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Homework Help: Integrating dP/dr over the Sun

  1. Jan 29, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider the Sun to be a sphere of hydrogen gas of uniform density equal to its
    average density (1440 kg/m3).
    a) Integrate the equation of hydrostatic equilibrium for dP/dr from the Sun’s radius to the
    core to estimate the central pressure in Pa and in atmospheres. Assume the pressure at the
    surface is zero. [Note: your estimate will fall far short of the true value that can be
    derived using a more realistic density profile, about 250 billion atmospheres, but that’s ok
    for our purposes]

    2. Relevant equations

    dP/dr = -Gmp/r^2 (p = density)

    3. The attempt at a solution

    I replaced m with 4/3pir^3p which yields
    dP/dr = -4piGrp^2/3
    and integrated from R to 0 yielding 2piGp^2R^2/3
    and filling in the values and Radius of the sun, I get 1.4e6 atm of pressure.
    Does this make sense? (Is it consistent with what the question is asking)
  2. jcsd
  3. Jan 29, 2009 #2
    bump - need help please
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