# 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?

May 27, 2018

#### 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:

• ${\lambda}_{\text{max}} = \frac{b}{T}$ where $b$ is another constant

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

Which means:

${L}_{1} / {L}_{2} = \frac{{A}_{1}}{{A}_{2}} = 81$

For spherical bodies:

$\frac{4 \pi {r}_{1}^{2}}{4 \pi {r}_{2}^{2}} = 81 \implies {r}_{1} / {r}_{2} = 9$

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