Saturday, January 5, 2013

Density of the Universe

The density of the universe seems to be about 10-30 grams per cubic centimeter (source). With a proton having a mass of about 1.67 * 10-24 grams, we have about one proton per million cubic centimeters, i.e. one proton per cubic meter. Since electrons are much less massive than protons, this is also approximately equal to about one hydrogen atom per cubic meter.

So if the mass of the universe were spread evenly throughout space, how much could a container fit? A ten-liter container would thus hold about one-hundredth of a hydrogen atom. Not a lot!
Imagine all the mass of the universe was the size of marbles--how far apart would they be? Assuming all matter is divided up into pebbles, and assuming a pebble has a mass of about 4 grams, this means that we would need 4 * 1030 cubic centimeters (4 * 1015 cubic km) of volume for every pebble to get the right matter density for the universe. This is a lot; assuming equally spaced pebbles, this means that the average distance of one pebble to its closest neighbor is about 1.6 * 1010 cm, or 160,000 kilometers. To put this into perspective, if one pebble is the earth, and another the moon, there would only be one pebble sized distance between them.

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