# Relativity in a Rotating Space Station

1. Jun 30, 2013

### kaikalii

A common solution to the problem of artificial gravity in space is to have the space ship or station rotate, and the centrifugal force would "pull" objects toward the outside.

What I haven't seen considered is that the station would have to have some kind of central motor attached to a central part of the station that would not rotate in the same way as the rest.

Imagine two of these space stations orbiting Earth. They are exactly the same in all regards, except that in the first, the spinning section is significantly more massive than the center, and in the second the center is significantly more massive than the spinning section. In both stations, both outer sections rotate at the same rate relative to the center. This leads me to believe that both stations would have the same amount of artificial gravity. However, relative to the Earth, the outer section of the second station would be spinning significantly faster than in the first station, leading me to believe that the second station would have significantly greater artificial gravity than the first.

My question is, which is correct? How does the relativity of the rotational velocity of the outer sections relate to the non-relativity of the actual acceleration felt by people aboard the station?

2. Jun 30, 2013

### Spinnor

Why can't the whole station rotate as one? See,

Last edited by a moderator: Sep 25, 2014
3. Jun 30, 2013

### Staff: Mentor

Why would you need that. Once it is spinning, conservation of angular momentum will keep it spinning as long as there is no external torque.

Edit: the appropriately named Spinnor beat me to it!

4. Jun 30, 2013

### WannabeNewton

+1 for the Kubrick reference.

Last edited by a moderator: Sep 25, 2014
5. Jun 30, 2013

### kaikalii

Perhaps I should revise my question to something far simpler. If there is a ring-shaped space station that is spinning relative to Earth, but is stationary relative to a person standing on the inner surface, what kind of acceleration does the person experience?

6. Jul 1, 2013

### BruceW

he experiences an acceleration away from the centre of the ring. I'm not sure what you're getting at...

edit: well, he 'experiences acceleration' in the sense that if he drops his keys, they will accelerate away from the centre of the ring.

7. Jul 1, 2013

### kaikalii

But in his frame of reference, isn't the entire station stationary, and therefore there would be no centrifugal force accelerating him?

8. Jul 1, 2013

### Fredrik

Staff Emeritus
In what one would normally call "his frame of reference", the station isn't stationary.

The station is only stationary in a coordinate system that has its origin at the center of the ring and is rotating with the ring. In that coordinate system, a person standing on the inside of the outer wall is stationary. He will however feel himself getting pushed towards the inside of the outer wall, and if he drops something, it will "fall" towards the wall.

9. Jul 1, 2013

### Staff: Mentor

There is a reference frame where the station is stationary, but this reference frame is not an inertial reference frame. The principle of relativity asserts the equivalence of different inertial reference frames, not non-inertial frames.

10. Jul 1, 2013

### BruceW

I think I see your line of thought. You are thinking that logically, there is no physical reason to favour the 'spinning station' coordinate system or the 'stationary station' coordinate system. But there is a difference. In the 'stationary station' coordinate system, he will see the stars spinning around. It is the structure of the universe that tells us the important difference between the two coordinate systems.

11. Jul 1, 2013

### Bill_K

It is the LOCAL structure of the universe that is the difference between inertial and noninertial frames. The stars have nothing to do with it.

12. Jul 1, 2013

### D H

Staff Emeritus
He experiences an acceleration toward the center of the ring, not away from it. What he feels is the floor of the space station pushing up on his feet and that upward force propagating non-uniformly throughout his body. This feeling is exactly what an accelerometer tells him; the accelerometer reports a centripetal acceleration. This also is exactly what those falling keys tell him. Those falling keys represent a local inertial frame. They appear to be falling down, but from the perspective of the falling key frame, he is accelerating upward.

A ring laser gyro will tell him something else: The station on he is standing on is rotating. This explains those falling keys. His frame of reference is a non-inertial frame. It is an accelerating frame thanks to the rotation. It is also a rotating frame, and that means he might be feeling some other effects. He might feel light headed (quite literally!) if the radius of the space station is short enough so as to create a significant gravity gradient between his feet and his head. (NASA has done studies on this. A rotating space station would have to be quite large so as to avoid creating that nauseating light headed feeling.)

This locally observed rotation is also consistent with non-local experiments such as looking at the stars tell him.

Yes and no. Either we are exceedingly lucky to live in a region of space where the local structure agrees with what the remote stars (or even better, pulsars) tell us, or there is something to do with it. The general relativistic explanation is that we don't live in a region of strongly curved space-time and that the universe as a whole is at most rotating at a very small rate.

13. Jul 1, 2013

### BruceW

I'm not sure if reference frame is really the correct terminology here. But the stars are important. They give us a big clue about what is the most likely metric tensor that describes the universe. If we did not assume FLRW metric, then the person in the space station would not be able to say if he was experiencing a pull due to the rotation of his space station, or if it was due to the 'non-flatness' of the metric tensor.

edit: alright, granted, without any evidence it would probably be best to assume a flat metric tensor. But light from the stars (and other radiation) give us explicit evidence. That's why they're important.

14. Jul 1, 2013

### DiracPool

Two questions, 1) Would people walking around and moving objects, etc. inside the spinning ring constitute a torque acting on the rotation and thus affecting the angular momentum? And 2) Why hasn't NASA or any other countries equivalent ever even tried at least a "proof of concept" mini-model of this in low Earth orbit to test these things and to give us kids back home the thrill of seeing it?

15. Jul 1, 2013

### WannabeNewton

The net angular momentum of the whole system (ring + people) will still be conserved; the internal torques in question will cancel out.

16. Jul 1, 2013

### DiracPool

Does that mean that once the system is set spinning at a particular angular velocity, no additional external torque would be required to maintain that velocity regardless of the peoples moving around inside?

17. Jul 1, 2013

### bahamagreen

What it means is that the rotating station is going to need a control system to maintain a constant level of "artificial gravity".

A system of tanks and pumps could do it - there will be a water supply there.

Otherwise, the distribution of mass would vary both in its radius from the central axis and in its symmetry around the central axis.

The control system needs to maintain superposition of the central axis (structural) with the actual axis of rotation.

Failing that, the rotation speed and orientation of the axis of rotation will vary as people shift from standing to sitting, and as they move themselves and equipment around the structure - the resulting cyclic variations in "AF" will make people sea sick.

Just imagine having an all hands meeting in one chamber... a compensating distribution of mass needs to balance that.

* Who thinks people walking in to the direction of rotation will feel different than those walking against the direction of rotation?

Last edited: Jul 1, 2013
18. Jul 1, 2013

### DiracPool

Good question. You could really mess people up and put those flat walking escalators like they have in the airports around the inside of the rim and not tell anyone which ones are on or off.

19. Jul 1, 2013

### WannabeNewton

No I meant the whole system not the ring itself. When the people shift from standing to moving they will change the rotational speed of the ring and the orientation of the rotation axis because they will exert a torque about the center due to the tangential force they apply when shifting from sitting to moving and a torque that will "tip over" the rotation axis due to the normal force they exert on the ring floor. I think this is what bahamagreen was referring to but I may be wrong of course. Hopefully he can correct me if so :)

20. Jul 1, 2013

### Mentz114

I remember a shot in Kubric's 2001 where a crew member of the spacecraft is jogging around the inside of a cylinder. Easy shot to fake if the cylinder is rotating and the actor just keeps pace so he stays at the bottom. The camera goes round with the cylinder so in the replay the guy seems to run around the inside of a stationary ring.
A new take on 'frame of reference' ?

21. Jul 2, 2013

### BruceW

I think this has been answered already, but no, the total angular momentum is conserved, so if the people inside all ran in one direction, it would cause the angular velocity of the space station to change. But since the space station needs to be pretty big to pull off this 'artificial gravity' thing, I would assume that the effect of people running around to be negligible. (unless there are a lot of them and they all decided to run the same way all at once).

22. Jul 2, 2013

### Staff: Mentor

No, they would not exert a net torque, so the angular momentum would be the same. However, it could change the moment of inertia and therefore the angular velocity.

Cost.

23. Jul 2, 2013

### bahamagreen

Yes. Even lateral mass displacements ("north/south") perpendicular to the tangent line of rotation direction ("east/west") at same radii will tip the rotation axis.

It does seem peculiar that one who runs against the direction of rotation at a relative speed to the floor that approaches the speed of rotation will be able to step "up" and float indefinitely above the floor in an inertial reference frame... those standing "still" on the floor will see the floater appear to zoom around the station floating across the floor without effort.

24. Jul 2, 2013

### D H

Staff Emeritus
1) As bahamagreen noted, the spinning ring would need some kind of control system to maintain stability. Physicists tend to ignore subtleties that engineers have to pay attention to. There's an implicit assumption in this thread that the space station has an axis of symmetry and that the angular momentum is perfectly aligned with this axis of symmetry. In reality, the space station will have three distinct principal moments of inertia (i.e., it will not have an axis of symmetry) and the angular momentum will not be perfectly aligned with any one of the station's principal axes.

With regard to moving objects around, there will have to be rules and procedures on doing that. Move things around too much and the control system will lose stability and/or controllability. That loss of controllability would give the astronauts on the ring an close and personal demonstration of what "the polhode rolling without slipping on the herpolhode lying in the invariable plane" means. Think of what happens inside your washing machine starts the spin cycle when the jeans happen to all be on one side of the wash bucket and the shirts on the other.

2) NASA has done and continues to do lots of experiments in this area. For example, see http://www.google.com/#q=Artificial+Gravity+Biomedical+Research+site:nasa.gov. These experiments don't need to be performed in space. That would be very expensive.

There are two key human factors problems with using rotation to provide artificial gravity. The Coriolis effect is one of them. It's not just walking. Even a simple motion such as reaching out with ones hand to push a button on a console can be quite confusing if the ring has too short a radius. The finger does not hit the button.

The other problem is gravity gradient. Too short a radius and the difference between what one feels at foot level versus eye level is disconcerting. To reduce these human factors issues to a tolerable level, studies performed in the 1960s indicated that the ring would have to be 112 meters in diameter or more. More recent studies suggest that training can mitigate these problems to some extent. A huge, 100+ meter diameter ring might be overkill.

25. Jul 2, 2013

### pervect

Staff Emeritus
Rather than a huge ring, what about a couple of boxes connected by a strong tether? As I recall, the stable state of rotation will be the one with the least energy for the given, constant amount of angular momentum. WHich means around the long axis. I think tether systems have other applications for catching payloads, too. If I can think of it, I"m sure someone at Nasa has too, but I don't t think I've ever read much discussion about it.