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Chapter 03 - Ancient Astronomy
CHAPTER 3
ANCIENT ASTRONOMY
CHAPTER OUTLINE AND LECTURE NOTES
1. Mesopotamian Astronomy
Physicists will no doubt recognize that the method used by the Babylonians to calculate the
positions of the planets is similar to Fourier decomposition.
2. Egyptian Astronomy
Perhaps because so few written documents about Egyptian science and mathematics have
been found, there is a controversy about the nature of science in ancient Egypt. The main
issue is whether Egyptian science contributed to Greek science or whether it was primarily
devoted to engineering applications.
3. Early Greek Astronomy
The timeline in this section is important to combat the notion that the Greek astronomers
were all contemporaries of one another. Many historians of science consider the era of the
Milesian astronomers to be the beginning of science. Certainly Anaximander’s model of the
cosmos was the first known explanatory model in history. Some of the ideas of the early
Greek astronomers, such as that motion must be on circles and the central position of the
Earth, were accepted for 2000 years.
4. Later Greek Astronomy
I’ve found that many students think anyone who lived before 1900 (or perhaps even 1980)
was hopelessly ignorant and dull. I love to use the accomplishments of the later Greek
astronomers to teach them otherwise. Students seem impressed by Aristarchus’s work
showing the enormous size of the solar system and Eratosthenes’s determination of the size
of the Earth. I use a demonstration I copied from Carl Sagan’s “Cosmos” series to
demonstrate Eratosthenes’s method. Place a flat sheet with two sticks on it in sunlight and
show that the lengths of the shadows of the sticks are the same. Then bend the sheet into an
arc and show that the shadows have different lengths. The greater the curvature of the
cardboard, the greater the difference in the lengths of the shadows. Some students need a
lot of help in understanding how the model of Ptolemy (or that of Copernicus, for that
matter) reproduces the retrograde motion of a planet. If you’re lucky, you may have an old
Ealing film loop on retrograde motion in your physics lecture demonstration materials. The
film loop shows a lighted ball moving on an epicycle and deferent as seen first, from above,
and then from a fixed-view camera at the center (the Earth).
5. Chinese and Mesoamerican Astronomy
Many cultures have produced interesting and significant astronomical results. The reason
that I haven’t emphasized them more in the text is that they didn’t lead directly to
contemporary astronomical ideas.
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Chapter 03 - Ancient Astronomy
KEY TERMS
astrology — A pseudoscience that holds that people and events are influenced by the
configurations of the Sun, Moon, and planets with respect to each other and the stars.
deferent — One of the circles on which a planet moved according to the Ptolemaic model of
the solar system.
epicycle — One of the circles upon which a planet moved according to the Ptolemaic
(geocentric) model of the solar system. The center of the epicycle moved on a larger circle,
called the deferent.
equant — In the Ptolemaic system, the point from which the motion of the epicycle around the
deferent appears uniform.
geocentric — Centered on the Earth. In the geocentric model of the solar system, the planets
moved about the Earth.
precession — The slow, periodic conical motion of the rotation axis of the Earth or another
rotating body.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. One way would be to have two kinds of years—one with 13 months = 325 days and another
with 14 months = 350 days. There would have to be 1 long year for every 4 short years.
2. One sphere carrying the Sun rotated eastward once per year. A second, tilted by 23.5° with
respect to the first, rotated westward once per day.
3. During some eclipses the curvature of the Earth’s shadow would be more pronounced than
during other eclipses.
4. Another explanation is that the diameter of the Earth’s orbit is tiny with respect to the
distance to the stars.
5. Mars could be seen at gibbous or full phase. Venus could be seen at either new and
crescent or full and gibbous phases, depending on whether its deferent was smaller or larger
than that of the Sun.
6. Yes. No.
7. Yes, in fact there would be little difference in the apparent motion of the planet.
8. In both cases, when the epicycle is on the part of the deferent farthest from the equant.
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Chapter 03 - Ancient Astronomy
Problems
1. 11 synodic periods = 12 years
2. 6188 seconds of arc = 1.72°
3. 62,000 m = 62 km
4. 4.8 m
5. Its angular diameter is reduced to 1/3 of its original value.
6. 1.25
7. 3.9
8. 19,200 km
Figure-Based Questions
1. Saturn
2. 21° , 8°, 6.6 times Earth’s distance
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