Scales that defeat intuition
Every orbit one force allows, and the number that picks between them
Circle, ellipse, parabola, hyperbola. A single inverse-square force permits exactly these four, and one number decides which — including whether the body ever comes back.
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.
StarlightThe triangle that reaches the stars, and stops
Parallax is the only distance measurement in astronomy that assumes nothing. It is also the only one with a hard ceiling, and everything beyond that ceiling rests on it.
StarsThe diagram that sorted the stars, by plotting two things against each other
Plot brightness against colour for a few thousand stars and they do not scatter. They fall on a narrow band with two islands off it, and explaining that structure is most of stellar astronomy.
StarsMass decides everything, by a power of three and a half
Two stars of the same mass are almost the same star. Double the mass and the output multiplies by eleven — which is why a modest range of masses produces a colossal range of stars.
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 speed that does not come back, and the √2 that separates it
Escape speed is exactly the square root of two times circular speed, at every distance from every body. Being in orbit is already 71% of the way to leaving.