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Homework Help: Hertzsprung-Russell Diagram question

  1. Dec 7, 2016 #1
    1. The problem statement, all variables and given/known data
    From first principles show that the relationship between the luminosity, size
    and surface temperature of a star can be expressed as:

    $$ \frac{l}{l_0}=(\frac{R}{R_0})^2(\frac{T}{T_0})^4 $$

    2. Relevant equations
    $$L_0$$= Luminosity of sun
    $$R_0$$=radius of sun
    $$T_0$$=surface temp of sun

    $$F=\frac{L}{4 \pi R^2}$$
    $$F=\sigma T^4$$

    3. The attempt at a solution
    $$F=\frac{L}{4 \pi R^2}$$

    $$L=4\pi R^2F =4\pi R^2\sigma T^4$$

    So this is as far as I get. Is it just a matter of doing a luminosity for the sun and then just putting $$L/L_0 $$ or is there more to it. Have I got the wrong end of the stick. Any help would be very much appreciated. Thank in advance
  2. jcsd
  3. Dec 7, 2016 #2


    User Avatar
    Science Advisor

    Yes. That's really all there is to it.
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