the red supergiant Betelgeuse

2. Giants and Supergiants (10 pts.) a) Near the end of the Sun’s life, the Sun’s radius will extend nearly to Earth’s orbit. Estimate the volume of the Sun at that time assuming the Sun is a sphere. Using that result, estimate the average density of the giant Sun. How does that density compare with the density of the Sun today and to the density of Earth’s atmosphere at sea level (about 10−3 g / cm3)?

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 1010LSun?

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?