B) the distance of the red supergiant betelgeuse is approximately 427 light years. if it were to explode as a supernova, it would be one of the brightest stars in the sky. right now, the brightest star in the sky other than the sun is sirius (which has a luminosity of 26lsun and is 26 light years away). how much brighter than sirius would the betelgeuse supernova be (from our point of view) if it reached a maximum luminosity of 10^10lsun? c) there have been some claims that when betelgeuse explodes it will be like having a second sun in the sky. compare betelgeuse’s brightness to the sun’s brightness at earth. is this likely to be correct?

b) Betelgeuse would be times brighter than Sirius

c) Since Betelgeuse brightness from Earth compared to the Sun is the statement saying that it would be like a second Sun is incorrect

Explanation:

The start brightness is related to it luminosity thought the following equation:

(1)

where is the brightness, is the star luminosity and , the distance from the star to the point where the brightness is calculated (measured). Thus:

b) and where is the Sun luminosity () but we don't need to know this value for solving the problem. is light years.

Finding the ratio between the two brightness we get:

c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is . Then

Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.