Definition · Plain-language
Kepler’s laws of planetary motion
Kepler’s three laws of planetary motion describe how planets orbit the Sun: in ellipses, sweeping equal areas in equal times, with a fixed relationship between orbital period and distance.
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First law: orbits are ellipses
Johannes Kepler published his first two laws in 1609 and the third in 1619, derived from painstaking analysis of planetary observations. The first law states that each planet moves around the Sun in an ellipse — a stretched circle — with the Sun located at one of the two foci, not at the centre. This overturned the ancient assumption that orbits must be perfect circles. Because the Sun sits off-centre at a focus, every planet’s distance from the Sun varies over its orbit, swinging between a closest point (perihelion) and a farthest point (aphelion).
Second law: equal areas in equal times
The second law states that an imaginary line joining a planet to the Sun sweeps out equal areas in equal intervals of time. The practical meaning is that a planet does not move at a steady speed: it travels faster when it is nearer the Sun and slower when it is farther away, so that the area swept stays the same in each equal slice of time. This is actually a consequence of the conservation of angular momentum. Earth, for example, moves slightly faster in early January, when it is closest to the Sun, than in early July.
Third law: period and distance
The third law links a planet’s orbital period to its distance from the Sun: the square of the orbital period is proportional to the cube of the semi-major axis of its orbit, written T² ∝ a³. In plain terms, planets farther from the Sun take disproportionately longer to complete an orbit — not just because their path is longer, but because they also move more slowly. This is why Neptune takes about 165 Earth-years to orbit once while Mercury takes only 88 days. Newton later showed all three laws follow from his law of universal gravitation, and they apply to any body orbiting another, including moons and satellites.
Key facts
At a glance
- Definition: three laws describing how planets orbit the Sun
- First law: orbits are ellipses with the Sun at one focus
- Second law: a planet sweeps equal areas in equal times (faster when nearer the Sun)
- Third law: T² ∝ a³ — period squared is proportional to distance cubed
- Published: by Johannes Kepler, 1609 and 1619
- Explained by: Newton’s law of universal gravitation, and applies to any orbit
Common misconceptions
What people often get wrong
Often heard: Planets orbit the Sun in perfect circles.
Actually: Kepler’s first law shows orbits are ellipses with the Sun at one focus. Most planetary orbits are only slightly elliptical, but they are not perfect circles.
Often heard: A planet moves at the same speed all the way round its orbit.
Actually: By the second law a planet moves faster when closer to the Sun and slower when farther away, sweeping equal areas in equal times.
Often heard: Kepler’s laws apply only to the planets of our Solar System.
Actually: They follow from gravitation and apply to any orbiting body — moons, comets, artificial satellites and exoplanets around other stars.
Going deeper
