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Planet of Only H2O: Continued

by Wolfman29
Tags: continued, planet
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Wolfman29
#1
Jan5-13, 10:48 PM
P: 10
Hey everyone. I am a lurker here, and I have posted once, I think; however, I literally stumbled upon a very interesting question posed here: http://www.physicsforums.com/showthread.php?t=174274/

Anyway, I decided to see if I could expand upon and get a more "exact" solution for this problem.

The first problem I encountered in my research was the several different types of ices, their density, and how the pressure/temperature is related to it. The point in my work at the moment is one in which I have a fairly good piecewise representation describing the density of the H2O at various pressures and temperatures. Because I am working under the assumption that I want the surface of my planet to be approximately 17 degrees C, I am using only Ice VI, Ice VII, Ice X, and Ice XI (even though Ice XI may be unnecessary - come on, we aren't in the TPa range here).

The problems I am encountering in making my model more accurate for the density of H2O are the following:

How do pressure, temperature, and density, affect liquid water, explicitly? I have a model that I am currently using that seems to make some sense at lower temperatures (between 0-200 degrees or so), however, after a certain point, because my function describing density is dependent solely on pressure, I am getting ridiculously high densities for water, which would not be the case, because said properties of water are only in under high pressure, and therefore high temperature, water, which we all know would have a lower density than if it only depended on pressure.

There seems to be little research on the nature of the more unusual crystalline ice structures: how do their densities change with pressure and temperature? Is the transition between two structures instantaneous or is it more gradual, and if it is gradual, over what range does the transition occur?

I will edit when I come up with more progress, if I come up with my progress.

My goal is to see what a model of this planet would look like. Would it have an Ice X core, with an Ice VI/Ice VII mantle, followed by a liquid water crust? How thick would the atmosphere have to be? How massive must the planet be in order to stay together, given the varying masses throughout the planet? What would be the temperature of this planet's core?

I hope you guys can help me out with this, it is making for an interesting pursuit!
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Wolfman29
#2
Jan11-13, 09:14 PM
P: 10
So I may have been getting somewhere with this - a friend of mine is a TA for a graduate student who is doing his doctoral research on water under high pressures/temperatures, so he may be able to help me. But I would prefer a second opinion! :D
Whovian
#3
Jan11-13, 09:58 PM
P: 642
I'm no expert, but I can make a guess based on the fact that, in deep bits of the ocean, there's liquid water below freezing due to enormous pressure.

Due to the coldness and low pressure of space, the surface should be made of ice. Since it's pure water, any atmosphere can't exist. As we get deeper, pressure increases, and so, if the planet is large enough and the planet has some temperature, the pressure will eventually be large enough to force the water into ice. I don't know what'll happen as t->∞, but, again, I'll have a guess that it'll keep cooling closer and closer to absolute zero (as will space,) and as such the planet will eventually turn into solid ice, and eventually, later, go into bizarre matter states such as superfluidity.

Note that (guessing again) large enough planets of water can't exist, even ignoring the mass from space that can accumulate on them, since a large enough planet will eventually have enough pressure to sustain nuclear fusion, and thus different elements and molecules will arise in it.

Again, this is just a guess and more qualitative than quantitative, but I hope this helps a little! Anyone, feel free to correct me, I'm sure there are hundreds of errors in this post.

Wolfman29
#4
Jan11-13, 10:07 PM
P: 10
Planet of Only H2O: Continued

Well, you forget that we can have a water vapor atmosphere! That will protect the water/surface from the vacuum of space. I am assuming that it will have an H2O atmosphere due to evaporation/sublimation. That will be my next project - I will figure that out after I figure out the liquid/solid part.

I *think* that you could have a planet of water, considering you can have a planet of gas.

However, thanks for the post. Was helpful.
Borek
#5
Jan12-13, 02:58 AM
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Saturated vapor pressure over the solid ice surface is at best that of a triple point, 612 Pa - or 0.006% of the atmospheric pressure on Earth. In a lab setting that already classifies as a low vacuum.
0xDEADBEEF
#6
Jan12-13, 08:40 AM
P: 824
Water is not very compressible. On another forum I found a formula for the pressure dependence of liquid planets http://lofi.forum.physorg.com/Planet...pth_27621.html It seems to be a standard problem in Astronomy.

All liquids turn solid if enough pressure is applied. Water has the unusual property to expand when forming Ice I (normal ice) therefore it can turn liquid again when pressure is applied. At very high pressures water will always turn solid (again). When compressed enough at constant temperature water will turn into Ice VI or Ice VII (for most cases). At higher pressures it will then turn into Ice X and later Ice XI. http://en.wikipedia.org/wiki/Ice#Phases

From the first link I would think that water planets with a radius above 3000 km will have a solid ice core.
Wolfman29
#7
Jan12-13, 02:26 PM
P: 10
@Borek - why couldn't it be over a liquid water surface? Wouldn't that allow for higher air pressures, i.e. at least significantly higher than the triple point?

@0xDEADBEE - I think they are just using standard pressure formulae, without recognizing that water is compressable, the same problem I am running into; however, I may look into assuming it isn't compressable and then just fudging the numbers, assuming slightly higher density as depth increases.
Borek
#8
Jan12-13, 03:16 PM
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For a liquid water you need temperature above 0C. Even then the pressure starts quite low (after all, it starts with the triple point pressure).
Wolfman29
#9
Jan12-13, 03:30 PM
P: 10
Yes - I am assuming a surface temperature of about 20 degrees.
0xDEADBEEF
#10
Jan12-13, 07:41 PM
P: 824
You get about 2% compression at 50 MPa that really isn't all that much, unless you really want to go to the limit where the planet will have a solid core. And I don't know if there are even measurements for the density or the bulk modulus at these pressures. I imagine it is already hard enough creating those pressures in the lab.
Wolfman29
#11
Jan13-13, 02:20 AM
P: 10
I do plan on going to the limit where the planet will have a solid core. I just did a quick calculation, and for a 3000km radius planet, we are looking at more than 1 GPa at the core, assuming constant density
Borek
#12
Jan13-13, 03:38 AM
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Quote Quote by Wolfman29 View Post
Yes - I am assuming a surface temperature of about 20 degrees.
Question is whether the atmosphere made solely of water vapor at this temperature will be high enough to provide insulation. As I understand it (I can be wrong though) in the Earth atmosphere the layers radiating into space are those cold, high layers. As they are cold, they radiate relatively slowly, and the layers below isolate them from the warmer Earth surface. In effect the process of radiation cooling is slower than what you would expect from the average temperature of the Earth surface. Having only water in the atmosphere you will be not able to reproduce this situation, and the radiative loses will be much higher, making it difficult to maintain warm surface.
Wolfman29
#13
Jan13-13, 10:34 AM
P: 10
Hmm. Interesting. I suppose this would require doing the math to calculate the thickness of the planet. This model is getting significantly more complex than I predicted, significantly more quickly. I wonder if there are any greenhouse effect models for this kind of situation out there?
Rap
#14
Jan13-13, 01:47 PM
P: 789
Quote Quote by Wolfman29 View Post
Hmm. Interesting. I suppose this would require doing the math to calculate the thickness of the planet. This model is getting significantly more complex than I predicted, significantly more quickly. I wonder if there are any greenhouse effect models for this kind of situation out there?
Is there a reason you cant have a solid iron planet with an ocean of water? Or is the planet being entirely water a necessary part of the problem?
Wolfman29
#15
Jan13-13, 05:16 PM
P: 10
Ideally, the planet would be entirely water. That's the hypothesis. With an iron core, we can have internal heating, no unusual forms of ice, etc. That's probably a fairly easy problem to solve.
Rap
#16
Jan13-13, 08:28 PM
P: 789
Quote Quote by Wolfman29 View Post
Ideally, the planet would be entirely water. That's the hypothesis. With an iron core, we can have internal heating, no unusual forms of ice, etc. That's probably a fairly easy problem to solve.
Ok, I thought maybe it was a very simple model of earth. Where would internal heating come from?
Wolfman29
#17
Jan13-13, 11:06 PM
P: 10
Actually, I am working on a model with no internal heating. I would just place it close enough to its sun to keep it at a constant temperature.
Mordred
#18
Jan13-13, 11:50 PM
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Cant help you much on this one even though Europa is covered in ice it may provide some directions.


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