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 seeing Santa 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.

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 video 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, 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, you'll fall right back in and oscillate back and forth

in the hole ... forever.

I don't know about you, but I definitely have better things to do with my time.

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.

Not too shabby!

How would you want to travel across the world?

Leave me a comment to let me know.

On a separate note: Have any of you been to Vidcon?

What did you think of that incredible experience?

Life Noggin Studios just produced an AMAZING documentary about the convention, and you

need to check it out!

There's a link in the description if you're on mobile.

Make sure you come back every Monday for a brand new video.

As always, I'm Blocko and this has been Life Noggin.

Don't forget to keep on thinking!