[drbaba]

Yes. You can think of it as: If you’re surrounded by an equal amount of mass in every direction (because you’re at the center of a set of spherical mass shells), then the gravitational force in every direction will cancel out.

[pbhjpbhj]

Agreed.

>If you’re surrounded by an equal amount of mass in every direction

Which is a reasonable approximation for being 'out in space', but perhaps not an entirely intuitive one.

[sliken]

Indeed, and as a related situation. You could be inside a black holes event horizon and experience zero gravity/acceleration. You just need two blackholes to cancel out the gravity.

[Ntrails]

I feel like being in the middle of two black holes would be more like being ripped apart than zero gravity/accel.

[Qwertious]

So if a cup of water were in the centre of the earth, and every layer of the earth above the centre wasn't there to compress it, then it would explode out!

Seems perfectly reasonable, if a bit useless.

[yorwba]

If a cup of water at room temperature were on the surface of the earth and every layer of the earth above it wasn't there to compress it (so no atmospheric pressure) the water would violently boil immediately. If the cup is very tall or you're talking about a cup of very cold ice, the water's own gravitational pressure could keep the bottom stable, but to prevent the top from boiling/sublimating off, you'll need a lid to keep it pressurized.

Moving the experiment to a zero-gravity environment doesn't change the pressure considerations much.

[pja]

No, it won't explode.

If you somehow made a spherical hole in the middle of the earth and placed a cup of water inside the hollow (anywhere inside, doesn't have to be the centre) it will just sit there: Newtonian gravity is 0 inside a uniform spherical shell of mass. (Einsteinian gravity is probably mostly 0 but you'll get frame dragging effects if the shell is rotating I would imagine.)

You can do the maths to prove this yourself if you want.

[nimchimpsky]

no it would be weightless, as all the gravity would cancel each other out.