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On the Shores of the Cosmic Ocean

In my astronomy classes I have often used the claim that there are "more stars in the heavens than all the grains of sand on all the beaches on Earth." The claim is certainly not original with me, but I had always accepted it without question. Then one day began to wonder if it is really true. After all, there must be a really big number of sand grains on all the planet's beaches!

So I decided to find out. Obviously I couldn't count all the sand grains, but I could do an order of magnitude calculation. Of course, sand comes in a variety of sizes. One standard definition is that medium sand is 0.25 to 0.5 millimeters in diameter, and fine sand is 0.25 to 0.125 millimeters. I chose, arbitrarily, to consider sand grains of 0.25 millimeters as an average. To further simplify matters I considered that each sand grain is a perfect cube, which allows for efficient packing.

Now all I had left to do was determine the volume of all the Earth's beaches! Simple, right?

Whoa, not really! First off, the best estimate I could find is that there are about a million and a half kilometers of shorelines on Earth. Not all of them have beaches per se, and some that do, have only very short beaches. Rather than stack the deck against the stars, I estimated that all the Earth's shorelines had a beach 50 meters back from the water. On the average, this may be an exaggeration. Next, how deep do you consider the beach to be? What is the definition? Who knows? A meter is about as deep as any summer beachcomber would ever dig, so I finally decided on that figure as the depth.

So, what is the number of sand grains, 0.25 millimeters cubed, that will fit in 1.5 million kilometers of beach, 50 meters broad and a meter deep? You can do the math yourself, or just accept my answer:

4.8 x 1021
That's 4,800,000,000,000,000,000,000!

Thus there is likely to be something less than 5 thousand billion billion grains of sand on the Earth's beaches! If I had just a penny for every billion grains of sand, I would be the world's richest person with nearly 50 billion dollars!

OK, this must be far more than all the stars in the sky, right? Let's see.

Until recently, the total number of galaxies in the Universe was estimated to be about 10 billion. However, the Hubble Space Telescope has provided a much clearer view of the Cosmos, and today's estimate is that there are 50 billion galaxies. Generally speaking, our Milky Way can be considered fairly average with the mass equivalent to 100 billion stars. There certainly can be some argument here that not all of a galaxy's mass is in the form of stars. There may be super-massive black holes in their cores, as well as other unseen matter. Nevertheless I think it is legitimate to consider the Milky Way our yardstick here.

So 50 billion galaxies all roughly equivalent to the Milky Way (100 billion stars) amount to how many stars altogether?

5 X 1021

That's still slightly more than all the grains of sand on Earth's beaches (even considering my rather generous assessment of shoreline fill). How many more? Oh, about 200 billion billion more stars than grains of sand. But of course, this is just an estimate. Still the old cliché seems vindicated. All of a sudden I'm really beginning to feel small and very insignificant!

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