A distant asteroid is discovered that takes 50 years to orbit the Sun once. According to Kepler's third law, what is the average distance of this asteroid from the Sun?
A) 2500 au
B) 50 au
C) 353 au (square root of 125,000)
D) 13.6 au (cube root of 2500)

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period (in years) is proportional to the cube of the average distance from the Sun (in astronomical units, au). For an orbital period of 50 years, $50^2 = 2500$, the cube root of 2500 gives the average distance, which is approximately 13.6 au.

A Distant Asteroid Is Discovered That Takes 50 Years to Orbit