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What are Kepler’s three laws of planetary motion?

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Illustration showing the eight planets of the solar system in order from the Sun-Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune-depicted to scale by size, with labeled diameters in miles and kilometers. The Sun is partially visible on the left for comparison. — Solar system The planets (in comparative size) in order of distance from the Sun.

German astronomer Johannes Kepler derived three laws of planetary motion in the early 17th century based on the precise observations of Tycho Brahe. These laws describe the movement of planets in the solar system as follows:

First Law (Law of Ellipses): All planets move in elliptical orbits, with the Sun situated at one of the two foci.123
Second Law (Law of Equal Areas): A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. This implies that a planet moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion).124
Third Law (Law of Harmonies): The squares of the sidereal periods of the planets are directly proportional to the cubes of their mean distances from the Sun. Mathematically, this is expressed as $T^{2} \propto a^{3}$ , where $T$ is the orbital period and $a$ is the semimajor axis of the orbit.123

These empirical laws were later explained by Isaac Newton through his law of gravitation.12