Kepler's Three Laws of Planetary Motion: Overview
Johannes Kepler published three laws describing how planets orbit the Sun. These laws, derived from Tycho Brahe's observational data, replaced the ancient assumption of circular orbits and remain foundational to astronomy and spaceflight.
First Law: The Law of Ellipses
Each planet moves in an ellipse with the Sun at one focus.
Before Kepler, all astronomers (including Copernicus) assumed orbits were circles or combinations of circles. Kepler showed they are ellipses—slightly flattened circles with two focal points. The Sun occupies one focus; the other is empty. For most planets, the eccentricity is small, so the orbits look nearly circular, but the mathematical distinction matters enormously for precise prediction.
Full details: Kepler's First Law
Second Law: The Law of Equal Areas
A line segment joining a planet to the Sun sweeps out equal areas during equal intervals of time.
This means planets move faster when they are closer to the Sun and slower when they are farther away. At perihelion (closest approach), a planet is at its maximum speed; at aphelion (farthest point), it is at its minimum. The underlying reason is conservation of angular momentum.
Full details: Kepler's Second Law
Third Law: The Harmonic Law
The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.
Where T is the period, a is the semi-major axis, and k is a constant that depends on the mass of the central body. This law links all the planets together under a single mathematical relationship and is essential to exoplanet detection and determining the mass of distant objects.
Full details: Kepler's Third Law