Hertzsprung-Russell Diagram question

[Taylor_1989]

Homework Statement

From first principles show that the relationship between the luminosity, size
and surface temperature of a star can be expressed as:

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

Homework Equations

$$L_0$$= Luminosity of sun
$$R_0$$=radius of sun
$$T_0$$=surface temp of sun

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

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

 

[phyzguy]

Is it just a matter of doing a luminosity for the sun and then just putting \rm L/L0 ?

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