Section   15.1The Solar System: An Overview

1. (Exercises 1 and 2) If a tenth planet were to be orbiting the Sun, it might have a semimajor axis of about 150 AU. If this planet did exist at this distance from the Sun, how long would it take to complete one orbit around the Sun?

Use the textbook's Eq.15.1 for Kepler's third law:

T² = k R²

For the data given:

T² = 1 year² / AU³ (150 AU)³

T² = 3,375,000 years²

Taking the square root of both sides gives us the actual period in years:

T = 1840 years

2. (Exercises 3 and 4) Calculate the length R of the semimajor axis of a planet whose period is 16 years.

Use Eq.15.1, T² = kR³.

Rearranging for R, R3 = T2/k =

Taking the cube root of both sides, R = 6.0 AU

Return to Previous Page