The Virtuosi (Posts about sand)https://thephysicsvirtuosi.com/enContents © 2019 <a href="mailto:thephysicsvirtuosi@gmail.com">The Virtuosi</a> Thu, 24 Jan 2019 15:05:03 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rss- Grains of Sandhttps://thephysicsvirtuosi.com/posts/old/grains-of-sand/Jesse<div><p><a href="http://3.bp.blogspot.com/-87-vnzGa9Po/TiRR2qFWprI/AAAAAAAAAF0/KsfRQhoL5Ds/s1600/SandUDunesUSoft.jpg"><img alt="image" src="http://3.bp.blogspot.com/-87-vnzGa9Po/TiRR2qFWprI/AAAAAAAAAF0/KsfRQhoL5Ds/s320/SandUDunesUSoft.jpg"></a></p>
<p>Have you ever sat on a beach and wondered how many grains of sand there
were? I have, but I may be a special case. Today we're going to take
that a step further, and figure out how many grains of sand there are on
the entire earth. (Caveat: I'm only going to consider sand above the
water level, since I don't have any idea what the composition of the
ocean floor is). I'm going to start by figuring out how much beach there
is in the world. If you look at a map of the world, there are four main
coasts that run, essentially, a half circumference of the world. We'll
say the total length of coast the world has is roughly two
circumferences. As an order of magnitude, I would say that the average
beach width is 100 m, and the average depth is 10 m. This gives a total
beach volume of $$ (100 m)(10 m)(4 \pi (6500 km) )= 82 km^3$$ That's
not a whole lot of volume. Let's think about deserts. The Sahara desert
is by far the largest sandy desert in the world. Just as a guess, we'll
assume that the rest of the sandy deserts amount to 20% (arbitrary
number picked staring at a map) as much area as the Sahara. According to
wikipedia the area of the Sahara is 9.4 million km^2. We'll take, to an
order of magnitude, that the sand is 100 m deep. 10 m seems to little,
and 1 km too much. That amounts to \~1 million km^3 of sand. We're
going to assume that a grain of sand is about 1 mm in radius The volume
occupied by a grain of sand is then 1 mm^3. Putting that together with
our previous number for the occupied volume gives $$ \frac{1\cdot
10^6 km^3}{1 mm^3}=\frac{1 \cdot 10^{15}}{1\cdot
10^{-9}}=1\cdot 10^{24}$$ That's a lot of grains of sand. Addendum:
Carl Sagan is quoted as saying</p>
<blockquote>
<p>"The total number of stars in the Universe is larger than all the
grains of sand on all the beaches of the planet Earth"</p>
</blockquote>
<p>If we just use our beach volume, that gives a total number of grains of
sand as \~1*10^20, which is large, but not as large as what we found
above. Is that less than the number of stars in in the universe? Well,
that's a question for another day (or google), but the answer is, to our
best estimate/count, yes.</p></div>carl saganorder of magnitudesandhttps://thephysicsvirtuosi.com/posts/old/grains-of-sand/Mon, 18 Jul 2011 11:33:00 GMT