# Size of the universe vs. the amount of atoms in earth

Heres a question raised during lunchtime:

If all the atoms in the planet earth, where the size of the earth as we know it, how much of the universe would it take up?

just curious =]

One-millionth of one percent.

Given the average atomic diameter of 2.5 x 10[sup]-10[/sup] meters, and the diameter of the Earth is 1.2756 x 10[sup]7[/sup] meters, the Earth would be 6.880 x 10[sup]7[/sup] light years in diameter if all its atoms were expanded to the size of the Earth currently. If the diameter of the universe is 20[sup]26[/sup] meters, then the expanded Earth would take up 4.0703 x 10[sup]-57[/sup]% of the universe’s volume.

Only off by 8 orders of magnitude, Achernar.

Silly me…I divided by mistake. Should be 50 orders of magnitude. :smack:

Check your math, and don’t mix up light-years with meters. I think you’ll find your answer is about 27 times larger than mine. A factor of 8 is due to my using the radius of the universe where you used diameter. A factor of 1.3[sup]3[/sup] = 2.2 is due to my universe’s dimension being bigger (13.7 Glyr). The remaining 1.5 is due to our assumptions about the atoms in the earth. I agree with you on the first difference, so I change my answer to:

eight-millionths of one percent.

You’re right. I had anticipated finding a diameter of the universe in light-years, so I converted to that first. Surprisingly I found one in meters, and used that, but did not convert back. The new, corrected result is 2.76 x 10[sup]-8[/sup]%, or about 27-millionths of a percent.

Most of the measures came from this site.