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?

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.