When we look at the Milky Way overhead and see denser regions of stars, it’s normal to wonder how densely packed in they all are.
In this article, we’re going to work out if galaxies are just full of empty space, or if they are as densely packed as eyes make them appear.
How We’ll Answer the Question
Before diving in, we need to think about what we’re going to work out.
First of all, there is no such thing as truly empty space (link opens a Dr. Becky video in a new tab where she explains why space is never empty).
When we talk about empty in this article, we mean empty of ‘normal’ matter, more properly known as baryonic matter. We’ll be ignoring dark matter, dark energy, quantum fields, etc.
We’re also going to ignore all the matter that is not in stars.
This may seem a silly assumption but we know that the Sun is so vast that it accounts for practically all the matter in our solar system. On this basis, factoring in planets, comets, dust, etc, will prove too complicated and have very little basis on the outcome.
Finally, we’re going to base our answer using data from the Milky Way galaxy. There is a huge variety of galaxy shapes, sizes, and types out there, but we’re confident that our home galaxy can act as an ‘average’ to effectively answer the question.
The way we’ll work out whether galaxies are mostly empty space is as follows:
- Work out the volume of the Milky Way
- Calculate the average volume of a star, using the sun
- Work out the total volume of stars in the Milky Way
- Compare the total stellar volume to that of the Milky Way
If we find that the volume of stars is less than half the volume of the Milky Way, we’ll be confident to say that galaxies are mostly empty space.
How Big Are Galaxies?
Galaxies come in a variety of sizes, from 3,000 to 300,000 light-years in diameter.
For the sake of simplicity, we’re using the Milky Way as the basis of our calculations, so let’s say that an ‘average’ galaxy is 100,000 light-years in diameter.
Although galaxies are flat, they do have a measurable thickness. The Milky Way is about 1,000 light-years thick, so we’ll use that in our math.
We now have the measurements we need to calculate the volume of the galaxy, using the formula for the volume of a cylinder: πr² h
= 3.141 x 75,000² x 1,000
The volume of the Milky Way =17,671,458,676,443 cubic light-years, where one cubic light-year is a cube with sides that are one light-year long.
Next, we need to calculate the average volume of a star using the same units.
What is the Volume of the Sun?
We considered the size of the sun in this article, which opens in a new tab. What we found was that our local star is about 900,000 miles in diameter, which is the distance light travels in just under five seconds.
To keep everything aligned, we need to turn five light-seconds into light-years. When we do that, we find the sun has a diameter of about one-six-millionth of a light-year (1/6,307,200).
Its radius, which we need to calculate its volume, is half that, so 1/12,614,400 of a light-year.
The formula for the volume of a sphere is 4/3π r³
The volume of the sun =0.0000000000000000000214 cubic light-years
What is The Total Volume of Stars in a Galaxy?
Our penultimate step is to multiply the volume of the sun by the number of stars in the Milky Way galaxy to get the total volume of all its stars.
Estimates of stellar numbers vary between 100 billion and 400 billion. We’ll use 200 billion as a ‘halfway house’ selection.
When we multiply the volume of a star (our sun) by 200,000,000,000 stars (in the Milky Way), we get a total stellar volume.
The total volume of all the stars in the Milky Way =0.00000000428 cubic light-years. In other words, the total volume is less than one 100-millionth of a cubic light year.
We are now ready for step four – to answer the original question.
Are Galaxies Mostly Empty Space?
The proportion of a galaxy that is empty of regular baryonic matter is staggering. The volume of the Milky Way is ~17 trillion cubic light-years. The volume of all the stars in the Milky Way is less than one 100-millionth of a single cubic light-year.
It’s hard to get clear in our mind’s eye just how little space the stars occupy compared to the size of the galaxy. Another way of visualizing it is to line up all of the stars in a galaxy and see how long the line would be.
Assuming each of our 200 billion stars has a diameter of five light-seconds, laid end to end, they would form a line 32,000 light-years long – about a third of the diameter of the Milky Way.
Recall that the Milky Way is a circle 100,000 light-years across. Our line of suns is just 5 light-seconds wide.
That stellar line is also only five light-seconds deep, compared to the Milky Way which is 1,000 light-years deep. In other words, our ‘flat’ galaxy could fit more than six billion suns stacked one on top of the other!
We don’t see distant galaxies as empty space because of their distance and the limits of the human eye.
However, when we look overhead at night and only see a few thousand pinpricks of light (click here to learn how many stars we can see), it’s more obvious that there is a lot of ‘nothing’ out there.
We know that our nearest star is over four light-years away. Scientists believe this is an average gap between stars, which further emphasizes the emptiness of space.
However, what we didn’t expect, and perhaps you didn’t either, was to learn just how incredibly empty a galaxy is when you measure the amount of its volume which is occupied by stars.
By volume, our galaxy is well over 99.99% empty space.
Even if we had factored in planets and other matter, we would still have clearly demonstrated that the Milky Way is an incredibly barren place.
Written by Adam Kirk