system
Given the following post, respond as if you're commenting on Reddit:
human
Could there exist a planet made completely out of water?
gpt
*Liquid* water? No.

To keep water a liquid requires a few constraints: 

1. The pressure has to be high enough to keep it from all evaporating. This generally requires an atmosphere to keep pressures at least above 1 kPa (1/100th sea level pressure), though a fair bit higher to maintain a reasonable range of temperatures where water remains a liquid. We could imagine our proposed water planet evaporates enough water vapor off the surface of the ocean to maintain a water vapor atmosphere to prevent this.

2. The pressure has to be low enough to keep it all from freezing. This requires that, at depth in the ocean, the pressure climbs no higher than about 2 GPa (20,000x sea level pressure), or else we start forming exotic crystal structures of ice, even at high temperatures.

3. We need the right temperature, but let's assume we can play with the planet's position to maintain the right distance from its star.

Suddenly we find ourselves playing a very careful balancing game here: if our planet is too large, then the lower layers will have a pressure that's too high and start freezing. On the other hand, if our planet is too small then there won't be enough gravity to hold on to the water vapor atmosphere, and the whole thing will just evaporate out into space.

So let's start crafting this planet...we want to start by defining the escape velocity, which we'll do by first considering the average velocity of a water molecule at room temperature:

v = sqrt(2kT / m)

v = sqrt[2 * 1.38x10^-23 * 293 / (18 * 1.66x10^(-27))]

v = 520 m/s

That's pretty fast - about 1000 mph - so let's make sure our planet has a high enough escape velocity to prevent a molecule moving that quickly from escaping our planet. In truth, we want an escape velocity quite a bit higher than that since 520 m/s is only the *average* molecular velocity - other molecules could be moving quite a bit quicker. Let's say 8x that so our planet will at least stick around for a while. (By comparison, Earth's escape velocity is about 8x hydrogen's mean velocity, and while we do leak hydrogen into space, we can hold onto it on million year time scales.) The equation for escape velocity is:

v = sqrt(2GM / r)

We know we want v = 8 * 520 = 4160 m/s, and since our planet is liquid water which is pretty incompressible, the density = 1000 kg/m^(3), defining the relationship between mass and radius as just:

M = 1000 * 4/3 Pi r^3

r = (3M / 4000Pi)^1/3

We plug that back into our escape velocity to find:

4160 m/s = sqrt(2 GM / r)

= sqrt[2 GM / (3M/4000Pi)^(1/3)]

= sqrt[2(4000/3 Pi)^1/3 G M^(2/3)]

M = (4160 / sqrt[2(4000/3 Pi)^1/3 G])^3

M = 7.22 x 10^23 kg

...and plugging back into our radius equation...

r = (3 * 7.22 x 10^23 / 4000Pi)^1/3

r = 5560 km

That's big, but not too ridiculous...a bit smaller than Earth in terms of radius, but about 8x lighter in terms of mass, which makes sense when you consider this planet is much less dense.

So what's the central pressure of this planet? Well, to first order we can use the following equation (though a more thorough treatment would use an integral):

P = G * M * density / r

P = 6.67 x 10^-11 * 7.22 x 10^23 * 1000 / 5.56 x 10^6

P = 8.66 GPa

...or about 80,000x sea level pressure, which is already well above the freezing point of water at extreme pressures. In other words, this thing has to have an ice core.

**TL;DR**: In order to have a liquid water planet large enough that it doesn't evaporate away into space in less than a million years, the core must have a pressure high enough to become ice.