Too Many Stars

I need people to check my math on this.

A few weeks ago, Bill and I were on the way to Flagstaff, and we got to talking about the size of the Universe. Bill mentioned a recent survey of the cosmos which estimates that there are about 300 septillion (3.0 x 1023) stars (the 23 is supposed to be a superscript; blogger apparantly can't do superscripts), which is roughly three times the previous estimate of 100 septillion (3 x 1023) stars.

We tried to figure out how to represent that as something that we could more easily grasp, like if each star was a grain of sand laid out in a perfectly uniform carpet with the grains touching, how big an area would that cover? We decided it would probably be something ridiculously huge, like the area of the entire North American continent. Just driving the 100 odd miles between Holbrook and Flagstaff, imagining the number of grains of sand flying by on either side of us, it seemed like an awful lot.

Nope. I finally sat down to do the math.

Lets make all the sand grains about 0.5 mm in diameter. This makes for 400 grains/cm2, or 4 x 1012 grains/km2.

1 x 1023 grains of sand (representing stars) divided by 4 x 1012 grains/km2 = a total area of about 2.5 x 101o km2.
3 x 1023 grains of sand (representing stars) divided by 4 x 1012 grains of sand/km2 = a total area of about 7.5 x 101o km2.

However, the total land surface of the entire Earth is only about 1.5 x 108 km2....

Which means you would need between about 167-500 Earths (depending on which estimate for the number of stars that you use), with the entire land surface covered with a uniform carpet of sand one grain deep and with all the grains touching, to equal the number of stars in the visible universe.

If you drain all the water off the Earth so that you can cover the entire surface are of the Earth (which is about 5.1 x 108 km2), you would only need 49-147 Earths.

That is a shitload of stars. And they were ALL MADE JUST FOR US. Don't you feel fortunate?