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.
