The sky as a clock
Equal areas in equal times, which is angular momentum in disguise
Kepler's second law is a statement about the area a radius line sweeps. It looks like an odd thing to have noticed, and it turns out to be a conservation law arriving eighty years early.
OrbitsThe law that links period to size, and weighs everything
Kepler found that the square of the period goes as the cube of the orbit. Newton found the constant of proportionality, and that constant is a mass — which is how every mass in astronomy has been obtained since.
The observed skyThe sphere that is not there, and why it is still the right model
The stars are at wildly different distances and the celestial sphere is a fiction. It is also the most useful fiction in observational astronomy, because for pointing at things, distance is exactly the information to throw away.
The observed skyThe Sun's path, and the tilt that makes the seasons
Summer is not when the Earth is closest to the Sun — that happens in January. It is when the Sun climbs higher and stays up longer, and both come from a 23.4° tilt.
The observed skyPhases are not shadows, and eclipses are
Half the Moon is lit at every instant of every month. The phase is which part of the lit half faces the Earth — and confusing that with a shadow is the commonest error in astronomy.
StarsWhy the biggest stars die first, and take the galaxy with them
A star thirty times the Sun's mass has thirty times the fuel and burns it forty thousand times faster. It lasts a few million years, and everything heavier than iron exists because of it.
SpaceflightThe cheapest way between two orbits, and why it is so slow
Two burns and a long coast is the least fuel that will move a spacecraft between two circular orbits. It is also, for anything beyond the Moon, an unreasonably long wait.