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

`R = 2.1R_(\bigodot)`

Explanation:

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

`L = T^(4) * R^(2)`

By solving the above equation for R we have:

`R = (√(L))/(T^(2))`

With
`L = 70L_(\bigodot)` and
`T = 2T_(\bigodot)` we have:

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

`R = (√(70))/((2)^(2))`

`R = 2.1R_(\bigodot)`

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

I hope it helps you!