Gravity & Orbits: Falling Forever
The apple and the Moon obey one law. An orbit is not an escape from gravity — it is falling, aimed well enough to keep missing.
Builds on: 1.1 Newton's Three Laws: The Operating System0.3 Projectiles: Two Motions That Ignore Each Other
One law, every mass
Newton’s deepest claim wasn’t F = ma — it was that the force pulling the apple down and the force holding the Moon in orbit are the same force, with one universal rule:
Two features carry everything. It is universal — you attract your coffee cup (feebly; G is tiny, and it takes a planet’s worth of mass to make gravity obvious). And it follows an inverse square: triple the distance, one-ninth the force. Distance is measured from the centre, which is why climbing a mountain barely changes your weight — you were already 6,371 km from Earth’s centre.
Small g from Unit 0 is just this law evaluated at Earth’s surface. Big G is the universe’s setting; little g = 9.81 m/s² is Earth’s local consequence. On the Moon the same G delivers g ≈ 1.6.
Newton’s cannonball
Newton’s own thought experiment turns projectiles into orbits. Fire a cannonball horizontally from a high mountain: it falls and lands. Fire faster: it lands farther, because the Earth’s surface curves away beneath it. Fire fast enough — about 7.9 km/s — and the ground curves away exactly as fast as the ball falls toward it. It falls forever and never lands. That is an orbit.
So the ISS astronauts are not “beyond gravity” — at 400 km up, gravity is still 89% of surface strength. They float because station and crew are falling together, endlessly, around the planet. Weightlessness is free fall with good aim.
Faster, slower, gone
- Too slow — the fall wins; the path bends into the ground.
- Circular speed — fall and curve match: a circle.
- Faster — the orbit stretches into an ellipse, swinging far and returning.
- 11.2 km/s — escape velocity: gravity slows you forever but never to zero. Goodbye.
Henry Cavendish measured G in 1798 with lead balls on a delicately twisting rod — detecting the gravity of furniture-sized masses. With G known, g = GM/r² could be solved for M: his tabletop experiment weighed the planet (6 × 10²⁴ kg) — and he titled the paper accordingly.
⚗️ Lab — Newton's Cannonball
A mountain, a cannon, a planet that curves away. Find every fate.
- Increase launch speed step by step: longer arcs, then the magic speed where the ball misses the ground forever.
- Push past circular speed and watch the circle stretch into an ellipse.
- Find escape velocity — the speed where the ball leaves and never comes back.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.