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Relativity in a Rotating Space Station

  1. Jun 30, 2013 #1
    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. jcsd
  3. Jun 30, 2013 #2
    Why can't the whole station rotate as one? See,

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

    Dale

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    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!
     
  5. Jun 30, 2013 #4

    WannabeNewton

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    +1 for the Kubrick reference.
     
    Last edited by a moderator: Sep 25, 2014
  6. Jun 30, 2013 #5
    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?
     
  7. Jul 1, 2013 #6

    BruceW

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    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.
     
  8. Jul 1, 2013 #7
    But in his frame of reference, isn't the entire station stationary, and therefore there would be no centrifugal force accelerating him?
     
  9. Jul 1, 2013 #8

    Fredrik

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    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.
     
  10. Jul 1, 2013 #9

    Dale

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    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.
     
  11. Jul 1, 2013 #10

    BruceW

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    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.
     
  12. Jul 1, 2013 #11

    Bill_K

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    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.
     
  13. Jul 1, 2013 #12

    D H

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    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.
     
  14. Jul 1, 2013 #13

    BruceW

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    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.
     
  15. Jul 1, 2013 #14
    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?
     
  16. Jul 1, 2013 #15

    WannabeNewton

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    The net angular momentum of the whole system (ring + people) will still be conserved; the internal torques in question will cancel out.
     
  17. Jul 1, 2013 #16
    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?
     
  18. Jul 1, 2013 #17
    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
  19. Jul 1, 2013 #18
    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.
     
  20. Jul 1, 2013 #19

    WannabeNewton

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    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 :)
     
  21. Jul 1, 2013 #20

    Mentz114

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    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' ?
     
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