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Re: [Phys-L] Halfway point ???



On 04/03/2015 08:19 AM, Donald Polvani wrote:
range of atmospheric dust particle "sizes" as 0.001 to 30 microns
mean radius of earth = r_e = 6371 km
mean "radius" of proton = r_p = 0.86 fm

Then arithmetic mean of r_e and r_p is about 3200 m
Geometric mean is about 2 microns
Harmonic mean is about 2 fm

1) I estimated this one in my head: The proton is a
little less than one fermi, i.e. 10^-15 meters. The
earth is a little less than 10^7 meters (in accordance
with the original /definition/ of the meter). So
the span there is 22 orders of magnitude. The square
root of that is 11 orders of magnitude. So the
geometric mean ought to be 10^11 fm, i.e. 10^-4 m,
i.e. 100 microns ... or a little less.


2) Whenever I see a mistake, I try to figure out where
it came from. Similarly, whenever I see an ill-posed
question, I try to figure out where it is coming from,
to figure out what question /should have been asked/.

In the present case, it seems plausible that a factor
of "kilo" got dropped from the size of the earth,
early in the calculations.

My number for the geometric mean is bigger by a factor
of √1000; I get 74 microns, which is still a bit
too big to qualify as a dust particle.

Also consistent with this hypothesis, my number for
the arithmetic mean is bigger by a full factor of
1000; I get 3186 km (not m).


3) Doing order-of-magnitude estimates is a useful
technique. In some cases it solves the problem all
by itself. In other cases is serves as a valuable
check on other methods.


4) BTW, if you take the geometric mean of the /masses/
you get something even bigger, almost 0.1 kg, which
is waaay too big to qualify as a dust particle.