P2 = a3

In 1619, Kepler discovered a basic relationship to relate the planets’ orbits to their relative distances from the Sun. We define a planet’s orbital period, (P), as the time it takes a planet to travel once around the Sun. Also, recall that a planet’s semimajor axis, a, is equal to its average distance from the Sun. The relationship, now known as Kepler’s third law, says that a planet’s orbital period squared is proportional to the semimajor axis of its orbit cubed, or

P² ∝ a³

When P (the orbital period) is measured in years, and a is expressed in a quantity known as an astronomical unit (AU), the two sides of the formula are not only proportional but equal. One AU is the average distance between Earth and the Sun and is approximately equal to 1.5 × 10⁸ kilometers. In these units,

P² = a³

Kepler’s third law applies to all objects orbiting the Sun, including Earth, and provides a means for calculating their relative distances from the Sun from the time they take to orbit.