The conic-family generator
Circle, ellipse, parabola and hyperbola, all sharing a focus and a closest approach. The eccentricity alone decides which one a body is on, and whether it returns.
3 essays call
conic-family. The drawing above is what it returns with no arguments at all; every
call below passes it something, because a placement that passes nothing draws whichever member
of the family the generator happens to default to rather than the one its essay argues about.
Where it is called
Every figure listed here is the same construction drawn at different numbers, so a correction to one is a correction to all of them.
Orbits
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.
Orbits
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.
Spaceflight
Stealing speed from a planet, which does not notice
A flyby cannot change a spacecraft's speed relative to the planet. It changes its direction — and adding the planet's own motion back turns that into free velocity.