Global Positioning System Reference
In-Depth Information
we would slide o√ it. Furthermore it was stationary, because if it moved we
would feel the motion. And it was the center of the universe, because the
stars rotated around it. Another early, pre-Socratic philosopher, Thales of
Miletus, may have considered the earth to be a disk resting on water. We
will meet Thales again; he had some more progressive ideas about geodesy.
His student Anaximander (early sixth century BCE) thought of the earth as
a cylinder, with a height three times its diameter. The axis of this cylinder
was oblique to the axis of the sun, and the earth was at the center of a
celestial sphere that contained the stars.
Pythagoras was a young man when Anaximander was expounding his
cylindrical thoughts. Whether or not Pythagoras heard of these ideas I do
not know, but if he did hear of them, he would have disagreed: on aesthetic
grounds the earth must be a sphere and must follow a circular orbit about
the sun. Aristotle, a couple of centuries later, agreed, but on altogether
more down-to-earth grounds. Aristotle believed in confirming philosophi-
cal hypotheses via observation, and he saw several indications that the
planet he resided on was a sphere. The shadow that the earth cast on the
moon during a lunar eclipse was circular, and this was true whether the
moon was high or low in the sky. The only object which casts a circular
shadow when lit from di√erent angles is a sphere. Furthermore, the man-
ner in which a ship at sea disappeared from view, in whatever direction it
was seen, argued for a spherical earth. The known stellar constellations
appeared lower in the night sky as one traveled farther south—and new
constellations appeared in the southern sky.
Eratosthenes (276-195 BCE) is widely known as the founder of geod-
esy. He is given credit for the first measurement of the earth's radius. For
him, qualitative observations were insu≈cient: he wanted measurements,
and this is why he is so highly regarded by geodesists. I will explain his
method and that of two later luminaries. Eratosthenes was librarian at the
famous library of Alexandria, on the coast of northern Egypt (fig. 2.3).
Farther south, on the Tropic of Cancer, was the city of Syene (modern
Aswan). Eratosthenes describes a deep well at Syene and tells us that the
bottom of the well was lit by sunlight at noon on the day of the summer
solstice, and so the sun was directly overhead Syene at that time. In Alex-
andria, he set up a
gnomon
(a sta√ or rod set perpendicular to the ground to
cast a shadow) and measured the length of its shadow at noon on the
summer solstice. He states that Syene was a distance of 5,000 stadia due
south of Alexandria. From this information and the length of the rod's
