The Apple and the Moon

An apple falls. The Moon does not fall. Everyone had always treated those as two different kinds of event: earthly motion down here, heavenly motion up there.

A young man sent home from Cambridge by the plague asked whether they are the same event. Whether the Moon is falling too, and only misses the Earth because it is moving sideways fast enough.

Answering that took him twenty years, a new mathematics, and a book another man had to pay to print. It is still the physics we fly spacecraft with.

Galileo had shown how things fall on Earth. Kepler had found three rules the planets obey, by fitting decades of measurements.

But a rule is not a reason. Nothing said why an ellipse, or what was doing the holding. The fashionable answer was Descartes: invisible whirlpools carrying the planets like leaves in a stream.

Others suspected a force falling off with the square of the distance. Hooke, Halley and Wren discussed it in a London coffee house. None could prove what orbit it would produce.

He was born at Woolsthorpe on Christmas Day 1642, so small they did not expect him to live. His father was already dead, and his mother soon left him with his grandmother.

He went up to Trinity College, Cambridge, in 1661 as a sizar — a student who paid his way by serving wealthier ones.

Then the plague closed the university. He went home for two years, alone, and invented the calculus, worked out the composition of light, and began on gravity. He was a professor at twenty-six, and published almost none of it for twenty years.

Everyone knew a prism made colours. The accepted explanation was that glass stains light.

Newton closed the shutters, let one narrow beam in, and put a prism in its path. The patch on the far wall was not a round spot but a long band, always in the same order.

Then he settled it. He let through one colour only, and sent that through a second prism. It came out the same colour.

The glass makes nothing. White light is already a mixture, and the prism only sorts it. Press the buttons and run the three steps.

If a lens bends each colour by a different amount, then every lens telescope must blur its images with coloured fringes. No careful grinding can fix that.

So Newton built a telescope with no lens to focus with. He cast and polished his own metal mirror, barely two inches across, and got a short instrument that worked as well as a much longer one.

The Royal Society saw it in 1671 and elected him. His first paper, on colour, went out the next year — and was attacked by Robert Hooke. Newton withdrew, and refused to publish his optics as a book until Hooke was dead.

The Moon is about sixty Earth radii away. If gravity thins out as the square of the distance, the pull out there should be sixty squared — three thousand six hundred times — weaker.

An apple at the surface accelerates at nine point eight metres per second squared. Divide by three thousand six hundred and you get about two and three quarter thousandths.

Work out what the Moon actually needs to keep curving around us, from its distance and its month-long period, and you get the same number. One force, doing both jobs. Move the test mass and watch the pull change.

Newton put the whole idea into one picture. Stand a cannon on a mountain so high there is no air, and fire it horizontally.

Fire gently and the ball lands nearby. Harder and it lands further. Harder still, and the curve of the ball starts to match the curve of the Earth.

At about seven point nine kilometres a second it never lands at all. It keeps falling, the ground keeps curving away beneath it, and it comes back round and hits you in the back. Past eleven point two it leaves for good. Press a speed and fire.

In January 1684 Hooke, Halley and Wren agreed the force probably falls off as the square of the distance. None could show what orbit that produced. Wren offered a prize; nobody collected it.

That August Halley rode to Cambridge and asked Newton directly. Newton answered at once: an ellipse. He had calculated it. Then he could not find the paper.

In November nine pages arrived in London, titled On the motion of bodies in an orbit. Halley read it and understood that this was not a paper but the beginning of a book. He spent three years getting it out of Newton.

The Principia came out in July 1687. The Royal Society had spent its budget on a book about fish, so Halley paid the printer out of his own pocket.

It opens with three laws of motion, then claims that one force, weakening with the square of distance, holds between every pair of masses in the universe.

From that, Kepler’s rules fall out as consequences. So do the tides and the bulge at the Earth’s equator. The word is universal: the same rule for an apple, the Moon, and a comet nobody has seen yet.

A theory earns its keep by sticking its neck out. Newton’s did it twice, after he was dead.

Halley used the new mathematics on comet records, concluded that three sightings were one object on a long ellipse, and predicted its return for 1758. He died in 1742. On Christmas night 1758 it came back.

Then in 1846 Uranus was drifting off course. Le Verrier assumed Newton was right, calculated where the unseen planet had to be, and posted the position to Berlin. Galle found Neptune within the hour, less than a degree away.

It is tempting to make him the first modern scientist. His own papers do not allow it.

He spent decades on alchemy, with a furnace in his garden at Trinity, and wrote more on biblical prophecy than on physics. When Keynes read those papers in 1936 he said Newton was not the first of the age of reason but the last of the magicians.

He was also a ferocious enemy. He fought Hooke over optics and over credit for gravity, and Leibniz over the calculus, long past Leibniz’s death.

In 1696, at fifty-three, he left Cambridge to run the Royal Mint.

England’s silver coinage was being clipped and forged into worthlessness. Newton ran the recoinage and went after the forgers personally, gathering evidence in taverns and prosecuting cases himself.

He became rich, became President of the Royal Society in 1703, and was knighted in 1705 — the first person knighted for scientific work. He died in London in 1727, aged eighty-four, and was buried in Westminster Abbey, the first scientist given that.

The man who found Neptune also found the crack. Mercury’s ellipse creeps round, and about forty-three arcseconds a century of that creep had no Newtonian cause.

Le Verrier reached for the move that had worked before and proposed another hidden planet. Astronomers looked for fifty years. It was not there.

In 1915 Einstein’s general relativity gave the missing forty-three almost exactly, by treating gravity not as a force but as curvature in space and time. Newton was not wrong so much as approximate.

The question in the orchard was whether the sky and the ground obey the same rules. The answer was yes, and it is the foundation under everything that followed.

Kepler’s laws stopped being brute facts; the tides and the shape of the Earth came from one equation. And it is still the working tool — flight plans to Mars and the orbit of every satellite over your head use Newton’s mechanics.

He wrote to Hooke, in the middle of their quarrel, that if he had seen further it was by standing on the shoulders of giants. In context the line is barbed — and true.

The chapter stills here are AI-generated; the portrait, the printed pages, Newton’s own diagram and the spacecraft photographs are real. Sources below.