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Gravity inside the Earth

  1. Jul 15, 2005 #1
    It seems common sense that as you go deeper into the Earth (eg with your feet towards the center) you will feel increasing pressure from the matter on top of you, that's what happens in deep sea.

    It may also seem common sense that the very centre of the Earth must be an ingravity place, because you have just the same amount of matter in any direction surrounding you. Is this correct?
    But if so, even being in zero gravity does anyway still mean that you have huge pressure from every direction? Shouldn't gravity from the surrounding matter "pull you outward in every direction" instead of pulling you down as it does in the surface?

    Is there a relationship between gravity and pressure in this context?

    Thanks!
     
  2. jcsd
  3. Jul 15, 2005 #2
    the force is zero, so i am assuming the pressure would be zero as well.
     
  4. Jul 15, 2005 #3

    Doc Al

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    While your "weight" (the gravitational force exerted on you by the mass of the Earth) will be zero at the center, the pressure you would experience (the weight of the earth pressing down on you) would be quite high.
     
  5. Jul 15, 2005 #4

    krab

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    But if you are in a rigid vessel (as in a submarine), this pressure won't be felt. The deeper you go in this vessel, the less gravity you feel. At the centre of the earth, you would be weightless as in free fall in space. But it is doubtful that you could design a vessel that could withstand the pressure at the centre of the earth; it's thought to be liquid there and very hot.
     
  6. Jul 15, 2005 #5
    Thanks
    But rather than just feeling weightless, shouldn't u actually feel a pull outwards in every direction, kind of getting swollen?
     
  7. Jul 15, 2005 #6
    I remember reading in Brian Greene's "The fabric of the cosmos" something about pressure contributing also to gravity, but don't know if this has anything to do in this context
     
  8. Jul 15, 2005 #7

    krab

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    No. Even the tiniest mass increment is pulled in all directions at once, so the forces simply cancel. You are thinking as analogous a situation where one end of something is pulled one way and the other end is pulled the opposite way. That's not the case here.
     
  9. Jul 15, 2005 #8

    BobG

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    Gravity and pressure are two separate things, but they are somewhat indirectly related.

    Gravity is due to the mass below you. Any mass further away from the center of Earth than you will be cancelled out. The only way you could experience any outward gravity is if left side of your body was only gravitationally affected by the mass on the left side of your body and the right side of your body was only affected by the mass on the right side. It doesn't work that way. Each and every molecule in your body would be affected by a balanced gravitational field, so your body wouldn't feel any outward gravity.

    Pressure is due to the weight of anything above you. In the sea, you feel the weight of all the water above you trying to replace your personal space with water. If you had a tunnel to the center of the Earth, it wouldn't be the weight of rocks above you that would increase the pressure - it would be the weight of the air above you. Air's not very dense, so the pressure increase wouldn't be as extreme as diving underwater. Of course, eventually you'd hit molten rock hot enough to melt your tunnel and then you would suddenly feel the pressure of all the matter above you trying to replace your personal space with molten rock. In other words, pressure depends on what's above you and wouldn't necessarily match the decrease in gravity.
     
  10. Jul 15, 2005 #9
    General Relativity inside Earth

    Although the idea of getting to the center of earth to safely test in a one atmosphere environment can only be done in a thought experiment. We can confirm the direction of these changes for real in a deep submersible like “The Challenger” that reached depth of 11 Km in Mariana Trench. I’m sure it measure greatly increasing pressure outside, and would measure the weight of a mass inside becoming lighter at depth.

    But a good question would be is it lighter because of LESS gravity?
    Or is it lighter even though gravity is the SAME or even GREATER just that as it is now being applied from multiple directions the weight decreases but maybe “gravity” does not ‘decrease’.

    That is to ask : What is the affect on General Relativity here?
    For example in a GPS system adjustments must be made for clocks in satellites running faster than the Master Clock on the surface due to GR and weaker gravity at altitude causing the orbiting clock to run faster. (Even larger SR adjustments for the speed of the orbiting clock slowing its time down must also be made).
    But will the lower altitude at 11 Km below the surface continue the GR affect of slowing time down as we near the center?
    Somehow that does not seem right to me. I’d think that the “gravity” for GR would be getting smaller inside the Earth and clocks would start to run faster again as they go deeper into the mass of Earth. (Meaning the GR time effect at the center of earth would be the equivalent of a deep space vacuum).
    How does the details of GR address this?
    Has it been confirmed by any direct tests of clocks taken to depth to confirm expectations by anyone??
    I’d think the GPS system in place now would be sensitive enough to detect which type of correction is required.

    Randall B
     
  11. Jul 15, 2005 #10
    That's interesting. If so, at what depht would the time-slowing reach its peak and start running faster again while moving towards the center?
     
    Last edited by a moderator: Jul 16, 2005
  12. Jul 15, 2005 #11
    Keep in mind, gravity ONLY attracts, it does not repel. Therefore, at the center of the earth, you cannot be pushed away in every direction because gravity only attracts.
     
  13. Jul 16, 2005 #12
    I got that, I was not thinking about gravity repeling. I was thinking about gravity attracting from allover around you, instead of the familiar attraction just from one direction.
    At the center, gravity certainly attracts you "outwards", each lump of the earth's matter is exerting gravity pulling you away from the center.
    What I missed to realise is that all this attraction anyway cancels eachother out so the net effect you feel is zero.
     
    Last edited by a moderator: Jul 16, 2005
  14. Jul 16, 2005 #13
    In any case, if our own weight reduces to zero as we move towards the center, that should also apply to all the other matter forming the earth.

    The "weight of the earth pressing down on you" will then actually be much less than what common sense suggests when we think about all that mass in terms of the weight it would have in our familiar environment at the surface, right?

    Just by the way, applied to black holes this reasoning must not work because all their matter is concentrated at the very center, as you approach the center you are never "in between" part of the matter and the center. We can not say if the very center is zero gravity or infinite gravity, or whathever else ....
     
    Last edited by a moderator: Jul 16, 2005
  15. Jul 16, 2005 #14

    ZapperZ

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    Yes, but there's still the weight closer to the surface that's still pressing down on the mass below it. So even if the weight of the earth that's closer to the center is getting smaller, it is still being pushed inwards by the mass on top of it.

    This means that if you only consider gravitational attraction as the source of your force, then we can say, via the Gauss's Law equivalent, that gravitational force acting on you at the center of the earth is zero. However, if you want to include the pressure of the earth surrounding you due to its weight, then this part is no longer zero due to all the weight of the earth from the surface down.

    Zz.
     
  16. Jul 16, 2005 #15
    Doesn’t this mean using General Relativity that time would be running more in sync with deep space at the center. Since the effect of GR and gravity slowing time down as you approach the earth down to the surface level, would reverse as you go below the surface, deeper into the earth until the direct force of gravity is cancelled out completely for space at the center.
    Randall B
     
  17. Jul 16, 2005 #16

    Doc Al

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    Why would gravitational time dilation reverse as you go below the surface? As you go beneath the surface, gravitational potential continues to decrease. Therefore I would expect a clock beneath the surface to run slowly as measured by a clock on the surface.
     
  18. Jul 16, 2005 #17
    I don’t understand your logic, As compared to a surface clock, clocks at higher altitudes further away from the earth run faster than the surface clock due to the gravitational potential decrease. So how do you reason that when going below the surface also results in a gravitational potential decrease, but results in time running more slowly there???

    It’s the surface clock that is experiencing the maximum gravitational potential thus it should have the Max time dilation.
    RB
     
  19. Jul 16, 2005 #18

    Janus

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    No. Gravitational time dilation is related to difference in Gravtational potential not local Gravitational force. Sitting at the center of the Earth you are deeper in Earth gravity well than you are at the surface (IOW, it takes work to lift you from the center to surface), thus time runs slower at the center than at the surface.
     
  20. Jul 16, 2005 #19

    Janus

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    I think you are having a problem with what "Gravitational Potential" means.

    Quite simply, a difference in gravitational potential is proportional to how much engery it take to move from one point to another.

    Example: you have a uniform gravity field of one g. (one that does not decrease in strength with height. You have two clocks of equal mass sitting at different heights in that field. The two clocks will have different gravitational potentials even though they both experience exactly 1g, and according to GR, the one that is above the other will run faster.

    Thus a clock sitting at the center of the Earth is not at the same potential as one in space, even though they experience the same gravitational force locally.
     
    Last edited: Jul 16, 2005
  21. Jul 16, 2005 #20
    Thanks Janus,
    I think I see the point; it’s the total energy required to move back out to deep space that is always increasing as you move towards the center the per unit increase may get smaller below the surface as compared to the rate above the surface but still an increase. I’ll ponder on it a bit but I think I see the point.

    Still be nice if someone has documented experiments done at deep water depths demonstrating time dilation running slower at depth vs. surface.
    Do you know if anyone has tried?

    Plenty have been done confirming faster time at higher altitudes.
    RB
     
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