Global Positioning System Reference
In-Depth Information
The one figure who stands out in this period is Claudius Ptolemy, a
Roman who wrote in Greek and lived in Alexandria, the home of Eratos-
thenes 350 years earlier. We will meet Ptolemy again, in more auspicious
circumstances. He has been called the father of modern geography because
of his contributions to mapping, but his influence on geodesy was baleful.
Recalculating Posidonius's results, Ptolemy used a value for the stadion
that was only
5
⁄
7
of the what we now believe it to be, and so determined a
measurement for the radius of the earth that was 17% too small. He also
wrongly believed that Asia stretched halfway around the world instead of a
third of the way. The result of these errors came home to roost one and a
half millennia later, when Columbus consulted Ptolemy's writings and
concluded that Asia was far closer than was actually the case.
8
During the European Dark Ages, the flame of geodesy was carried for-
ward elsewhere. In Tang China around 725 CE, a government-appointed
Buddhist monk named I-Hsing (Yi Xing) set about determining the size of
the earth by setting up stations across China to measure the length that
corresponds to a degree of arc. Such measurements anticipated Al-Mamun
by a century and, we will soon see, became very fashionable in Europe a
thousand years later. I-Hsing arranged for measurements to be made of the
lengths of the midsummer and midwinter shadows from gnomons and of
the altitude of Polaris. From these he made estimates of the length of a
meridian arc.
9
This investigation took place in a flat-earth culture and
stands out more for the advanced nature of the investigations than for the
influence they had on geodesy.
Now we come to Al-Biruni (973-1048 CE, shown in fig. 2.6). His
method for estimating the earth's radius was di√erent from the three con-
He advocated the view that earth moved around the sun. He also estimated the distance to
the moon, as follows. Assuming that the moon went around the earth at constant speed in a
circular orbit, he measured the time it took for the moon to pass through the earth's shadow
during a lunar eclipse. Knowing the size of the earth and the moon's orbital period, he
determined that the earth-moon distance equals 60 earth diameters—pretty close to the
true value. Aristarchus's views, and the questions he asked, would not be seriously enter-
tained in Europe again for close onto 1,900 years. To learn more about Aristarchus, see, for
example, Heath (1981).
8. You might well ask why medieval Europeans consulted ancient texts to determine the
size of the earth, rather than simply go out and repeat the experiments themselves. Good
question. Christian dogma may not have been so pervasive as to insist on a flat earth, as we
have seen, but it did discourage innovation and independent query. See, e.g., Boorstin
(1983).
9. An analysis of I-Hsing's achievements is provided in Beer et al. (1961).
