What Would Happen If the Earth Was Hollow and How Do We Know It’s Not?
There was a fun question on reddit (but it was removed). The question asked about the physics of a hollow Earth. I mean, the question wasn’t completely clear and left off some important details — but I’m going to answer it anyway. In fact, I’m going to make up some different versions of this question and answer them.
Gravity and a solid Earth.
OK, we are going think about a hollow Earth— but we need to stop for a moment and talk about gravity. Let’s model gravity as an attractive force between objects that have mass (instead of modeling it as a curvature in space-time). With that, we can calculate the gravitational force per unit mass due to some other tiny mass. This would be called the gravitational field (it’s the vector g with units of Newtons per kilogram).
The gravitational field due to this tiny little mass depends on both the value of the mass (m) and how far you are from that mass (r). It’s a vector that points towards the mass and we can write it as the following expression.
Here, G is the universal gravitational constant with a value of 6.67 x 10^-11 N*m²/kg². Also, notice that there is an r-hat in there. If r is a vector from the mass to where you want to find the gravitational field, r-hat is a unit vector that makes…
