Isaac Newton: The Laws That Govern the Universe

In the summer of 1665, Cambridge University sent its students home. The Great Plague was killing thousands across England, and there was little point pretending lectures could continue. One of those students — a 22-year-old from Lincolnshire named Isaac Newton, who had shown some mathematical aptitude but nothing extraordinary — returned to his family's farm in Woolsthorpe.

He stayed for 18 months. During that time, he invented calculus, developed the theory of universal gravitation, proved that white light contains all colors, and laid the foundations for classical mechanics. When Cambridge reopened, he returned as a man who had already solved much of physics.

An Unremarkable Beginning

Isaac Newton was born on Christmas Day 1642 — though by the Gregorian calendar, it was January 4, 1643. He was premature, small enough (according to family legend) to fit inside a quart pot. His father had died three months before his birth; his mother remarried when he was three and left him with his grandmother for nearly a decade. This abandonment marked him. Newton was throughout his life solitary, paranoid, and ferociously competitive — traits that may have made him difficult to know but also drove him to prove himself with extraordinary intensity.

He showed early mechanical aptitude — building model windmills, sundials, and water clocks — but was academically undistinguished until his teens. At Trinity College Cambridge, he was officially studying the scholastic philosophy curriculum inherited from Aristotle. Unofficially, he was reading Descartes, Galileo, and the Flemish mathematician Frans van Schooten. He was teaching himself the frontier.

The Plague Years: A Solitary Revolution

When Newton retreated to Woolsthorpe in 1665, he took notebooks. What followed is extraordinary not just for what he discovered but for how he discovered it.

The problem of planetary motion had been bothering natural philosophers since Copernicus. Kepler had shown in the early 1600s that planets move in ellipses around the sun, and had formulated empirical laws describing how they move. But why they moved that way — what force caused it — was unknown. Many guessed it had something to do with the sun's influence decreasing with distance, but nobody had the mathematics to prove it.

Newton's breakthrough required two simultaneous inventions. First, he needed a new kind of mathematics that could handle continuously changing quantities — velocity, acceleration, force varying with position. He invented it: the method of fluxions, which we now call calculus. (Leibniz independently invented calculus in the 1670s, leading to a bitter priority dispute that consumed much of Newton's later life.)

Second, he needed to apply that mathematics to the question of gravity. He made an inspired guess: suppose the force of gravity decreases as the square of the distance from the center of the Earth. This is the inverse-square law. Then he calculated whether that law could simultaneously explain the fall of objects near Earth and the orbit of the Moon.

The apple story — Newton watching an apple fall and being struck by inspiration — is almost certainly embellished (Newton himself told different versions at different times). But the underlying insight is real: Newton was the first to recognize that the Moon is essentially falling toward Earth continuously, and that its orbital motion is the same phenomenon as a thrown stone. Gravity doesn't stop at the atmosphere. It reaches the Moon. It reaches everything.

His calculation in 1665–66 nearly worked. There was a small discrepancy, which Newton set aside. He returned to the problem in 1679 with better data on Earth's radius, recalculated, and found perfect agreement. The Moon's orbital motion was precisely what you'd expect from an inverse-square gravitational force.

The Principia: Writing the Rules of the Universe

By 1684, Newton had shown the inverse-square law, but hadn't published any of it. Astronomer Edmond Halley visited Cambridge to ask a question: if the gravitational force follows an inverse-square law, what shape orbit would a planet follow? Newton immediately said: an ellipse. Halley asked how he knew. Newton said he'd calculated it. Halley pressed him for the calculation. Newton couldn't find his notes. He promised to redo it and send it.

What followed was two years of the most intense writing in scientific history. Newton essentially locked himself in his study and wrote the Philosophiæ Naturalis Principia Mathematica — the Mathematical Principles of Natural Philosophy. It was published in 1687 and contained, among other things:

• Three laws of motion: A body remains at rest or in uniform motion unless acted upon by a force (inertia); force equals mass times acceleration (F = ma); for every action there is an equal and opposite reaction.
• Universal gravitation: Every particle of matter in the universe attracts every other particle with a force proportional to their masses and inversely proportional to the square of the distance between them.
• Derivations of Kepler's laws from these principles, explanations of tides, the precession of the equinoxes, the shape of Earth, and the motion of comets.

The Principia was written in Latin, in the geometric style of classical mathematics, and was difficult enough that even contemporary mathematicians struggled with it. It sold out immediately.

Why It Was Revolutionary

Newton's achievement was not just new discoveries but a new kind of knowledge. Before the Principia, natural philosophy was largely qualitative — describing phenomena in words, arguing about what causes what. After the Principia, it was mathematical — deriving precise quantitative predictions from a small set of fundamental laws.

The three laws of motion created a framework applicable to everything from falling apples to orbiting planets to the paths of artillery shells. For the next 200 years, Newtonian mechanics was the dominant framework of physics — used to design bridges, predict eclipses, and navigate ships. When French mathematicians like Laplace extended Newton's methods in the 18th century, they could predict the positions of planets centuries in advance.

The conceptual revolution was equally profound. Newton's laws implied that the universe runs according to deterministic mathematical laws — that everything that happens is, in principle, calculable from the current state of the universe. This vision of a "clockwork universe" dominated scientific thinking until the quantum revolution in the 20th century.

Legacy and Impact Today

Newtonian mechanics is still the physics of everyday life. Building a bridge, calculating the trajectory of a rocket, designing a car's suspension — all of this uses Newton's laws. The Apollo moon landings were navigated with Newtonian mechanics. GPS satellites require relativistic corrections to Newton (Einstein's relativity shows that Newton's laws break down near the speed of light or in strong gravity), but for most practical engineering at ordinary speeds, Newton's equations are exact enough.

Newton himself went on to become Master of the Mint, devoting much of his later career to reforming England's currency and personally prosecuting counterfeiters. He served as president of the Royal Society for 24 years and was knighted in 1705. He never married and left no direct descendants.

He died in 1727. At his funeral, Voltaire — visiting from France — was so struck by the honor accorded Newton that he returned to France determined to spread Newtonian natural philosophy across Europe. The Enlightenment owed much to the idea Newton had demonstrated: that the universe is governed by laws that human reason can discover.

Key Takeaways

• Newton's 18-month plague exile was one of the most productive scientific retreats in history, producing the foundations of calculus, optics, and gravitational theory.
• His key insight was that the Moon's orbital motion and the fall of objects near Earth are the same phenomenon — both caused by universal gravity following an inverse-square law.
• The Principia (1687) established that the physical universe could be described by precise mathematical laws, creating the template for modern physics.
• Newton's three laws of motion remain the foundational framework for classical mechanics and are still used in engineering today.
• His work implied a deterministic, law-governed universe — a vision that dominated science for two centuries.

FAQ

Did an apple really fall on Newton's head? Almost certainly not. The apple story was told by Newton in old age (often to visitors he wanted to impress) and has been retold in increasingly dramatic forms. The likely truth: Newton may have observed falling apples and used the image to illustrate the insight that gravity extends beyond Earth's surface. The dramatic strike on the head appears nowhere in contemporary accounts.

What is the inverse-square law? The inverse-square law states that the gravitational force between two objects decreases as the square of the distance between them. If you double the distance, the force drops to a quarter; triple the distance, it drops to a ninth. This law correctly describes how gravity weakens with distance and can be derived from the geometry of three-dimensional space.

Did Newton really invent calculus? Yes, Newton independently invented calculus (which he called "the method of fluxions") around 1665–1666. Leibniz independently invented it in the 1670s with different notation. Both deserve credit. The bitter dispute over priority between Newton and Leibniz — partly stoked by Newton himself — was one of the uglier episodes in scientific history.

Why was the Principia so revolutionary? Before the Principia, natural philosophy described phenomena qualitatively. Newton showed that a small number of mathematical laws could precisely predict the motions of planets, moons, comets, and earthly objects. He unified terrestrial and celestial mechanics under a single framework — and proved it with calculations accurate enough to confirm by observation.

When did Newtonian mechanics break down? Newton's laws are extremely accurate at ordinary speeds and scales. They break down in two regimes: very high speeds (approaching the speed of light), where Einstein's special relativity applies; and very strong gravitational fields or cosmological scales, where general relativity is needed. At the atomic scale, quantum mechanics replaces classical mechanics. But for everyday engineering, Newtonian mechanics remains exact to any practical precision.

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