Chapter 15

15.1  Why do most nearby stars turn out to be low-mass, low-luminosity stars?

Because most stars are low-mass, low-luminosity stars!

15.4  Consider a hypothetical star similar to our Sun being one of the fist stars that formed when the Universe was still very young.  Would you expect it to be surrounded by planets?  Explain.

No.  The raw material to make planets didn't exist until the first generation of massive stars had exploded as supernovae, spreading the heavier elements they made around the universe.

15.10  T Corona Borealis is a well-known recurrent nova.
             a.  Is it a single star or a binary system?  Explain.
             b.  What mechanism causes a nova to flare up?
             c.  How can a nova flare-up happen more than once?

a.  Only binaries can be novae, so it's a binary system.
b.  Hydrogen from its partner is deposited on the surface of the white dwarf.  When the hydrogen layer reaches 10 million K, fusion starts with a bang!
c.  As long as the hydrogen being deposited doesn't push the white dwarf over the Chandrasekhar limit (causing a Type I supernova) and as long as hydrogen keeps being deposited, novas can happen over and over again.

15.13  A white dwarf has a density of approximately 109 kg/m3.  Earth has an average density of 5500 kg/m3 and a diameter of 12,700 km.  If Earth were compressed to the same density as a white dwarf, how large would it be?

The white dwarf is 109/5500 = 1.82 x 105 times denser than Earth.

The density of a sphere increases as its volume and radius decrease and the volume is related to the cube of the radius.  So the radius would have to be decreased by the cube root of 1.82 x 105 which is 56.67.  

So Earth's diameter would have to be 12,7000 km / 56.67 = 224 km.