What does Kepler's Third Law of planetary motion state?

Kepler's Third Law of planetary motion establishes a fundamental relationship between the period of a planet's orbit around the Sun and its average distance from the Sun, as measured by the semi-major axis of its orbit. The law states that the square of the orbital period (in years) of a planet is directly proportional to the cube of the semi-major axis of its orbit (in astronomical units, AU). This relationship can be mathematically expressed as:

(Period of orbit in years)² = (Semi-major axis in AU)³.

This law reveals important insights into the gravitational effects causing orbital motion and indicates that planets farther from the Sun take significantly longer to complete one orbit compared to those closer to the Sun.

Other formulations, such as those involving distances in kilometers or periods in days, do not align with Kepler's original findings and principles. The use of AU (astronomical units) and years ensures the law accurately reflects the dynamics of the solar system as originally described by Kepler. This understanding allows astronomers to calculate orbits and predict planetary positions based on their distances from the Sun, showcasing the elegant relationship between these two quantities.