Can anyone help me understand how to find the radius of a star using luminosity and temperature ratios?

The bright star Rigel in the constellation of Orion has a temperature about 3 times that of the Sun, and a luminosity 64,000 times that of the Sun. What then is Rigel's radius compared to the radius of the Sun?Can anyone help me understand how to find the radius of a star using luminosity and temperature ratios?http://ceres.hsc.edu/homepages/classes/a鈥?/a>

Lr/Ls = (Rr/Rs)^2 (Tr/Ts)^4 where r is Rigel, s is Sun.

64000 = (Rr/Rs)(Rr/Rs)(3)^4

sqrt(64000/81)=(Rr/Rs)

sqrt(1000)(8/9)=(Rr/Rs)

28.11 = (Rr/Rs)Can anyone help me understand how to find the radius of a star using luminosity and temperature ratios?starryskin's answer is spot on with the formula!



However, Rigel's temperature is only 11,000K which is more appropriate of a B8Ia star while the bolometric luminosity climbs to 66,000 solar. So the correct radius should be around 70 solar radii (70.93 here). 3x that of the sun would be like a B3 star.



http://en.wikipedia.org/wiki/Rigel

http://www.astro.illinois.edu/~jkaler/so鈥?/a>



Clear skies!