Fall, orbit, or escape

Everything in this unit comes down to one launch and three possible fates. From a fixed starting point, speed and launch direction decide which one you get; hold the direction tangential for this comparison:

• Too slow → the ellipse dips into the planet and you crash.
• Just right → a clean, closed orbit.
• Too fast (past escape velocity) → you leave and never return.

The beautiful part: you can feel where the boundaries are by testing. Nudge the speed up until a crash becomes an orbit; keep going until the orbit opens into an escape. You are mapping the same thresholds — the surface-intersection boundary and escape speed; circular speed is a particular orbit inside the bound range — that engineers compute for real missions.