Date: Wed, 29 Sep 2004 07:40:20 -0500 (CDT) From: "P.E. Robinson"
To: Michael Milligan Subject: Re: being cheap You can borrow my copy if... you can give me a quantitative answer to this: are there more stars in the universe than grains of sand on the Earth?
One of my students asked me this, and I told him that I thought stars would win...but I figured you have probably actually thought about this... -p- On Tue, 28 Sep 2004, Michael Milligan wrote: > Hey folks! > > Being as it's expenseive and hard to find, and since you (hopefully) > only take grad e+m once and always do the homework with other people > anyway, I never bothered to acquire a copy of Jackson. > > Yet, as fate and my big mouth would have it, I've landed a line of > research that would be made easier by having one handy for the next few > months. I.e., while I'm in Israel. > > Anyone feel like loaning me their copy for a while? It'll be about as > likely as I am to come back in good condition. > > Thanks, > ...Milligan
Ah, a challenge. The best way to win a book. Or, as I've found, a good way to annoy students while teaching them about scientific notation. Naturally, if contrary to the usual wisdom, sand throws down.
Pity he had to add the "on the Earth" bit, because I was all ready to throw in the snarky point that there are vastly more grains of sand than stars. Figure an Earthlike, water-eroded planet contains around <N> grains. Well, it's got to be true that more than 1/<N> stars will harbor such a planet. Especially when we consider just how big that is.
The question Paul really asked, though, is how
Giving the stars the benefit of the doubt, let's say a typical grain of sand occupies a cubic millimeter (they're generally a little smaller). That puts 1018 grains in a cubic kilometer.
Let's say a typical beach extends 100 m inland. I don't know how deep the sand generally is, but I'd imagine 10 m is a reasonable estimate. That gives a beach a cross-sectional area of about .001 km2. A book and documentary by PBS suggests there are 1.6 million km of coastline on Earth; we'll call it 1 million since not all of that is sandy beach, for a total of 1000 cubic kilometers of beach sand, or about 1021 grains.
Already we're up to the lower value of N*; to push <N> over the top, consider that continental shelves are also sandy, if submerged, and extend 1-10 km from the shore. So chalk up
Now, just to be mean, we'll throw in the deserts, where the