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?

1 Answer
May 27, 2018

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:

  • #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