Answer to Question #89386 in Astronomy | Astrophysics for Peace Adejumobi

Question

You have discovered a new star in the Milky Way: Your new star is red and has 3/5 the temperature of our Sun. The new star emits a total power that is 100,000 times greater than the power
emitted by our Sun.
(a) Determine the spectral type (i.e. spectral classification) of the new star.
(b) How many times bigger is the radius of the new star compared to the radius of our Sun?

Answer 1

The effective temperature of our Sun is around 5780 K.

The temperature of the new star is 3470K - it is M spectral class

As its luminosity $10^5$ times greater than luminosity of Sun, looking at Hertzsprung–Russell diagram, we deduce this is red supergiant.

They are typically several hundred to over a thousand times the radius of the Sun.