Laws of motion

Classical mechanics is the claim that motion obeys a small set of exact rules. A body left alone keeps its velocity forever; a force changes that velocity in proportion to the force and inversely to the mass (F = ma); and every push is answered by an equal push back. To these three laws Newton added a fourth statement — that any two masses attract with a force that weakens as the square of the distance between them. The consequence is startling: if you know the forces on an object and its position and velocity right now, you can in principle calculate exactly where it will be at every moment forever after. Motion became a calculation.

Before Newton, the heavens and the Earth were governed by different rules. In the inherited Aristotelian picture, celestial bodies moved in perfect circles for reasons of their own, while earthly things fell in straight lines toward the ground. Newton's single law of gravitation covered both: the apple's fall and the Moon's orbit are the same phenomenon at different distances, and Kepler's three empirical laws of planetary motion drop out as theorems. This is the first time one mathematical law was shown to run the whole cosmos, and it made the universe predictable. Edmond Halley used the theory to forecast that the comet of 1682 would return in 1758 — and it did, arriving on Christmas night, sixteen years after Halley's death.

Nearly all of engineering runs on these laws: structures, machines, ballistics, the tides, the wobble of the Earth's axis. They gave later mathematicians a machine to extend — Laplace's celestial mechanics, the prediction of Neptune from Uranus's stray motion in 1846 — and they set the template every physical theory since has followed: a law of nature written as an equation whose solutions are checked against measurement. Even where the framework later broke down — at very high speeds, where relativity takes over, and at atomic scales, where quantum mechanics does — it survives as the exact limit those theories reduce to in ordinary life.