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The universe the size of earth

I was wondering, if the entire 180 billion light year (800 sextillion mile) universe was the size of the earth, using the same scale how large would the earth be? does anybody know the size of the earth using this model/scale. assuming that the universe was the size of the earth, how large would earth be to this scale? please give suggestions. thank you.

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Answer #1

Hope I’m not getting suckered into answering a homework question ;)

Anyway, lets take your estimate of the universe being 800 sextillion miles across. That would be 8*10^23.

The Earth’s average diameter is 7,917.5 miles, lets call it 8,000 or 8*10^3 for a round number.

Since the 8s cancel out the Earth is 10^3/ 10^23 the size of the universe which comes out to 10^-20.

Divide the size of the Earth by the ratio of the size of the universe and Earth:

810^3miles/10^20 = 810^-17 miles= 510^-12 inches= 1.310^-3 angstroms

The smallest atom hydrogen1 is about 0.25 angstroms so the Earth in this model would be about 5 thousandths of the size of the smallest atom. Probably off by a bit since I rounded and approximated everything but unless I gained or lost a power of ten somewhere it should be in the ballpark.

Makes you appreciate how mind boggingly large the universe is eh?

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