[0] Introduction: What do we see out there? What we know, what we think and what we are clueless about.
[1] First solved problem: Gravitational few body dynamics and the motion of the planets and the moon. In particular, deriving the 1/r^2 law from observations and resolving the challenges posed by the large precession of the moon (surprisingly large 3-body effect) and mercury (general relativity).
[2] Second solved problem: Structure of Stars and White Dwarfs: How do they work? How do we know? Calculating the main properties roughly (analytically) and accurately (numerically) and comparing to observations.
[3] A little about stellar evolution.
[4] Some things we know about stellar explosions (supernovae). In particular, demonstrating that supernovae contribute significantly to the abundances of elements heavier than helium and therefore are important for our existence.
[5] Some things we know about extremely compact objects- neutron stars and black holes.
[6] The distance ladder and a little about galaxies.