Answer to Question #90270 in Astronomy | Astrophysics for Shivam Nishad

Question

In the H-R diagram, three stars are found to be having luminosities L1, L2 and L3 such that
L1 > L2 > L3. Determine the ordering relation of their radii if the effective temperatures of these stars are the same.

Answer 1

As the temperatures of the stars are equal, according to Stefan-Bolzman law, their the energy radiated per unit area are equal for all three stars.

$$j_1=j_2=j_3$$

As luminosity is :

$$L=jS=4\pi r^2 j$$

And as:

$$L_1>L_2>L_3$$

These all fact implies that

$$r_1>r_2>r_3$$