A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite? A) 60.8 hours B) 12.0 hours C) 33.1 hours D) 9.80 hours E) 27.0 hours

Question

Quizplus · Accepted Answer

We can use Kepler's third law which states:

(T1/T2)^2 = (R1/R2)^3

where T = period and R = orbital radius.

Solving for T2, we have:

T2 = T1 * (R2/R1)^(3/2)

Plugging in the given values, we have:

T2 = 18.0 hours * (3.00 × 10^17 m / 2.00 × 10^17 m)^(3/2)

T2 ≈ 33.1 hours

Therefore, the answer is (C) 33.1 hours.

A Planet Has Two Small Satellites in Circular Orbits Around