Answer to Question #310380 in Astronomy | Astrophysics for K12

Question

Question:- Like everything in Minecraft game, an Astronomer started thinking what will happen if our Sun would have been a square of similar luminosity.

a. If the Sun was a cube, what would be its surface temperature?

b. In what interval, does its magnitude lie as seen from the Earth?

Hint: The volume for Cube Sun remains the same as usual.

Answer 1

The current temperature of the Sun surface is $T_1=5772\:\rm K$. The temperature is related with luminosity by an equation

$$L=\sigma T^4A$$

Hence

$$T\sim\sqrt[4]{L}$$

(a) When the luminosity of Sun would have been a squared, then

$$T_2=T_1\sqrt[4]{2}=5772\:\rm K*\sqrt[4]{2}=6864\:\rm K$$

(b) The current visual brightness of the Sun $m_1=-26.74^m$. When the luminosity of Sun would have been a squared, then

$$m_2=m_1-2.512\lg 2\\ =-26.74^m-0.756^m =-27.50^m$$