Ephemerides, timely positions of planets, from Babylon to Kepler

Gingerich, Owen

An ephemerides is a tabulation of planetary positions, the most sophisticated outcome of observing the heavens even prior to the advent of writing. Before planetary positions could be recorded, there had to be a reference frame, such as a particular horizon, or a list of star patterns. With the beginning of writing, records could be kept and patterns noted. The oldest such records are the so-called Venus Tables of Amizudaga, which give positions of Venus around 1700 BC, although the surviving copies are closer to the 7th century BC. Relatively abundant astronomical records survive from around 750 BC, and these anchored period relations up to the time of Tycho Brahe and Kepler.

It will be less confusing to start somewhere in the middle of this sequence, around AD 1320. We first distinguish four types of related volumes or scrolls. First there are treatises, the detailed “how to” texts, of which Ptolemy’s Almagest (AD 150) or Copernicus’ De revolutionibus (AD 1534) are the premier examples. Second are the tables, which expand and tightly organize the numbers from the treatises. Examples are the Ptolemaic-based Alfonsine Tables introduced around AD 1320, and the Copernican-based Prutenic Tables (AD 1551). Third are the ephemerides, which are calculated from one of the tables. These ephemerides can be very thin, for just one year, or very thick, even with as much as half a century of daily positions. Finally there are the light-weight almanacs, for just a year. (Occasionally an ephemeris is titled as an almanac.)

Throughout the Middle Ages and the Islamic period very little was done to improve the positions predicted by the tables. Instead, a vast effort was undertaken to make the tables easier to use. Contrary to popular mythology, there was an almost negligible effort to improve the Ptolemaic positions.

The advent of printing made it reasonable to print a set of ephemerides. An individual astrologer might possibly wish to have the birth configurations for a hundred patrons, but this could hardly justify the computation of a thousand or more daily positions. The situation changed completely in 1474 when the leading mathematician of the 15th century, Regiomontanus, had become a printer. His planetary positions were reprinted over and over up through 1506.

The first major change in the layout of tables came with Johannes Kepler’s Rudolphine Tables of 1628, which improved the accuracy of the predictions by two orders of magnitude (something based on Tycho Brahe’s extensive and accurate positions and Kepler’s physical insights). Kepler’s mentor Michael Maestlin advised him to forget about all that physics stuff and use geometry, which is what astronomers were supposed to do.

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