Newton publishes the Principia

The story

A question about orbits

In January 1684 in London three members of the Royal Society, Edmond Halley, Christopher Wren and Robert Hooke, were discussing a question that fascinated them: what force keeps the planets in their orbits? Kepler had discovered that the planets move in ellipses, but nobody could explain why. Halley suspected that the force depended on the inverse of the square of the distance from the Sun, that is, that it became four times smaller if the distance doubled, but he could not prove it. Wren, according to tradition, offered a prize to anyone who could, and nobody won it.

In August 1684 Halley made a journey to Cambridge to ask for help from a professor of mathematics who lived a secluded life and published almost nothing: Isaac Newton. He asked him what curve a planet would follow if it were attracted by a force of this kind. According to the story handed down, Newton answered at once: an ellipse. He had already done the calculations, years earlier, but could no longer find the papers. He promised to do them again.

Eighteen months of work

Newton was born in 1642 at Woolsthorpe, in England, into a farming family. He was a solitary boy, fond of mechanics and of building things. At the University of Cambridge he devoted himself to mathematics and physics, and in the years 1665–1666, when the university closed because of the plague, he worked at home and made important discoveries: calculus (a new kind of mathematics for studying things that change), the nature of white light, gravitation. The story of the falling apple is linked to that period: Newton himself told it when he was old, but the apple hitting him on the head is a legend.

After Halley's visit, Newton shut himself in his study and for about eighteen months worked almost without a break, forgetting his meals, according to one of his assistants. The result was a work in three books, in Latin, full of geometrical proofs: the “Philosophiae Naturalis Principia Mathematica”, that is, “Mathematical Principles of Natural Philosophy”. Halley oversaw the printing and paid for it out of his own pocket, because the Royal Society had no funds. The book came out in July 1687.

Three laws and one force

In the Principia Newton set out three laws of motion. The first says that a body at rest stays at rest, and one in motion keeps moving in a straight line at the same speed, unless a force makes it change. The second says that the force acting on a body is equal to its mass multiplied by its acceleration. The third says that to every action there is an equal and opposite reaction: if you push a wall, the wall pushes you.

Then he set out the law of universal gravitation: every body attracts every other body with a force that is greater the greater their masses are and smaller the greater the square of the distance is. The same force that makes an apple fall makes the Moon go around the Earth and the planets around the Sun. From these laws Newton derived Kepler's three laws, explained the tides as an effect of the attraction of the Moon and the Sun, predicted the slightly flattened shape of the Earth and studied the motion of comets.

A difficult book

The Principia were extremely hard to read, even for experts: few people in Europe understood them at once. Newton had written them in a deliberately complicated way, by his own account, to avoid arguments with people who did not understand. But the predictions were so exact that the book soon won everyone over. In 1705 Halley, using Newton's laws, predicted the return of a comet in 1758: it really did come back, though he was already dead, and today it bears his name.

Newton was also involved in quarrels: with Hooke, who claimed that he had had the idea of the inverse-square force, and with the German philosopher Leibniz, who had developed calculus independently. In 1699 he became Master of the Mint, in London, and in 1705 Queen Anne knighted him. He died in 1727 and had a solemn funeral in Westminster Abbey.