@kurzgesagt

4 months ago

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

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