Stars or Sand? Are there more Grains of Beach Sand or Stars in our Visible Universe?

This began as a simple question, but it has intrigued enough people that I decided to feature it as an article and expand it so we can have some fun.

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Carol Charming:

“I have heard people say that there are more stars in the universe than there are the grains of sand ‘on the beach.’

What size is the beach and are the grains of sand coarse or fine? Or does the saying go “all the grains of sand on all the world’s beaches,” something I simply can’t believe to be true.”

Carmel (Charmel) Beach has many more grains of sand than our Milky Way has Stars

Carmel (Charmel) Beach has many more grains of sand than our Milky Way has Stars

Disclaimer —
You and I will work through to get an answer, but be warned — There will never be a definitive, conclusive, absolute, precise or final answer to this question.

For either counting stars or sand grains — there simply is no measurement, or accurate calculation or mathematical proof or method of counting – nor will one ever conceivably exist.

Its even worse than that — we can’t even get approximate numbers with much confidence.

We can only roughly estimate the number of stars in our own galaxy. Estimates easily vary by 150 times (more than two orders of magnitude) and estimates of the number of grains of beach sand are even worse.

So if we can credibly estimate either the number of stars or sand grains within say four or five orders of magnitude of the other estimate – we’ll be doing well. However, as mentioned above, this essentially guarantees that answers to this question will be off by a few magnitudes; or they will have, in more diplomatic terms, “a high variance” or “a large margin of error.”

Even using the best available evidence and methods – no one can credibly claim their answers to either estimate of stars or sand grains are within 20 percent (and 20 percent of a trillion stars / sand grains is an error of 200 billion.

That’s more than ten magnitudes larger than a measuring error of one star or one grain of sand). And that’s my estimate on the best numbers we can ever do.

What we can do instead is try to use reasonable methods, use the broadest range of assumptions (lowest and highest) and use the most credible methods available to get estimates for both sand grains and for star counts.

Then, after we have estimates (with each having its own range of variance) the only way I can reasonably imagine deciding there are more stars than sand, or more sand than stars, is if one estimate comfortably exceeds the other by six or more magnitudes; a million times larger or smaller.

* And so, because of the gigantic estimation errors inherent in this exercise – you might take a big breath (now let it out) and try to keep a sense of humor in mind while reading this.

 

With that disclaimer in mind, shall we start ? 

1. Stars: We are going to multiply estimates of stars in our galaxy with an estimate of the number of galaxies — even though the number of stars in a galaxy can vary by more than five magnitudes; from 10 million to a trillion stars (and we really don’t have a good grasp on how many galaxies there are.)(For this article we’ll use the definition of a Star as “a luminous body” and embarrassingly ignore dark stars like Brown and Red Dwarfs which make up a HUGE portion of our own galaxy.)

2. Sand: Next we’ll measure actual sand grains and then estimate how many grains fit in cubes of increasing sizes.

3. Then we’ll see how many sand grains we need to represent our own Milky Way galaxy. Finally we’ll ball park estimate the size of beaches on the West Coast of North America. (This “back of an envelope” type of analysis is sometimes called a “Fermi Estimate.”)

Estimating Stars

Using some credible methods and thoughtful analysis some astrophysicists estimated there are 300 sextillion stars in our visible universe as of 2010. That’s 3 with 23 zeros after it. 300,000,000,000,000,000,000,000 !

Instead, we’re going to play with a method for calculating and estimating stars that is probably less credible than taking one of our important numbers “off the shelf,” but since there is no reasonable way to find out if any answer is even close. So instead of worrying about accuracy, how about if we have a little more fun on the way. (Besides, that 300 sextillion estimate is fairly controversial.)

We are going to multiply estimates of stars in our galaxy with an estimate of the number of galaxies — even though the number of stars in a galaxy can vary by more than five magnitudes; from 10 million to a trillion stars

 

Milky Way Credit: Wikipedia

Milky Way Credit: Wikipedia

There are (very) roughly 125 to 225 billion galaxies we can now detect in our Visible Universe, and there are very roughly 50 to 400 billion stars in our Milky Way galaxy (and compared to most spiral galaxies our Milky Way is big, having an extra large number of stars like our neighboring spiral galaxy Andromeda).

This estimate is confounded by at least two problems. Every time we look deeper into the universe (Hubble Deep Field and Extreme Deep Field images) we see another magnitude (sometimes several magnitudes) of galaxies. The multitude of nearly invisible “Low Surface Brightness Galaxies” some of which are the largest galaxies we know of.

The “off the shelf” estimate of  300 sextillion stars in our visible universe has the same two problems.

Even though our Milky Way is rather large for its spiral type of galaxy, spiral galaxies have dramatically fewer stars than elliptical galaxies.

Estimating Sand Grains

Sand can vary enormously in its size and the number of grains in a cube.

Fortuitously enough I just happen to have a small spice jar filled with Carmel beach sand which I can measure with a vernier caliper.   Carmel Beach sand has roughly 1,000 grains per foot (1).

1,000 grains of sand by 1,000 grains of sand on a flat surface = 1 Million grains of sand in a square foot.

Sand Grains per Cubic Millimeter, Credit: Biocyclopedia.com

Sand Grains per Cubic Millimeter, Credit: Biocyclopedia.com

Now put the vertical dimension of 1,000 grains high = 1 billion grains of sand (one cubic foot).

So One Billion grains of Carmel Beach sand is a cube only ~ 1 foot on a side.

So if you believe our galaxy has about 50 billion stars that means you only need about 50 cubic feet of Carmel Beach sand (a cube about 3.7 feet on a side) to represent each shining star in our galaxy.

Remarkably small isn’t it ?

Just for fun we can call this – One cubic “Sand-Galaxy.”

You can keep this for reference —

“You could easily fit a galaxy of sand in a car.”

Even if you multiply that by 2 (to represent 100 billion stars) – you might still fit that in a Van and maybe a large SUV.

Sand car Credit: Skoda

Sand car Credit: Skoda

However if you believe our Milky Way has closer to one trillion stars, you’d need 20 cubic sand-galaxies to represent the stars in our home galaxy. That size galaxy of sand will take a good sized truck. (10 ft x 10 ft x 10 ft = 1,000 cubic feet of sand)

Number of Galaxies
Next, because we don’t have a good or simple way to “average” the number of stars in a galaxy (good data doesn’t exist) lets (falsely) assume all galaxies have the same number of stars as our Milky Way.

(One could reasonably argue that there are a lot more or a lot less stars than the answer this method will produce. There might be less stars because lots of spiral galaxies are smaller than ours. There might be more stars because spiral galaxies have less stars than other kinds of galaxies such as elliptical galaxies. A reasonable alternative at this point would be to estimate of the total number of stars described above)

There are several “estimates” (all less than fully convincing) of the number of galaxies visible from here; they come in at (very) roughly 50 to 100 billion to maybe a trillion galaxies.

Next, lets see how big a cube of sand made up of one billion Milky-way type “sand-galaxies” is.

Surprisingly the smallest version is a cube of sand only a third of a cubic mile in size ~ about 3,700 feet on a side. (a cubic mile ~ 150 billion cubic feet, 3,700 cubed ~ 50  billion cubic feet)

That 3,700 foot wide cube of sand represents one billion galaxies. So lets call it a “one billion galaxy sand-cube.”

Lets use Carmel Beach for comparison.
Its pretty close to a mile long (5,280 ft) and in the summer, lets estimate maybe 200 feet wide and 30 feet deep. That comes to ~32 million cubic feet. That’s about 1/1,550 th of what we need.

Book

Book “Sandcastles Made Simple” (Click image to order this Book)

So we’d need about 1,550 Carmel beaches to make a “one billion galaxy sand-cube.”

If we counted all the sand in Carmel Bay – we’d might get enough for a whole “one billion galaxy sand-cube.”

(Question: Can you identify SWAG when you see it ? SWAG or SSWAG=Scientific Sounding Wild Ass Guess

I can imagine there is easily enough sand under Carmel Bay to make a few hundred Carmel beaches. I’m not quite as confident there are as many as 1,550 Carmel beaches in the bay though.

For the next step of star estimation lets get another reference point.

To represent the 50 to 100 to 1,000 billion (trillion) galaxies – you just multiply the “one billion galaxy sand-cube” by 50, 100 or 1,000. Again, really not that much more (not that many Carmel beaches).

Even the biggest estimate of a trillion galaxies “only” needs 500 cubes of sand about 3,700 feet on a side (billion galaxy sand-cubes); or 500 Carmel Bays.

I estimate there are almost that many cubes of sand (of about 3,700 feet on a side) on the beaches of California alone (I’ve seen a lot of them from an airplane and a sailboat), but your estimate on this point is as good as mine. 

If we include the vast beaches of Baja California and (half vast?) beaches of Oregon and Washington – we should easily exceed 500 Carmel Bays worth of sand purely with the West Coast alone. 

If we then take into account the thousands of miles of beaches on America’s East Coast, the Brazilian Amazon Coast, Africa and Australia – that seems to easily, and maybe even dramatically exceed, the needed 500 Carmel Bays.

However, we must now ask — does the sand grains estimate exceed the stars estimate by my original threshold of six magnitudes more of one than the other? While it seems likely, I’m not sure. Its maybe too close to call.

So by this rough estimate, there might be more grains of sand on our planet’s beaches than there are stars in our known visible Universe.

Beaches Plus: If you want to expand on the original question and include all the sand grains on the ocean bottom (ignoring all the sand on deserts) – then finally, I think the number of sand grains wins by far more than 6 magnitudes.

Short Answer: Using this analysis method, there might possibly be more grains of sand on the world’s beaches and ocean bottoms than there are stars in our (visible) Universe.

So Carol, your sense of the relative numbers of each was right. Or at least it is consistent with the method we used to arrive at this conclusion.

However, remember this is a very rough, back of the envelope estimate with a few major assumptions that could change the estimates by magnitudes. One might reasonably reach a different answer with a different method and different assumptions.

Aren’t you glad you asked :-)

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References and further reading:

1. Using 1,000 grains per foot is just a rough approximation. Carmel Beach sand grains typically measured ~11 to ~14 thousands of an inch with a vernier caliper (though a few grains are much larger and some much smaller). Fourteen (14) thousands of an inch is roughly 857 grains per foot. Eleven (11) thousands of an inch is about 1090 grains per foot.

Physical properties of soil” is a source for size of soil grains of sand (and clay).

Universe’s Star Stock Rises: The number of stars in our universe just tripled, according to astronomers’ most recent estimates.

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More fun reading:

Finally – if you like this, perhaps you’ll enjoy seeing our Earth from orbit from the live camera in the International Space Station .

Children's Book (Click image to order this Book)

Children’s Book “Stars” (Click image to order this Book)

(Tip: If you buy a book through the link in the article above it won’t cost you a penny more but I’ll eventually get a tiny payment that helps pay for this website’s costs to provide you with this information online – for free. It is appreciated.)

For more technical reading

The study that estimated the total number of stars — “A substantial population of low-mass stars in luminous elliptical galaxies, by Pieter G. van Dokkum & Charlie Conroy

How many galaxies are there in the universe? by Maria Temming in Sky and Telescope, 2014

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