A hypothetical moon is orbiting Saturn in a circular orbit that has exactly 3 times the period that an object orbiting in one of one of the gaps in Saturn's rings would have. As measured from the center of Saturn at what fraction [to 3 decimal places] of that moon's orbital radius does the ring appear? [Hint: Use Kepler's 3rd Law]

Answer 1

Kepler's third law says that, for all objects orbiting the same large mass,
P^2/R^3 = constant
P is the period; R is the orbit radius.

If the moon's period is 3 times the ring gap object's period
[R(gap)/R(moon)]^3 = [P(gap)/P(moon)]^2 = 1/9
[R(gap)/R(moon)] = cube root of 1/9

Answer 2

[R(gap)/R(moon)] = cube root of 1/9 = 0.481