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chornedsnorkack
2011-Jun-06, 11:18 AM
The Roche limit, in terms of primary radii, for a fluid secondary is about 2,423 times the cube root of the ratio of densities.

An implication thereof is that which is the density ratio required for the Roche limit to be inside the primary?

Cube of 2,423. Which is over 14.

Not exactly common for ratio between low pressure, high temperature condensed substances.

The density of iron is about 8. The heavier elements (gold, platinum) are strong siderophiles as small alloying component and do not much increase the density of iron.

Iron crosses the Roche limit for any primary whose density is more than about 0,55. Which means any planet in Solar System - specifically including Saturn. Although Saturn is 11 times less dense than iron, iron would cross Roche limit at about 1,1 Saturn radii.

Shouldnīt then a planet have rings of multiple materials - inner iron rings, outwards stone rings, and in outer Solar System, where ice does not evaporate, clean white ice rings outside the stone rings?

StupendousMan
2011-Jun-06, 12:39 PM
The first thing you need to do is figure out the origin of the rings. Do they begin as tiny little particles like sand and remain that size as they are captured to form rings? Or do they begin as large bodies, many kilometers in diameter, which migrate closer and closer to the planet before breaking up into the little ring particles?

Tell us which of these two extremes is closer to the story you are trying to describe, and we can take it from there.

chornedsnorkack
2011-Jun-06, 01:09 PM
The first thing you need to do is figure out the origin of the rings. Do they begin as tiny little particles like sand and remain that size as they are captured to form rings? Or do they begin as large bodies, many kilometers in diameter, which migrate closer and closer to the planet before breaking up into the little ring particles?



Large bodies. As they migrate inward under tidal forces (whether orbiting faster than primary rotation or in the opposite direction) they would deform and be stretched until, at Roche limit, the force of gravity at certain points of surface becomes zero and pieces start floating off these spots.

As the remaining core becomes smaller and denser (due to losing less dense surface pieces, like stones or icebergs) it continues moving inwards continuously shedding mass from surface until iron core is left. Since the iron core is uniform in composition and density (hard siderophiles like nickel and gold dissolve in iron) the iron core would disintegrate into iron ring, at which point (since the mass is uniformly spread along ring) there should be no more tides.

Rhaedas
2011-Jun-06, 02:16 PM
Would the body come apart like that, or would it be more of a catastrophic fracturing of the entire object? Smaller bodies break apart easily, but are there models for planetary sized bodies and how they would act?

HypersonicMan
2011-Jun-06, 03:27 PM
A recent paper on the origin of Saturn's rings by Robin Canup (you can read about it here: http://www.sciencenews.org/view/generic/id/67342 ) invokes this very mechanism. In Canup's scenario, a big differentiated satellite of young Saturn (Titan-sized) spiraled in to the planet due to gas forces in the sub-Saturn nebula until it reached the Roche limit of ice. The icy mantle was then stripped off to form the ice-rich rings we know and love. However, the young Saturn was much hotter than it is today and its radius was much larger. In fact its radius was so large that the Roche limit for rock (and iron) was inside the atmosphere. So before the remaining rock & metal-rich core of the satellite could get tidally stripped to form an inner ring, it was swallowed up by Saturn.

StupendousMan
2011-Jun-06, 06:02 PM
Okay, following your idea, we start with a large, differentiated single body. Its orbital radius gradually shrinks until it reaches the neighborhood of the Roche limit. Fine.

The Roche limit itself is derived from a simple comparison of gravitational forces. It doesn't include any of the forces which hold ordinary rock or ice or matter together. When the body reaches, say, the Roche limit for iron, it will begin to break up. But how large will the pieces be? You need to figure out the size at which the inter-molecular forces become small compared to self-gravitational forces. Do you know how to do that?

HypersonicMan
2011-Jun-07, 09:24 PM
For large objects, gravitational forces dominate over intermolecular forces (material strength). The transition from strength-dominated to gravity dominated happens for objects larger than about a kilometer in diameter. So if I had to guess, I'd say ~1 km is probably about the size of the chunks (the minimum of the strength vs. size curve). Of course the real physics is likely to be more complicated, as there are likely to be fractures and whatnot. However, once the icy mantle gets tidally stripped from the rest of the body, it goes into orbit and forms the rings. Then the chunks will collide with each other and grind down to even smaller sizes.