Isaac Newton · Science
Newton’s law of universal gravitation - that every body attracts every other with a force proportional to their masses and inversely proportional to the square of the distance - which unified the heavens and the earth under a single law.
The most famous story in the history of science tells of Newton watching an apple fall in his garden and wondering whether the same force that pulled the apple to the ground might reach all the way to the Moon. Whether or not the apple is literally true, it captures Newton’s revolutionary insight. Before Newton, the heavens and the earth were thought to be utterly different realms, governed by different principles: earthly bodies fall, but the Moon and planets move eternally in their orbits by some quite different, celestial cause. Newton’s great unifying idea was that there is no such division - that the same force which makes an apple fall to the ground also holds the Moon in its orbit around the Earth, and binds the planets to the Sun. The force that pulls the apple down and the force that keeps the Moon circling are one and the same: gravity, a universal force of attraction between all bodies. The Moon, Newton realized, is in effect perpetually falling toward the Earth - but moving sideways so fast that it keeps missing, circling endlessly. This single, breathtaking idea - that one force governs both the falling apple and the orbiting Moon - abolished the ancient division between heaven and earth and united the whole physical universe under a single law.
Newton did not merely assert that one force governs heaven and earth - he found its precise mathematical law. The law of universal gravitation states that every body in the universe attracts every other body with a force that is (1) proportional to the product of their masses - the more massive the bodies, the stronger the attraction - and (2) inversely proportional to the square of the distance between them - the farther apart, the weaker the attraction, falling off as the square of the distance. Double the distance, and the force becomes one quarter as strong; triple it, and one ninth. This is the famous inverse-square law. In a single, simple formula, it captures the gravitational attraction between any two bodies in the universe - apple and earth, earth and moon, sun and planet, star and star. The law is universal: it applies to every body everywhere, from a falling apple to the most distant galaxy, all governed by the same simple mathematical relationship. From this one law, Newton could calculate the strength of gravity between any two bodies, and so determine their motions. The inverse-square law of gravitation is one of the most powerful and far-reaching laws ever discovered - a single equation governing the gravitational dance of the entire cosmos.
With the law of universal gravitation, Newton could explain and calculate an astonishing range of phenomena, in the heavens and on the earth, from a single principle. He derived Kepler’s laws of planetary motion. He explained the orbits of the Moon and the planets, and of comets - showing that comets, long regarded as mysterious omens, are bodies moving on elongated orbits under the Sun’s gravity, returning periodically (as Halley’s comet was later found to do, exactly as Newton’s physics predicted). He explained the tides - the twice-daily rise and fall of the seas - as the effect of the gravitational pull of the Moon and Sun on the Earth’s waters. He explained the slight bulge of the Earth at its equator, and the slow wobble of its axis (the precession of the equinoxes). All of these - planets, moons, comets, tides, the shape of the Earth - Newton showed to be consequences of his single law of gravitation. This was what he called the System of the World: a unified, mathematical account of the entire physical cosmos, in which the motions of all the heavenly bodies and many terrestrial phenomena are derived from a few simple laws. Never before had so much of nature been brought under so few principles. It was the supreme achievement of the Scientific Revolution and one of the greatest in the history of human thought.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned Newton’s law of universal gravitation. State the law in your own words and explain how it unified the falling of bodies on Earth with the motions of the Moon and planets.
Leads to Johannes Kepler.
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