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.

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    $\begingroup$ See astronomy.stackexchange.com/questions/13112/… but @anders answer below is much better than those there. $\endgroup$
    – James K
    Mar 30 '21 at 9:47
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    $\begingroup$ 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. $\endgroup$ Apr 6 '21 at 3:15

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.


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