If the whole observable Universe is as big as planet Earth, how big would Earth be?

If the whole observable Universe is as big as planet Earth, how big would Earth be?

• Take a look at the other question that you asked about the relative size of earth and the milky way. Then look up the size of the observable universe. You will be able to show your understanding of that answer by doing the same calculations for the observable universe, and then you can write your own answer for this question. – James K Jan 27 at 8:39
• @JamesK I don't understand this math – larry909 Jan 27 at 9:46
• It is multiplication and division. Please read the answer there again, carefully. You can understand the maths if you think about it. – James K Jan 27 at 10:35

1 Answer

• The radius of the observable Universe is 41.5billion light years (ref).
• A light year is $$9.5\cdot10^{12}$$ km.
• The radius of the Earth is 6371 km.

So the answer is $$6371 km \cdot \frac{6371 km}{41.5\cdot10^9\cdot9.5\cdot10^{12}km} = 1.03\cdot10^{-16}km = \underline{\underline{1.03\cdot10^{-13}m}}$$.

The size of the atoms are $$\approx 10^{-10}m$$.

• @PM2Ring Your link states 28.5e+9 ly diameter, which is 14.25e+9 ly radius. I calculated here with radius of 13.7bln ly, the difference is imho not significant in this context, but I fixed it. – peterh says reinstate Monica Jan 27 at 8:49
• It says 28.5 gigaparsecs, or 93 billion light years, for the diameter. Also see physics.stackexchange.com/questions/57402/… although that does get a bit technical. – PM 2Ring Jan 27 at 8:54
• @PM2Ring Uhm, it seems it is not my day :-) I fixed it again. – peterh says reinstate Monica Jan 27 at 9:14
• It's always a good day to learn new stuff. ;) – PM 2Ring Jan 27 at 9:16
• @larry909 $10^-{10}$ is 0.0000000001 . $10^{-13}$ is 0.0000000000001. The answer is around a tousandth of an atom. – peterh says reinstate Monica Jan 27 at 10:15