Suppose that you are inside a room, and your task is to determine whether you are on the surface of Earth or inside some kind of space station where artificial gravity is achieved by rotation. You are provided with any tools you want (as long as they don't help you communicate or observe outside the room). The perceived gravity matches that of Earth, so that alone cannot be done to determine the answer.
Ok, that's a relatively interesting problem in itself, but not the actual problem I'm posing, as the solution is rather trivial: You can use, for example, a
pendulum or a rotating wheel which can also rotate on a perpendicular axis in order to determine whether the gravity is achieved by rotating a space station or not. (To people who haven't studied lots of physics it might not be self-evident why this is so, though.)
But a pendulum or rotating wheel will also show rotation on Earth too: After all, the Earth is rotating once every 24 hours, which the pendulum/wheel is going to show. The difference is, of course, that the space station is going to rotate significantly faster (probably in the order of minutes instead of 24 hours), which is what gives it away.
So the problem I'm presenting consists of two parts:
1) Assume that there's no physical limit (imposed by material strength, etc) to the size of the space station. To make the problem more difficult, let's build a space station which makes one full rotation in 24 hours, like Earth, and produces the same perceived gravity like that. Question: What would the radius of the space station have to be in order to achieve this (iow. it makes a full rotation in 24 hours and the perceived gravity at the outer edge is the same as on the surface of the Earth)?
2) In this situation, is there any way of determining whether you are in such a spacestation or on Earth?
