Accepted Answer
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)³Moon #2: (orbital period)² / (9.378 x 10^3 km)³If Kepler knew what he was talking about ... and Newton showed that he did ... then these two fractions are equal, and may be written as a proportion.Cross multiply the proportion:(orbital period)² x (2.346 x 10^4)³ = (1.262 days)² x (9.378 x 10^3)³Divide each side by (2.346 x 10^4)³:(Orbital period)² = (1.262 days)² x (9.378 x 10^3 km)³ / (2.346 x 10^4 km)³ = 0.1017 day²Orbital period = 0.319 Earth day = about 7.6 hours.
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