CHAPTER 3



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.

1. 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.

1. 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.

1. 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).

1. 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.

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.

1. 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.

1. During some eclipses the curvature of the Earth’s shadow would be more pronounced than during other eclipses.

1. Another explanation is that the diameter of the Earth’s orbit is tiny with respect to the distance to the stars.

1. 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.

1. Yes. No.

1. Yes, in fact there would be little difference in the apparent motion of the planet.

1. In both cases, when the epicycle is on the part of the deferent farthest from the equant.

Problems

1. 11 synodic periods = 12 years

1. 6188 seconds of arc = 1.72°

1. 62,000 m = 62 km

1. 4.8 m

1. Its angular diameter is reduced to 1/3 of its original value.

1. 1.25

1. 3.9

1. 19,200 km

Figure-Based Questions

1. Saturn

1. 21° , 8°, 6.6 times Earth’s distance

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