Number the Stars

My uncle asked me an interesting physics-related question the other day, so I thought I’d share the question and my answer on the blog:

Q: If a trillion seconds take 30,000 years and there are three trillion stars in the universe, it would take ninety thousand years to count them at one per second. So how do we know?
Before you click through to my explanation, why not take a few minutes to think about how you might answer this?  How DO we count that which is essentially uncountable?

A hint, by way of another question: How would you count the number of grains of sand on a beach?  What’s your strategy for those “guess how many candies are in this jar” type of games?

Now, after you’ve mulled it over for a little bit, here’s my response:

A: You’re right, there’s no way we could ever actually count all the stars.  For one thing, there’s too many, a lot more than 3 trillion: latest estimates put the number around 70 sextillion, a 7 followed by 22 zeros, which is more than twenty billion times bigger than 3 trillion, and it would take 2 quadrillion years to count that high, one number per second.

The second problem is that, in all but the closest galaxies, we can’t see most of the individual stars, so we couldn’t count them if we wanted to.  In fact, there are about 100 billion galaxies in the known universe, so we can’t even count them one by one.

What astronomers have to rely on is the large-scale uniformity of the universe.  That is, no matter which way we look, on a large enough scale, the universe looks the same.  On small scales, this is obviously untrue, as we see stars surrounded by huge amounts of empty space, but the uniformity sets in on truly unimaginable (but still measurable) cosmic scales.  The discovery of the uniformity of the universe was one of the most shocking discoveries of the 20th century, and led to the inflationary model of the big bang.

(Actually, there’s a stronger statement, called the cosmological principle, which says that the universe, on large scales, is homogeneous and isotropic.  That is, it’s the same in any sector of the universe, and it doesn’t matter what direction you look.)
Anyway, we can put this uniformity of the universe to good use in estimating the number of stars.  If you wanted to know how many grains of sand there are on a beach, you would see how many grains of sand there are in a cubic inch, and then measure the size of the beach and extrapolate from there.  If the sand was balled up in little dirt clods, you’d count how many grains of sand are in the average clod (analogous here to a galaxy), and then multiply that by the number of clods.

By studying our own galaxy, astronomers know a lot about the distribution of stars of different sizes and brightnesses, so they can measure the brightness of a distant galaxy and estimate the number of stars it contains.  They do this for a small section of the sky, and then extrapolate to the whole sky, just as you would do with grains of sand on a beach.

When scientists report a number for a measurement, they always give an uncertainty, indicating that this number is accurate plus or minus a certain fraction.  Of course, newspaper articles, etc. never report these.  But because the number of stars has been estimated rather than literally counted, that’s why they give a big round number, rather than saying it’s 70 sextillion and two or something.

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4 Responses to “Number the Stars”


  1. 1 Exoplanetology June 29, 2009 at 3:52 PM

    If there’s no way “we can ever actually count all stars”, then the prospect of counting all exoplanets is even more mind-blowing.
    Thanks for this post. You have inspired wonder in me. Now “Number the Planets” is a blog post begging to be written. 🙂

  2. 2 excitedstate June 29, 2009 at 6:53 PM

    With a lot more data about planets outside of the solar system, we might be able to hazard a guess as to the number of planets. We would need an idea of the percentage of stars with planets, and then go from there. A problem is that we can only see fairly large planets with current techniques.

    But we would also want to know whether there is a correlation between the type of star and the likelihood that it would have planets. Then we should be able to number the planets based on our numbering of the stars.

    Of course, this exciting search is just getting started.

  3. 3 Lab Rat July 12, 2009 at 3:01 AM

    I was always terrible at those ‘guess the number of sweets in the jar’ games. i just used to say the biggest number I could think of and then add five to make it more ‘realistic’.

    Great post…I had wondered before how they calculated things like star and planet numbers, i’d just assumed there were some kind of rapidly scanning computers hooked up to telescopes of something 🙂

  4. 4 María August 25, 2009 at 5:15 PM

    I’ve always asked myself that question. Now it’s the first time i’ve really thought about it and i got it before reading yor solution! I’m so happy hehehe (i took your advice :)).

    Now i’d like to make a question about stars. Star blinks, so Could astronomers get confused about if it’s caused by the diversion of ligth or if it’s because that star is a binary star? or that’s impossible?

    Thank you!


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