<p>@anders answer below is <em>not</em> better. The solar-wind water accumulated primarily in the building blocks that became Earth, then to an extent the pre- and primordial-atmosphere’d Earth. The pebbles/boulders/planetesimals had, collectively, far greater surface area.</p>
<p>Still, we can’t literally answer the question, because much of this water is now hydrides, locked in the iron of the core, plus more locked in the minerals below the transition zone. We have poor constraints on these mineral compositions, much less the dissolved ions they carry. Even above the transition zone, we have only constrained the water level by its geoelectric implications, and its implications on tectonics (impurities will soften rock).</p>
<p>Figures for mantle water vary from, I’ve seen, one ocean (that is, 1x Earth’s visible, surface seas) to eleven ocean. A year or two ago, a paper posited that the evidence so far gives ~1 ocean in the core.</p>

CC BY-SA 4.0
2022-08-18T21:36:43.523Z
Indeed! The assumption that majority of captured hydrogen is in the ocean may not be correct.
ZAB
CC BY-SA 4.0
2022-08-19T06:25:22.780Z
This answer doesn't answer the question, merely point out that any answer is going to be uncertain. If you think there are X times the surface water inside earth and the hydrogen from the sun is equidistributed, then it just means that the fraction of solar hydrogen in the cup is 1/(1+X) of what it otherwise would have been. This does not change the order of magnitude, presumably.
Anders Sandberg
CC BY-SA 4.0
2022-08-01T22:48:26.460Z
2022-08-01T22:48:26.460Z
caInstrument
<p>Here is a way of getting a rough upper bound: the density <span class="math-container">$\rho$</span> of the solar wind is about 4 atoms per cm<span class="math-container">$^3$</span> (that we can assume are hydrogen), and it travels at <span class="math-container">$v=400-500$</span> km/s. That means that were the Earth to catch every atom directed at it it would gain <span class="math-container">$\pi R_\oplus^2 \rho v$</span> atoms per second, <span class="math-container">$2.0$</span> to <span class="math-container">$2.5\cdot10^{14}$</span>. Which gives us a mass flow of <span class="math-container">$3.4$</span> to <span class="math-container">$4.3\cdot 10^{-13}$</span> kg/s. Earth has been around for 4.5 billion years, so over that time at most about 49 to 61 tons of hydrogen have arrived.</p>
<p>The total amount of liquid water on Earth is <span class="math-container">$V=1.386\cdot 10^9$</span> km<span class="math-container">$^3$</span> (which doesn't count the sizeable amount of water bound in rocks). About 11.19% of this mass is hydrogen, so the weight of hydrogen is <span class="math-container">$0.1119 V\rho_{water}=1.55\cdot 10^{20}$</span> kg. So the ratio between hydrogen from Earth and from the sun is about <span class="math-container">$2$</span> or <span class="math-container">$3\cdot 10^{15}$</span>.</p>
<p>Still, in a half liter (about 27.7 mol water) there are <span class="math-container">$3.33\cdot 10^{25}$</span> hydrogen atoms, so there should be about 11 to 16 billion solar hydrogen atoms in the cup if this estimate is right.</p>
<p>Maybe Earth's magnetic field captures more atoms, which might increase the value. Likely most solar wind is instead pushed away and the true value is much lower. But I am pretty confident there are <em>some</em> solar atoms in the cup.</p>

CC BY-SA 4.0
2022-08-18T21:47:53.980Z
@caInstrument below raised an interesting point. We need also estimate how much of that captured hydrogen is now in the ocean. Some of it could have been deposited in crust and even deeper layers of the Earth.
ZAB
CC BY-SA 4.0
2021-03-30T09:00:33.537Z
2021-03-30T09:00:33.537Z
Anders Sandberg
<p>A great fraction of solar wind is protons or Hydrogen ions. Some part of it is captured by Earth. I am wondering how much water in my half a liter cup is made of hydrogen from the Sun.</p>

CC BY-SA 4.0
2021-03-30T09:47:07.440Z
See https://astronomy.stackexchange.com/questions/13112/is-solar-wind-a-source-of-water?rq=1 but @anders answer below is much better than those there.
James K
CC BY-SA 4.0
2021-04-06T03:15:24.497Z
This question and the one @JamesK refers to are close enough to be duplicates of each other. As this one has the best answer, I've voted to close the other as a duplicate of this one.
Chappo Hasn't Forgotten
<the-sun><solar-wind>
How much water on the earth is made from hydrogen comes with solar wind?
ZAB
# How much water on the earth is made from hydrogen comes with solar wind?

(Asked by: username_0 on 2021-03-30)

A great fraction of solar wind is protons or Hydrogen ions. Some part of it is captured by Earth. I am wondering how much water in my half a liter cup is made of hydrogen from the Sun.

**Tags:** the-sun, solar-wind
> **Comments:**
> **username_1**: See https://astronomy.stackexchange.com/questions/13112/is-solar-wind-a-source-of-water?rq=1 but @anders answer below is much better than those there.  
> **username_2**: This question and the one @JamesK refers to are close enough to be duplicates of each other. As this one has the best answer, I've voted to close the other as a duplicate of this one.  

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## 2 answers

### Answer by username_4 on 2021-03-30. Score: 16 | Accepted answer

Here is a way of getting a rough upper bound: the density $\rho$ of the solar wind is about 4 atoms per cm$^3$ (that we can assume are hydrogen), and it travels at $v=400-500$ km/s. That means that were the Earth to catch every atom directed at it it would gain $\pi R\_\oplus^2 \rho v$ atoms per second, $2.0$ to $2.5\cdot10^{14}$. Which gives us a mass flow of $3.4$ to $4.3\cdot 10^{-13}$ kg/s. Earth has been around for 4.5 billion years, so over that time at most about 49 to 61 tons of hydrogen have arrived.

The total amount of liquid water on Earth is $V=1.386\cdot 10^9$ km$^3$ (which doesn't count the sizeable amount of water bound in rocks). About 11.19% of this mass is hydrogen, so the weight of hydrogen is $0.1119 V\rho\_{water}=1.55\cdot 10^{20}$ kg. So the ratio between hydrogen from Earth and from the sun is about $2$ or $3\cdot 10^{15}$.

Still, in a half liter (about 27.7 mol water) there are $3.33\cdot 10^{25}$ hydrogen atoms, so there should be about 11 to 16 billion solar hydrogen atoms in the cup if this estimate is right.

Maybe Earth's magnetic field captures more atoms, which might increase the value. Likely most solar wind is instead pushed away and the true value is much lower. But I am pretty confident there are *some* solar atoms in the cup.

> **Comments:**
> **username_0**: @caInstrument below raised an interesting point. We need also estimate how much of that captured hydrogen is now in the ocean. Some of it could have been deposited in crust and even deeper layers of the Earth.  

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### Answer by username_3 on 2022-08-01. Score: -1

@anders answer below is *not* better. The solar-wind water accumulated primarily in the building blocks that became Earth, then to an extent the pre- and primordial-atmosphere’d Earth. The pebbles/boulders/planetesimals had, collectively, far greater surface area.

Still, we can’t literally answer the question, because much of this water is now hydrides, locked in the iron of the core, plus more locked in the minerals below the transition zone. We have poor constraints on these mineral compositions, much less the dissolved ions they carry. Even above the transition zone, we have only constrained the water level by its geoelectric implications, and its implications on tectonics (impurities will soften rock).

Figures for mantle water vary from, I’ve seen, one ocean (that is, 1x Earth’s visible, surface seas) to eleven ocean. A year or two ago, a paper posited that the evidence so far gives ~1 ocean in the core.

> **Comments:**
> **username_0**: Indeed! The assumption that majority of captured hydrogen is in the ocean may not be correct.  
> **username_4**: This answer doesn't answer the question, merely point out that any answer is going to be uncertain. If you think there are X times the surface water inside earth and the hydrogen from the sun is equidistributed, then it just means that the fraction of solar hydrogen in the cup is 1/(1+X) of what it otherwise would have been. This does not change the order of magnitude, presumably.  

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