Titan, the largest satellite of Saturn, orbits Saturn with a semimajor axis of 1.22 × 10⁹ m and an orbital period of 1.38 × 10⁶ s (about 16 days). Use the formula in Box 4-4 to compute the combined mass of Saturn and Titan. What is the result, in kilograms?

Question

Quizplus · Accepted Answer

Using Kepler's third law, $ M = \frac{4\pi^2a^3}{GT^2} $, where $ a = 1.22 \times 10^9 $ m, $ T = 1.38 \times 10^6 $ s, and $ G = 6.674 \times 10^{-11} $ m³/kg/s², the combined mass is approximately $ 5.65 \times 10^{26} $ kg.

Titan, the Largest Satellite of Saturn, Orbits Saturn with a Semimajor