The law that describes the relationship between a planet's average distance from the Sun and its orbital period is Kepler's Third Law of Planetary Motion.

Here's what it states:

* The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

In simpler terms:

* The further a planet is from the Sun, the longer it takes to complete one orbit. This relationship is not linear, but rather a cube-square relationship.

Mathematically:

* T² ∝ a³

Where:

* T = orbital period (in years)

* a = semi-major axis (average distance from the Sun in astronomical units (AU))

Example:

* Earth has an orbital period of 1 year and a semi-major axis of 1 AU.

* Mars has an orbital period of 1.88 years and a semi-major axis of 1.52 AU.

* Notice that the ratio T²/a³ is approximately the same for both Earth and Mars, which confirms Kepler's Third Law.

This law revolutionized our understanding of planetary motion and provided a powerful tool for studying the solar system.