Clearly both numbers are very large. Can modern astronomy confirm or deny this assertion?
It's an example of a “Fermi question,” in which a student is asked to make a rough, yet reasonable, estimate of a mathematical quantity from basic principles, usually in the shortest amount of time, and usually during some sort of oral exam. It tests both knowledge and imagination, and it can be fun.
The label is in honor of physicist Enrico Fermi, who would set his students to estimating things like the number of drops of water in Lake Erie, or how many piano tuners there are in Chicago, just to exercise their minds.
Several astronomers have done this analysis, just for fun, and you can find their results on the Web. Shall we give it a try ourselves?
First, we'll consider the sand. How big is a sand grain? Many of the folks who have done this say a diameter of one millimeter is about right. That may be a bit on the large side, but it's reasonably close. Just to keep things simple, we'll also assume all sand grains are tiny cubes (this is only an estimate we're doing, right?). Then one cubic meter of sand (several bags worth) would contain a billion grains.
How big is a beach? Would you agree an average beach might be about 20 meters (roughly 20 yards) wide, from dry land down to the water? This will vary with different beaches, but 20 meters seems like a good guess.
How deep should we go? One authority claims 10 meters (about 10 yards), but this seems a bit much to me. I'm going to say my beaches are only one meter deep: below that, it seems to me you'll run into rock, or plain dirt (and here is where an expert will make a better Fermi guess than a beginner.)
Finally, how long are all the beaches in the world? This question is more subtle than you might expect. If you have a small map of the world, and run your pencil around all the coastlines, you'll get a total mileage figure. But if you have a larger scale map, you'll see more ins and outs — the coast will “wiggle” more — and you'll invariably get a larger number.
This pattern of increasing length will continue as you look closer and closer (look up “fractal” in your dictionary), and it's not easy to estimate. Here's a method some people have tried. The circumference of the Earth is approximately 25,000 miles. Can we guess that the coastlines will total 10 times that amount? Then we end up with 250,000 miles.
At this point, I decided to cheat, simply because I'm not well-versed in geology or geography. I looked it up.
It turns out I was on the low side by a factor of four: there are actually about a million miles of coastline on the Earth. On the other hand, not all of it is beach sand. I used about half a million miles; it may not be in the ballpark, but at least it's in the right county.
If you multiply all these numbers together, you get a total of 20 billion billion sand grains. We can call it 20 quintillion, or a 2 followed by 19 zeroes (that's 2 x10E19 for you science types). Two other folks who have done this get answers of 8 quintillion and 100 quintillion, so at least I'm in the middle of the spread.
Now we look at the stars. First, a disclaimer: we're going to count up all the stars we can detect with our various powerful instruments, not just those we can see with the naked eye in the night sky. Our unaided vision, under ideal conditions, can see only about 6,000.
For us astronomers, counting stars is relatively easy. From studies of our Milky Way galaxy by many astronomers over the past century, we can safely say the number of stars in our home galaxy is somewhere between 200 billion and 600 billion.
Our galaxy is somewhat larger than average, though. Let's assume 100 billion stars is a good average for a galaxy.
How many galaxies are there? First we must decide that we'll only consider galaxies we can actually detect. If, as current theory holds, the universe is infinite, clearly the number of galaxies, and therefore the number of stars, is also infinite. Let's limit ourselves to only what we can see!
Some years ago, the Hubble Telescope stared at a chosen small patch of sky, less than a degree across, near the Big Dipper, for many hours, to see how many galaxies it could possibly detect in that tiny area. We can then multiply that number by how many such patches would fill up the entire sky.
The result: we could detect and study about 100 billion galaxies … if we had sufficient time, and lots of Space Telescopes!
Now we multiply the two numbers together. The total number of observable stars comes out as 10,000 quintillion (10E22), or 10 sextillion, which is 500 times the number of sand grains we calculated above.
Even if we've erred by quite a bit in any our assumptions, it's true: there are more stars than grains of sand on the beaches.
Keith Johnson is director of the Edelman Planetarium at Rowan University. The star show “Stars: The Powerhouses of the Universe” is playing on Sunday afternoons at 3 p.m. More information is available at www.rowan.edu/planetarium/.