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

the Moon?

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.

Light ray

Exits at the

same angle

Corner cube prism (three-dimensional)

A B

C

If the length of AB is known, the lengths of AC

and BC can be determined by finding ∠BAC

and ∠ABC.

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