Question

A certain star has a temperature twice that of the Sun and a luminosity 61 times greater than the solar value. What is its radius, in solar units?

Answer 1

We can use the Stephan-Boltzmann Law to relate the temperature (T), size (R), and luminosity (L) of a star to each other. The radius of the star (R) is related to luminosity (L) and temperature (T) through the relation

$R = \frac{\sqrt{L}}{T^2}$

If the temperature of the star is twice times the sun and 64 times the luminosity of our sun we have that

$T= 2T_{sun} \rightarow 2units$

$L = 61L_{sun} \rightarrow 61units$

Replacing we have

$R = \frac{\sqrt{61}}{2^2}$

$R = 1.95$ solar units

Therefore the radius is 1.95 solar units.