Question

A certain star has a temperature twice that of the Sun and a luminosity 70 times greater than the solar value. What is its radius, in solar units

Answer 1

Answer:

$R = 2.1R_{\bigodot}$

                         

Explanation:                          

The radius (R) is related to temperature (T) and the luminosity (L) as follows:    

$L = T^{4} \times R^{2}$      

By solving the above equation for R we have:

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

With $L = 70L_{\bigodot}$ and $T = 2T_{\bigodot}$ we have:

$R = \frac{\sqrt{70L_{\bigodot}}}{(2T_{\bigodot})^{2}}$

$R = \frac{\sqrt{70}}{(2)^{2}}$

$R = 2.1R_{\bigodot}$

Therefore, the radius is 2.1 times that of the Sun.

I hope it helps you!