Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Earth's interior heat vs Gravity

  1. May 29, 2008 #1
    Earth’s interior is much hotter than the surrounding environment (i.e., empty space) so there must be a tendency of the Earth to expand - yet the Earth’s volume remains essential constant. This is so because an equilibrium has been achieved in which the heat-driven expansion is balanced by a gravity-driven contraction. My question: How is this described mathematically? How do we numerically describe the equilibrium between the amount of HEAT inside the Earth and GRAVITY?

    Thanks
     
  2. jcsd
  3. May 30, 2008 #2
    Maybe I should post this question to another thread??? Any suggestions? Maybe Gerneal Relativity? Or one more oriented towards thermodynamics??

    Thanks
     
  4. May 31, 2008 #3
    I’m curious as to the lack of responses to my question. Is this a “stupid question”? Is this simply of no interest to anybody? FWIW I spent this morning plotting (MATLAB) osculating circles per exercises in Faber’s “Differential Geometry and Relativity Theory” and read the same text while relaxing with my Saturday afternoon cigar today. Meaning – I am really looking for assitance.

    Thanks
     
  5. May 31, 2008 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    What makes you think this is so? Asteroids have lost all of their internal heat, and do not have a tendency to expand. Solids are not gases.
     
  6. May 31, 2008 #5

    DaveC426913

    User Avatar
    Gold Member

    Uh, well I guess I can see his point. If the Earth were magically supercooled, it would shrink a certain amount. If it were heated, it would expand. Since it is being heated, it is larger than it would be if at ambient temperature.

    But the OP seems to feel that expansion would be on-going, which is not true. As you point out, a solid is not the same as a gas.

    If you have a simple sphere of steel and you heat it a certain amount, it will expand a certain amount. And then it will stop expanding. Heat it hgiher and it will expand more. And then stop. There is surely a linear relationship between the sphere's temperature and its volume.

    Note that the cessation of the expansion occurs independent of gravity.

    So, to answer the OP's question, the Earth will have a certain expansion due to its temperature, but it is not a continual expansion, just like the steel sphere. And all this happens before factoring gravity in.
     
    Last edited: May 31, 2008
  7. Jun 1, 2008 #6
    Good point - a solid is not a gas. As to the steel sphere analogy, I understand that the sphere will stop expanding whether gravity is not present. However, it seems to me that the resultant volume will be less if gravity (or any other pressure inducing force) is present. I would be surprise to learn that the steel sphere would occupy the exact same volume when placed in the vacuum of outer space (no outside pressure) or placed at the bottom of the ocean (very high outside pressure). I would expect a small volume difference based on where equilibrium is achieved.

    Thanks
     
  8. Jun 1, 2008 #7

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    OK. Now you're getting somewhere. Solids are compressible. The bulk modulus of a solid describes how that solid reacts to pressure. One way to visualize this: Think of the individual atoms or molecules that comprise a solid as being connected via springs. Just as laying down on your bed compresses the springs in your mattress, squeezing a solid makes the atoms/molecules that form the solid squeeze a little closer together. You sink in a little bit when you lie down on your mattress. That sinking stops at the point where the spring compression balances out your weight. The same thing happens when you apply pressure to a solid. The springs in a solid ball of steel are just a whole lot stiffer than the springs in your mattress.

    Another thing happens to rock when it is compressed. Some rocks change chemical composition above some critical temperature/pressure. The rocks we know on the surface simply do not exist deep beneath the Earth's surface.
     
  9. Jun 1, 2008 #8
    "The bulk modulus of a solid describes how that solid reacts to pressure."

    What is the equation governing how the bulk modulus describes how a solid reacts to pressure?

    Thanks
     
  10. Jun 1, 2008 #9

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    RTFI. Documented very well here. I told you the exact phrase to use in the referenced website.
     
  11. Mar 13, 2009 #10
    So a heat source without mass would not create a gravitational field?

    I appologize if this is a stupid question.
     
    Last edited: Mar 13, 2009
  12. Mar 13, 2009 #11

    DaveC426913

    User Avatar
    Gold Member

    Well, I'm not sure how you could have a "source" of heat that has no mass, but I suppose if you could it would simply be a collection of EM waves in the IR band (though that's not technically a "source" of heat). That being the case, there would be heat but no mass, therefore no gravity.

    It is mass that generates gravity. Heat has nothing to do with it.
     
  13. Mar 14, 2009 #12

    Ich

    User Avatar
    Science Advisor

    No, energy greates gravity (ok and pressure and shear stress and momentum...), and heat is a form of gravity. EM waves gravitate.
     
  14. Mar 14, 2009 #13
    Your statements are flawed, as well as absurd.

    "Heat" isn’t a form of "gravity". Regardless of the intensity of the heat energy released, it’s never going to attract an object though, it could potentially incinerate it.

    Additionally, EM waves "radiate", not "gravitate".
     
  15. Mar 14, 2009 #14

    DaveC426913

    User Avatar
    Gold Member

    Yeah, this is all just weird.
     
  16. Mar 16, 2009 #15

    Ich

    User Avatar
    Science Advisor

    Yes, I made an error:
    should read: heat is a form of energy.
    EM waves also carry energy, so both heat and EM waves gravitate.
     
  17. Mar 16, 2009 #16

    DaveC426913

    User Avatar
    Gold Member

    What? What do you mean by "gravitate"?
     
  18. Mar 16, 2009 #17

    Ich

    User Avatar
    Science Advisor

    They attract other objects via gravitation. IOW, they are a source of spacetime curvature.
     
  19. Mar 16, 2009 #18

    DaveC426913

    User Avatar
    Gold Member

    What does this have to do with the original question?
     
  20. Mar 17, 2009 #19

    Ich

    User Avatar
    Science Advisor

    Nothing.
     
  21. Mar 17, 2009 #20

    DaveC426913

    User Avatar
    Gold Member

    Then shutting the thread down would be in everyone's best interests. I think the OP's question has been answered.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Earth's interior heat vs Gravity
  1. Earths gravity (Replies: 20)

  2. Earth's gravity (Replies: 1)

Loading...