Answer to Question #185255 in Astronomy | Astrophysics for Abdussomod

Question #185255

A star has twice the diameter and twice the surface temperature of our sun.how will it's luminosity compare with that of our sun


1
Expert's answer
2021-04-26T17:12:07-0400

The luminosity of the star is

"L = 4\\pi R^2 \\cdot \\sigma T^4"

"D=2D_{Sun} \\Rightarrow R=2R_{Sun}" , "T=2T_{Sun}"

Then "L = 4\\pi (2R_{Sun})^2 \\cdot \\sigma (2T_{Sun})^4 = 4\\cdot 4\\pi R^2_{Sun} \\cdot \\sigma \\cdot 16 T_{Sun}^4 = 4 \\cdot 16 \\cdot( 4\\pi R^2_{Sun} \\cdot \\sigma \\cdot T_{Sun}^4) = 64 L_{Sun}"


Answer: The luminosity will be 64 times higher.


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