Counting all the grains of sand on earth
The Sunday Nation
Nairobi,
12 May 2013
George Gitau was
watching a documentary on TV and he heard them say that “That
there are more stars in the Universe than the total grains of sand on
Earth!”
The commentator went ahead to explain that “the
Milky Way [Galaxy] has 220 Billion stars and it is estimated that the
known universe has 220 Billion galaxies.”
So, George wonders whether the product of
multiplying 220 billion galaxies by 220 billion stars is a bigger number
than all the grains of sand found on earth.
First things first: what is 220 billion time
220 billion? The answer is 48,400,000,000,000,000,000,000! For
simplicity, let’s round that to 50,000,000,000,000,000,000,000; that is,
the number 5 followed by 22 zeroes; or if you prefer, 50,000
billion-billion. This is surely a large number, but how does it compare
with the grains of sand on Earth?
The Earth has a diameter of about 12,800km;
this gives a total surface area of about 500 million square kilometres.
But two-thirds of the surface is covered by water, thus land is about
170 million square kilometres.
To find the total volume occupied by sand, we
multiply this land surface area by the average depth of sand. This
varies from a few hundred metres in the hot deserts to under one meter
on rocky ground. I would put the average at, say 20 metres.
Therefore the total volume of sand on earth is
about 3.4 million cubic kilometres; or 3.4 trillion cubic metres – the
number 34 followed by 11 zeroes.
Now the average brain of sand measures about
1mm across. Even though no grain looks the shape as another one, we can
safely estimate that the average volume is about one cubic millimetre.
So the question now is: how many cubic
millimetres are there is 3.4 trillion cubic metres? One cubic metre has
1,000 x 1,000 x 1,000 cubic millimetres (c-mm); that is
1,000,000,000c-mm.
Therefore, there are 3.4 trillion multiplied
by one billion grains of sand on earth. Interestingly, it easier to do
that calculation with pen and paper than with a calculator… this is how.
The first number is 34 followed by 11 zeroes;
the second is one plus 9 zeroes. Doing the multiplication means simply
adding the numbers of zeroes; thus 9 + 11 = 20. So the answer is 34
followed by 20 zeroes.
For the purpose of comparison with the number
of stars in the universe, we may round the last answer from 34 to 30.
Thus instead of, we now have 30 followed by 20 zeros; which simply 3
followed by 21 zeroes.
Now we can do the comparison. The stars are 5
plus 22 zeros while the grains of sand are 3 with 21 zeroes. Therefore,
it seems like the TV documentary was correct: there are more stars in
the universe that grains of sand on earth – ten times more!
Another way of thinking about it is that there
are ten stars in the universe for each grain of sand on earth. That’s
mind-boggling!
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