Question

20. Consider two Stars A and B with temperatures Ta and TB and radii Ra and RB respectively. If TA

Answer 1

Answer:

$L_A = 9 L_B$

Explanation:

The formula that relates the luminosity of a star (L) to its radius (R) and the temperature (T) is

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

For star B, we can write:

$L_B=\frac{R_B^2}{T_B^4}$

For star A, we have

$T_A = 2 T_B\\R_A = 12 R_B$

So the luminosity of star A is

$L_A=\frac{R_A^2}{T_A^4}=\frac{(12 R_B)^2}{(2 T_B)^4}=\frac{144 R_B^2}{16 T_B^4}=9\frac{R_B^2}{T_B^4}=9 L_B$