I'm experiencing a mild fit of nerd-rage here and I'm hoping someone can help. I was watching a documentary and it made a claim I've heard a few times before: that a teaspoon of material from a neutron star would weigh 900 times the Giza pyramid. But according to most of the sources I'm seeing, the Giza pyramid weighs about 6 million tons, and a teaspoon of neutron star weighs about 10 million tons (though a few sites claim wildly different answers, including this question which claims 20 billion and this one claims a teaspoon weighs a billion tons). How goes 6 million x 900 = 10 million? I would expect the numbers to vary a bit but why are they so wildly different? What am I missing?
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$\begingroup$ Can you add the source where you got the 10 million tons figure from? $\endgroup$– probably_someoneCommented Dec 5, 2018 at 1:44
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2$\begingroup$ The variation probably comes from people not converting between SI and cgs units correctly. An average density for a neutron star would be about $5 \times 10^{17}$ kg/m$^3$. Choose your volume and calculate. $\endgroup$– ProfRobCommented Dec 5, 2018 at 7:20
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I'm not sure what resources you're using, but a teaspoon of neutron star material has a mass of quite a bit more than 10 million tons.
The density of neutron star material is roughly $4\times 10^{17}$ kg/m$^3$; this is the same order of magnitude as the typical density of an atomic nucleus, and is also what you'd get if you divided the neutron mass by the volume of a sphere of radius $1$ fm.
Multiplying this by $5$ cm$^3$ - approximately the volume of a teaspoon - yields a mass of $2 \times 10^{12}$ kg $= 2$ billion tons. Comparing this to the $6$ million tons estimate for the Great Pyramid gives us a ratio on the order of a few hundred.
