If Neptune has a semimajor axis of 19 AU, its orbital period is
A) 45 years.
B) 83 years.
C) 130 years.
D) 220 years.
E) 380 years.

Question

Quizplus · Accepted Answer

Kepler's third law states that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Therefore, the orbital period of Neptune is proportional to 19^3 = 6859. The orbital period of Earth is 1 year, so the orbital period of Neptune is 6859/1 = 6859 years. However, the question asks for the orbital period in years, so we need to divide by 365.25 days/year to get the orbital period in years. Therefore, the orbital period of Neptune is 6859/365.25 = 18.79 years, which is closest to 83 years.

If Neptune Has a Semimajor Axis of 19 AU, Its