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Will a cloud collapse?

  1. Mar 6, 2013 #1
    1. The problem statement, all variables and given/known data
    A cloud consists of 8 solar masses of hydrogen gas (H2). Its temperature is 20 K and its radius is 0.6 light years. Will it collapse?


    2. Relevant equations
    jeans mass


    3. The attempt at a solution[/b
    I've tried to use jeans mass to solve this however I am finding the formula difficult to understand
     
  2. jcsd
  3. Mar 6, 2013 #2

    vela

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    Show your work.
     
  4. Mar 6, 2013 #3
    So far I'm using the formula
    3/2kT <GMm/R
    And (3KT/2Gm) x k >mj

    I'm substituting m=2.167x10^-27
    G=6.67x10^-11
    K=1.38x10^-23
    T=20
    R=0.6

    However I'm not sure what it is exactly that I'm gaining from using these formulae?
    I'm getting that (3kT/2Gm) x R = 1.115011357 x 10^15 ???
    I'm aiming to get an answer of
    Jeans mass = 1.05 x 10^31 kg
    Which is less than 8 solar masses (1.6 x 10 ^31) so it will collapse?
     
  5. Mar 6, 2013 #4

    haruspex

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    I struggled to follow your logic above. Seem to be a few typos:
    (3kT/2Gm) x R = Mj ?
    √((3kT/2Gm) x R) = 1.115011357 x 10^15 ?
    Also, I don't see online a formula with that 3/2 factor. I see one with 15/4pi, another that approximates that to 1. Anyway, using your 3/2 I get that the Jeans length/radius = 0.84, which suggests to me it won't collapse. (I'm a bit confused over whether the Jeans length is a radius or a diameter, but if it's a diameter then the actual radius is much too large to collapse.)
     
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