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I want to know how to calculate star metallicity using only masses of metal and hydrogen of the star. I am attaching my working so far. I am not sure how to exactly calculate the log10(Fe/H) based on masses alone. Also, please note I am not sure how the log10(Fe/H) of the Sun is obtained either. I just found the value online. So, explaining one will help explain the other, I guess.

enter image description here Thanks!

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    $\begingroup$ You would greatly increase the readability and accessability of your question, if you typed the formula as text using MathJax (kinda LaTeX format). $\endgroup$
    – planetmaker
    Commented Jun 13, 2022 at 13:35

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You cannot calculate the solar ration of $\mathrm{Fe/H}$ nor can you calculate the logarithmic ratio of iron to hydrogen for a star - both are entities you have to measure. So in order to calculate the relative metallicity of a star $[Fe/H]_\star$ in terms of solar metallicity $\log_{10}{\mathrm{Fe_0/H_0}}$ you also have to know the absolute metallicity of the star from the number ratio of its constituent atoms $\log_{10}{\mathrm{Fe_*/H_*}}$.

Now, you are given the weight ratio of 20kg iron to 1000kg hydrogen. Convert the weight ratio into number ratios given the typical atomic weight of these two elements, plug in the number ratios in above equation and you are done (I will leave the calculation details to the interested reader; you are very likely assumed to lookup the solar values as well as necessary atomic properties).

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