![]() If you go out in the early evening and observe the western horizon just after sunset when the stars are first becoming visible, there will be some constellation of stars there. However, there is a second motion of the sun that is not as obvious, but was observed and tracked by the Babylonians. This apparent motion of the sun is caused by the earth’s west to east rotation. As everyone knows, the sun rises in the east and sets in the west every day. The ecliptic is more accurately defined as the apparent annual path of the sun through the stars. Under this model the ecliptic is a great circle on the sphere at any one time half of it stretches across the sky in a rough east to west direction. At any one time only half the sphere is visible the other half is below the horizon. To visualize the ecliptic we can think of the sky as a huge “celestial sphere” with the earth in the center and with the stars plastered to its inside surface (see Figure 1 below). By carefully observing their wanderings over many years, the ancient Babylonians observed that all the planets seem to move along roughly the same path through the stars. Ancient people believed the planets to be heavenly bodies whose motions could influence events on earth thus it was important to chart and predict their motions through the stars. The ancient Babylonians were the first to pay careful attention to the wanderings of the planets. We now know them to be the five planets of our solar system that are visible to the naked eye-Mercury, Venus, Mars, Jupiter, and Saturn. These “stars” became known as “wandering stars,” or planets. The fact that constellations do not change their size or shape led ancient people to notice that some “stars” do not stay put within any constellation. The Big Dipper always looks the same, no matter when we observe it, although it might be in a different part of the sky or pointing in a different direction. Ancient people observed these changes and noticed a very important fact-while constellations do move around in the sky, they never change their size or shape. Even in the course of a single night, they can be observed to change their position as the earth rotates. Another well-known constellation is Orion, whose belt forms three bright stars visible in the winter sky of the northern hemisphere.Īs the earth moves around the sun, constellations move around in the sky, sometimes disappearing from view for weeks or months. One well-known constellation is the Big Dipper if one “connects the dots” formed by the stars of the Big Dipper, the resulting shape looks like a large ladle, or “dipper.” The Big Dipper is actually part of a larger constellation known as Ursa Major, or the Great Bear. In gazing at the nighttime sky, ancient people noticed that the stars occur in distinct groupings, which we call constellations. To understand what a planetary model does, we must first consider the sky at night. We shall see that trigonometry is exactly the ingredient that makes such geometric models-both ancient and Copernican-quantitatively useful. I show how to find the parameters of this basic model and how to use the model to compute planetary positions. ![]() In this paper I describe the prototype of the Greek and Indian models for planetary motion-the basic “epicycle-deferent” model invented by Apollonius of Perga. Working with these historically significant models-both ancient and Copernican-requires a good knowledge of basic trigonometry, a fact which is left out of most history books, with the result that few people are aware of their mathematical underpinning. Computation with these models was a major impetus behind the development of trigonometry, and Copernicus’s attempt to simplify and refine them led to the “sun-centered” geometric model of the Copernican Revolution. For these two reasons, ancient civilizations such as the Babylonians, Greeks, Indians, Chinese, and Mayans systematically observed the sky and worked out mathematical schemes to describe what they found there, thereby establishing the science now known as mathematical astronomy.Īncient mathematical astronomers in Greece and India in particular employed a variety of geometrical models to describe the pattern of movements within the sky, models that were further developed by the Islamic civilization. The regular movements of the sun, moon, and stars provided humanity with its first clocks and calendars, while the irregular but still patterned motions of the planets inspired the idea that their wanderings may influence events here on earth. Since ancient times, human beings have observed the sky and the movements of the objects-sun, moon, stars, and planets-within it.
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