Global Positioning System Reference
In-Depth Information
FIGURE 2.4.
Two ways of
measuring the size of the
earth, from ancient Greece.
(a) Eratosthenes measured
the length of a shadow at
Alexandria while the sun
was directly overhead at
Syene. (b) Posidonius
measured the height of the
star Canopus (which sat on
the horizon when seen from
Rhodes) at Alexandria and
then calculated the earth's
radius using the known
distance between Alexandria
and Rhodes.
shadow, he derived mathematically the radius of the earth.
4
Eratosthenes'
measurement geometry is illustrated in figure 2.4a.
Eratosthenes found the radius of the earth to be 40,000 stadia. The
definition of a stadion is ambiguous. It is supposed to be the length of an
athletics stadium, but these varied in di√erent parts of the ancient Greek
world. The consensus of historians is that a stadion was 185 m, which
makes Eratosthenes' estimate for the earth's radius a little shy of 7,400 km.
This is too big by 16%, we now know—but it is a great achievement given
the limited resources he had available. The main point is that he used
measurement and observation in order to quantify; he did not settle for a
mythological or a philosophical and qualitative explanation for the earth's
physical shape and size.
4. The ratio of the length of the gnomon shadow to gnomon height is tan
a
. The angle
a
is
also equal to
d/R
, where
R
is the radius of the earth (see fig. 2.4a). When
a
and
d
are known,
R
can be determined.
