The Moon is falling. It has been falling for four billion years and has never once hit the ground — because it keeps missing.
The weakest force in the universe built every star, planet and galaxy. Let's chase it through history — and fly the orbits yourself.
Gravity is pitifully feeble — a fridge magnet beats the entire Earth in a tug of war over a paperclip. But it has two advantages nothing else has: it is always attractive, never cancelling out, and it reaches across infinite distance. Given enough mass and enough time, it wins everywhere.
Newton's insight was that the force pulling an apple down is the same force holding the Moon in the sky, and it obeys one line: F = G M m / r² — every mass pulling every other mass, everywhere, forever.
A satellite isn't beyond gravity — it's in freefall. It simply moves sideways so fast that the ground curves away beneath it as it drops.
Go fast enough and gravity can never reel you back in. That threshold — escape velocity — is why rockets are enormous and why black holes are black.
Everything below is hands-on. No sliders for the physics — you fire Newton's cannon, sling a planet into an ellipse, chase escape velocity on three worlds, and fly real satellite missions.
Plague had closed Cambridge, and Isaac Newton, twenty-three, was thinking in his mother's orchard. The famous apple didn't hit his head — but watching one fall, he asked a question nobody had thought to ask: how far up does this pull reach? To the treetop, certainly. To the clouds. Why not… all the way to the Moon?
If so, the Moon is falling too — constantly, forever — and only misses the Earth because it also races sideways. To explain it, Newton drew a cannon on an impossibly tall mountain. Fire slowly and the ball lands nearby. Fire faster and it lands further. Fire fast enough and the Earth's surface curves away exactly as fast as the ball drops. It falls forever, and never lands. That is an orbit.
Pull the slingshot — set both speed and aim — then release. Find the vector where falling becomes flying.
The Space Station orbits at about 7.8 km/s — roughly 28,000 km/h — circling the Earth every 90 minutes. Astronauts float not because gravity is absent up there (it's about 90% as strong) but because they and the station are falling together, endlessly missing the planet.
For two thousand years everyone knew the planets moved in perfect circles — the heavens were divine, and circles were perfect. Johannes Kepler inherited the superbly precise observations of Tycho Brahe and spent eight brutal years trying to fit Mars to a circle. He got agonisingly close: his best circle was wrong by just eight minutes of arc, about a quarter the width of the Moon.
A lesser man would have blamed the data. Kepler trusted Tycho's instruments more than Plato's philosophy, threw out the circle, and found the ellipse. Three laws followed: orbits are ellipses with the Sun at one focus; a planet sweeps equal areas in equal times, so it races at perihelion and dawdles at aphelion; and T² ∝ a³ ties every orbit in the solar system together.
Sling the planet with your own hand and watch it carve an ellipse — sweeping equal areas as it goes.
Kepler wrote that those eight minutes of arc "pointed the way to a complete reformation of astronomy." Refusing to explain away an inconvenient measurement is arguably the moment science grew up — and it handed Newton the data he needed to deduce the inverse-square law.
Throw a ball up and it returns. Throw it harder and it goes higher. Is there a speed beyond which it simply never comes back? Yes — and it depends only on the world you're standing on: v_esc = √(2GM/R). On Earth, 11.2 km/s. On the Moon, a modest 2.4. On Jupiter, a brutal 59.5.
In 1783 an English country rector named John Michell followed the logic to its end. If a star were massive and compact enough, its escape velocity would exceed the speed of light — and the star would be invisible, since no light could ever leave it. He called them "dark stars." He had described a black hole, 130 years before Einstein, using nothing but Newton.
Tune the launch speed on three worlds and find the exact threshold where gravity loses its grip forever.
Squeeze the Earth to the size of a marble and its escape velocity would exceed 300,000 km/s — nothing, not even light, could leave. That radius is the Schwarzschild radius, and Michell's 18th-century "dark star" turned out to be a real object at the centre of nearly every galaxy.
In 1945, long before any rocket reached orbit, the writer Arthur C. Clarke published a short paper pointing out that a satellite at exactly 35,786 km would circle the Earth once every 24 hours — perfectly matching the planet's spin, and so appearing to hang motionless in the sky. Three such satellites, he noted, could relay signals to the whole world. Every television dish on Earth now points at that ring, which is officially called the Clarke Orbit.
You have Mission Control. Three flights are on the board: a stable low orbit, Clarke's geostationary ring, and a one-way trip out of Earth's grip altogether. Everything depends on the single vector you draw at launch.
Three missions. Draw the burn, read the telemetry, and fly them clean.
On 4 October 1957 a polished metal sphere the size of a beach ball became the first object humans placed in orbit, transmitting a simple beep that amateur radio operators worldwide could hear. Within twelve years the same equations put people on the Moon.
Everything you just flew by hand — the cannonball that finally missed the ground, the planet that raced at perihelion, the throttle that crossed the point of no return, the ring where satellites hang still — comes from a single inverse-square line written in a plague year.
Every mass pulls every other, weakening as the square of distance.
Ellipses with equal areas swept in equal times; period tied to size.
Cross this speed and gravity can never reel you back.
The same equation that drops an apple keeps the ISS aloft, times your GPS, steers Voyager out of the solar system, spins the galaxies, and once — long ago, in the dark — pulled scattered hydrogen together tightly enough to ignite the very first star.
The weakest force in nature, given enough time, builds everything. That's the whole chapter.