Final answer:
To find the mean distance of a planet with an orbital period of 8 years from the Sun, one applies Kepler's third law. Squaring the orbital period gives 64, and taking the cube root yields an average distance of 4 astronomical units (AU).
Step-by-step explanation:
The question relates to the calculation of a planet's average distance from the Sun using Kepler's third law, which states that the square of the orbital period (P2) is proportional to the cube of the semimajor axis, or mean distance from the Sun (a3). For a planet with an orbital period of 8 years (P = 8), we would square the period to get 64 (P2 = 82 = 64). To find the mean distance (average distance) we would take the cube root of 64, which is 4. Therefore, a planet with an orbital period of 8 years has an average distance from the Sun of 4 astronomical units (AU).