A planet whose distance from the Sun is 3 A.U. would have an orbital period of how manyEarth-years?
A)3
B) $\sqrt { 27 }$
C) $\sqrt { 3 }$
D)9
E)81

Question

Quizplus · Accepted Answer

According to Kepler's third law of planetary motion, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This can be expressed as $T^2 \propto a^3$, where $T$ is the orbital period in Earth years and $a$ is the semi-major axis in astronomical units (A.U.). For a planet 3 A.U. from the Sun, $a = 3$, so $T^2 = 3^3 = 27$, and thus $T = \sqrt{27}$.

A Planet Whose Distance from the Sun Is 3 A Would