Rotating Space Station & Gravity: A General Relativity Exploration

[Dr. Keith]

It is easy to see how a rotating space station can simulate gravity through the centripetal force. Examples are swinging a cup of water in an arch, or theme park rides.

I saw another discussion about this very topic and it got me interested and I was researching it, however everything I found suggested that there would be some wierdness, such as throwing a ball in the air wouldn't return to your hand like if you were on earth.

But the main thing that I would like to discuss is the assumption that an object within the space station would have to be touching the floor of the station in order to pick up the acceleration and "feel gravity".

This makes perfect intuitive sense, however:
According to General relativity, a rotating disk's circumference divided by its radius is NOT equal to $$2 \pi$$ like normal circles. This is due to the warping of space, which is the same thing that happens around massive objects like planets.

So I'm starting to think that an object just floating in the middle of the space station will actually feel a gravitational pull to the sides without touching it, according to general relativity.an interesting thought, if my idea is correct:
If you were to throw something past the center of rotation it will fall outward in the other direction, which is inversely related to planets, if you cross the center you will fall inward in the opposite direction you were falling.

 

[russ_watters]

Objects don't need to be touching the sides, they just need to be moving. You could throw an object into a type of orbit by throwing it backwards at the speed of rotation of the station. But since the air inside is moving with the station (due to friction), the object would "slow down" and fall back to the side of the station.

 

[jcsd]

As Russ states there's no requirement for objects to touch the floor.

For the purposes of your question, the relativistic effects in a spinning space station are too small for be interested in.

What the spinning space station is a good example of is how Einstein arrived at the equiavlence principle. In this case the space station uses a suitable non-inertial frame to simulate gravity. This is possible because gravitational force and pseudo-forces and experinced by a body are both proportional to it's mass. It was this simlairity between pseudo-forces and gravitational force that led Eisntein to the equiavlence principle and from there to spacetime curvature.

 

[Dr. Keith]

So say you were on the floor and the station was rotating at an extremely high rate, fast enough to notice such relativistic effects.

Would the person on the floor notice any differences whatsoever compared to being stationary on earth? say they threw a ball straight in the air (but not past the center) would it return to their hand?

 

[DaveC426913]

I rather suspect that any possible anomalies in the ball-throwing would be (oh let's go with understatement) ... overshadowed ... by somewhat more blatant side-effects of rotating at relativistic speeds.

 

[DaveC426913]

But the main thing that I would like to discuss is the assumption that an object within the space station would have to be touching the floor of the station in order to pick up the acceleration and "feel gravity".

It is possible, with a great amount of effort, to arrange it so that an object inside a rotating space station does not experience the artifical gravity - but it is not easy to do.

You see, anything in the space station will have acquired, as an initial state, the rotation of the space station. So, touching the floor or not, you're going to have the inertia - and it's the inertia that creates the artifical gravity.

The only way to NOT acquire that initial rotation is to be non-rotating when you first enter the space station. If you remain in vacuum (say, in a space dock that takes up one end of the station), you're golden - you will float weightless. you could maneuver yourself all the way down to the outer-inner hull of the space station - which would be whizzing by fairly quickly - and experience no artificial gravity.

But as soon as you enter a chamber with air, you're doomed to pick up its rotation.


One thing of note:

You could, in your socks and shirtsleeves, float yourself easily enough simply by running in a counter-rotatory direction. You would cancel your rotational inertia, causing you to experience less weight, and in fact, could run yourself right into midair and float there until air drag spun you up again. Running in rotatory direction OTOH, will get VERY difficult very quickly until you trip and fall.

 

[DaveC426913]

If you were to throw something past the center of rotation it will fall outward in the other direction, which is inversely related to planets, if you cross the center you will fall inward in the opposite direction you were falling.

No. Your ball will follow a perfectly straight path as seen by from a non-rotating FoR.

Now, the path it will follow from a FoR rotating with the station will be quite different, but I do not think it will be what you think it will be. For instance, it will not slow down as it nears the centre and it will not pick up speed as it "falls" to the opposite wall.

Exercise for the math adept: If the thrower tosses the ball and runs around the station to catch it when it lands, what path will the ball appear to follow from the thrower's point of view? (We assume the thrower treats the floor he is on as always horizontal and not curved.)

At first blush, I would guess the ball would appear to follow a circular (not parabolic) arc from throw to catch.

At second blush: Draw a straight line on a polar grid, convert the polar grid to a cartesian grid. Yeah, I think you get a circular arc.

 

[Dr. Keith]

I agree with your circular arch.
It appears that a perfect gravity simulation can't be achieved through a rotating body.

However, I would assume that the anomalies get lesser as the radius of the space station is increased.

But I'm still not sure if anyone has answered my question. I am aware of how things would appear from a classical euclidean view, but I am just curious if (air resistance aside) a rotating object creates an actual gravitational field.
Because gravity, according to general relativity is due to the warping of spacetime, and Einstein showed that the space around a rotating disk is warped as well.