Final answer:
The average distance of a comet from the Sun with an orbital period of 8 years is 4 AU, calculated using Kepler's Third Law of Planetary Motion.
Step-by-step explanation:
The student asks about the average distance of a comet from the Sun, given that the comet has an orbital period of 8 years. To calculate this, we can use Kepler's Third Law of Planetary Motion, which states that the square of the period of any planet (or comet) is proportional to the cube of the semi-major axis of its orbit. Since we know the period in years, we can find out the length of the semi-major axis in astronomical units (AU), with one AU being the average distance between the Earth and the Sun, approximately 150 million kilometers.
Kepler's Third Law of Planetary Motion formula is:
P^2 = a^3
Where P is the period in years and a is the semi-major axis in AUs. Plugging in the period (P) of 8 years, we get:
8^2 = a^3
64 = a^3
So the cube root of 64 gives us the average distance:
a = 4 AU
Thus, the average distance from the Sun for this comet is 4 AU, which corresponds to option (a).