Relativity in a Rotating Space Station

[kaikalii]

A common solution to the problem of artificial gravity in space is to have the spaceship 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?

 

[Spinnor]

...

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.

...

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

 

[Dale]

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.

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!

 

[WannabeNewton]

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

+1 for the Kubrick reference.

 

[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?

 

[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.

 

[kaikalii]

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.

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

 

[Fredrik]

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

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.

 

[Dale]

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

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.

 

[BruceW]

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

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.

 

[Bill_K]

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.

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.

 

[D H]

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.

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.

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.

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.

 

[BruceW]

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.

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.

 

[DiracPool]

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.

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?

 

[WannabeNewton]

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

 

[DiracPool]

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

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?

 

[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 into the direction of rotation will feel different than those walking against the direction of rotation?

 

[DiracPool]

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

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.

 

[WannabeNewton]

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?

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 :)

 

[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' ?

 

[BruceW]

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?

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).

 

[Dale]

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?

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.

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?

Cost.

 

[bahamagreen]

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 :)

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.

 

[D H]

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?

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 anyone 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.

Who thinks people walking into the direction of rotation will feel different than those walking against the direction of rotation?

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.

 

[pervect]

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.

 

[D H]

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.

It's the shortest axis, not the longest. See [post=3350918]this post[/post].

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.

Yep. You don't need a rotating ring. A livable module and a counterweight connected by a truss or tether will do quite nicely, and yes, NASA has thought of it.

 

[pervect]

It's the shortest axis, not the longest. See [post=3350918]this post[/post].

That's what I meant, I worded it poorly. Basically energy = I omega^2, and angular momentum = I omega. Thus the lowest energy state for a given value of angular momentum (which must be conserved) will be the one with the lowest rotation rate - or the maximum moment of inertia, as E = L*omega, or L^2/I.

Being at a true global minimum of energy guarantees stability under all circumstances - as you point out, there are some theoretical circumstances where a rigid body can be stable and not in the global low energy minimum (by being in a local minimum). But it turns out to be a poor idea in practice, there are paths to the true global minimum energy state that exist for real bodies that are not totally rigid, which make the apparent stability of some of the solutions an illusion.

I believe there was an actual failure when a satellite was launched and tumbled, because it was rotated along the "wrong" axis. But I don't recall the details.

Yep. You don't need a rotating ring. A livable module and a counterweight connected by a truss or tether will do quite nicely, and yes, NASA has thought of it.

Has anything actually been done with this idea - or is there just not enough need for artificial gravity to make it worth the effort?

 

[bahamagreen]

The idea of the long tether is that there is no rotation relative to the Earth's surface.

Two platforms in orbit separated and tethered by a perpendicular cable will each enjoy an accleration; the lower orbit platform will be trying to orbit the Earth faster than the upper platform. Since the tether is tensile "ridgid" the lower platform is being held back from going as fast as it would without the tether; the upper platform would be going slower if not pulled forward... the pulling back and up on the lower platform and the pulling forward and down on the upper platform gives both platforms an "AF'.

The effect is dependent on the length of the tether; which makes an angle to the vertical normal from the Earth's surface - the lower platform leading the upper platform in orbit. Nominal useful AF occurs on the order of the tether being hundreds of miles, which is good because a long conductive tether cutting the Earth's magnetic field lines at high speed (about one orbit per hour) is a source of power and the orbital elevation of the center of mass of the whole system may be increased or decreased by discharging this power either at the low or high end of the system...

 

[pervect]

I do recall there were some experiments with conductive tethers - but as I recall, if you took power out of the system, it came from the orbital energy, which made the orbit decay faster. You could also do the reverse IIRC - pump power into the tether (power from solar cells, for example) to help mantain the orbit against drag - without using propellant.

 

[D H]

The idea of the long tether is that there is no rotation relative to the Earth's surface.

That's one use of tethers. There are others. A formation of tethered satellite used for long baseline interferometry, for example. Rotation is a big no-no for this usage. Pervect's tethered system for artificial gravity is another. Here a paltry 90 minutes per rotation is useless. Tethered satellites make for great thesis projects and grant proposals. The applications are limitless!

Tethers are one of the many technologies for which NASA had lots of plans that were shelved when paper confronted reality. That's one of the key problems with perpetually low TRR concepts. The technology looks great on paper, in the lab, and even in mockup. Reality has a nasty way of saying otherwise. Tethers are one of those technologies.