Assuming you mean a liquid ocean of water which beings sufficiently adapted could potentially swim all the way through, it would have to be small because water when compressed enough becomes ice - unless it has a hot core, which it might have soon after formation, or tidally heated.

So, the easiest case first, if you don’t need it to have enough gravity to hold an atmosphere, I don’t see why not. Basically you want a large comet, in an orbit which keeps it permanently liquid. We could create such a world artificially in our solar system with mega engineering by diverting a comet into just the right orbit around the Sun.

However, unless we add something extra to the picture, it wouldn’t last long. The problem is that water evaporates rapidly in a vacuum.

Calculation indented

With surface temperature of 273.15 °K (0 °C) and using the equation for mass loss of liquid water in a vacuum of

(pe/7.2) * sqrt (M/T) kg / m² / sec (equation 3.26 from Modern Vacuum Physics)

where M is the molar mass, 0.018 kg for water, T is the temperature in kelvin, pe is the vapour pressure, which for water at 0 °C (273.15 °K) is 611.3 Pa, (Vapour pressure of water at 0 °C), so putting all those into the formula we get:

(611.3/7.2) * sqrt(0.018/273.15) = 0.689 kg / m² / sec.

So you lose 24*60*60*0.689 or about 59.529 tons a day

Compare calculation results here: Modern Vacuum Physics where they use the vapour pressure for water at room temperature 295 K to calculate (2300/7.2) * sqrt(0.018/295) = 2.495 kg / m² / sec.

So at room temperature you lose 24*60*60*2.495 or about 215.6 tons a day

So you lose about 60 meters a day thickness of liquid water exposed to a vacuum, or about 21.9 kilometers thickness of water per year.

The rate of loss goes up if the temperature increases and at 295 K, or 22 C, it’s 215.6 meters per day and 78.7 km per year.

So, a liquid water comet would not last for long. That is unless you get a constant influx of other comets bringing more water to it.

LARGER PLANET WITH SIGNIFICANT GRAVITY

What if the object is large enough to retain liquid water for long periods of time?

That’s only possible if it has at least enough gravity to retain a significant amount of atmosphere, even if the atmosphere is just water vapour, or oxygen (after dissociation of the water by radiation).

But then - it will surely have a solid ice core. In that case, if the water is also salty, it might well have a “club sandwich” type pattern of alternating layers of ice and water as suggested for Ganymede, of various types of ice, with some of them “snowing upwards”

Images from: Possible 'Moonwich' of Ice and Oceans on Ganymede (Artist's Concept) and for paper, see Ganymede׳s internal structure including thermodynamics of magnesium sulfate oceans in contact with ice

But even Ganymede is not large enough to retain a permanent atmosphere to protect the surface layer of water if there is no returning flux of water and it just gets dissipated into the vacuum of space right away. Of course in practice it will build up a water vapour atmosphere, so we’ll get to that, but let’s see what the figures would be without that.

Its diameter is 5,268 km so if brought close enough to the Sun to have a permanently liquid surface layer, and if there was no atmosphere to protect it, it would vanish completely in 67 years.

It could build up a temporary atmosphere however, as the water evaporated. It’s gravity is similar to the Moon’s. Geoffrey Landis says here that the gravitational escape lifetime for the Moon is of the order of thousands of years for heavier gases like oxygen and nitrogen.

Air Pollution on the Moon

So, for a first rough calculation, just to get an order of magnitude type estimate, let’s suppose it warms up enough and the escape of water vapour is enough to build up an Earth pressure atmosphere. How much water would you need to build up an Earth pressure atmosphere of water vapour on Ganymede?

Its radius is 1,635 km. So surface area is 4×π×1,635^2 or 33,592,736 km². For an Earth pressure atmosphere we need (9.807/1.428)×10 tons per square meter, or around 68.676 tons per square meter, and multiply also by 10^6 for the number of square meters per square kilometer, that’s 33,592,736*10^6*68.676 tons or around 2.3×10^15 tons or 2.3 quadrillion tons.

It would take thousands of years to lose that atmosphere, and then it can be replenished from below. A water planet the size of Ganymede would have a mass of (4/3)*π*1,635,000^3 = 1.83*10^19. So assuming ten thousand years for an Earth pressure atmosphere to dissipate that makes it 10000*1.83*10^19/(2.3×10^15) or about eight million years. It would evaporate more quickly as it got smaller, and so less able to hold onto an atmosphere. But this is all very approximate anyway.

You’d need a more detailed calculation here to find out how much pressure of atmosphere it would actually build up through evaporation of the water. However, the mass loss would still be similar to the terraformed Moon even if it had a higher pressure atmosphere. So the amount of the atmospheric pressure it builds up doesn’t really matter much. So our rough calculation may be better than you’d think. The main thing to do is to replace that 10,000 years by a more exact figure for the gravitational escape time for water vapour for a moon this size with a reasonable pressure atmosphere.

It seems at least possible that a water planet the size of Ganymede could last for tens of millions of years. For millions of years anyway, while, surely it couldn’t last for billions of years.

ANOTHER SOLUTION - “DIRTY OCEAN” WITH ORGANICS

There is another solution though. If you are willing to do it artificially, you could cover the entire surface of a small comet with a low density liquid which also has a low evaporation pressure.

Indeed, comets are rich in organics anyway, so if you could bring a comet to just the right distance from the Sun, not too far, not too close, then as it melted, it would develop a layer of scum like that. And that might well be habitable too, with organics and an oxygen rich ocean too, due to similar processes to the ones that make Europa’s ocean oxygen rich.

Organics with a high evaporation rate would disappear leaving only those with a low evaporation rate, and perhaps solid layers as well.

If you have life there, the surface could be covered in algae

Brookmill Park: lake with algal bloom (C) Stephen Craven

Or if the water is very salty, haloarchaea

File:San Francisco Bay Salt Ponds.jpg

The algae right on the surface would die, but algae just below would be shielded from the vacuum and UV light by the dead layers above.

Or if it is constructed artificially, you can cover the surface with a low density ionic fluids. These are salts that melt at very low temperatures and then have very low rate f evaporation. So long as it is less dense than water it will float. Many ionic fluids are high density but some are lower density than water. These are examples, though I don’t know how well they would fare in a vacuum: Hydrophobic and low-density amino acid ionic liquids

So if you are okay with your planet being a tiny comet sized object, and your water can be a bit “dirty” with organics, which means it can also support life, I’d say yes, it does seem possible.

CONSTANT INFLUX OF COMETS

Another solution, without the layer of ionic liquids or similar, is to have a constant influx of comets to replenish the water. I can imagine some scenarios where that could work, e.g. soon after formation of a solar system. It also might work for a while later on in a white dwarf star with material brought into it through destruction of its Oort cloud and perturbing effects of an extra planet, see Our Solar System Could Lose One Or More Of Its Gas Giants Billions Of Years In The Future - and that would also help keep it hot. In a situation like that maybe even quite a large minor planet would stay hot enough to stay liquid all the way through.

So we have two ways to keep it liquid without it evaporating away to nothing in the vacuum of space even if it is quite small, too small to retain an atmosphere. So, how large can it be?

EXAMPLE OF EUROPA

Europa’s ocean may be as much as 100 km thick, with a surface layer 10 - 30 km thick.

Based on that, you could have a minor planet made of ice, 260 km in diameter, and consisting entirely of water, I think, with a surface layer of organic ionic fluids or a scum of organics in solid form floating on the surface. That could last for billions of years.

That makes it about the same size as 88 Thisbe

Vesta’s double that diameter

Vesta, Ceres and the Moon to scale at 20 km per px

I’m just using the figures for Europa and the depth of its subsurface ocean, which is kept liquid by tidal heating, and assuming the situation is similar - so this is just a rough estimate as it would depend on what you have by way of an energy source to keep your planet or moon warm.

Tidal heating could be a way to keep your planet liquid just as for Europa, so if you make it so that it orbits a hot Jupiter - those are planets like Jupiter that end up in orbits close to their sun, and they may well have liquid water moons.

Or put your planet close enough to its sun and you can have liquid water moons just because the surface is heated to above melting point and that would keep the whole moon at that temperature..

HOW LARGE CAN A PLANET BE AND CONSIST ENTIRELY OF WATER?

The problem with making a planet entirely of water is that if the water is compressed enough it turns into ice VI or ice VII no matter how hot it is, within reason.

Phase diagram by Cmglee, wikipedia. Ice outside of Earth can be in many different phases. For instance in the outer solar system it is often so cold that it is in the very hard orthorhombic phase, where it behaves more like rock than what we think of as ice. However ice on Mars is likely to be in the Ih phase similar to Earth life. The Mars surface is close to the triple point of solid / liquid / vapour in this diagram.

There the Ice VI (ice-six) triple point with liquid water and Ice V is at -0.16 °C, 632.4 MPa. So 632.4 MPa is as high pressure as you can get with liquid water at around 0 °C

That’s 6324 bars or the pressure at a depth of about 63.24 kilometers in a liquid ocean under Earth gravity.

Obviously a water planet smaller than Earth is going to have a lot less gravity than Earth. It’s tricky to work out the pressure at the center - it’s caused by all the layers above pressing down on it. The top layers of course contribute most pressure but all of them do right down to the central layers that have almost no effect. The maximum pressure is at the centre.

We want the maximum diameter of a planet with the pressure at the center low enough to remain liquid at various temperatures. I assume uniform density as water isn’t very compressible. Calculation indented:

The equation is here: How to find the force of the compression at the core of a planet?

P = (2/3) * π * G * ρ^2 * R^2

There using SI units, the density of water, ρ = 1000 kg / m3, Pascal is the SI unit for pressure, and meter is the SI unit for length.

There P for Ice V at -0.16 °C, is 632.4 MP = 632.4*10^6 Pascals

G = 6.674×10^−11 N⋅m² / kg²

Want to solve for R.

So R = sqrt ( 632.4*10^6 / ((2/3) * π * 6.674×10^−11*10^6 )) meters.

= 2,127,029 meters or around 2,127 km

Trying another figure from that table, 355 K or 81.85 °C, pressure of 2.216 gigapascals, then it’s

sqrt ( 2.216*10^9 / ((2/3) * π * 6.674×10^−11*10^6 )) meters.

or about 3,982 km.

So we can have an ice free planet of pure water with temperatures of -0.16 °C and radius of around 2,127 km and at temperature of 81.85 °C and radius of about 3,982 km.

That’s for fresh water. A salty ocean would stay liquid at lower temperatures and higher pressures.

Compare the diameter of our Moon of 3,474 km, so it seems you could have a planet that’s a bit larger than our Moon, entirely of water, and still be habitable for at least some microbes. Indeed Hyperthermophiles have optimal temperatures above 80 °C (176 °F).

SUMMARY

So, in short, I think this scenario could actually exist in nature, if you don’t mind having an ocean rich in organics, covered with a thin layer of organics, and make it a moon orbiting a gas giant rather than a planet on its own, to help keep it liquid through tidal heating, and make it perhaps around the size of 88 Thisbe

This is just a rough estimate. Would be interesting if someone was to do a paper on it - has anyone?

Would a liquid water world the size of Vesta or even Ceres be possible, with tidal heating to keep it warm? Can a hot Jupiter have a moon of pure ice? (I don’t see why not if it formed far enough away from its host star originally, but would be interesting to know how likely that is).

Alternatively, it could be possible if the world is kept hot and liquid by impacts of numerous comets - perhaps for quite some time in the early stages of formation of a solar system.

STACK EXCHANGE DISCUSSION AND STAR TREK VOYAGER EPISODE

See also stack exchange discussion here, where I’ve just added this answer (a copy of the original text which I wrote here)

Could a planet made completely of water exist?

The original question there is motivated by a story in Star Trek Voyager about a planet made entirely of water with the water prevented from escaping by a “containment field”

Thirty Days (episode)

Originally answered as Is it possible that a planet is entirely made of liquid much like Saturn and Jupiter are made entirely of gas?

(Don’t suggest a merge as “liquid” can be understood more generally as any liquid including liquid nitrogen, liquid helium etc)

Check out my book for more:

Simple Questions - Surprising Answers - In Astronomy,

It is a compilation of some of my quora answers, including this one.