Kepler's Laws of Planetary Motion
The three empirical laws describing planetary orbits: ellipses, equal areas in equal times, and the relation between period and orbit size.
Kepler's three laws of planetary motion, published by Johannes Kepler in 1609 and 1619, describe how planets move around the Sun. They were derived from the extraordinarily precise naked-eye observations of Tycho Brahe, especially of Mars, and they replaced the ancient assumption of perfect circular orbits. Kepler's achievement was empirical and mathematical: he found the patterns before anyone could explain why they held.
The first law states that every planet moves in an ellipse with the Sun at one focus. An ellipse has two foci; the Sun occupies one, so a planet's distance from the Sun varies over its orbit — closest at perihelion, farthest at aphelion. The second law states that a line from the Sun to a planet sweeps out equal areas in equal times: a planet moves fastest near perihelion and slowest near aphelion. This is a statement of angular momentum conservation. The third law connects the whole system: the square of a planet's orbital period T is proportional to the cube of its orbit's semi-major axis a, T² ∝ a³, with the same constant for all planets of the Solar System.
Newton's law of gravitation, published in the Principia of 1687, derived all three laws from a single inverse-square force — the first law follows from the mathematics of conic sections, the second from angular momentum conservation, and the third from the force's strength. Newton's laws of motion thereby turned Kepler's empirical rules into consequences of mechanics, one of the great unifications of science.
Kepler's laws remain the working tools of orbital mechanics. Satellites, spacecraft, and the planets of other stars all obey them: the transit method detects exoplanets by the periodic dimming they cause, and the measured wobble of stars reveals planetary masses through the same orbital relations. The laws also explain tidal locking: a moon's rotation gradually synchronizes with its orbit because the tidal bulge it raises is dragged by the varying orbital speed that Kepler's second law describes.
Tags
astronomy gravity kepler orbital mechanics