aljalloh94
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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
​

Respuesta :

skyluke89

Answer:

[tex]L_A = 9 L_B[/tex]

Explanation:

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

[tex]L=\frac{R^2}{T^4}[/tex]

For star B, we can write:

[tex]L_B=\frac{R_B^2}{T_B^4}[/tex]

For star A, we have

[tex]T_A = 2 T_B\\R_A = 12 R_B[/tex]

So the luminosity of star A is

[tex]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[/tex]

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