One of astronomy’s lovelier aphorisms, popularized by astronomer Carl Sagan, is that there are more stars in the universe than grains of sand on all the beaches on Earth.
Thank you for reading this post, don't forget to subscribe!That’s hard to grasp, which is the point. When you stand on a beach, you can see a lot of sand. Extrapolating that to the entire planet multiplies that sum immensely. Yet according to the adage, the number of stars in the cosmos is even larger—truly an unfathomable amount.
I’ve heard this dictum many times over the years, expressed in many ways. But like many such brain-freeze-inducing sayings, it’s worth asking a very basic question: Is it true?
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The answer is a little irritating: probably not, but it depends on a lot of assumptions you have to make, some of which are hard to pin down.
This sort of huge-yet-quantifiable query is called a Fermi problem—think of it as a back-of-the-envelope calculation—after the physicist Enrico Fermi, who was famous for (among many, many other things) looking at ways to estimate big numbers in a nigh-incalculable problem accurately enough to get somewhere within the ballpark of the right answer. Generally, when astronomers broadly estimate things, we like to be accurate to within a factor of 10—meaning the number we get is within one tenth of to 10 times bigger than the true answer. This is what astronomers call an order of magnitude. Don’t fret over, say, a factor of two or three; that’s close enough for this sort of sanity check.
So with that amount of fuzziness to our answer in mind, let’s turn to sand and stars.
First, let’s look at the astronomy. Our Milky Way, as an example, is a large galaxy composed of hundreds of billions of stars. It’s actually rather hard to nail that number down because we’re inside the galaxy, and our view of much of it is blocked by gas and opaque dust—and stars can have a very wide range of luminosities. Let’s conservatively call it 200 billion.
Now we just have to multiply by the number of galaxies in the observable universe to know how many stars there are. A team of astronomers working on this question published its results in 2016 and stated that there are approximately two trillion galaxies in the universe.
So we can multiply 200 billion by two trillion and get the answer, right? Well now, cool your hyperjets for a sec. It’s a little more complicated than that. The astronomers who calculated this estimate actually considered any galaxy that had a total mass of stars that was more than a million times the mass of the sun.
Compared with the Milky Way, that’s less massive by a factor of 200,000! So we can’t just use the Milky Way as our template. The good news here is that, like stars, low-mass galaxies probably vastly outnumber much beefier ones, so their larger number makes up for their more modest stellar population. Using the one million solar masses per galaxy is probably close enough—remember, we’re not worried about factors of a few here and there.
But there’s another issue. One million solar masses doesn’t mean one million stars per galaxy! The sun is unusually massive compared with most stars, the majority of which are actually smaller red dwarfs. Stars as hefty as or heftier than the sun only make up about 10 percent of all stars, so out there in the universe there are closer to 10 stars for every one solar mass. We need to multiply that galactic one million solar masses by 10, which gives a result of 10 million stars per galaxy on average.
Therefore we can estimate the total number of stars as 10 million x 2 trillion = 20 million trillion = 20 quintillion, or 2 x 1019, stars. The cosmos is not lacking in stars.
But how does that compare with sand? It’s time to turn to estimates that are decidedly more down-to-earth.
The easiest way to estimate the number of grains of sand on all the world’s beaches is to determine the volume of sand on those beaches, say, in cubic meters and then multiply that by the number of grains of sand in a cubic meter. Those numbers aren’t too hard to find.
How much sand is in a cubic meter? That depends on the size of the grain of sand, which ranges from less than 0.1 millimeter up to about 2 mm. Let’s call it 1 mm on average. A cubic meter would then contain 1,000 x 1,000 x 1,000 = 1 billion grains of sand.
Wow! That’s a lot. It would only take a couple of hundred cubic meters of sand—roughly the volume of a typical house—to equal all the stars in the Milky Way! It doesn’t take much beach sand to equal even a big galaxy such as ours.
From there, though, the numbers get fuzzier. For example, how big is a beach? Well, we can throw out some decent guesses: let’s say the amount of beach exposed from the edge of the ocean to higher ground is 50 meters and goes 10 meters deep. Now we just need the length of all the beaches combined.
To my surprise, that number has been calculated: the total length of shoreline around all the continents is about 2.5 million kilometers. Not all of that is sandy, but it turns out that fraction has been determined as well: about 30 percent of global (nonicy) shoreline is sand. We could get fussy and exclude Antarctica from the first number, but eh, it’s close enough.
That gives us 750,000 kilometers of sandy beach, or 750 million meters.
To find the total volume of sand, we can calculate that 50 meters wide x 10 meters deep x 750 million meters long = 375 billion cubic meters. If we go with a billion grains of sand per cubic meter, that means there are 375 billion x 1 billion = 375 quintillion grains. Call it an even 400—we’re being rough here—so that’s 4 x 1020 grains of sand.
Huh. That’s about 20 times as many stars as there are in the observable universe, in fact. That’s pretty close—much closer than I’d have thought! This also means that, on its face, the aphorism is wrong.
My assumptions were pretty rough, however, and that could change the numbers a lot. Take grain size: grains at the smaller end are 0.1 mm and could outnumber the bigger 1 mm grains. If so, that means there are a trillion per cubic meter, multiplying the number of grains of sand by a thousand. Even if I over- or underestimated the length and depth of sand on a beach by a factor of a few, sand hugely wins over stars by a factor of many thousands.
On the other hand, 10 million stars per galaxy may be a bit too scanty; it’s possible that most galaxies have far more stars than that. Still, it’s not likely to offset the huge advantage sand has. If I had to bet, I’d wager against stars and put my money on sand.
Mind you, that’s just the sand in beaches. Look at the ocean floor and surface deserts and that number goes up a lot. There’s probably hundreds of times as much sand in the Sahara Desert alone as all the other beaches on Earth combined. (I’ll leave that math as a fun exercise for you.)
I’ll admit this result surprised me. That’s the beauty of Fermi problems; you can get ballpark figures pretty quickly and check to see if your intuition is correct—or at least get an idea of how far it’s off.
And for any given problem, it’s likely to be off; our brain didn’t evolve to deal with such huge numbers, so it’s easy to get it wrong. But that’s what math and science are for: to keep us from fooling ourselves.
