With a ring like this...

Suppose that you found, somewhere in deep space, a planet that is pretty much like Saturn, i.e., it is a ball of gas together with a ring. The ball of gas is not still stood, it is moving along the ring's symmetry axis. If the maximum distance between the center of mass of the ball and the center of the ring is much smaller than the ring's radius, what is the period of the ball's movement?

Details and assumptions:

• Express your answer to the nearest integer in hours.
• The mass of the ring is $5.6846 \times 10^{26}$ kg.
• The radius of the ring is $2.4 \times 10^{8}$ m.
• The gravitational constant is $6.67 \times 10^{-11}$ Nm²/kg².