## 2011-12-07

### How much matter does the universe contain?

A single look at the night sky will reveal there's far more nothing than something out there. The tiny specks of light are stars, made of something, and the vast oceans of blackness surrounding them are nothing. The universe contains gigantic amounts of void, but how much, I wonder. To visualise this, I decided to picture all the matter in the universe clumped together. Not super-tightly, like in a neutron star, but still put together closely so that the density is 1 kilogram per litre: the density of water. The main reason I chose this density is, of course, that it makes it very easy to calculate. So if we pack all matter in the universe together like this, is the result larger or smaller than a single galaxy?

Before I answer this question, I should point out I will give large numbers first in the scientific notation, then give their name according to the long scale. I'm using the long scale because it's more sensible and because it's the scale I grew up with using. But for people who are more keen on the short scale (the one generally used in English-speaking countries) I will put the short scale name of large numbers in parentheses. A second thing I should point out is that I'll be using all the matter in the observable universe, not the entire universe.

First of all, we have to find out the total mass of matter in the universe. Wikipedia gives several estimates of the mass of the universe. I will be using the calculated mass based on the critical density, 1.53×1053 kg, as it seems to be the best corresponding to our observations of the universe. Basing the mass of the universe on stars alone is silly due to the presence of dark matter, and assuming a steady state-universe requires the pretty big assumption that our universe is a steady-state universe.

So, since we assumed the density of water for our clump of all matter, that means it's 1.53×1053 litres in volume. 153 octilliard (153 septendecillion) litres is unimaginably huge, so we'll have to use bigger units to make this more imaginable. Let's start with converting to cubic metres. Thanks to space being three-dimensional, a cubic metre contains not ten, but a thousand litres. So that means this clump of matter is  1.53×1050, 153 octillion (153 sexdecillion) cubic metres in volume.

We can get closer to imaginable numbers by converting to cubic kilometres. Similarly to how a cubic metre contains a thousand litres, a cubic kilometre contains a milliard (billion) cubic metres. That means our clump of all matter is 1.53×1041, 153 sextilliard (153 duodecillion) cubic kilometres.

To get closer to home, we'll convert to cubic megametres. The megametre is a pretty rarely used unit, but it's equal to a thousand kilometres. The clump of matter has a volume of 1.53×1032, 153 quintillion (153 nonillion) cubic megametres.

To take another step, I'll now convert to cubic gigametres. A gigametre is a million kilometres, a bit more than a journey to the moon and back. We divide by a milliard (billion) and get 1.53×1023,153 trilliard (153 sextillion) cubic gigametres.

We're still not using imaginable numbers, so we convert to cubic terametres. A terametre is a milliard (billion) kilometres, 1.5 times the distance from here to Jupiter. The clump of matter is 1.53×1014,153 billion (153 trillion) terametres. Hey, that's approaching numbers we use (on occasion) in our daily lives.

But let's take another step and convert to petametres, one billion (trillion) kilometres. I would like to give an example of how big this is, but there are few meaningful distances close to a petametre. It's 220 times the distance from here to Neptune, or a fiftieth of the distance from here to the nearest star (aside from the Sun). All the matter in the universe taken together is, if my calculations are right, 1.53×105, 153000 cubic petametres.

While a hundred-and-fifty-thousand is quite a low number, we can use cubic lightyears instead. A lightyear is approximately ten petametres. Actually, it's 9,5 petametres, but considering how rough our estimate of the universe's mass was I think we can get away with rounding it to ten, thus putting a thousand cubic petametres in a cubic lightyear. One final calculation, and we get 153 cubic lightyears. A cuboid of five by five by a little over six lightyears. That's all the matter in the universe. Not only would it fit inside a single galaxy, if its centre was at the Sun's position it wouldn't even reach the nearest star. That's all the matter in the universe, everything else is void.

But where is all this void exactly? You might think the gigantic gaps between galaxies are where it is, but these are actually relatively small. The Milky Way is a hundred thousand lightyears across, though only ten thousand lightyeard thick, and the nearest big galaxy is at two million lightyears, only twenty times the Milky Way's own diameter. If we count dwarf galaxies the nearest other galaxy is much closer even. If you imagined the big galaxies as coins, they would be less than a metre apart.

The real distances that are responsible for all this void are the distances between stars. When I tried to give an example of the size of a petametre and failed we already saw there is a huge gap between distances within a solar system and distances between stars. Our Sun is 1.4 million kilometres across, but the nearest other star is more than four lightyears away. If we imagine the Sun as a grape in the centre of Amsterdam, the nearest starsystem consists of two grapes and a grain of pepper located near Brussels. And that's a good comparison for interstellar distances: a piece of fruit in every European capital. Those distances are mainly responsible for the huge amounts of void in the universe.