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Rotation & Mathematics

  1. Oct 31, 2009 #1
    Hello!

    I am certain that a lot of debate and good debate must have gone in this direction. I do not know where on the net I can get to read about it.

    Case 1 (the very usual one)

    Telling rotation in absence of a reference frame. How does a person who cannot see any reference point in the sky tell if earth is rotating?

    Case 2

    Moons phase locking. Why moons (moons of almost all the planets) are phase locked, and planets closer to Sun rotate much slower?

    Case 3

    Why planets rotate?

    Case 4

    How exactly did the celestial bodies turn spherical?

    Case 5

    WMAP image of the universe, why does it look like any other celestial object, spherical, oblate and having edges?

    I know that non-mathematical explanation for these events exist.

    Regards
    Shahin
     
    Last edited: Oct 31, 2009
  2. jcsd
  3. Oct 31, 2009 #2

    HallsofIvy

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    Basically, relativity add nothing to those explanations. They involve such relatively low masses and low speeds that relativistic effects are neglegible.
     
  4. Oct 31, 2009 #3
    Because (without an external reference frame) GR cannot tell if a body is rotating or not, and going by the shape of the universe does it not suggest that it (universe) is rotating?

    A rotating universe justifies its expansion.

    My basic question really is if rotation is out of scope for GR/Mathematics, I know GR rules out a rotating universe, however even if it were rotating, GR could not tell?
     
  5. Oct 31, 2009 #4
    Well, physical evidence of the earth's rotation include observations of polar flattening and the equatorial budge, and an experiment by Foucault involving the famous Foucault Pendulum demonstrates the existence of the Coriolis effect.
     
  6. Oct 31, 2009 #5
    Thank you for your reply. I knew one can tell rotation, as it causes 'centrifugal force' that would cause weight reduction.

    One can tell about rotation (in absence of an external reference frame) by identifying and detecting the effects of rotation. (The same does not apply to linear motion.)

    I can see one effect of rotation on universe, exansion of the universe, is there any observational evidence that suggests universe should not be rotating?

    Can you please also tell what theory we have for the phase locking of moon, why they lost their angular momentum?

    Shahin
     
  7. Oct 31, 2009 #6
    Case 1:

    I would say that there is no way to tell if the planet is rotating without a reference point to go by.


    Case 2:

    Moons are phase locked because they are caught inside LaGrange points. Planets closer to the sun would rotate slower because of the imbalance between the sun's gravitational pull and that of other celestial objects.


    Case 3:

    The reason planets rotate is that they are unevenly influenced by the gravity of other celestial bodies. There may be bodies in space that don't rotate.


    Case 4:

    I can't exactly explain why stars are spherical, but given that there is no erosin in space I would say that the most likely reason for the spherical shape of solid objects in the universe is meteoric impacts.


    Case 5:

    I think the WMAP image looks like that because that is how the lens is shaped. I don't think we should assume from those images that the universe is spherical or finite.
     
  8. Oct 31, 2009 #7

    Dale

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    Use a gyroscope or ring interferometer.
    Conservation of angular momentum.
    It is an Aitoff or Hammer projection. Like one way of drawing a map of the globe on a flat piece of paper. It is not an indication of the shape of the universe.
     
    Last edited: Oct 31, 2009
  9. Nov 1, 2009 #8
    ernestpworrel/DaleSpam, thank you for your relies.

    I think I agree with you and I am hppay to close this case. *I* think Foucault pendulum experiment cannot tell whether the earth is rotating or it is just the pendulum rotating about stationary earth's orbit, again perhaps moon is also a bit oblate in shape but it does not rotate. Similarly you would need different tyeps of experiments to conduct if you were to tell if the galaxy we are in is rotating about its axis or not, and despite having done that you would not be able to tell if it is the galaxy rotating about its axis or is this just you rotating about stationary galaxy's orbit?

    I think this is the essence of relativity and this was once explained to me by my professor (I did go thrugh G. 't Hooft's Introductory GR available online but could not find my answer). If anyone disagrees please reopen. I am sure there should be some good material available online.

    I am happy to close this one as well.

    I am happy to close this one as well.

    However I would like some more input on Case 2 and Case 3.

    OK, as far as I understand LaGrange points, this tells about a possibility that a small body can be stationary in space.

    This does not explain the whole thing. Bodies closer to Sun rotate slowly, bodies farther from Sun rotate much faster, and moons of nearly all the planets are phase locked. This indicates more towards a fact they were rotating in the past but they lost their angular momentum. Somewhere I have read about rotation braking as well.

    As it looks to *me*, bodies under large gravitational force of another body gradually loose their angular momentum.

    This one is a bit difficult to appreciate. I have another exlanation that says they planets received their initial angular momentum from the rotating gases they were formed of. There is yet another that says planets started rotating because of meteor fall. Take a look at Saturn and let me know if the above two exlanations justify its rotation.

    The question really is how did they start rotating (defying conservation of angular momentum)? Can I have an explanation which is mathematical or testable?

    Regards!
     
  10. Nov 1, 2009 #9
    Calm down. You seem to be in a hurry to close all those 'cases'. Don't spoil the fun.

    The start of rotation doesn't defy conservation of angular momentum. Imagine a clay ball going straight with a particular speed. It hits an arm of a straight rigid pole. The arm is so designed such that it can rotate around the pole with a bearing arrangement. Completely inelastic collision. The clay ball sticks to the arm. The arm starts rotating. Where did this angular momentum come from? The thing is that the clay ball which was going straight in fact had an initial angular momentum w.r.t the pole axis. Angular momentum is a mathematical function. R X mv. So rigid and indifferent. It doesn't care whether a particular particle is executing rotation about some axis. As far as there is a reference point, a reference frame and a particle with some speed in a particular direction measure from this frame, angular momentum can be found.
    For planets, the centripetal force to capture random gas molecules and make them rotate along with the already swirling ones was provided by gravity.
     
  11. Nov 1, 2009 #10

    Dale

    Staff: Mentor

    Hi ernest, sorry about this, I was content to let your answers slide, but the OP seems to accept them readily. Unfortunately you are incorrect in pretty much every response.
    Yes, you can. A sensitive gyroscope or http://en.wikipedia.org/wiki/Ring_laser_gyroscope" [Broken] has to do with tidal effects, not the LaGrange points.
    No, they rotate due to conservation of angular momentum, not uneven gravity. As a planet or a solar system is formed the initial dust cloud has some overall angular momentum just by chance (it would be an incredible coincidence for it to have 0 angular momentum). That angular momentum must be conserved and results in the angular momentum both of the orbits and the spin of the planets.
    That is not relevant for objects like stars or gas giants. The short answer is that a spherical shape is a minimum energy configuration.
    You are correct, you should not assume anything about the shape or size of the universe from those images, but it is not due to the lens, it is simply a projection.
     
    Last edited by a moderator: May 4, 2017
  12. Nov 1, 2009 #11

    D H

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  13. Nov 1, 2009 #12
    @Dalespam and DH
    Just because the laws take on a simpler form doesn't mean its the only acceptable frame right. This isn't a matter of consensus. Do you guys mean to say rotation is absolute?
     
  14. Nov 1, 2009 #13

    D H

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    Correct. There is nothing wrong with using a rotating or accelerating frame.

    In the sense that one can measure whether a frame is rotating with respect to an inertial frame, yes.
     
  15. Nov 1, 2009 #14
    So its absolute rotation w.r.t an inertial frame. Not a 'stand alone' absolute rotation. A frame detecting its own motion is meaningless.
     
  16. Nov 1, 2009 #15

    D H

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    There is a big difference between motion (i.e., velocity) and acceleration. If you are in an isolated spacecraft (or a windowless elevator car), there is no way to tell from experiments conducted inside the vehicle how fast the vehicle is moving or how it is oriented. There are however experiments that will tell you whether it is accelerating or rotating. In that sense, acceleration and rotation are absolute.
     
  17. Nov 1, 2009 #16
    Ok. Let me be clear in my argument. Please correct me if i go wrong somewhere.
    What i have understood is that position,displacement, velocity, acceleration etc are all quantities that can be inferred by the observer in a frame about other bodies. An observer detecting his own motion seems ridiculous to me(by motion i mean all the parameters associated. Position, velocity, acceleration, jerk, everything). It shatters the concept of a reference frame.
    Its similar to saying that me along with the train is moving forward seeing the whole platform moving back. Just an accumulation of experiences that makes me think "No kidding. The platform can't move back".
    When you're saying he can detect his frame's rotation, you mean w.r.t an inertial frame. But that is a narrow minded thinking i would say. Like a person "deciding" that he is an eccentric viewing the society going around monotonously.

    I m sorry if my line of thinking is absurdly wrong. Would be happy if you could correct me.
     
  18. Nov 1, 2009 #17

    D H

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    sganesh88, to measure your position, velocity, orientation you do need some external reference. To measure acceleration or rotation you don't. The external reference is in a sense built into space-time. Google Mach's Principle.
     
  19. Nov 1, 2009 #18

    Dale

    Staff: Mentor

    It should be clear from Newton's second law that acceleration is fundamentally different than position and velocity. The equation f = m a = m x'' is second-order in position. So it should be no surprise that position and its first derivative (velocity) are relative and its second derivative (acceleration) and higher are absolute.

    Acceleration (rotation is a type of acceleration) can be measured with a variety of physical devices, this is the basis of http://en.wikipedia.org/wiki/Inertial_guidance_system" [Broken].
     
    Last edited by a moderator: May 4, 2017
  20. Nov 2, 2009 #19
    I think all that results due to the very way we define an inertial frame. Going by that line of reasoning, we could also say that the distance between two points,difference in velocities between any two particles and a host of other quantities as absolutes. All these are absolutes w.r.t an inertial frame. They are not universal absolutes.
    I am just skeptical about the special status you guys attribute to the "acceleration" factor.
     
  21. Nov 2, 2009 #20
    Whats the role of GR in this? Doesn't it say that both inertial and non-inertial frames are equivalent? That should mean that the results of the equipment that supposedly detect "your" rotation could be attributed to the motion of some other object.
    For example the detectors on the under side of the mouse could say to the CPU that the mouse is moving. We could create the same result by moving the mouse pad.
    Does a statement "the ball is rotating" cut off from reference to any frame make sense? Nature wouldn't give preference to acceleration this way i feel. :-O
     
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