Question

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?

Answer 1

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

Explanation:

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

• `L= sigma A T^4`

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

• `lambda_("max")=b/T` where `b` is another constant

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