Final answer:
To determine the orbital period of an asteroid orbiting the Sun at 16 AU, we apply Kepler's Third Law that relates the orbital period squared to the semi-major axis cubed; the calculation yields an orbital period of 64 years.
Step-by-step explanation:
The question is asking how long it takes for an asteroid to orbit the Sun at an average distance of 16 astronomical units (AU). To find the orbital period, we can use Kepler's Third Law of Planetary Motion, which states that the square of a planet's orbital period (T) is directly proportional to the cube of the semi-major axis of its orbit (a). The law is often expressed as T2 = a3, where T is in Earth years when a is in AU. For an asteroid orbiting at 16 AU, the calculation would be T2 = 163. Thus, T = √(163) which equals to 64 years for a complete orbit around the Sun.