If a planet were to exist in the solar system in a circular orbit with a radius of 3 au, about how long would it take to orbit the Sun once?
A) 5.2 years
B) 2.1 years
C) 27 years
D) 3 years

Question

Quizplus · Accepted Answer

According to Kepler's Third Law, the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. This can be expressed as T^2 ∝ r^3. If we take Earth's orbit as a reference (1 AU and 1 year), for a planet orbiting at 3 AU, the period T can be calculated as follows: T^2 = (3)^3 = 27. Therefore, T = sqrt(27) ≈ 5.2 years.

If a Planet Were to Exist in the Solar System