# How does gravity affect pressure under water?

How different would being under water in Europa differ from being under water on Earth? Would it be possible to dive deeper on Europa with a submarine than on Earth and by how much?

• In order to answer this you'd need to know the density of Europa's oceans, which I don't believe anyone knows. Water pressure is created by the weight of the column of water above the depth in question, and this is directly related to its density. But if one assumes the density to be about equal to Earth's oceans, then the diving depth would simply be the ratio of Earth's and Europa's gravity (Earth = 9.78, Europa = 1.314). – BillDOe Nov 28 '18 at 21:39
• @BillDOe How compressible do you think water is? – ProfRob Nov 28 '18 at 22:17
• @BillDOe Why do you think there would be a meaningful difference in density? (Obviously, if you get deep enough you'll start seeing effects but long before you get appreciable compression you'll get phase changes.) – Loren Pechtel Nov 29 '18 at 4:49
• I was thinking about dissolved solids in Europa's oceans possibly increasing the water's density and therefore weight, not the compressibility of water. Ocean water on Earth, for instance, is more dense that fresh water. – BillDOe Nov 29 '18 at 20:15

For a liquid, hydrostatic pressure is $$\rho g h$$ where $$\rho$$ is density (this is always the same for all water) g is gravitational acceleration and h is depth.

The gravitational acceleration on Europa is 1.3 $$\text{m/s}{}^2$$ (compared with 9.8 $$\text{m/s}{}^2$$ on Earth). But on Europa there is 20km of ice floating on the water.

As a rough estimate, the gravity in Europa is 1/10 that on Earth, so the pressure at the bottom of the ice/top of the water would be comparable to the pressure at 2km in the Earth's Oceans.

Since we can build submarines that can operate at 10km, we could reasonably suppose that we could operate submarines down to about 100km on Europa, which takes us to the rocky surface. However we have no way to pass through 20km of ice crust to reach the water layer. Building the submarine may be the easy part!

• A hot submarine could melt its way through, a bit like a dark stone on a glacier ;-) – Chappo Hasn't Forgotten Monica Nov 29 '18 at 0:03
• Nice answer. Is 20 km of ice a pretty good estimate? I thought it was a lot less certain. – userLTK Nov 29 '18 at 1:28
• @Chappo Yup. Put a nuclear reactor (not merely a RTG) on board, melt your way down. – Loren Pechtel Nov 29 '18 at 4:50
• To be fair, the density does change due to pressure and impurities - the difference is small, but whether it's negligible depends on what you're trying to calculate. In this case, it's definitely dwarfed by the difference in gravity and the ice layer, though (unless there's something very weird about Europa's oceans, which is a distant possibility). – Luaan Nov 29 '18 at 7:46
• what kind of radio or other communication device is needed to transmit through 20km of water ice? – Alonda Dec 1 '18 at 18:08