12.4  Although we tend to think of our Sun as an "average" main sequence star, it is actually hotter and more luminous than average.  Explain.

Most stars are smaller and therefore cooler and less luminous than the Sun is.  So the "average" star is cooler and less luminous than the Sun.

12.5  Albiero, a star in the constellation of Cygnus, is a binary system whose components are easily separated in a small telescope.  Viewers describe the brighter star as "golden" and the fainter one as "sapphire blue."
a.  What does this tell you about the relative temperature of the two stars?
b.  What does it tell you about their respective sizes?

a.  The brighter, golden star is cooler than the fainter, blue star (blue stars are hotter than yellow stars).
b.  The golden star is larger than the blue star.  Since it's cooler, it has to be much larger to be brigher.

12.9  Star masses range from 0.08 M_Sun to about 100 M_Sun.
a.  Why are there no stars with masses less than 0.08 M_Sun?
b.  Can you guess why there are no stars with masses much greater than 100 M_Sun?

a.  Smaller objects cannot get hot enough to burn hydrogen in their cores.
b.  Very large stars are thought not to form because of the stellar wind which starts after fusion begins.  Also, such a huge star may well blow itself up!

12.13 Sirius, the brightest star in the sky, has a parallax of 0.379 arcseconds.  What is its distance in parsecs?  In lightyears?
(I added problem 13)

1/p = d, where p is the parallax in arcseconds and d is the distance in parsecs,

d = 1/0.379 = 2.64 parsecs.

1 parsec = 3.264 lightyears, 2.64 parsecs is 8.61 lightyears.