Which is denser? And what about, say, density of galaxies in the universe vs. atomic nuclei in your body?
Almost certainly the density of the nuclei in your body. The number of atoms in your body is probably within a few orders of magnitude of Avogadro’s number (~10[sup]23[/sup]), while the number of stars in the Milky Way is “only” around 10[sup]11[/sup] or so. The volume of your body is obviously much smaller than the Milky Way. In other words, your body contains zillions of times more objects in a volume that’s skillions of times smaller, so its density (in terms of objects per volume) will be bajillions of times higher.
ETA: The number of galaxies in the observable Universe is also on the order of 10[sup]11[/sup], so the same kind of logic applies in that case.
Here are some rough orders of magnitudes for volumes I found with a quick search, all in m^3:
Hydrogen nucleus: 10^-33
Human body: 1
Sun: 10^27
Galaxy: 10^61
Observable universe: 10^80
So a human is ~10^33 times larger than a hydrogen nucleus, a galaxy is ~10^34 times larger than a star, and the observable universe is only 10^19 times larger than a galaxy.
Oops, that wasn’t actually what the OP was asking for.
There’s about 10^27 atoms in a human body, and if I use the 10^11 figures MikeS gave:
10^27 * 10^-33 / 1 = 10^-6 atoms per unit volume in a human
10^11 * 10^61 / 10^80 = 10^-8 galaxies per unit volume in the universe.
So if we scaled an atom to the size of a galaxy, a human would be roughly 2 orders of magnitudes denser than the universe.
A neutron star would seem to be denser at first though.
Careful there — you’re computing the fraction of the volume occupied by the objects (e.g., total volume of nuclei divided by volume of human body), rather than the number per unit volume (e.g., number of nuclei per unit volume.) If you’re interested in the latter figure (which I think the OP was), then you need to leave out the 10[sup]-33[/sup] in the first equation and the 10[sup]61[/sup] in the second. Obviously, this will substantially affect your numbers.
Yes the OP is badly worded. Clearly the human body is a lot denser than the galaxy which is mostly empty space. I think the question might be if we expanded the human body to the size of the galaxy, would the average distance between atoms be smaller or larger than the average distance between stars.
Of course the human body is much more uniform in density than a galaxy so the average distance between neighboring atoms in a human body is more nearly constant than the average distance between stars in a galaxy.
Yeah you’re right, I didn’t think through my calculations enough so the ones on my second post can safely be ignored. I’m not sure that the number of objects per volume is what the OP was looking for, though, unless it was in which case a human has about 10^96 times more atoms per volume than the universe has galaxies.
There would be 10^16 times more atoms in a human body than stars in a galaxy, so I would expect the average distance would be similarly higher.
But on the other hand if we expanded an atomic nucleus to the size of a star (a 10^60 fold increase), then a human similarly scaled would be about a tenth the size of a galaxy.
I don’t think the OP was asking that, because that’s trivial. There are umpteenillion atomic nuclei per cubic centimeter in your body, but only an umpteenillionth of a star per cubic centimeter in the Galaxy.
If the OP meant for the volumes to scale as well, then we have to first decide how we’re scaling the volumes, and there are many reasonable ways to do that.
This is a helpful way to picture it, thanks.