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Robert Walker

Right, using that phase diagram:

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).

It would evaporate quickly though. I make it that a planet of water the size of Ganymede would evaporate away entirely probably within a few tens of millions of years. But it could slow down a lot if covered in a thin layer of organics as seems quite likely.

More on all this in my answer to: Do water planets exist?

About the Author

Robert Walker

Robert Walker

Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.
Studied at Wolfson College, Oxford
Lives in Isle of Mull
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