Billions and Billions

July 28, 2008 – 10:09 pm

So, I recently got the idea of "billions and billions" in my head, thanks to memories of Carl Sagan, and wondered how many "billions and billions" is, particularly in respect to the Milky Way galaxy.

According to the Physics Factbook, the consensus among modern theorists seems to be that the number of stars in our galaxy is around 100 billion give or take a handful.

Of course, stars are massive. Our own sun, which is not one of the bigger classes of stars masses 1.9891 * 10³⁰ kilograms or 332,946 times the weight of the Earth. So 100 billion stars is obviously pretty massive.

But what if you had 100 billion grains of sand, or 100 billion popcorn kernels--as many as all the stars in the galaxy?
How much would they weigh?

Well, the popcorn question was easily answered with a trip to the kitchen. I flipped open my digital scale, placed a little paper cup on it, zeroed it out, and started adding random kernels until I got what I considered to be a nice round number of 3.5 grams. I then took the cup off the scale and counted it out, coming up with 15 unpopped popcorn kernels, weighing in at an average of 0.233333 grams per kernel.

Let's do that math... multiply 0.233333 by 100 million (that way we get kilograms without having to do the extra division later) and we have 23,333,333 and 1/3 kilos of popcorn or 25,713 and 1/3 short tons (2,000 pounds - known normally as "a ton" in the U.S.). Now compare that to the weight of just one Nimitz class aircraft carrier at full load, which weighs 97,000 tons. So as many popcorn kernels as there are stars in the galaxy weighs a little more than 1/4 of an aircraft carrier.

But when we get to sand, well, that's tricky. If you check out what the Physics Factbook has to say about the weight of a grain of sand, you get all sorts of talk about grain size, composition, and numbers ranging from as low as 0.01 milligrams to about 23 milligrams. So 100 billion grains of the biggest, heaviest sand would be about 5,074,168 pounds or 2,302,254 kilos. But at the smallest measurement, .01 milligrams per grain (i.e. it takes 100,000 grains to make a gram of sand, which seems pretty ridiculous), you'd come up just short of 1,001 kilos (1,000.98) or 2,206 pounds.

If we take an average of the upper and lower bounds of the two more reasonable ranges on the Physics Factbook's page, we come up with 8.71 milligrams. One hundred billion of those grains of sand would weigh in at 871,000 kilos, or 959.84 short tons of sand.

Can you come up with any rough equivalents for 100 billion? If so, post them in the comments below.