Rudolphine Tables

• 1. Introduction

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  The Rudolphine Tables arrived in the world in September 1627, the culmination of decades of calculation, war, exile, and debt. Johannes Kepler, the man who finally brought them to print, had spent years roaming the German countryside trying to collect money he was owed, survived a siege that nearly burned the manuscript, and quarreled bitterly with his printer in Ulm. The tables he produced were the most accurate planetary tables in history up to that point, precise enough to forecast astronomical events years into the future.

  What questions do they raise? Why did it take so long to publish a book that astronomers across the world, from India to China, were begging to read? How did two astronomers who disagreed about the very structure of the solar system manage to produce a work that would outlast both of them? And what was the strange inheritance battle that Kepler had to fight off even as the ink was drying?

• 2. Centuries of Imprecision

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  The Alphonsine tables, first produced in the 13th century, were the standard reference for planetary positions for more than three hundred years. Astronomers, astrologers, and calendar makers relied on them to place the planets among the twelve constellations of the zodiac and to construct horoscopes. They were built on the Ptolemaic, geocentric model of the solar system, and they were not very accurate. No better option existed, so they endured.

  In 1551, Erasmus Reinhold produced a rival set called the Prutenic Tables, building on the heliocentric system that Nicholas Copernicus had described in De revolutionibus orbium coelestium. The Prutenic Tables embraced the new cosmology but matched the old tables in precision. A heliocentric model alone was not enough to improve the numbers. What was missing was better raw observation of the sky.

• 3. Brahe's Island and His Data

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  Tycho Brahe built his observatory on the island of Hven during 1576-1596, supported by the Danish king Frederick II. Without a telescope, Brahe used elaborate instruments to fix the precise positions of planets and stars. The measurements his team produced were more accurate than anything available before.

  When Frederick II died, Brahe moved to Prague and was named the official imperial astronomer under Emperor Rudolf II. Kepler joined him there in 1600, and Rudolf directed both men to publish the tables. The two astronomers held opposing views of the cosmos: Brahe favored a geo-heliocentric model in which the Sun and Moon orbit Earth while the planets circle the Sun; Kepler argued for a fully Copernican, Sun-centered system. Brahe died in 1601 before the disagreement was resolved, and Kepler inherited both the imperial mathematician's post and the accumulated observational data. Studying that data, Kepler derived his three laws of planetary motion, publishing them in 1609 and 1619.

• 4. War, Debt, and One Printer

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  Kepler completed the tables near the end of 1623, but publication proved nearly as arduous as the calculations. He wrote to a Venetian correspondent who had been pressing him for the work: "I beseech thee, my friends, do not sentence me entirely to the treadmill of mathematical computations, and leave me time for philosophical speculations which are my only delight." Kepler first sought to recover money owed to him by the imperial court for his work. Sent from Vienna to three further towns as the debt was transferred from one account to another, he eventually raised 2,000 florins out of the 6,299 owed to him. That sum covered the paper. He paid for the printing himself.

  The original plan was to print the book in Linz, where Kepler was living. The Thirty Years' War intervened. Soldiers garrisoned the town, then a peasant uprising laid siege to it, and the manuscript came close to being destroyed in a fire. Kepler moved the project to Ulm, where he quarreled repeatedly with a printer named Jonas Saur. Despite everything, the first edition of a thousand copies was finished in time for the annual Frankfurt Fair in September 1627.

  Even during publication, Kepler faced pressure from Tycho Brahe's relatives, who repeatedly tried to take control of the observations and claim a share of the profits from the tables.

• 5. What the Book Contains

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  Written in Latin, the Rudolphine Tables recorded the positions of 1,005 stars measured by Tycho Brahe, along with more than 400 additional stars drawn from Ptolemy and the astronomer Johann Bayer. For most of these stars, the positions were accurate to within one arc minute and included corrections for atmospheric refraction. The book also provided tables and directions for tracking the Moon and the five classical planets of the solar system.

  Kepler included tables of logarithms and antilogarithms, a computational tool that John Napier had described in 1614, along with worked examples for calculating planetary positions. A world map was tucked into the book as well. A scroll on the lower left panel of that map explained how to use a lunar distance measurement, by observing the edge of the Moon's disc against a known star or a lunar eclipse, to calculate longitude at any point of observation. The map is notable for being among the first to show the Dutch discoveries of the west coast of Australia, including Eendracht Land and Dedels Land. Kepler apparently derived that geographic information from a publication by Jodocus Hondius II, issued in Amsterdam in 1625, which itself drew on an unpublished 1622 map of the Indian Ocean by Hessel Gerritz. A time scale running along the Equator on Kepler's map converts hours to degrees of longitude, at the rate of fifteen degrees per hour.

• 6. The Tables in Use

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  The dedication page of the Rudolphine Tables honored Emperor Ferdinand II, though the book took its name from Rudolf II, who had been dead for fifteen years by the time it appeared. The reach of the work spread quickly. Adam Schall von Bell, a Jesuit missionary in China, used the tables to complete a reform of the Chinese calendar in 1635.

  The truest test of the tables' accuracy came in the years after publication. They were precise enough to predict a transit of Mercury, which the astronomer Pierre Gassendi observed in 1631, and a transit of Venus, which Jeremiah Horrox observed in 1639. Predicting transits years in advance demanded a level of exactness that no earlier planetary tables had achieved, and the Rudolphine Tables delivered it.