Re: [OT] Stars versus sand grains

From: Terry Pinnell (terrypinDELETE_at_THESEdial.pipex.com)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 10:08:57 +0100

"Terry Given" <the_domes@xtra.co.nz> wrote:

>something like 10^60 atoms in the entire universe.

As Phil pointed out, well established at the much higher figure of
about 10^80.

>If the earth is a sphere of 12,760km diameter, then the surface area of said
>sphere is 4*pi*r^2 = 511*10^12 m^2. A gross over-estimate would be 1km deep
>sand over the whole planet, ie volume = 0.5*10^18 m^3.
>
>for a grain of sand 1mm diameter, 1cm * 1cm * 1cm = 10^3 (not 10^6) grains
>per cm^3. lets assume this, ie 10^9 grains per m^3.
>
>therefore there are around 10^27 grains of sand on earth - and thats being
>pretty bloody generous. This number is likely to be an over-estimate, but
>not by more than 2-3 orders of magnitude. So its probably a fair comparison
>to the total number of stars in the universe.

Thanks for going to that trouble. It prompted the following
calculations of my own.

After further googling I've still not found anything that could be
called a 'consensus' for the star number. But say it's 10^22. FWIW,
that's about ten times more than one I've seen mentioned by several
sources, of '100 billion galaxies, each averaging 10 billion stars'.
(Of course, they may each have been quoting the same source...) As
you'll have seen from my follow-up, 1mm was a typo: should have been
0.1mm. And even that's probably far too large. Examined a few grains
under a microscope, and most were more like 0.01 mm. So my current
best guess would be say 0.02 mm. IOW, you could get 50 typical grains
of sand between the 1mm divisions on a ruler.

Using 5*10^14 m^2 as a crude approximation for Earth's surface area
would imply that a sand depth as little as 1 m covering the Earth
would then contain about 6*10^28. That's a million times *more* than
the star number. For the original assertion to be true would imply a
depth of only 0.00016 mm - far less than one grain's diameter!

This is all very crude, but reinforces my suspicion that for all its
familiarity the 'sand/stars' assertion might possibly be exaggerated.
Or, of course, the number of stars is many orders of magnitude larger
than any estimate I've seen so far. Or sand is a *lot* rarer than I'd
imagined.

Note that I've ignored packing limitations. That would reduce the
number of grains possible in any volume to a maximum of about 74% of
the superficially-calculated one; hardly significant for this
question! And needless to say, I'm also ignoring issues like 'the
universe is infinite', or 'there are an infinite number of universes',
or 'it's all in the mind', etc, etc!

>on an unrelated note, I tried doing some design calcs at a friends house the
>other day (I had an idea :) and borrowed a shitty little calculator. no
>sqrt() function, and couldnt handle numbers < 1/1000000. no use to me :)
>
>cheers
>Terry

I often use the 'Calculator' key on my PC keyboard to bring up the
built-in Windows utility. Or load up Excel, as I did to prepare the
following table.

                        Number in
Grain size Number in 'handfull' Number if covers Earth at:
in mm 1 cubic cm of 100 cm^3 1 metre depth 1 mm depth
---------- ---------- ----------- ------------- -----------
0.10 1.E+06 1.E+08 5.E+26 5.E+23
0.05 8.E+06 8.E+08 4.E+27 4.E+24
0.02 1.E+08 1.E+10 6.E+28 6.E+25 

-- 
Terry Pinnell
Hobbyist, West Sussex, UK