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The Webfooted Astronomer - October 2001


Minutes: Hooked on Gnomonics!

By Greg Donohue

THE next new members’ meeting is October 27 at Karl and Judy Schroeder’s home. Peter Hirtle announced that Telescope Makers will meet Saturday, September 29.

Loren Busch, Astronomical League Correspondent (ALCOR), talked about the Astronomical League (AL), of which the SAS is a member. The AL is the largest association of amateur astronomers and astronomy clubs in the world. In addition to a youth program, the AL has an extensive amount of material that can be checked out for use at club meetings.

In addition to the Reflector newsletter, the Astronomical League’s Web site has a collection of white papers to help amateur astronomers and clubs. The Astronomical League is probably best known for its many observing clubs and awards. Among these are the Messier club, double star club, and the new Earth Orbiting Satellite club, to name just a few. For more information on the Astronomical League, visit their Web site or contact Loren Busch.

Jim Evans, physics professor at the University of Puget Sound, discussed the material culture of ancient Greek and Roman astronomy. Professor Evans authored “The History and Practice of Ancient Astronomy.”

In ancient times, astronomy played a much more central role in people’s lives than it does today. In ancient Greece, astronomy played a central role, with important ties to mathematics, philosophy, religion, astrology, medicine, and politics. Examining the material culture of ancient astronomy can help make the case for its centrality to the peoples of antiquity. In the first century A.D., Geminus divided the mathematical arts into two broad areas, pure and applied mathematics. Pure mathematics includes number theory and the properties of numbers. Geminus divided applied mathematics into six divisions: practical calculation, geodesy, the theory of musical harmony, optics, mechanics, and astronomy.

A subdivision of mechanics was sphere making, specifically the making of mechanical images of the heavens. This included such things as globes representing the celestial sphere, and armillary spheres. Some of these devices were very elaborate, containing intricate gear-work, and some were even powered by flowing water.

Astronomy is broken down into gnomonics (sundials), meteoroscopy (position of celestial bodies), and dioptrics. Astronomy was seen as a branch of mathematics.

Those objects that survive from antiquity fit into sphere making, sundials, and other time-telling devices. Objects associated with religion, politics, and astrology have also survived.

The oldest extant celestial sphere is a marble globe some 2-3 feet in diameter that now resides in the National Museum in Naples. The globe shows the constellations, and also the principal circles of the celestial equator, the tropic circles, and a triplet of rings representing the zodiac. This globe probably dates to around 70 BC, and is likely a Roman copy of a Greek original from a couple of hundred years earlier.

Another smaller bronze globe from the Roman era around the second or third century AD was discovered about a 12 years ago. While these are the only two celestial globes that have survived, ancient literature contains many references to these types of devices, and there are many images of them on coins.

Armillary spheres served much the same purpose as the three-dimensional globes. But rather than being solid objects, armillary spheres used bands to represent the sky. They were more fragile, and so none of them survived from antiquity. But they are mentioned by Greek writers, including Geminus. Some armillary spheres were equipped with sites, and used as observing instruments. Tyco Brahe used a derivative of this type of instrument for his observations.

Gnomonics is the making of instruments to tell time, the most notable example being sundials. The simplest design for a sundial would contain a hemispherical cavity with a gnomon (the dial) to cast a shadow into the hollow. However, in practice it was difficult to create a good hemispherical cavity in stone. An example of such a sundial built from soft stone was excavated from the ruins of Pompeii.

Entire or partial hemispheres were still hard to make, so the conical dial, in which the surface on which the shadow was cast was the inner surface of a cone, was common. Many more conical dials have survived than have spherical dials.

An extraordinary example of an elaborate timekeeping device from the first century BC is the Tower of the Winds in Athens. This octagonal building, designed by the Macedonian astronomer Andronicos, still stands today. A vertical sundial adorns each of the building’s eight faces. A wind vane (which no longer exists) atop the building would tell which of the eight winds was blowing. And evidence points to the possibility that the building once housed an elaborate water clock.

Two incomplete writings regarding the mathematics and design of sundials, including one by the architectural writer Vitruvius, have survived, reinforcing the notion that gnomonics was indeed an active area of mathematical pursuit.

Vitruvius also described another class of devices called anaphoric clocks, and pieces of two of them have come down to us from antiquity. The same theory for projecting the constellations and horizon on the anaphoric clock underlies the astrolabe, a two-dimensional model of the celestial sphere. In ancient times, the most important “practical” application of astronomy for working astronomers was generating horoscopes. Astrology was not an important part of early Greek astronomy; it only came into prominence after the Greeks came into contact with the Babylonians, in the first or second century AD. And the minting of coins with the images of rulers and celestial events was often used to influence political sentiments and consolidate positions of power.

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