.
It's a stable configuration.
Any minor deviation and the forces will bring them back.
In astronomy, configurations like this are governed by gravity
and they're called "resonances."
We usually label them with some kind of ratio.
For example, three of Jupiter's moons have a 1:2:4 orbital resonance.
That means in the time it takes one moon to go around once,
the others go around two and four times, respectively.
But today's video isn't about orbital resonance.
It's about spin-orbit resonance.
Rather than multiple objects having a ratio between them,
there's a ratio between the spin and the orbit of a single object,...
kind of like how the planet Mercury has a 3:2 spin-orbit resonance with the Sun.
That means for every three rotations or spins,
there are two full orbits.
For some places on Mercury, that means you could have two sunrises or sunsets in a single day,
which is kind of weird.
Our own moon has a special kind of spin-orbit resonance called "synchronous rotation."
That means the ratio between the spin in the orbit is one to one.
The time it takes to spin around once equals the time it takes to orbit once,
so the same side of the Moon always faces the Earth.
If you took a picture of the Moon every day for a month,
the resulting GIF would look like this.
And, yes, I pronounced it GIF.
It's "graphics interchange format."
Graphics. GIF.
Anyway, synchronous rotation is actually a very common phenomenon, even in our own solar system.
Both of Mars's moons do it.
All four of Jupiter's big moons do it.
Some of Saturn's moons even do it.
It happens a lot, is what I'm saying.
All it takes is time, but how much time depends on the circumstances.
In fact, if the two objects were perfectly spherical,
none of this would ever happen.
It's the imperfections that make spin-orbit resonance possible;
which, if you ask me, is the most interesting part of this whole process.
It's the imperfections that make it beautiful.
Contrary to what we tend to think, no object is ever perfectly rigid.
I've mentioned in a previous video that Earth has an equatorial bulge because it spins.
Well, the Moon spins too, which means it also bulges at the equator.
Those graphics are extremely exaggerated though.
The Earth's oblateness is only about 0.3%.
The Moon's is about 0.1%.
We're exaggerating for clarity.
Now, spin is not the only thing that can cause bulge...
(Laughing)
There are other things that can cause bulging.
It had to be said. I know.
Somebody had to say it.
Let's try to get through this line again.
Now, spin is not the only thing that can cause bulging.
Gravity can do it too.
The Earth and Moon are pretty far apart, but they still pull on each other.
That gravitational tug can and will cause bulging along the line between them.
That's not necessarily along the equator of either object,
so we can't call it an equatorial bulge.
We call it a "tidal bulge."
"Tidal" as in the tides.
This effect is most noticeable with the oceans.
The Earth's gravity may hold the ocean down,
but the moon's gravity pulls it a little to the side.
That, combined with a massive amount of fluid pressure, causes a bulge in the ocean.
(Springy Sound Effects)
This doesn't just happen with liquids though.
The Earth may be solid rock, but it can be deformed in exactly the same way.
Remember, nothing is perfectly rigid.
Not only does the ocean bulge, but all the rock underneath it does too,
just not as much.
How does this cause that synchrotron radiation though?
It's synchronous rotation, also known as tidal locking.
And hi, where have you been?
Do you really want to know the answer to that?
Actually, no, never mind.
Anyway, synchronous rotation occurs because of torque.
You know how forces can cause a change in speed?
Well, torque is like a rotational force.
It can cause a change in rotational speed.
For any spin orbit resonance to occur, there must be torque.
In our case, that comes from the fact that tidal bulges can't change instantly.
If the Moon is rotating quickly,
it's bulge is going to lag behind of the planet-moon line.
That means the forces on either side don't line up.
You get a torque opposite the rotation, which slows it down a bit.
It's not a lot. Those bulges in the animation are exaggerated.
But if it happens over and over again for 100 millineer...
milla millineers?
We're the millineers! Yeah. (Laughing)
The millineers!
But if it happens over and over again for 100 million years,
those little slowdowns are going to add up.
One snowflake may be pretty insignificant,
but a bunch of them is an avalanche.
(Scream)
Planetary systems tend to be around for billions of years.
That's billions with a "b."
The rotation of our own Moon had enough time to slow down
until the bulge was always along the planet-moon line.
That's when its spin equals its orbit.
A similar thing would happen if the Moon started out slower instead.
If it's rotating slowly,
its bulge is going to get ahead of the planet-moon line.
That means the forces on either side still don't line up,
but this time you get a torque along the rotation, which speeds it up a bit.
The end result is the same though: synchronous rotation.
How long did it take to tidally lock like that?
Getting a number is actually kind of tricky.
We do have an equation for it,
as long as we make a crap-ton of approximations.
There are actually so many approximations
that I don't feel entirely comfortable using it,
but it's the best we've got.
The general problem is so complex that it's completely unsolvable.
What this equation can do though, is give us an idea of what factors are involved
and how important each one is.
We've got some things you'd probably expect:
the rotation speed of the moon,
the radius of the moon,
the orbital radius of the moon,
the mass of the planet,
and the gravitational constant of the universe.
All things we either know or can find by taking a few measurements.
Unfortunately, these two we often don't know very well.
Something called the tidal love number, which measures the elasticity of the moon;
and the specific dissipation function, which tells us how much energy is lost to heat.
We do know them for our moon, which is how I knew it took 100 million years.
If you're trying to calculate this for any other object, just give up now.
We can see some patterns in this equation though.
If the elasticity is zero, meaning the moon is perfectly rigid,
then time is infinite.
Tidal locking never happens because no elasticity means no bulges.
The more energy that gets dissipated, the longer it's going to take.
We can also see the radius and the orbital radius are to the fifth and sixth powers, respectively.
That makes the time particularly sensitive to those values.
A moon orbiting much closer to its planet is going to tidally lock a lot sooner.
What about the planet's bulge? Oh! That's a great question!
Earth rotates about 27 times faster than the moon orbits,
so its own tidal bulge gets ahead of the planet-moon line,
and the tidal forces slow the rotation.
Given enough time, the Earth could slow down enough that it would tidally locked to the Moon.
The same side of the Earth would always face the Moon.
How long would that take? Don't get your hopes up.
A generous lower-bound says it'll take at least 50 billion years.
Considering the Sun will go red giant in 4 to 5 billion,
there isn't nearly enough time.
But this has happened elsewhere in our Solar System.
Pluto and its moon Charon do this.
They're much closer to each other in distance, size, and mass than the Earth-Moon system,
so it took a lot less time.
Tidal locking with the Sun will take even longer.
This scenario doesn't stand a chance of happening,
but we have seen it happen outside our own solar system.
In the TRAPPIST-1 system, several of its planets are tidally locked to the star.
It's a small red dwarf, so the planets are a lot closer to each other and to the star.
Plus, red dwarfs last for like 1,000,000,000,000 years.
That's the kind of system where we'd expect to see an eyeball planet like this.
The lit side would be a desert hellscape,
the dark side a frozen wasteland.
Life would only be possible in the thin boundary between the sides.
It would be a land of eternal dusk,
with dangers lurking in every shadow...
kind of like life on the internet.
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So would you like to live on a tidally locked planet?
Please share in the comments.
Thanks for liking and sharing this video.
A special thanks goes out to my Patreon patrons and YouTube members
like OnlineBookClub and Christopher Schiele for their generous support.
Don't forget to subscribe if you'd like to keep up with us.
And until next time, remember it's OK to be a little crazy.
What did I say? I said, don't at me.
But fine! I'll clarify.
Saying superconductors have zero resistance is sacrificing accuracy in favor of simplicity.
Is their resistance below our ability to measure?
Yes, but that doesn't make it zero.
Anyway, thanks for watching.