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Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion - The Wandering Stars

Sandra M. Caravella (New Jersey City University)

To understand what a planetary model does, we must first consider the sky at night. In gazing at the nighttime sky, ancient people noticed that the stars occur in distinct groupings, which we call constellations. 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. Another well-known constellation is Orion, whose belt forms three bright stars visible in the winter sky of the northern hemisphere.

As the earth moves around the sun, constellations move around in the sky, sometimes disappearing from view for weeks or months. Even in the course of a single night, they can be observed to change their position as the earth rotates. 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. 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.

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. These “stars” became known as “wandering stars,” or 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.

The ancient Babylonians were the first to pay careful attention to the wanderings of the planets. 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. 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. That path became known as the ecliptic.

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). At any one time only half the sphere is visible; the other half is below the horizon. 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.

Figure 1

The ecliptic is more accurately defined as the apparent annual path of the sun through the stars. As everyone knows, the sun rises in the east and sets in the west every day. This apparent motion of the sun is caused by the earth’s west to east rotation. However, there is a second motion of the sun that is not as obvious, but was observed and tracked by the Babylonians. 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. (In reality, the air pollution and artificial light of modern times obscure the stars at the horizon just after sunset, but in ancient times, from whence these ideas originate, these stars were easier to see.) If you did this over the course of a complete year, you would observe that the constellation in that part of the sky at that time of the evening changes. In ancient times you would see (roughly) the constellation Capricorn in January, Aquarius in February, Pisces in March, Aries in April, Taurus in May, Gemini in June, Cancer in July, Leo in August, Virgo in September, Libra in October, Scorpio in November, and Sagittarius in December. These, of course, are the well-known signs of the zodiac; in fact, this is where the zodiac comes from. The sun, moon, and planets all appear to wander through the constellations of the zodiac. More specifically, the sun completes one cycle through the zodiac in one year, moving in an apparent circle around the earth. This circle is the ecliptic.

Sandra M. Caravella (New Jersey City University), "Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion - The Wandering Stars," Loci (August 2010), DOI:10.4169/loci003120