An asteroid follows a circular orbit around the Sun with a radius of 5 AU.Which of the following is closest to its orbital period?
A) 3 years
B) 11 years
C) 25 years
D) 125 years

Question

Quizplus · Accepted Answer

Using Kepler's Third Law, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit, $T^2 \propto a^3$. Given that the Earth's orbit is 1 AU and it takes 1 year to orbit the Sun, for an asteroid at 5 AU, its orbital period can be calculated as $T^2 = (5)^3 = 125$, so $T = \sqrt{125} \approx 11$ years.

An Asteroid Follows a Circular Orbit Around the Sun with a Radius