## The armillary sphere

In order to better visualize in three dimensions the relationship between the Earth perceived as the center of the universe and the sky around it, the ancients created an instrument called the armillary sphere. There is evidence that Eratosthenes used an armillary sphere in the 3rd Century bc to determine the angle in the sky between the celestial equator and the ecliptic. Scholars at the great library in Alexandria also used this instrument to visualize the heavens, compute the coordinates of the stars on the celestial sphere, and make calculations involving angular distances between heavenly bodies. At about the same time during the Han dynasty (207 bc-220 ad) in China, the armillary sphere was developed and became an important astronomical tool. Its popularity continued in Islamic countries during the 8th to 15th Centuries ad, when several treatises were written on its construction and use. During the Renaissance, the armillary sphere continued to be used for education and calculation, and one of the first European makers of this instrument was Johannes Regiomontanus (1436-1476), who we shall meet in Section 3.8.2. During the Age of Exploration (1400 to 1800), the armillary sphere was used in training navigators; in fact, it became an important symbol of Portuguese exploration during the heyday of their activities in the 15th and

16th Centuries, often appearing figuratively on banners and paintings. Most armil-lary spheres were geocentric, with the Earth appearing in the center, and it was not until the 18th Century that Sun-centered armillaries were produced. But, by then, advances in spherical trigonometry and the development of the telescope and other instruments that could more accurately determine the positions of heavenly bodies in the sky led to the armillary sphere becoming more of a decorative piece than a tool for celestial calculations.

The armillary sphere consisted of a number of nested rings, or armillaries (which means "bracelet" in Latin). These were of varying diameters and represented the principal celestial spheres. One of these rings was fixed and was connected to the base of the instrument; this represented the observer's horizon. The other rings could be moved or pivoted around an axis to match the latitude and longitude of the area in the sky being observed. Usually, there were rings representing the meridian, the celestial equator, and the ecliptic. In some larger versions, there were also rings representing the orbits of the Sun and planets. Many of the rings were calibrated in degrees. In the center was a sphere representing the Earth. Most armillary spheres that were used for observation and calculation were large and made out of brass, but those that were primarily used for demonstrational purposes were smaller and often constructed of cheaper material such as wood rather than metal.

A schematic of this instrument is shown in Figure 1.4. Imagine yourself way out in space looking back on the rest of the universe. There in the center is the Earth ("Terra", in black), oriented with the north pole pointing directly up. At a 23j degree angle around the Earth is the ecliptic ("Ecliptica") with the 12 constellations of the zodiac. In parallel to the spherical Earth, the universe itself can be conceived of as a sphere, with many of the circles on the Earth being projected onto the universal sphere. Thus, the projection of the equator is the celestial equator (here the "Aequienoctoalis"). Note also the projections of the Tropics of Cancer and Capricornis, the Arctic and Antarctic Circles, and the Arctic and Antarctic Poles. Like the Earth, the sky may be divided into 360 degrees, going up or down from 0 to 90 degrees from the celestial equator. In this diagram, the orientation shows east ("Oriens") to the left and west ("Occidens") to the right. Just as on the Earth, many of the circumference lines on the celestial sphere whose center is the center of the universe/Earth are called the "great circles'', and they include the ecliptic, the celestial equator, and the horizon (which here is shown parallel to the celestial equator).

Note that there is a place in the sky where the great circle of the celestial equator crosses the great circle of the ecliptic. For the ancients, this location occurred at the positions of the equinoxes, when the Sun was in the constellations of Libra and Aries (see Figure 1.3). In fact, the place when the Sun first entered the constellation Aries was called "first point of Aries'', and this had great significance for ancient astronomers and astrologers and was considered the 0-degree point of celestial longitude in the sky. In the last 2,000 years, a wobbling of the Earth's axis has caused a "precession" of the heavens so that the place in the sky where the celestial equator and ecliptic cross is now in the neighboring constellation of Pisces, as is shown in Figure 1.4. Nevertheless, the first point of Aries continues to have special meaning

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Figure 1.4. A figure of an armillary sphere, from Lorenz Fries' 1522 edition of Ptolemy's Geographia. 37.3 x 24.9 cm (page size). Note the central Earth and the projections of its great circles into the sky. See text for details.

for astrologers. In fact, the great north-to-south circle that goes through the two equinoctial points has a special significance and appears on some star charts as the "Equinoctial Colure''. In a complementary manner, the great circle that goes through the two solstitial points is called the "Solstitial Colure''. (For a view of the first point of Aries on a celestial globe, see Figure 8.2.)