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Flux that reaches a certain radius in a star

  1. Nov 23, 2013 #1

    ppy

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    I know the radiative flux travelling through the atmosphere of a star obeys the equation:

    dF/dr=-opacity*F*density

    If we have an isothermal atmosphere the density decreases with radius such that density is proportional to 1/r^2.

    If the flux entering such an atmosphere from the core of the star at radius r0 is F0 show that the flux that reaches radius r is

    F(r)=F0 *e^opacity*(r^-2 -r0^-2) where the opacity is a constant.

    I do not understand i'm guessing I need to integrate the 1st order ODE but how can I do this when flux is on both sides of the equation and where does the exponential come from in the answer?

    Help!!
    Thanks :) Note: for some reason the symbols tab is not working on my laptop
     
  2. jcsd
  3. Nov 23, 2013 #2
    if you divide your first eqn by F and multiply by dr you get 1/F dF = - opacity * density dr

    which gives 1/F dF α -opacity * 1/r^2 dr where α means proportional to, which since opacity is a constant you can write (i think)

    1/F dF = -opacity * 1/r^2 dr

    integral both sides to give ln(F/Fo)=-opacity [1/r0 - 1/r]

    do exp of both sides

    F = F0 exp (opacity (1/r - 1/r0))

    not sure why it gives r^-2 , maybe ive done it wrong, im guessing thats where the exponential comes from anyway!
     
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