Final answer:
To find the average distance from the Sun of a planet with an 8-year orbital period, we can use Kepler's third law of planetary motion.
Step-by-step explanation:
To find the average distance from the Sun (in astronomical units) of a planet with an orbital period of 8 years, we can use Kepler's third law of planetary motion. According to Kepler's third law, the square of the orbital period (T) is proportional to the cube of the average distance from the Sun (d). Mathematically, this relationship can be expressed as T^2 = k * d^3, where k is a constant.Given that the orbital period (T) is 8 years, we can substitute this value into the equation: (8 years)^2 = k * d^3. Simplifying, we get 64 years^2 = k * d^3.Since we don't have the value of k, we can't calculate the exact distance. However, we can compare the distance of the planet to the distance of another known planet with a similar orbital period:For example, if we know that the average distance from the Sun of another planet with an orbital period of 8 years is 2 astronomical units (AU), we can use this value to determine the distance of the planet in question.