How Big Is the Universe?

As we learned last time, the solar system is an almost unfathomably vast place. But compared to the rest of the universe in which we and everything else live, the solar system is actually rather quaint and cozy. Because the universe is not just almost unfathomably vast—it's truly unfathomably vast.

But that's not going to stop us from trying to come to grips with exactly how big it is! Just as we did last time with the solar system, today we're going to build a scale model of the entire universe to help us get a better feeling for the immensity of the numbers behind it.

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Recap: How Big Is the Solar System?

Before we head for the stars, let's quickly recap what we learned last time about the size of the solar system. In a nutshell, we learned that the solar system—which consists of our friendly neighborhood star (the Sun), Earth, the seven other planets, as well as a bunch of comets, asteroids, and other fun stuff—is really, really big.

To get a feel for just how big, we imagined shrinking the Sun down by a factor of 57.3 billion to the size of a US quarter coin, and then placing this model Sun on the goal line of a 100 yard long American football field. In this model, the planet Mercury sits at about the 1 yard line, the planet Venus sits at the 2 yard line, Earth sits just short of the 3 yard line, and Mars sits between the 4 and 5 yard lines.

To get to the giant planets in the outer solar system, we have to start hiking. On this football field, Jupiter sits at about the 15 yard line, Saturn sits at the 27 yard line, Uranus sits at the 45 yard line on the other side of the field, and Neptune is way down at the 15 yard line on the opposite side of the field from the Sun. Remember, we Earthlings are only about 3 yards away from the Sun at this scale. So Neptune is really far away!

How Far to the Stars?

Here's where things start to get a little crazy. The truth is that the incredibly long distance between the Sun and Neptune is really only "incredibly long" when we're talking about sizes within our solar system. Because as soon as we step out of those friendly confines, and instead think about the distances to the stars, we see that Neptune is, comparatively, right next door.

To see what I mean, let's take a look at the closest star outside of our solar system: Proxima Centauri is one of a trio of stars orbiting each other in a group known as Alpha Centauri. How far away is this star? It's about 24.8 trillion miles away from Earth. That sounds like a lot, but it's hard to imagine just how far that is when dealing with such large numbers.

So let's think about our football field scale model. On that model, where the Sun sits on one goal line and Neptune sits at the 15 yard line on the opposite side of the field, Proxima Centauri would be about 433 miles away. There is a lot of space out there between the stars!

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How Big Is the Milky Way Galaxy?

As it turns out, even the distance to this nearest star is tiny from some perspectives. As you may know, our solar system and all of the stars you see in the night sky all live in what's called the Milky Way Galaxy. And in comparison to all of the sizes we've looked at so far, the Galaxy is truly enormous.

How big is it? The center of the Milky Way Galaxy is about 145.9 quadrillion miles from Earth. That's so far that light, which travels faster than anything else in the universe, takes almost 25,000 years to reach us from the center of the galaxy.

To gain a little perspective on just how far this is, let's go back to our football field model. In that 57.3 billion-to-1 scale model, in which Proxima Centauri is located 433 miles away, the center of the Milky Way Galaxy would be about 2.5 million miles away. For comparison, that's more than 100 times around the Earth's circumference!

Are these numbers starting to make you feel tiny yet? We're not done…

How Big Is the Universe?

While the Milky Way is big, it turns out there are hundreds of billions of galaxies like it in the visible universe. Which means that the visible universe itself must be vastly bigger. And indeed it is.

At this point, our football field model (with the Sun shrunk to the size of a quarter) begins to fail us. After all, we've already had to travel around the Earth 100+ times to model the size of the Milky Way, so trying to model the size of the entire universe at this scale just won't do. Instead, let's shrink the entire Milky Way Galaxy down to the size of that quarter—this gives us a 37 billion trillion-to-1 scale model!

The edge of the visible universe would be over 130 football fields away.

If we put our quarter-sized Milky Way Galaxy model down on a goal line, the nearest really large galaxy—known as Andromeda—would sit just short of the 1 yard line. The Milky Way and Andromeda are the most prominent of the 50 or so nearby galaxies that sit in what's called the Local Group. And this group is just one of a number of clusters of galaxies in what's called the Virgo Supercluster. On our model, the center of the Virgo Supercluster—from which light takes over 50 million years to reach us—would sit at about the 15 yard line.

But, cosmically speaking, the Virgo Supercluster is still pretty much right next door. Because at this scale, the edge of the visible universe would be over 130 football fields away. And all of that space, over those 130 football fields, is speckled with more than 100 billion galaxies, each of which are speckled with hundreds of billions of stars. Many of these 10 billion trillion stars are no doubt orbited by planets...and perhaps some of these planets are inhabited by other intelligent beings thinking thoughts similar to these about the vastness of the universe.

Wrap Up

OK, that's all the math (and astronomy) that we have time for today.

Please be sure to check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Spiral galaxy and solar system images courtesy of Shutterstock.