Interesting astro/phys question I'd like the naswer to

[ajm133]

I'm a normal adult male (abt 6ft tall, 180 pounds), if my density was that of the mean density of the universe, what would be my volume?

 

[mgb_phys]

It depends a little bit on what definition of universe (which is a whole more complicated question) but assuming the observable universe that is a sphere about 90Bn lyr in diameter and so has a volume of around 3 x 10 ^80 m^3.
It contains around 100Bn galaxies, each with a few 100Bn stars so 10^22 stars.
A star has a mass of around 2x10^30kg so the universe weighs about 10^52kg
So the density is about 10^(80-52) = 10^-28 kg/m^3 (assuming just stars ignoring dark matter etc)

If you weigh 80kg then at that density you would fill a volume of around 8x10^29m^3 or a radius around 10^10m = 10 million km. By comparison the Earth is only 150million km from the sun

edit thanks sylas - I hit sqrt instead of cube root!

 

[sylas]

I'm a normal adult male (abt 6ft tall, 180 pounds), if my density was that of the mean density of the universe, what would be my volume?

Roughly 8.3*10²⁷ cubic meters. (I'm using the mass density, including dark matter, which is about 27% of critical density.)

That's about the same as a sphere with a radius of 8 million kilometers.

Congratulations -- Sylas

 

[sylas]

Argh. We both made errors in the above. mgb_phys calculated the radius incorrectly, and I stuffed up some calculations. Let me try my method again, and show the working.

Critical density of the universe is about 10^-29 g/cm³, or in SI units, 10^-26 kg/m³.

In the current consensus model of cosmology, this is 27% matter and 73% dark energy. Most of the matter is "dark matter"; ordinary matter makes up about 4.5% of the total.

So the ordinary matter density is about 4.5*10^-28 kg/m³. That's about four times what mgb_phys estimates. There's a lot of matter in clouds of dust and hydrogen, which partially accounts for this, perhaps, and the masses of stars, and sizes of galaxies vary a lot.

Including dark matter, the total matter density is about 2.7*10^-27 kg/m³.

Thus 81 kg would fill out about 3 * 10²⁸ m³. If you ignore the dark matter, this becomes more like 1.8 * 10²⁹ m³.

The volume of a sphere is 4πR³/3, so the radius of the sphere with volume 3 * 10²⁸ m³ is about 2 million kilometers. That is how much volume you would take at the matter density of the universe.

Using just the ordinary matter density of the universe (the same stuff you are made of) your volume blows out to that of a sphere with radius about 3.5 million kilometers.

By comparison, the radius of the Earth is about 6400 kilometers, and the radius of the Sun is about 700,000 kilometers.

Cheers -- sylas