system
Given the following post, respond as if you're commenting on Reddit:
human
What would happen (in terms of gravity) if you stood in a spherical room, underground, in the center of a planet, such as Earth?

i have been thinking about this for a while, and i have no idea what would happen. would you float, like in space? would you be pulled to all of the walls at once? would you float into the center of the room, and be stuck there?

i have asked most of my friends this question, and everybody just gives me one of the answers above.
gpt
In a spherical room at the centre of the Earth, there would be no gravity at all. You'd float anywhere in the room. This is because inside any spherical mass distribution, mass that is at a larger radius than you're at combines to pull on you in such a way that doesn't affect the gravity you feel at all. Or, in other words, only mass below you contributes to the gravity you feel. So, if you're in a spherical room at the centre of the Earth, there's nothing "below" you ("below" = at a smaller radius), so you feel no gravity. 

The *reason* why it works like this is a little harder. First, imagine you're exactly at the centre of the room. All the walls pull on you equally, so you float there. This is hopefully clear. Now, if you move to the side, you get closer to a portion of the Earth (call it portion A), and further away from another portion (portion B). Now, this would be easier with a diagram, but portion B is actually larger than portion A. So B is a "large and far away" mass, and A is a "small and close mass". It should be obvious that these two objects pulling opposite to each other might cancel each other out, and if you work through the maths, it turns out that they do. This works anywhere in the room, and in fact you could have an entire hollow Earth and feel no gravity anywhere inside it.