# How can the observable universe be so small if there are so many stars in it?

The observable universe has a radius of about 46.5 billion light years. That’s big but I just wonder how that can be big enough to fit in everything we know exists in the universe. There are hundreds of billions of galaxies and each galaxy has billions of stars.

Plus there are vast spaces between galaxies. And galaxies tend to cluster up into local groups, so there would be even bigger gulfs of empty space between these local groups.

If the observable universe was only 46.8 billion light years, and there were this many and galaxies stars that need to fit inside, wouldn’t everything be much closer together?

• What you're saying is based on intuition alone, and your intuition is simply wrong when it comes to big numbers. Most likely, you are vastly underestimating the size of 1 light-year. – Florin Andrei Nov 10 '15 at 19:52
• An overly simple example. The United States is 3,000 miles across and there are 300 million people who live there. That's 100,000 people per mile or 20 people per foot. That's the same error. On the US you have to consider square mileage not distance across, and in the Universe, you have to use roughly the cube of the distance across. 46,500,000,000 to the power of 3. That's a very big number. – userLTK Nov 11 '15 at 3:30
• Just do the math. – Eubie Drew Nov 14 '15 at 18:17

If you know the total number $N$ of galaxies, and you know the size $V$ of the (observable) Universe, then you can calculate the number density $n = N/V$ and mean distance (of the order $1/n^{1/3}$) between galaxies, and convince yourself that it actually works out fine.

However, the reason we know how many galaxies are in the observable Universe in the first place is the other way round:

1. Observe an average number density of galaxies (which of course varies quite a lot from dense clusters to voids).

2. Calculate the size of the Universe by integrating the Friedmann equation (using as input observed values of the densities of the constituents of the Universe; dark energy, dark matter, gas, stars, radiation, etc.).

3. Finally, multiply the two numbers to get the total number.

Note that when observing the number density, we must not look too far away from the local Universe, since this means looking back in time to a period where the number density was different from present-day's value.