68 Chapter 1 Is Earth the Center ofthe Universe?
Before the Corner Cube Prism
Before the arrival of the Apollo spacecraft, what
did scientists have to do to find the distance to
Triangulation is the most general method of
measuring the distance to a place that you can-
not actually go. This technique involves observing
an object at a distance from two different places.
In the figure to the right, the line at the bottom
(known as the baseline) represents the distance
between the two observation points A and B,
and C is the object being observed. In order for
triangulation to work, one must know the cor-
rect length of line AB. One then uses the angles
drawn from points A and B to point C in trigo-
nometric functions to determine the distances to
point C. This practice is said to have already been
established in ancient Egypt around 3,000 BC.
It was also actively used in Greece during the
era in which the sciences of geography and
astronomy developed rapidly (from 2,500 to
2,000 years ago). One famous example of the
successful use of triangulation was Eratosthenes’
measurement of the size of Earth (see page 20).
Hipparchus (who lived around 190–120 BC) was a Greek astronomer who measured
the distance to the Moon a generation after Eratosthenes did. Unfortunately, the method
he used to do this is no longer known. Scientists speculate that he probably measured the
angles at which the Moon was visible at the same time of day from two points a known
distance apart, but since there were no clocks in his day, he must have used a solar or lunar
eclipse to know to mark the exact same time at two different locations.
Hipparchus concluded that the distance to the Moon was about 59 to 72.3 times
the radius of Earth. Since we now know that the distance to the Moon is actually about
60 times the radius of Earth, his calculation was pretty good, all things considered.
Exits at the
Corner cube prism (three-dimensional)
If the length of AB is known, the lengths of AC
and BC can be determined by finding ∠BAC