MinutePhysics

WATCH: How long would it take to fall through Earth?

The answer is 42. Seriously.

BEC CREW
25 MAY 2016
 

If you stood on the surface of Earth at one point, and you had a tunnel running all the way to the opposite point on the globe, how long would it take to fall through and get to the other side? It could be as simple as calculating how fast the average human would fall a distance of 12,742 km (Earth's diameter), but thanks to the curvature of space-time, we have different degrees of gravitational force to contend with all the way down.

But this is actually something you can calculate, and when you see Henry from MinutePhysics show you how, you're going to feel mighty smart.

 

So first up, let's set the scene properly. We have a hole through the planet running from the North Pole to the South Pole, which negates the coriolis effect of Earth's spin. We've also sucked all the air out of the hole to prevent terminal velocity from seriously slowing down your trip.

Let's simplify it more by assuming Earth is perfectly spherical, and its density is the same all over.

If we want to calculate the speed of the drop, we can figure out the gravitational attraction pretty easily - it averages out across the entire sphere, where the parts closer to the centre experience a stronger pull, but these are cancelled out by the weaker pulls of the furthest away points. 

"If you're inside a spherical shell, then the gravitational pulls from all the different parts cancel out, and you experience zero effect from the shell," says Henry. 

Note: Except what we've just described isn't really Earth as we know it - it's a smaller spherical object with all its interesting parts shaved off. But you'll soon see why all that simplification was necessary. 

 

Now, get ready for some maths, because you're about to get hit by a whole lot of it. Don't be afraid to pause and rewind, because this stuff can be tough, and we're going at break-neck speeds here - not unlike our hypothetical stick figure friend plummeting through an airless hole through a shaved Earth.

Let's yada yada the maths part because Henry has got all that down (plus he has graphs!) and get to the answer: 42. Say what? 

Yep, the answer is 42 minutes to fall through a simplified Earth, and also around it, if you don't feel like going through the middle.

But we're cheating here, because Earth isn't the same density all the way through, and as we discussed yesterday, that means the gravitational potential of certain areas within the hole would have a marked influence on the speed of your fall. 

This requires a bit of "mathemagical dust", as the video above describes it, but when the dust settles, we finally get our better answer: approximately 37 minutes. It was a bit of a slog to get there, but feels pretty good to understand it now, right?

To find out how fast you'd actually be falling, check out the video that started it all:

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