Kepler's laws of planetary motion

In the early seventeenth century, Johannes Kepler used the exceptionally detailed planetary observations made by Danish astronomer Tycho Brahe to investigate how planets move. The orbit of Mars was especially difficult to reconcile with the circular paths assumed in older models. Kepler's analysis led him to describe planetary motion with three rules. He published the first two in Astronomia Nova (1609) and the third in Harmonices Mundi (1619).

The first law states that a planet follows an ellipse, with the Sun at one focus. A circle is a special case of an ellipse, so a planet's orbit can be close to circular without being exactly so. The second law says that a line joining the Sun and a planet sweeps out equal areas in equal intervals of time. As a result, a planet moves faster when nearer the Sun and slower when farther away. The third law relates orbital period to orbit size: for planets orbiting the Sun, the square of a planet's period is proportional to the cube of the semi-major axis of its orbit. When period is measured in Earth years and semi-major axis in astronomical units, the relation is commonly written P² ≈ a³.

Together, the laws summarize regularities in planetary paths and speeds without specifying the physical force that produces them. Newton's theory of universal gravitation later provided a physical explanation and a broader mathematical framework for orbital motion. In modern astronomy, Keplerian relationships help describe and compare the orbits of planets, moons, artificial satellites, and bodies orbiting other stars. More precise predictions must account for gravitational interactions between multiple bodies and, where necessary, effects beyond Newtonian mechanics.

The laws are useful approximations when one body's gravity dominates the motion of another and other influences are small. In a system of several planets, each body's gravitational pull perturbs the others, so their paths do not remain perfect, isolated two-body ellipses. Newton's generalized form of the period–orbit-size relation also depends on the masses of the orbiting bodies; the familiar solar-system form treats the Sun's mass as dominant. These qualifications do not diminish the laws' historical importance or their continuing value as a first model of orbital motion.