The surface temperature of Arcturus is about half as hot as the Sun’s, but Arcturus is about 100 times more luminous than the Sun. What is its radius, compared to the Sun’s?
1 Answer
Arcturus's radius is 40 times larger than the sun's radius.
Let,
We are given,
Now express luminosity in terms of temperature.
The power radiated per unit surface area of a star is
To get the total power radiated by the star (its luminosity) multiply the power per unit surface area by the surface area of the star
Luminosity of a star
Using this,
where
Rearranging the above equation gives
We are given that
Arcturus's radius is 40 times larger than the sun's radius.