Exploring Europa's Ocean: Questions & Answers

[MonstersFromTheId]

1) How firm is the data ;-) this week ;-) , (ya got to love how fast & furrious new info is coming in these days), that there IS an ocean under all that ice?
Last I read opinions were fairly split between "Pretty sure there's an ocean down there" & "Naw, more like a slushy mush. Picture a very big Slurpy".

2) If there IS an ocean down there, what would the pressures be like just under 90 + miles of ice considering that, being so much smaller than Earth, the gravity would be much lower.

3) How deep is deep? How deep would the ocean be, how would that compare with the depths of Earth's oceans, and again, given the lower gravity, how would pressures compare between the deepest parts of Earth's oceans, and the deepest parts of Europa's oceans?

4) How warm is "warm"? Obviously if there's a liquid ocean it's got to be comparitively toasty for the moon of one of the outer planets. But how warm? Just barely above freezing for salt water kind of warm? Where would the warmest place on Europa be, just under the ice, the very bottom of the ocean, no one has the very slightest clue?

5) How would radiation levels compare to those on Earth? I'd imagine that 90+ miles of ice and one hell of a lot of water would shield things quite nicely from the hellish radiation of Jupiter, then again maybe not.

 

[Nereid]

1) How firm is the data ;-) this week ;-) , (ya got to love how fast & furrious new info is coming in these days), that there IS an ocean under all that ice?
Last I read opinions were fairly split between "Pretty sure there's an ocean down there" & "Naw, more like a slushy mush. Picture a very big Slurpy".

Until we actually go there, dig a hole, and take a look-see, we won't be 100% sure.

However, AFAIK, no one has come up with a model of Europa - sans ocean - that accounts for the relevant, good data. To the extent that 'we can't possibly think what else it could be!' is 'firm', then it's firm (IOW, pretty much the same as a great deal else in astronony - even seen a neutron star up close & personal?).

BTW, the data are very 'firm'; it's the conclusions that are a little mushy.

2) If there IS an ocean down there, what would the pressures be like just under 90 + miles of ice considering that, being so much smaller than Earth, the gravity would be much lower.

Would you like to have a go at working this out for yourself? For example, how would you calculate (approximately) what the pressure is, 1 km under the surface of an Earth ocean?

3) How deep is deep? How deep would the ocean be, how would that compare with the depths of Earth's oceans, and again, given the lower gravity, how would pressures compare between the deepest parts of Earth's oceans, and the deepest parts of Europa's oceans?

Well, if we can work out 2), the this will be a piece of cake!

As to the depths, well, I'll let someone else google that for you.

5) How would radiation levels compare to those on Earth? I'd imagine that 90+ miles of ice and one hell of a lot of water would shield things quite nicely from the hellish radiation of Jupiter, then again maybe not.

Indeed. That much ice, the only detectable radiation would be from naturally occurring radioisotopes (e.g. ⁴⁰K, and U and Th), and the occassional cosmic neutrino.

 

[MonstersFromTheId]

Would you like to have a go at working this out for yourself?

Actually I would, but I'm not sure where to get the numbers, or exactly how to do it.

What I'd try is first to figure out the pressure generated by 90 miles of ice.

I'd do that by trying to figure out how much a 1 inch x 1 inch x 90 miles high column of ice would weigh on Europa to get the psi value at the bottom of the ice where the water starts.
Thing is, 90 miles is a lotta miles, and I'm not sure that even if I knew how much things weighed on Europa as compared to Earth that that value would be constant over 90 miles.
Take an average? Figure out how much the gravitational attraction is at the outer radius of Europa, then figure out what it'd be at R-90 miles and average the two?
The other thing is I'm not sure what the density of the ice should be. Salt water ice? My understanding is that the ocean under Europa's ice shell is suspected to be a salt water ocean, so, given that's it's REALLY cold on Europa, salt water'd prolly freeze dammed solid, but... how much salt/gal of water?
And even once I know that, does salt water ice have a particular density, or might it be a lot less dense since it's freezing under lower gravity?
I read someplace that ice cubes cut from Earth's poles is offered in posh bars because that ice, having been formed under ENORMOUS pressure, is denser, and doesn't melt as quickly as ice made in a freezer.
And now that I think of that, it makes me wonder if I'd be talkin *salt* water ice, or just water ice. Ice on Earth's poles doesn't have salt in it does it?
Would ice on Europa be salt water ice? Or just plain water ice?
OY!
Either way, if I could figure out how much a 1 inch square x 90 mile high column of ice (salt or pure water) would weigh on Europa, that'd be the water pressure at the "surface" of the ocean just under the ice.

But to figure out what pressures would be at the bottom of that ocean, I'd still have to know how deep it is, and I don't know that, (Does anyone? At least more or less?)

The pressure at the bottom of the ocean would be the weight (on Europa) of the 1 inch square x 90 mile column of ice + the weight of a 1 inch square x depth of the ocean column of SALT water, again, with both weights calculated with an average value of local gee over the height of the column?

OY YOY YOY!

As for what temperatures'd be, cripes, I've got no idea at all how that could be calculated.

 

[MonstersFromTheId]

More thoughts.

I'm not sure that the pressure just under the ice actually WOULD be equal to the ice piled over the water.
The ice shell is 90 miles thick. Again, that's a LOT of ice. And it's a shell, a sphere, with no edges of an "ice pack" to allow sideways pressures to be released in any way.
How do I know that quite a bit of that weight isn't supported by the sphereical shell acting as a kind of self supporting continiuos arch?
For all I know, if something like that were true, it's even concievable that the water pressure just below the ice is nearly ZIP.
Picture a ball of ice with a vacuum in the middle.
Not that I think there's a vacuum under Europa's ice shell, but think about it. As water freezes to ice it expands. Side to side expansion might force the ice "up" like stickin an extra brick into a arch.

This might not be as simple a question as I initially thought.

 

[Nereid]

Hi Monsters.

I do apologise for overlooking this thread and leaving it alone for so long.

Let's do some OOM (order of magnitude - a.k.a. back of the envelope) stuff, shall we? The great thing about this is we don't have to be too careful to 'get it all right', but we should be able to go through it a second time and get a lot closer, with just some tweaking.

Imagine a rigid tower, full of water. Assume the tower has a perfectly square cross-section (or circular, take your pick), is made of utterly rigid sides (which have no weight), and there are no 'floors' - it's water from ground to top. Assume too that it's perfectly 'vertical'.

The pressure on something at the bottom of the tower will be just the weight of all the water in the tower, right? So, how do you calculate the weight of water in a tower, 1 cm in cross-section, 10 km high? (Assume gravity doesn't change from bottom to top - remember, we're doing OOM)

What if the tower were full of ice, instead of water (assume it's cold enough so the ice doesn't melt under the pressure)?

So far all I've done is pace your thinking. The OOM part says "let's not worry about the differences in the density of water, by temperature or pressure, nor ice" Go for 1 gram per cc.

But we're talking Europa, not Earth, right? OK, so g (9.8 m/s²) comes from Newton, right? (you remember? G with a couple of m's, and an r^2)?) So the surface gravity on Europa can be worked out (OOM, remember?) from its mass, radius and G, right? Nine Planets (the website) gives 1565 km and 4.8x10²² kg.

So, a 90 mile layer of ice will certainly contain a not insigificant %-age of the total mass of Europa, but if we assume it's '1g/cc' all the way down, then it's easy to estimate (OOM) what %-age, right? And get an idea of how much g_Europa will differ, 90 miles down, from g_Europa on the surface, right?

The temperature/ice vs water bit is trickier. We could start with pure water - you've no doubt seen those phase diagrams, right? There are lines which show where the boundary between gas, liquid and solid occur (assuming equilibrium) and have the magic 'triple point'. From your estimates of the pressure at the bottom of 90 miles of Europan ice, what would the temperature need to be for (pure) water to be in equilbrium there?

{note to all other readers - how about you help Monsters out? Google up an answer or twenty to his/her question on the depth of the Europan ocean, hey?}