Kepler's laws: Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years. Saturn circles the Sun at a distance of 1.43 × 10¹² m. What is the orbital period of Saturn? A) 304 y B) 121 y C) 109 h D) 88.6 y E) 29.4 y

Question

Quizplus · Accepted Answer

Kepler's third law of planetary motion states that 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 expressed as $T^2 \propto r^3$, where $T$ is the orbital period and $r$ is the average distance from the Sun. Given the orbital period of Neptune and its distance, we can use the ratio of the squares of the orbital periods of Neptune and Saturn to the cubes of their respective distances to find Saturn's orbital period. The correct answer, after applying Kepler's third law and solving for Saturn's orbital period, is 29.4 years, which corresponds to choice E.

Kepler's Laws: Neptune Circles the Sun at a Distance of 4.50