Posted by Leslie on Thursday, November 15, 2012 at 12:48am.
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]

Physics  Astronomy  drwls, Thursday, November 15, 2012 at 3:02am
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

Physics  Astronomy  drwls, Saturday, November 17, 2012 at 2:26am
[R(gap)/R(moon)] = cube root of 1/9 = 0.481
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