Newton's Cannon: the Thought Experiment That Did 270 Years of Field Work
1687 (tested 1957)
Prediction
This one is a thought experiment and says so: in the Principia (1687) Newton asks us to fire a cannon from an impossibly tall mountain, horizontally, faster and faster. Faster means it lands farther away - until one speed where the Earth's surface curves away beneath the falling ball exactly as fast as the ball falls: it falls forever. That speed is recomputable from schoolbook numbers: v = √(g × R) = √(9.81 m/s² × 6,371,000 m) ≈ 7.9 km/s. Newton's own drawing - the cannon on the mountain, paths A to E - is in the book.
The test
270 years of applied patience: on 4 October 1957 Sputnik 1 went to orbit at about 7.8 km/s - the mountain was real, the powder was a rocket, and the ball was a 58 cm polished sphere beeping at 20 MHz. The predicted behaviour was observed: a fall that never arrives.
The result
Every orbit since - ISS, GPS, Starlink, the lunar missions with the Moon standing in for 6,371 km by adding a bigger number first - is Newton's picture with the friction caveat handled by going high enough that 'negligible' becomes true. The arithmetic still works exactly as drawn: stay at 7.9 km/s near the surface and you circle in about 84 minutes; go higher, need less speed, take longer. Low Earth orbit is the cannon's path E.
The reaction
The experiment is a reminder of what a good model owes no one: Newton never had to build it, only to notice that falling and orbiting are the same sentence said at different speeds - the insight the collection's gravity cards keep re-teaching. When the test finally came, it confirmed a prediction made before steel, before the calorie, before the word 'energy'. The beeping heard by radios worldwide was the scholium closing.
Why it matters
Thought experiments are load-bearing: this one designed an industry. It is also the cleanest demo in the collection of the difference between data and understanding - Tycho had better naked-eye data than anyone, Kepler turned it into laws, Newton read those laws as one falling apple shared by the Moon, and only then could anyone aim at orbit. When a card here says 'every number is recomputable', this card is the reason the phrase exists.