The Rudolphine Tables (Latin: Tabulae Rudolphinae) consist of a star catalogue and planetary tables published by Johannes Kepler in 1627, using some observational data collected by Tycho Brahe (1546–1601). The tables are named as "Rudolphine" in memory of Rudolf II, Holy Roman Emperor.
Star tables had been produced for many centuries and were used to establish the position of the planets relative to the fixed stars (particularly the twelve constellations used in astrology) on a specific date in order to construct horoscopes. Until the end of the 16th century, the most widely used had been the Alphonsine tables, first produced in the 13th century and regularly updated thereafter. These were based on a Ptolemaic, geocentric model of the Solar System. Although the Alphonsine tables were not very accurate, nothing else was available and so they continued to be used.
In 1551, following the publication of De revolutionibus orbium coelestium by Nicholas Copernicus, Erasmus Reinhold produced the Prutenic Tables based on a heliocentric model of the Solar System, but these were no more accurate than the earlier tables.
Tycho's data and Kepler's model of the Solar System
Tycho Brahe had spent much of his life obtaining measurements of the position of stars and planets to a much greater degree of accuracy than had been possible previously. He wished these observations to be the basis of a new and more accurate set of star tables. Kepler was able to prepare these new tables using Tycho's observations together with a heliocentric model of the Solar System and his own discovery of the elliptical orbits of the planets. Accurate computation was aided by the newly published system of logarithms, which simplified the calculations and made them less prone to errors.
Work on the tables began in 1600 when Kepler had joined Brahe, then mathematician and astronomer on the royal court in Prague, as the assistant. Both were given an order by Emperor Rudolf II for the calculation of new, more precise planetary maps. After Brahe's death next year, Kepler had become his successor and continued on the tables alone. The tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China. Apart from external hindrances, Kepler himself deterred from such a monumental enterprise involving endless tedious calculations. He wrote in a letter to a Venetian correspondent, impatiently inquiring after the tables: "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". They were finally completed near the end of 1623.
In his attempts to finance the printing of the tables, Kepler began by claiming the arrears due to him by Rudolph. From the Imperial Court in Vienna he was sent to three other towns to which the debt was transferred. After a year of roaming the country, he was eventually able to raise 2000 florins (out of 6299 owed to him), which sufficed to pay for the paper. The printing itself he decided to pay for from his own pocket. It was initially supposed to be printed in Linz, where he resided at the time, but the chaos of the Thirty Years' War (first the garrisoning of soldiers in the town, after which a siege of the revolting peasantry, which almost resulted in the burning of the manuscript) prompted him to leave. He began to enterprise anew in Ulm. There, after many quarrels with the printer Jonas Saur, the first edition of a thousand copies was completed in September 1627, in time for the annual book mart in the Frankfurt Fair. While publishing the Rudolphine Tables, Kepler was hard-pressed to fight off Tycho's numerous relatives. During the publication process, these relatives repeatedly tried to obtain control of the observations and the profit from the publication of the tables. They argued that Tycho's work should benefit his own family, and not one of Tycho's competitors. Kepler counter-argued that he and Tycho had been collaborating on the data for many years before Tycho's death. Kepler further asserted that he himself was responsible for most of the calculations and also for the organization of the data. In the end, Kepler did win control of the tables and published them himself, while the Brahe family got no benefit from them.
Tycho had intended that the tables should have a dedication to Emperor Rudolf II, but by 1627, when the tables were published, Rudolf II had been 15 years dead yet, so instead the tables were dedicated to Emperor Ferdinand II but are named after Rudolph II. They contain positions for the 1,005 stars measured by Tycho Brahe, and more than 400 stars from Ptolemy and Johann Bayer, with directions and tables for locating the planets of the Solar System. The tables included many function tables of logarithms and antilogarithms, and instructive examples for computing planetary positions.
For most stars these tables were accurate to within one arc minute, and included corrective factors for atmospheric refraction. The tables were sufficiently accurate to predict a transit of Mercury observed by Pierre Gassendi in 1631 and a transit of Venus observed by Jeremiah Horrox in 1639.