A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite? A) 4.50 × 10⁷ B) 3.90 × 10⁷ C) 9.24 × 10⁷ D) 8.00 × 10⁷ E) 7.27 × 10⁷

Question

Quizplus · Accepted Answer

Using Kepler's third law, which states that the square of the orbital period is proportional to the cube of the orbital radius, we can calculate the orbital radius of the second satellite. The ratio of the periods squared is equal to the ratio of the radii cubed: (16/12)^2 = (r2/6)^3. Solving for r2 gives approximately 7.27 × 10^7 m.

A Planet Has Two Small Satellites in Circular Orbits Around