# What mass distribution around a huge rotating cylinder would a person (who can't see the outside) at rest on the inner side of the cylinder infer?

In a rotating frame, the artificial gravity has a peculiar form. At the center, this "gravity" is zero, while it's increasing in proportion to $R^2$, where $R$ is the distance to the center.

Now imagine we find ourselves on the inner side of a huge rotating cylinder, on the inner side of which are villages, an infrastructure, flora, fauna, etc. Imagine a person throws a ball in such a way that the velocity of the ball is exactly opposite to the rotation velocity of the cylinder (or, more accurate, opposite to the rotation velocity of the person's hand when he starts the throwing). The ball is then standing still in the rest frame for a person who's not in the rotating cylinder frame. So a person in the rotating frame (of course standing on the ground, the inner side of the cylinder) sees the ball moving in a circle, (with a radius $R$ being about the same as the radius $R$ of the person's head) just a little above the cylinder's inner side.

Another effect would show itself if you would let loose a ball from a tower so the ball goes in free fall. The ball doesn't end up at a place exactly under the point where you let it fall. Off course, it ends up at the bottom (the inner side of the cylinder) but farther away from the tower than when it started to fall. And how strange a game of baseball would look like! You can even wonder if they can find the equations governing gravity, but let's assume they know.

Now to come to the question: How would persons inside the cylinder think the mass outside the cylinder is distributed to cause the gravitational behavior (just like a person in an accelerated lift thinks the gravity he feels is caused by a mass outside the lift)?

Will it be a rotating ring of mass (which is consistent with the circular motion of the ball, described above, because in that case, the ball is standing still with respect to the rotating ring of mass and the gravitational on a mass inside a spherical shell of mass is zero)?

EDIT

For the rotating bucket with water, you can say the rising water is caused by a massive enough rotating sphere around the bucket (so the rising is caused by frame dragging), as well that the rising is caused by the rotation of the bucket. Both cases are equivalent. This is not the same as the example above, but related though.

• Why would they think there's a distribution of mass outside the cylinder? They can detect that they're rotating! That many sci-fi authors propose using rotation to create forces that act "like gravity" on board of these rotating stations doesn't mean that the passengers could literally not tell that apart from actual gravity! – ACuriousMind Apr 11 '17 at 11:10
• But if people in the cylinder couldn't see what is outside the cylinder (and thus they can't detect that they are rotating), they might as well think that the gravitational force is caused by a mass distribution around the cylinder (like a person in an accelerating lift, who experiences a pseudo gravitational force and who can't see what's outside the accelerating lift might just as well conclude that a real mass is pulling him downwards: Einstein's equivalent principle). – descheleschilder Apr 11 '17 at 11:47

"Accelerating lift" analogy is only valid for a small region of space-time (see equivalence principles).

If they play baseball on the inner surface of a rotating cylinder, but the size of the baseball field is relatively small and they don't kick the ball too high and they don't play for too long, the difference between the pull they experience and some gravitational pull will be too small to measure.
In this case, since their measurements are local, they can choose any fictitious distribution of mass that produces the required pull (flat surface will do).

If they set on a task to find the exact mass distribution though, they will have to go farther (and higher and faster) until the non-gravitational effects (e.g. coriolis force) and overall structure of a distribution of the pull will become non-negligible and eventually they will realize that there is no gravitational field capable of producing observed accelerations.

• A rotating cylinder with a big enough mass around the cylinder in question can explain the gravitation the objects inside the cylinders experience. The frame dragging effect caused by the surrounding cylinder causes the inner cylinder to rotate (like a massive spinning cylinder around a bucket of water will cause the bucket to rotate). An infinite flat mass (causing a uniform gravity) will do for the uniform gravity (if the person goes an arbitrarily distance up or down in the lift the gravity experienced by him will remain the same) experienced by a person in a uniformly accelerated lift. – descheleschilder Apr 11 '17 at 16:08
• If you hit a ball so that it has the opposite angular velocity to the angular velocity of the cylinder, the ball will make trace out a circular trajectory according to the people in the inner cylinder. With respect to the outer cylinder, the ball isn't moving, so the gravity on the ball is zero (like any object in a stationary cylinder of mass, or in a hollow sphere of mass), consistent with the circular motion of the ball, while a ball moving with uniform velocity with respect to the outer rotating cylinder is subject to the frame dragging effect, also consistent with the f.d. effect. – descheleschilder Apr 11 '17 at 16:45