🚀 go-pugleaf

On 3/29/95 Richard Swanson challenged us to estimate some large numbers.

           Let me try to answer the first half of his first question.

>   How many grains of sand in all the beaches of the world?

Estimations of that kind are often referred to as "Fermi's method" because
Enrico Fermi was famous for making them. He often used this method in
scientific projects claiming that an educated guess is better than nothing
at the beginning of a project. (see Prelude to Physics, by Clifford Swartz).

I vaguely remember somebody saying that the size of the first nuclear reactor,
(called "atomic pile", University of Chicago, 1942), was initially estimated
by Fermi on the basis of guessed parameters. The cross sections of most
important nuclear reactions were not known at that time. Monitoring of Geiger
counters, when the reactor was being constructed, was essential to avoid a
catastrophy and to stop the chain reaction just when it started. The initial
predictions turned out to be resonable; the reaction started as expected.

Here is my way of answering the grains of sound question.

The diameter of the planet is about 25,000 miles or roughly 40,000 km.
Without looking at the map let's assume that the total length of shores is
five times the diameter, or 200,000 km. Without consulting anything I would
guess that about 25% of shores are beaches. This amounts to 5*10^7 meteres.
If the average width and depth of the beach is 30 meteres and 5 meteres,
respectively (I am not a geologist), then the volume of the sand is 7.5*10^9
cubic meters. If the average grain is about 1 cubic millimeters (10^-9 cubic
meters) then the total number of grains is 7.7*10^18. Rounding up my
estimation is 10^19 grains.

Hopefully, overestimated and underestimated guesses cancel and the order of
magnitude is about right; I would not bet my life on it.


>        How many atoms in the earth?

That question is easier to answer; the mass, the composition (% of each
element) and atomic weights are available.

             Ludwik Kowalski       kowalski@apollo.montclair