@kurzgesagt

Let’s look at some of your frequently asked questions for this one:

Why does halving the radius lead to ⅛ of the volume?

We halved the radius of the Earth, keeping the average density of the planet the same. This allows us to roughly estimate the mass by multiplying the new volume by the unchanged density. The volume of a sphere depends on the radius to the power of three (r^3) – so halving the radius actually means dividing the volume by 8. You can see the equation for this at 0:08

What if we removed the layers instead of halving the radius?

We went with the approach of halving the radius as it seemed to us to be more logical to simply shrink Earth instead of removing the outer layers until it was half the size.
Shrinking something in a scientifically correct way is a hard thing to do, this is something we learned during the development of our VR experience.
There are two methods: either you shrink things by removing their atoms while keeping the density the same, or you shrink them by reducing the distance between atoms while increasing the density. We opted for the first technique, simply because it keeps stuff more or less the way it is, so stones will just be smaller stones after shrinking them.

Removing layers would only mean three things:
1. Changing the average density of the Earth, making our calculations a bit more complicated.
2. The outer shell of Earth would now be the Earth's mantle, which is a scorching 1000–2000°C
3. All things on Earth would immediately burn up – from flora and fauna to buildings and us humans.
So this would be a pretty boring scenario.

Why is a day 48 minutes long?

For the duration of a day, we use the formula for angular momentum. It’s the product of angular inertia (how difficult it is to start and stop the rotation of an object) and angular velocity (how quickly an object rotates around an axis of rotation). Angular inertia is proportional to mass and the square of the radius. Halving the radius led to an eighth of the mass, so the angular inertia is divided by 32 – this comes from 1/8 (from the mass) multiplied by 1/4 (from the square of the halved radius). But angular momentum needs to be conserved, so the angular velocity has to change. It needs to cancel out the inertia loss by increasing to 32 times the speed. Thus, a day will be 32 times shorter. You can see the equation for this at 0:15 in the video.

We think that some of the most surprising and interesting scenarios we come up with are the result of playing around with these formulas and equations. We also checked these calculations carefully to make sure we did not make a mistake here. But if you still have objections, we're happy to discuss them here with you. After all, the battle of equations is half the beauty of physics! <3

@Astro_486

Finally kurzgesagt saying 'size still matters'

@doodlehates_uttp

Basically, things get bad

@Aixo235

we going to school for 40 days a week with this one

@edmdeathmachine

"size still matters" 💀

@iwannabeafishy

DIGLETT AND EGGXECUTOR CAMEOS LMAO

@wojciechgilicki6815

That alolan Exeggutor at the end is gold 😂

@charged_kaon

The smaller the size, the lower the attraction
😭😭😭

@coolbionicle

If the gravity is reduced then you shrinked the earth by removing mass and that means you also removed it's angular momentum. Unless you used that mass to propell the rotation of this new earth, said rotation should stay the same, otherwise for the first analogy to work you have to compress the earth, which would increase its gravitational acceleration at the surface.

@abherbitter

You can't change gravity/mass, and preserve angular momentum. Earth's rotation wouldn't speed up in this scenario because the mass it lost would have taken the rotational energy with it.

When a figure skater pulls in their arms, they don't lose their arms.

@hydralisk3534

If you’re shrinking the earth by just removing the outer layers and decreasing the mass (as opposed to condensing the same mass into a smaller volume) the earths spin would not increase

@oof7346

I kept looking for a "I'm sure it has a great personality" comment but now I'm disappointed

@calinacho7704

If you shrink it in such a way that it's mass also gets cut to one 8th, then it's speed of rotation wont change. (Unless youre deliberately imagining a scenario where the smaller earth magically inherits the entire momentum)

@thelightningboom8061

I love the Alolan Exeggutor in the background!

@juniper9836

correction: half the size of earth (in diameter) would not lead to things being half as heavy; this would scale with mass (which is determined by volume)

@Nee56abb

Listen, what if we don't shrink it or make it bigger

@ttongx9352

The moon probably wouldn't like that either

@OzGoodman

just love you guys I wish more people will make shorts like yours, amazing

@Tootall206

Doesn't add up. If the mass decreases the length of day doesn't change.

The increase in rotational speed only happens like that when the mass is brought closer to the center. Not when the mass is removed.

@R4Z4K1N

Well shrinking can imply compression or reduction, but each has its own respective effects. The difference is substantial in compression