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Acceleration of Gravity inside a planet

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the acceleration of gravity within the mantle (at some radius R) of a planet that has a core and a mantle, each with different constant density.

    Rp= radius of planet
    Rc= radius of core
    Pm= density of the mantle
    Pc= density of the core
    P= density

    I know what the answer is but I cannot get there!
    ANSWER=
    a= (-4/3)G(Pi)[((Pc-Pm)*Rc^3/R^2) + Pm*R]


    2. Relevant equations.
    Gravitational Potential Equations



    3. The attempt at a solution

    I have made 3 potential equations:

    (R>Rc):
    V= (-4(pi)GP/3R)*(R^3-Rc^3)

    (Rp>R>Rc):
    V= [(-4(Pi)GP/3R)*(R^3-Rc^3) + (-2(Pi)GP)*(Rp^3-R^3)]

    (Rp>R):
    V= -2(Pi)GP*(Rp^3-R^3)

    I cannot get to the correct answer any help would be great!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 13, 2008 #2
    You should use Gauss' law. Perhaps you know that law from electrostatics, where the law refers to electric fields and the total charge inside a volume. The gravitational equivalent refers to g and the total mass inside a volume.
     
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