What is the offical name for the critical radius in which rings can form a moon?

I think it's called the Rouch radius. Anything within the Rouch radius will fall back to a planet but anything at the rouch radius will form a moon.





Can someone please confirm my postulate?

What is the offical name for the critical radius in which rings can form a moon?
It's called the Roche limit. (Check the spelling; I've always seen it as "Roche" since I first an across the term 40 years ago.) A planet can actually have a moon within the Roche limit because Roche (after whom it's named) assumed that the materials forming the moon had no tensile strength but were held together by their gravitational attraction. He then calculated how close the moon would have to be to its primary for the tidal forces of the primary to prevail over the gravitational attraction of the moon's matter. He then expressed the limit in terms of the radius of the primary. There is no constant Roche limit as the size and denisty of the primary affect where the Roche limit is.





A planet can have a small moon within its Roche limit because the cohesiveness (stickiness? Gluiness?) of the small satellite becomes more significant that its gravitational attraction. Saturn's rings are well within the planet's Roche limit and so they can't form into a satellite. The Earth's Roche limit is about 18,000 miles.
Reply:In complex analysis, Rouché's theorem tells us that if the complex-valued functions f and g are holomorphic inside and on some closed contour C, with |g(z)| %26lt; |f(z)| on C, then f and f + g have the same number of zeros inside C, where each zero is counted as many times as its multiplicity. This theorem assumes that the contour C is simple, that is, without self-intersections.





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Reply:It's actually Rouche's theorem, and it's a complex one. It varies based on the size of the planet, the planet's rotation and revolution velocities, and any other gravitational force in the vicinity (i.e. other moons, planets, it's star, etc.) For instance, Saturn and Uranus still have rings because their rotation speed does not lend well to making moons with that debris.