Definition

Kepler's laws are three rules for how planets move around the Sun: orbits are ellipses rather than circles, a planet moves faster when closer to the Sun, and planets farther out take much longer to go around. Stated precisely, each planet orbits in an ellipse with the Sun at one focus; a line from the Sun to the planet sweeps equal areas in equal times, so the planet is fastest at perihelion and slowest at aphelion; and the square of the period is proportional to the cube of the average distance, $T^2 = a^3$ with $T$ in years and $a$ in AU. All three follow from Newton's gravitation: the inverse-square force yields conic-section orbits, conservation of angular momentum yields equal areas, and combining gravity with centripetal acceleration yields $T^2 = \dfrac{4\pi^2}{G(M + m)}\,a^3$, which reduces to the simple form when $M$ is the Sun and $m$ is negligible. The generalized third law is the primary tool for measuring masses throughout astronomy.