CHAPTER 4 | THE ORIGIN OF MODERN ASTRONOMY 55
at Alexandria in what is now Egypt. He ensured the continued
acceptance of Aristotle’s universe by transforming it into a
sophisticated mathematical model.
When you read The Ancient Universe on pages
56–57, notice three important ideas and fi ve new terms that
show how fi rst principles infl uenced early descriptions of the
universe and it motions:Ancient philosophers and astronomers accepted as fi rst prin-
ciples that the heavens were geocentric with Earth located at
the center and sun, moon, and planets moving in uniform
circular motion. It seemed clear to them that Earth was not
moving because they saw no parallax in the positions of the
stars.
Th e observed motion of the planets, the evidence, did not fi t
the theory very well. Th e retrograde motion of the planets was
very diffi cult to explain using geocentrism and uniform cir-
cular motion.
Ptolemy attempted to explain the motion of the planets by
devising a small circle, an epicycle, that rotated along the
edge of a larger circle, and the deferent, which enclosed a
slightly off -center Earth. An equant was a point from which
the center of an epicycle appeared to move at a constant rate.
Th at meant the speed of the planets would vary slightly as
viewed from Earth.Ptolemy lived roughly fi ve centuries after Aristotle, and
although Ptolemy based his work on the Aristotelian universe, he
was interested in a diff erent problem—the motion of the planets.
He was a brilliant mathematician, and he was mainly interested
in creating a mathematical description of the motions he saw in
the heavens. For him, fi rst principles took second place to math-
ematical precision.
Aristotle’s universe, as embodied in the mathematics of
Ptolemy, dominated ancient astronomy, but it was wrong. Th e
planets don’t follow circles at uniform speeds. At fi rst, the
Ptolemaic system predicted the positions of the planets well;
but, as centuries passed, errors accumulated. If your watch gains
only one second a year, it will keep time well for many years, but
the error will gradually become noticeable. So, too, did the
errors in the Ptolemaic system gradually accumulate as the cen-
turies passed, but, because of the deep respect people had for the
writings of Aristotle, the Ptolemaic system was not abandoned.
Islamic and later European astronomers tried to update the sys-
tem, computing new constants and adjusting epicycles. In the
middle of the 13th century, a team of astronomers supported by
King Alfonso X of Castile studied the Almagest for 10 years.
Although they did not revise the theory very much, they simpli-
fi ed the calculation of the positions of the planets using the
Ptolemaic system and published the result as Th e Alfonsine
Tables, the last great attempt to make the Ptolemaic system of
practical use.1
2
3
Aristotle, Aristarchus, and Eratosthenes were philosophers,
but the next person you will meet was a real astronomer who
observed the sky in detail. Little is known about Hipparchus,
who lived during the second century bc, about two centuries
after Aristotle. He is usually credited with the invention of trigo-
nometry, the creation of the fi rst star catalog, and the discovery
of precession (Chapter 2). Hipparchus also described the motion
of the sun, moon, and planets as following circular paths with
Earth near, but not at, their centers. Th ese off -center circles are
now known as eccentrics. Hipparchus recognized that he could
reproduce this motion in a model where the celestial bodies trav-
eled around a small circle that followed a larger circle around
Earth. Th e compounded circular motion that he devised became
the key element in the masterpiece of the last great astronomer
of classical times, Claudius Ptolemy.
The Ptolemaic Universe
Claudius Ptolemaeus was one of the great astronomer-mathema-
ticians of antiquity. His nationality and birth date are unknown,
but around ad 140 he lived and worked in the Greek settlement
SunlightAlexandria Well at Syene7 °
Earth’s
centerZenith at
Alexandria7 °■ Figure 4-7
On the day of the summer solstice, sunlight fell to the bottom of a well
at Syene, but the sun was about __ 501 of a circle (7°) south of the zenith at
Alexandria. From this, Eratosthenes was able to calculate Earth’s radius.