Field
Orbits
Kepler's three laws, and the family of curves a single force allows.
The orbit is an ellipse, and the Sun is not in the middle of it
Kepler's first law is usually drawn wrong. The interesting content is not the ellipse — it is the focus, and the fact that one of the two is empty.
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.
The 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.
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.