Kepler's laws of planetary motion

Kepler found his three laws by fitting decades of naked-eye observations of planetary positions, decades before Newton had any theory of gravity to explain them. The first law says orbits are ellipses with the Sun at one focus, not circles — a genuine break from millennia of assumed circular motion. The second says a line from the Sun to a planet sweeps out equal areas in equal times, which forces a planet to move fastest when nearest the Sun (at perihelion) and slowest when farthest (at aphelion) — an ellipse traversed at constant speed would violate this law. The third relates different planets to each other: the square of the orbital period is proportional to the cube of the orbit's size, T² ∝ r³, so a planet twice as far out does not orbit twice as slowly but nearly three times as slowly.

These were empirical regularities, discovered with no underlying mechanism — Kepler had found the pattern without knowing why nature followed it. Newton's achievement, decades later, was showing that all three laws fall out automatically from a single assumption: gravity pulls with a force proportional to 1/r². Elliptical orbits, the area law, and the period-radius relationship are not three separate facts about the solar system; they are three consequences of one force law, derivable together from Newton's mechanics rather than requiring three separate empirical rules.

This is one of the clearest examples in the history of physics of empirical law preceding — and then being explained by — physical theory, and it is exactly the same trajectory Newtonian gravitation itself would later follow when general relativity explained why mass produces that particular inverse-square attraction in the first place.