Suppose that a distant planet orbiting its sun has an orbital period of 8 years. What is the approximate distance from the sun to the planet?
A) 1 AU
B) 4 AU
C) 10 AU
D) 32 AU

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 law can be formulated as $P^2 = a^3$, where $P$ is the orbital period in years and $a$ is the semi-major axis in astronomical units (AU). For a planet with an orbital period of 8 years, $8^2 = 64$, so $a^3 = 64$. Taking the cube root of both sides gives $a \approx 4$, meaning the planet is approximately 4 AU from its sun.

Suppose That a Distant Planet Orbiting Its Sun Has an Orbital