Earth is mostly covered in oceans, but they only go a few kilometres deep. It's obviously not possible to have a planet the size of the earth to be made entirely out of water, because of the kind of pressures reached in the interior.

a. But say that we did, how far down from the surface would water remain water before presumably turning to ice under the pressure?

b. How large a 'planet' could we have made entirely out of water? Would it be able to attain the size of a small dwarf planet like Ceres?

  • $\begingroup$ Related (but not a duplicate): Does water turn solid under deep ocean because of high pressure? $\endgroup$ – John Rennie Jan 17 '19 at 18:10
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    $\begingroup$ I think maybe you should clarify - at least I think ice is a form of water. So you mean water = 'liquid water' $\endgroup$ – Stefan Jan 17 '19 at 18:39
  • $\begingroup$ @stefan: I'm not sure what you mean by clarify. The conventional sens of water is liquid water as you yourself acknowledge. What is it you want clarifying? $\endgroup$ – Mozibur Ullah Jan 17 '19 at 18:41
  • $\begingroup$ Ok, it might be a language thing. In my perception water can be solid, liquid or gas, but it might not be the standard way to see this. $\endgroup$ – Stefan Jan 17 '19 at 18:45
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    $\begingroup$ I deleted some slightly inappropriate comments and their responses. $\endgroup$ – David Z Jan 17 '19 at 21:29

Suppose we assemble a large mass of water in space, then it will form a sphere held together by its gravitational field. The question is then how large this sphere can become before the pressure at the centre causes the water to solidify to ice.

The calculation of the pressure at the centre is straightforward in principle, and is described in How to find the force of the compression at the core of a planet? The problem is that to do the calculation precisely we need to know how the density of water changes with pressure. There is no simple equation for this so we would need to do a numerical calculation. However if we make the approximation that the density of the water remains constant we can get an approximate equation for the pressure:

$$ P = \frac{2}{3}\pi G \rho ^2 R^2 \tag{1} $$

We can estimate the pressure at which water solidifies by looking at the phase diagram of water. The following phase diagram comes from London South Bank University web site:

Water phase diagram

The pressure at which the water solidifies to ice is strongly temperature dependent. At everyday temperatures it's around 800MPa to a GPa, and since this is an approximate calculation let's take a GPa as being a round number. Then using equation (1) we find that value of the radius $R$ for which the pressure reaches 1GPa is about 2700km.

So there's your answer. A ball of water at room temperature larger than 2700km would contain a solid ice core. In practice the density of the water increases with depth so the radius at which ice forms would be less than this. Though the relative density of ice VI is only around $1.3$ so it wouldn't be that much smaller.

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  • $\begingroup$ Whilst I agree about the principles of the calculation, you cannot assume the central temperature is anywhere near the values on your plot. $\endgroup$ – Rob Jeffries Jan 19 '19 at 10:47
  • $\begingroup$ Why are there different shades of green in the plot? $\endgroup$ – gerrit Jan 23 '19 at 14:21
  • $\begingroup$ Your planet also needs an atmosphere for the surface water to be liquid, an atmosphere consisting entirely of water vapour... except that UV radiation will cause photodissociation, and then hydrogen will escape by Jeans escape or be stripped away by the solar wind, resulting in an increase in oxygen, and the planet wlil no longer consist entirely of liquid water. $\endgroup$ – gerrit Jan 23 '19 at 14:24

The related question points out that water would become ice at a depth of around sixty km. This answers the first question. And this suggests we should expect a body of water a 120km in diameter to remain water all the way through. This is far smaller than a dwarf planet and more the size of a large asteroid.

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  • $\begingroup$ And would rapidly disappear through loss of water vapor since the atmospheric pressure possible would be essentially zero, and there is essentially no gravitational well to hold onto the water vapor. And it would have to be kept warm to keep it liquid given the enthalpy of vaporization. $\endgroup$ – Jon Custer Jan 17 '19 at 19:57
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    $\begingroup$ I'm afraid this is wrong. 60km depth of water is enough pressure to form ice in Earth's gravitational field i.e. at 1g. But a 60km radius ball of water would have a much smaller gravitational field so the pressure at its centre would be much lower. $\endgroup$ – John Rennie Jan 17 '19 at 19:58
  • $\begingroup$ @John Rennie: That makes sense to me. I guess that related question wasn't so related after all and made me slip up here. $\endgroup$ – Mozibur Ullah Jan 17 '19 at 20:00
  • $\begingroup$ @jon Custer: Yeah, I suppose thats why we don't see too many water asteriods, dwarf planets and planets! $\endgroup$ – Mozibur Ullah Jan 17 '19 at 20:01
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    $\begingroup$ @my2cts - Of course, even ultra-pure water is not transparent on the km scale, so it would indeed be visible. $\endgroup$ – Jon Custer Jan 17 '19 at 22:45

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