Question

A planet has two moons. The first moon has an orbital period of 1.262 Earth days and an orbital radius of 2.346 x 104 km. The second moon has an orbital radius of 9.378 x 103 km. What is the orbital period of the second moon?

Answer 1

Kepler's third law hypothesizes that for all the small bodies in orbit around the same central body, the ratio of (orbital period squared) / (orbital radius cubed) is the same number. 

Moon #1:  (1.262 days)² / (2.346 x 10^4 km)³

Moon #2:  (orbital period)² / (9.378 x 10^3 km)³

Equating the ratio:
(1.262 days)² / (2.346 x 10^4 km)³  = (orbital period)² / (9.378 x 10^3 km)³

Cross-multiply:
(orbital period)² x (2.346 x 10^4)³ = (1.262 days)² x (9.378 x 10^3)³

Divide each side by (2.346 x 10^4)³:

(Orbital period)² = [ (1.262 days)² x (9.378 x 10^3)³ ] / (2.346 x 10^4)³

               =  0.1017 day²

Orbital period = 0.319 Earth day = about 7.6 hours.