Formation of Saturn's Rings

It has been proposed that Saturn's rings formed when one or more small moons, originally orbiting outside Saturn's Roche limit, spiralled inwards over time due to tidal effects, crossed inside the Roche limit, and were disrupted.

1. Calculate the orbital angular frequency (in units of ) of a hypothetical moon travelling in a circular, prograde orbit at the Roche limit of Saturn. Compare your answer to Saturn's spin frequency (yes, we mean a number). If values for the needed quantities are not given in Shu's text then look in the appendices of the books listed as references in the syllabus.
2. Do tidal forces increase or decrease the orbital angular momentum of the hypothetical moon? Does the moon spiral in or out? Explain why using words and a diagram similar in style to the one on page 37 of the lecture notes.
3. Redo the previous question for a hypothetical moon in a retrograde orbit at the Roche limit of Saturn. Use a second diagram to illustrate your answer.
4. If the proposed scenario for ring formation is correct, in what sense (prograde or retrograde) do the rock fragments in the resulting rings revolve? Why?

One can measure the sense of revolution of Saturn's rings. It turns out that they revolve in the opposite sense to that predicted by the disruption scenario. Too bad for the scenario!

5. In a short paragraph, describe what you learnt from this problem, what you think the point of this problem is, and how it fits in to the material covered in lectures. (Please answer this seriously; it is a serious question, i.e. we will grade it!)