A star with the same color as the Sun is found to produces a luminosity 81 times larger. What is its radius compared to the Sun?

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Answer 1 · 2018-05-27T22:10:30

The star's radius is 9 times our Sun's radius

Luminosity, measured in energy delivered per unit time, is according to the Stefan–Boltzmann equation:

That black body colour is related directly to average temperature is summarised in Wien's Law:

So $T$ is a constant in this calculation, both black bodies have the same temperature.

Which means:

$L_1/L_2= ( A_1 )/( A_2 ) = 81$

For spherical bodies:

$(4 pi r_1^2)/(4 pi r_2^2)= 81 implies r_1/r_2 = 9$

The star's radius is 9 times our Sun's