You know what would be really cool - if we had a hole that travelled straight through the Earth from pole to pole.

I mean, you could go from Artic to seeing some penguins in Antarctica in no time at all -- well, assuming you’d survive that is.

But anyway, you might be wondering: how long would a trip like that actually take?

Well, let’s start off with some simplifications: firstly, we’re going to assume that the Earth has the same density everywhere, is a perfectly symmetric sphere, and the hole has no air in it - because otherwise, the air resistance will cause you to reach terminal velocity, meaning your speed would eventually plateau.

And the core temperature of Earth will cause no harm to you.

So with those assumptions out of the way, we’re ready to begin!

Let’s suppose you’re standing next to this super dangerous hole and fall in, so your initial speed is zero meters per second.

And like you’d normally experience if you fell into any hole, you’re going to accelerate down.

But how much you accelerate depends on how far you are in the hole.

See, when you are at the top of the hole, the entire Earth is below you, so you’ll experience the same gravitational acceleration as you normally would, 9.8 meters per second squared and you’ll start to speed up as you fall.

But then, things change.

Now, you are inside the hole, so some of the Earth is above you and some of it is below you.

And this means that the gravitational forces are both pulling you up as well as pulling you down.

So your acceleration is going to change.

Luckily for us, there’s a simple trick that we can make use of to figure out how much.

Let’s pretend that you are inside a spherical shell with a uniform density.

In here, no matter where you are, the gravitational forces from every part of that shell will cancel out.

To actually prove this, you’d need to know a super cool thing called calculus and add up the forces from every single tiny portion of the shell.

But to keep this topic from getting too math-heavy, just trust me that this works.

Now, as you are falling toward the center, the parts further from the center than you are form a spherical shell.

And we just said that all of the gravitational forces from that shell will cancel out.

So, this means that we can simply pretend that that part of the Earth isn’t there, and, instead, you’re standing on the surface of a smaller Earth.

So, as you fall, the Earth basically gets smaller and smaller and your downward acceleration decreases.

And once you reach the center, and you won’t experience any acceleration at all.

But remember: you are still falling down pretty quickly and you have great velocity, so you’ll zoom right past the center towards the other side.

And from here, instead of the Earth shrinking, it’s getting larger and larger as you fall down, since you are now moving away from the Earth’s center.

And with all that Earth above you, the acceleration will flip directions and will now be pointing up.

But since you are still traveling down, this means your velocity will start to slow, eventually reaching zero when you get to the other side of the hole.

And if you don’t jump out from other hole, you’ll fall right back in and oscillate back and forth in the hole ... forever.

But assuming you only travel through the hole once, using some physics, we’ll find that this whole trip will take you around 42 minutes.

Leave me a comment to let me know.

I mean, you could go from Artic to seeing some penguins in Antarctica in no time at all -- well, assuming you’d survive that is.

But anyway, you might be wondering: how long would a trip like that actually take?

Well, let’s start off with some simplifications: firstly, we’re going to assume that the Earth has the same density everywhere, is a perfectly symmetric sphere, and the hole has no air in it - because otherwise, the air resistance will cause you to reach terminal velocity, meaning your speed would eventually plateau.

And the core temperature of Earth will cause no harm to you.

So with those assumptions out of the way, we’re ready to begin!

Let’s suppose you’re standing next to this super dangerous hole and fall in, so your initial speed is zero meters per second.

And like you’d normally experience if you fell into any hole, you’re going to accelerate down.

But how much you accelerate depends on how far you are in the hole.

See, when you are at the top of the hole, the entire Earth is below you, so you’ll experience the same gravitational acceleration as you normally would, 9.8 meters per second squared and you’ll start to speed up as you fall.

But then, things change.

Now, you are inside the hole, so some of the Earth is above you and some of it is below you.

And this means that the gravitational forces are both pulling you up as well as pulling you down.

So your acceleration is going to change.

Luckily for us, there’s a simple trick that we can make use of to figure out how much.

Let’s pretend that you are inside a spherical shell with a uniform density.

In here, no matter where you are, the gravitational forces from every part of that shell will cancel out.

To actually prove this, you’d need to know a super cool thing called calculus and add up the forces from every single tiny portion of the shell.

But to keep this topic from getting too math-heavy, just trust me that this works.

Now, as you are falling toward the center, the parts further from the center than you are form a spherical shell.

And we just said that all of the gravitational forces from that shell will cancel out.

So, this means that we can simply pretend that that part of the Earth isn’t there, and, instead, you’re standing on the surface of a smaller Earth.

So, as you fall, the Earth basically gets smaller and smaller and your downward acceleration decreases.

And once you reach the center, and you won’t experience any acceleration at all.

But remember: you are still falling down pretty quickly and you have great velocity, so you’ll zoom right past the center towards the other side.

And from here, instead of the Earth shrinking, it’s getting larger and larger as you fall down, since you are now moving away from the Earth’s center.

And with all that Earth above you, the acceleration will flip directions and will now be pointing up.

But since you are still traveling down, this means your velocity will start to slow, eventually reaching zero when you get to the other side of the hole.

And if you don’t jump out from other hole, you’ll fall right back in and oscillate back and forth in the hole ... forever.

But assuming you only travel through the hole once, using some physics, we’ll find that this whole trip will take you around 42 minutes.

If you jumped into the tunnel, you'd fall down towards the center of the Earth, accelerating constantly, thanks to gravity.

By the time you reached the halfway point, after falling for 21 minutes, you'd be traveling at 28,000 kilometers per hour.

Once you crossed the halfway point, the velocity would carry you back up the other side of the tunnel for another 21 minutes.

This
time, however, gravity is slowing you down, so by the time you reach
the other end, you come to a perfect stop, just as you arrive at your
destination.

Not too shabby!

How would you want to travel across the world?Leave me a comment to let me know.

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