The moons of Saturn named Tethys and Dione have a 2:3 orbital resonance with Tethys orbiting closer to Saturn than Dione.If the semimajor axis of Dione's orbit is 380,000 km,what is the semimajor axis of Tethy's orbit?
A) 700,000 km
B) 570,000 km
C) 290,000 km
D) 250,000 km

Question

Quizplus · Accepted Answer

In a 2:3 orbital resonance, Tethys completes 2 orbits for every 3 orbits of Dione. Using Kepler's third law, the ratio of the semimajor axes is (2/3)^(2/3). Solving for Tethys' semimajor axis: a_Tethys = 380,000 * (2/3)^(2/3) ≈ 290,000 km.

The Moons of Saturn Named Tethys and Dione Have a 2:3