# Flux that reaches a certain radius in a star

1. Nov 23, 2013

### ppy

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. Nov 23, 2013

### rwooduk

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!