Final answer:
The average distance from the Sun of a comet with an orbital period of 82 years is approximately 19.1 astronomical units (AU), calculated using Kepler's Third Law of Planetary Motion.
Step-by-step explanation:
To calculate the average distance (in astronomical units, AU) of a comet from the Sun based on its orbital period, you can use Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period (P) of a planet (or comet) is directly proportional to the cube of the semi-major axis (a) of its orbit around the Sun (P² ≈ a³), where P is in years and a is in AU. For a comet with an orbital period of 82 years, you'd first square the period to get P² = 82² and then take the cube root to find the semi-major axis a.
Let's go through the calculation:
First, square the period P: (82 years)² = 6724 years²
Next, take the cube root to find the semi-major axis a: a ≈ ∛(6724 years²) ≈ 19.1 AU
Thus, the average distance of a comet with an orbital period of 82 years from the Sun is approximately 19.1 AU.