Question

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

= 2 TB and Ra= 12 RB, which statement about the stars' luminosities, LA and LB, is true?
using this formula: L=(R^2)(T^4)
a) La =LB
b) La = 2 LB
La=4 LB
d) La = 12 LB
e) La = 14 LB
​

Answer 1

`L_A = 9 L_B`

Step-by-step explanation:

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

`L=(R^2)/(T^4)`

For star B, we can write:

`L_B=(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=(R_A^2)/(T_A^4)=((12 R_B)^2)/((2 T_B)^4)=(144 R_B^2)/(16 T_B^4)=9(R_B^2)/(T_B^4)=9 L_B`