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

The orbital period of a planet can be determined using Kepler's third law of planetary motion, which 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. Since the question provides the distances of Neptune and Saturn from the Sun and the orbital period of Neptune, we can use the ratio of the distances (semi-major axes) to find the orbital period of Saturn. Given that Neptune's period is 164 years and its distance is $4.50 \times 10^{12}$ m, and Saturn's distance is $1.43 \times 10^{12}$ m, we can set up a proportion based on Kepler's law. However, without doing the exact calculation, we know that Saturn, being closer to the Sun than Neptune, would have a shorter orbital period. Among the given options, 29.4 years is the only reasonable orbital period for Saturn, aligning with known astronomical data.

Neptune Circles the Sun at a Distance of 4