Callisto is 1.76 times as far from Jupiter as is Ganymede.The orbital period of Callisto is 16.7 days.What is the orbital period of Ganymede?
A)About 3 days
B)About 7 days
C)About 10 days
D)About 13 days

Question

Quizplus · Accepted Answer

According to Kepler's Third Law of Planetary Motion, the square of the orbital period of a planet (or moon in this case) is directly proportional to the cube of the semi-major axis of its orbit. This law can be simplified to $T_2^2/T_1^2 = R_2^3/R_1^3$, where $T$ is the orbital period and $R$ is the distance from the central body. Given that Callisto is 1.76 times as far from Jupiter as Ganymede, and the orbital period of Callisto is 16.7 days, we can set up the ratio for Ganymede (let's call its period $T_g$) as follows: $16.7^2/T_g^2 = 1.76^3/1^3$. Solving for $T_g$ gives an orbital period of about 7 days for Ganymede.

Callisto Is 1