The sum of the masses of the Sun and Jupiter is equal to
A) the square of Jupiter's average distance from the Sun in AU divided by the cube of Jupiter's period in years.
B) the cube of Jupiter's average distance from the Sun in AU divided by the square of Jupiter's period in years.
C) the square of Jupiter's period in years divided by the cube of Jupiter's average distance from the Sun in AU.
D) the cube of Jupiter's period in years divided by the square of Jupiter's average distance from the Sun in AU.

Question

Quizplus · Accepted Answer

This is a direct application of Kepler's third law of planetary motion, which states that the square of the orbital period of a planet (in years) is directly proportional to the cube of the semi-major axis of its orbit (in astronomical units, AU). When Kepler's third law is expressed in terms of masses, it shows that the sum of the masses of two bodies (like the Sun and Jupiter) is proportional to the cube of the distance between them divided by the square of their orbital period.

The Sum of the Masses of the Sun and Jupiter