Final answer:
The distance of each planet from the Sun is related to its orbital period by Kepler's third law, which states that the square of the orbital period is proportional to the cube of the average distance from the Sun, showing that planets farther from the Sun have longer orbital periods.
Step-by-step explanation:
The relationship between the distance of each planet from the Sun and its orbital period is given by Kepler's third law. This law states that the square of a planet's orbital period (P) is directly proportional to the cube of its semimajor axis (a), which is the planet's average distance from the Sun. In mathematical terms, this is written as P2 ≈ a3, where P is measured in Earth years and a is measured in astronomical units (AU).
Using Kepler's third law, we can calculate the expected orbital period for planets at different distances from the Sun. For example, if we plot the relationship for mean distances from 0.1 to 32 AU, we create a Keplerian curve that shows how the orbital period increases with distance from the Sun. When we overlay the actual data for each planet in our solar system onto this theoretical curve, we find that the planets conform closely to this predicted relationship, corroborating Kepler's discovery over 400 years ago.