Aplanet 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?

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.

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