I Spy With My Little Eye

More Stars Than Grains of Sand…

Globular cluster NGC104M

Greetings, everyone. Today I’m going to continue where I left off last time. I had planned to examine the saying, “There are more stars in the sky than all of the grains of sand on all of the beaches of the world”, or however it goes. When I was researching this topic, there was so much mindless drivel to wade through that I was appalled. I got so disgusted that I threw a slipper at the cat.

Hmph. I try not to get so worked up anymore, but sometime I just reach my limit and,…wait, do I have a cat? I used to have a cat, but I haven’t seen him in at least 10 years, so it probably wasn’t him, hmmm. Well, I threw a slipper at something the size of a cat, anyway. And I see that I am wearing both of my slippers. Then what did I throw? Bah, it doesn’t matter. Where was I? Oh yes, sand and stars.

So, are there more stars than grains of sand yada yada yada? The short answer is: yes.

The long answer is a little more involved, but not so long that you’ll get bored and wander off, looking for more coffee and something nice to go along with it. I’ve been having vanilla wafers with my coffee lately, and they’ve been quite tasty. My wife doesn’t normally let me eat such things and constantly hides them from me, the tyrant! “They have too much sugar in them”, she says, and “do you want to go on insulin?” Bah! She’s always nagging, but those sugarless things that she brings home are bloody awful, the texture is more like clay than cookie, and…and

Ahem. The calculations are pretty straightforward once you’ve arrived at your base values.

The first thing we need is the number of sand grains on all of the beaches blah blah, and it just so happens that someone at the University of Hawaii has come up with just such a calculation. You can look at the equations themselves here:


Leave it to the scoundrels at U of H to come up with a project that involves going down to the beach, probably with some pretty graduate students, and playing in the sand. There was probably a subsection that called for drinking beer until you could no longer count, too. Hmph.

The value they arrived at is 7.5 x 1018 or 7.5 billion billion grains of sand. Sounds about right.

Next, we need the number of stars in a galaxy, and since the Milky Way is right there, we’ll use it. The estimates for the number stars in our galaxy varies all over the place, from 75 billion all the way to 400 billion, and the Milky Way is considered a small galaxy once you start looking. The accepted estimate for the Milky Way for a long time was 100 billion, or 1011 so we’ll double that to 2 x 1011 and call it good for now.

Now we need the number of galaxies in the visible universe. The estimates for this value are all over the place too, and it grows every time the Hubble space telescope takes a long exposure photograph. The most recent number I’ve read about is 4 x 1011 or 400 billion galaxies, so that’s what we’ll use.

A simple calculation:

(2 x 1011) x (4 x 1011) = 8 x 1022 or 80 billion trillion, and remember, this figure is probably quite low.

Since 8 x 1022 > 7.5 x 1018, we can safely say that there are more stars than grains of sand yada blah. A lot more, like 1000 stars per grain of sand more.

And there you have it.

An interesting side note: While I was researching this topic I came across someone who calculated it differently, but I can’t find the article again. He got some sand, sifted it so that all the particles were uniform, and figured out how many grains would fit in a cubic millimeter. He then took the number of stars in the visible universe, and calculated how many cubic millimeters they would make as sand, and mapped it over the surface area of the Earth. He figured that sand would bury the Earth to a depth of 450 kilometers or so. Since that isn’t the case, QED. I thought it was novel.


Google answers, of all places.

  • skitter

    What partial or whole measurement is extrapolated or averaged to come up with star estimates?

    • dmilligan

      The star estimates are from estimates of the number of stars in the Milky Way and are based on star density measurements of a an area and then extrapolated. Or, 'fancy guesswork and how dare you question a professional astronomer' type of values. It's dealing with those sort of values that got me disgusted with the data I was seeing. On the other hand, I wouldn't want to try and count all of those stars by hand either.

      • OA5599

        While your star estimates may be valid, I don't know that I'd trust sand guessing to the same people who took three years to count one birth certificate. I'll wait for Dr. Harrell or some other geologist to chime in on their math.

        • dmilligan

          Sounds good to me, I didn't think about asking Mike about it. He's playing in Yellowstone right now, so he probably won't be around for a week or so.
          But, I bet he agrees with the figure from U of H.

    • dmilligan

      I forgot to ask yesterday, but did I answer your question on star estimates to your satisfaction?

      • skitter

        Yes, thank you. My guesses were either some poor soul counting away, or somehow measuring the total radiation and then dividing by average star radiation (which would still require someone using all of their fingers and toes, in binary.)

  • PowerTryp

    Where do I sign up for your class on the physics of won ton burrito meals?

  • dmilligan

    Sorry, I mostly just shuffle papers, disrupt board meetings, and attempt to look respectable at alumni dinners. The last task is the hardest one.

  • Very interesting. I may want to be an astronomer. You basically just make SWAGs all day, publish it, and collect your $250 as you pass Go!

    Also, good Professor, my coworker thinks you're hilarious. I heard him chuckling under his breath and asked what was so funny and he said he was reading your post.

    • dmilligan

      Well, I'm glad that I can be entertaining and maybe pass on a tiny sliver of factual information at the same time. SWAGs do appear to be the order of the day in astronomy, but given the huge numbers of objects that they have to deal with and the difficulty in detecting them, they have to work with something. I poke fun at astronomers, but I admire them very much.

      • Oh, absolutely. And considering they are making new discoveries every time Hubble comes out of sleep mode, the best they can do is publish rough order of magnitude numbers. Besides, once you get above 10^8 or so, the human brain can't really comprehend it. At that point, the brain basically hears "infinity" and moves on. Otherwise, it'd go into a stack overflow and we'd be rebooting undergrads on a daily basis.

        • Deartháir

          You reboot undergrads with a pair of jumper cables attached to their nipples, right?

          • dmilligan

            If you install electrodes you get better contact. They last longer, too.

          • I prefer my undergrads come with nipple rings. Then the electrodes are pre-installed!

            Note: I have never asked any of our undergrad interns if they have nipple rings. I fear that would lead to my immediate dismissal for sexual harassment, despite my purely altruistic intentions.

          • dmilligan

            It's a safety issue in a physics lab. There are lots of high voltage power sources and energized equipment. Metal objects on the body can cause sudden arcing, severe burns and even death. All students should notify their instructors if they have metal piercings on their body, and their location. Otherwise, students will not be allowed into the labs without a full-body non-conductive hazmat type of suit, provided by the student.

            See how easy that is? You're welcome.

          • Unfortunately, the only danger in my cube farm is a lot of hot air spewing from certain, discreet sources.

          • Deartháir

            Beans, beans, the musical fruit…

  • BlackIce_GTS

    Tedious informational supplement: 10^18th is a quintillion, 10^22 is 10 sextillion.
    I can count to (10^45)-1*, because 10^45 is a 'quattuordecillion', and that's a hard word to remember.

    *Except I can't, because that would take 317 decillion (3.17×10^35) years (at the unreasonable rate of 1 number/second).

    • dmilligan

      Aha, you're one of those snotty little buggers that are always waving your hands during a lecture, aren't you? Didn't you ever wonder why the tires on your bicycle were always flat?

  • highmileage_v1

    I play around at this site very once in a while:
    &lt ;http://www.planethunters.org/>
    I don't know if I'm actually helping some struggling academic find a planet, but it is kind of fun.

    My nephew is doing something String Theory/ Quantum Mechanics/ Astronomy related these days. I sort of understand the general concepts, but the detail work is waaay over my head. I think he has a grant to play with a collider in Saskatchewan(?). (Saskatchewan has a collider? Who knew? Who would notice?)

    • Alff

      It makes me wonder what higher knowledge of the workings of the universe are to be gleaned from watching two moose butt heads.

      • dmilligan

        You never can tell with those sorts of things. I'll have to write up a proposal and submit to the budget committee. It's all in the name of Science [cue music, sparkly lights].

      • highmileage_v1

        I'm not sure what cosmic inspiration there is in Saska-bush although the stars are pretty when it's minus frickin' forty. As far as Prairie Moose go, I lived in Moose Jaw for a couple of years and never saw one of the critters…

    • mr. mzs zsm msz esq

      Yup it's where the Canadian Light Source is now, an experiment named EROS used to be there, I liked that name.

      • dmilligan

        I just checked on the website, and that's a nice looking facility with a good machine. Lots of things can be done at that facility. Thanks for the info.

    • dmilligan

      Donating your excess computer capacity Is a great thing to do, and every little bit helps. There is an insane amount of data that has to be analyzed, and it all takes CPU cycles.
      It's wonderful to hear that your nephew is getting involved in particle physics and cosmology and the egghead math that goes with it. Not many people are capable of doing that kind of research, so it's good to see new faces. I had no idea that Saskatchewan had a collider, but good for them. If nothing else, it is a good teaching tool.

      • highmileage_v1

        It is good to see him interested in something. He was aimless for a while; surfer, bartender, marketer, etc. Then he took a physics course out of curiosity and took a liking to the subject. His Prof was instrumental in cultivating his interest and managed to have him included in a number of research projects. After that, there was no stopping him.

        A buddy of mine is in the field as well. I remember being out one night with his telescope observing Halley's comet on its last transit. Fascinating.

      • Deartháir

        Saskatchewan does have a collider… problem is I'm not sure they really understood what it was they were supposed to be building. It's not quite on the same level as CERN:

        <img src="http://www.streetlegaltv.com/forum/attachments/2409d1242856238-pontiaccrash.jpg&quot; width="550">

        • dmilligan


  • Victor

    Dust in the Wind.