### How many earths fit in the observable universe?

• I was pondering our insignificance, when I wondered - how much smaller is our planet then the (observable) universe? And being as I don't know how to do the math, I'm asking it here.

So how many of our planet (in space it occupies - i.e. ignoring space between the space between the spheres) can fit inside the known/observable universe?

Really to me this question is pointless. I mean, the answer is obviously going to be a ridiculously big number, so what does it changes to you if it is 10^50 or 10^100??

i was trying to find something to compare it to, in order to better understand it and relay it.

• Gerald Correct answer

8 years ago

Without checking the numbers in detail, according to Wikipedia, the volume of the observable universe is about $3.5\cdot 10^{80} \mbox{ m}^3$, and the volume of Earth is about
$1.08321\cdot 10^{21} \mbox{ m}^3$.

By dividing the two volumes we get a factor of $3.2\cdot 10^{59}$, or written as decimal number: The observable comoving volume of the universe is about
320,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000-times the volume of Earth.

dats alot, woah!

Your answer assumes we are pulverizing the earth to *completely* fill the volume of a universe-sized container. Without getting into the complicated math behind forming optimal latices of congruent spheres, you should multiply your answer by a factor of pi/(3*sqrt(2)) or about 0.74048. The Kepler Conjecture says that is the highest density that can be achieved by any arrangement of spheres. Oh, and since the observable universe is also expanding at an accelerated rate, you should also update your answer every few hundred millions years just to be safe. Just saying.

@RobertCartaino That's why I just provided two valid digits; so the numbers should be valid more or less next week, too. ;) Btw. sorry for pressing Earth into a cube, next time I'll be more careful.

That's about the same as the number of atoms in the largest stars.

@SteveLinton So the Earth is to the universe as an atom is to a very large star.

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Content dated before 7/24/2021 11:53 AM

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