Each of the following lists two facts.Which pair can be used with Newton's version of Kepler's third law to determine the mass of the Sun?
A)Mercury is 0.387 AU from the Sun,and Earth is 1 AU from the Sun.
B)The mass of Earth is 6 × 10²⁴ kg,and Earth orbits the Sun in 1 year.
C)Earth rotates in 1 day and orbits the Sun in 1 year.
D)Earth is 150 million km from the Sun and orbits the Sun in 1 year.
E)Jupiter is the most massive planet and has a mass of 1.9 × 10²⁷ kg.

Question

Quizplus · Accepted Answer

Newton's version of Kepler's third law is expressed as T²=(4π²/GM)r³, where T is the period of orbit, r is the average distance of an orbiting body from the center of the central mass, M is the mass of the central body, and G is the gravitational constant. Using the fact that Earth is 150 million km from the Sun and orbits the Sun in 1 year, we can calculate the product GM using T and r. This value can then be used along with the fact that Mercury is 0.387 AU from the Sun and Earth is 1 AU from the Sun to solve for the mass of the Sun. Therefore, choice D can be used to determine the mass of the Sun.

Each of the Following Lists Two Facts