The Roche Limit And Earth Rings

[PacThePhoenix]

Many of you by know probably know what the Roche Limit is, if not, then here is a quick definition. The Roche Limit is the minimum distance from a parent body a satellite can orbit without being pulled apart by tidal forces. What this means is that if, for instance, the moon were to decay into an orbit within its Earth-Moon Roche Limit, it would be torn apart by Earth's gravity and be turned into rings (kinda like Saturn). For me, this is where the confusion starts. I've seen two different formulae regarding the Roche Limit and they are (in terms of mass):

Rigid Satellite: d = 1.26Rm(MM/Mm)^1/3

Fluid Satellite: d ~= 2.44Rm(MM/Mm)^1/3

d = distance, Rm = radius of satellite, MM = mass of parent, Mm = mass of satellite

Now, first of all, I realize that the Moon acts as a fluid satellite rather than a rigid one; no idea as to why though. The thing that interests me the most after running the numbers to discover that the Earth-Moon Roche Limit is ~18,500km is the question; what would the thickness of the ring be? My initial instinct would be that the inner limit of the ring would be defined by the first equation I provided while the outer limit would be defined by the second. Nevertheless,I'm sure that all you smarty-pants people will be able to figure this out, but also let me know if there is something that I'm missing or anything I got wrong. This is literally all I know about the Roche Limit .

[Scotius]

I always thought "fluid satellite" meant icy moons of giant planets. Contrary to our Moon, they are mostly water.

[Shpaget]

The inner limit would be the primaries surface, where some other forces would start to dominate the interaction.

[PacThePhoenix]

I originally thought the same @Scotius, From what I've read, which again could be wrong, it suggests that a large body such as the Moon would be considered a "fluid" satellite due to the fact that tidal forces stretch and squeeze the body on a regular basis (this is what causes bodies to be tidally locked), causing it to act more as a liquid... kinda. I honestly don't know .

[K^2]

3 hours ago, PacThePhoenix said:

Now, first of all, I realize that the Moon acts as a fluid satellite rather than a rigid one; no idea as to why though.

Gravitational forces for such a large body are much too strong for any sort of rigidity Moon has to matter. It's the same reason why Moon is roughly spherical. Which also answers the question of how large a body has to be to be considered fluid for purposes of Roche Limit. If it's spherical, it's basically a fluid.

[fredinno]

11 hours ago, PacThePhoenix said:

Many of you by know probably know what the Roche Limit is, if not, then here is a quick definition. The Roche Limit is the minimum distance from a parent body a satellite can orbit without being pulled apart by tidal forces. What this means is that if, for instance, the moon were to decay into an orbit within its Earth-Moon Roche Limit, it would be torn apart by Earth's gravity and be turned into rings (kinda like Saturn). For me, this is where the confusion starts. I've seen two different formulae regarding the Roche Limit and they are (in terms of mass):

Rigid Satellite: d = 1.26Rm(MM/Mm)^1/3

Fluid Satellite: d ~= 2.44Rm(MM/Mm)^1/3

d = distance, Rm = radius of satellite, MM = mass of parent, Mm = mass of satellite

Now, first of all, I realize that the Moon acts as a fluid satellite rather than a rigid one; no idea as to why though. The thing that interests me the most after running the numbers to discover that the Earth-Moon Roche Limit is ~18,500km is the question; what would the thickness of the ring be? My initial instinct would be that the inner limit of the ring would be defined by the first equation I provided while the outer limit would be defined by the second. Nevertheless,I'm sure that all you smarty-pants people will be able to figure this out, but also let me know if there is something that I'm missing or anything I got wrong. This is literally all I know about the Roche Limit .

Isn't the ring thickness usually very low?

[Spaceception]

Just now, fredinno said:

Isn't the ring thickness usually very low?

I'm pretty sure he meant how wide they would be (i.e. Would they look like Saturn's?), Although the OP author can correct me.

[fredinno]

Just now, Spaceception said:

I'm pretty sure he meant how wide they would be (i.e. Would they look like Saturn's?), Although the OP author can correct me.

That depends on its mass.

[Spaceception]

Just now, fredinno said:

That depends on its mass.

Well it's the Moon, so...

[fredinno]

Just now, Spaceception said:

Well it's the Moon, so...

That would be pretty big- maybe like Uranus', but it would be relatively unstable and decay eventually.

I'm not an expert though.

[PacThePhoenix]

What makes this a complicated question is the fact that we are theorizing if the Moon, a single satellite, turned into a ring. Saturn's rings are quite massive, most likely created through the destruction of several moons if it were the case, but could also be made simply of small debris. It's hard to say what Earth's rings would look like as we honestly don't know exactly how other planets got theirs. And yes, when I said thickness I meant how far would they stretch out (width, I guess) @Spaceception. The thing that my original hypothesis about the two equations determining the inner and outer boundaries makes me question is that if that were the case, the ring would be roughly 9,000km wide (very large :P).

[Nuke]

i bet things would not be fun on the surface while parts of the ring orbitally decayed.

[fredinno]

17 hours ago, Nuke said:

i bet things would not be fun on the surface while parts of the ring orbitally decayed.

Most would burn up, but you'd get a few impacts here and there. Livable, but not great.