Answered

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?  

Verified Answer :

AL2006

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

If 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)³

Divide 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 day²

Orbital period = 0.319 Earth day = about 7.6 hours.

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