Rudolphine Tables

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. The purpose of the Rudolphine tables was to be able to predict the positions of planets based off of calculations. His calculations did not agree with the Alphonsine tables nor Copernicus which motivated him to make a more precise table.

Previous tables

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. Tycho Brahe did not use a telescope, but did all observations by naked eye and used math calculations.[1]  He did not agree with the Copernican or Ptolemaic theories of planetary positions, so he created his own system. He believed the earth had a geoheliocentric motion while the planets have a heliocentric motion. He did have an Aristotelian view when it came to physics of the earth because it agreed with the Bible and he would not go against this.[2] He believed that with more accurate instruments and careful observations, the calculations produced, or models would be better. Tycho had died unexpectedly when working on the tables and Kepler took over the task. 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. Using Tycho's observations of Mars, he was also able to create a law of planetary motionAccurate computation was aided by the newly published system of logarithms, which simplified the calculations and made them less prone to errors.


Tycho Brahe was a Protestant living in the island of Hven, a Danish island. He had many connections to the upper class Danish people because of his family serving on councils, so he was able to get an education while growing up. In the university he attended, he was taught the Aristotelian system.[3] He had traveled due to the war taking place in his country and once it was over he returned home. He wanted to work with astronomy and physics so he had built a castle-like building that he used as an observatory and a home. The purpose of this observatory was to collect data for King Frederick II.[4] In his observatory he focused on making instruments as precise as possible to gain better results before he started to record observations. He made all observations with a naked eye and his instruments were used for calculations. In this observatory, he saw a new star which he published a book on.[5] He then wanted to move countries, but the King did not want to lose him as an astronomer, so he was given rule of the island, Hven. He built an observatory here which also doubled as his home. Here, he functioned as the royal astronomer, and made several key improvements to his instruments. He did work with many assistants that helped to compile all of the data. He also observed a comet during his stay here that he was able to propose a new theory behind after doing calculations and observations.[6]  After twenty years of living there, a new King was appointed that did not get along with Brahe so he was forced to leave. He decided to live in Prague. However, Prague was a Catholic ruled city and he had to convert before accepting a job from the emperor. He was funded by many people to make the move to this new city before he was employed by Rudolf II. He was then assigned by the emperor to make better astronomical tables and he planned to use the data he had already collected. Tycho and his assistants decided that they needed help organizing the data and he hired Johannes Kepler. to do this task. Kepler was also a Protestant and had to leave his city because of religious disagreement, but came to a Catholic city to work with Tycho. Kepler believed in the Copernican system of astronomy and disagreed with some of Tycho's systems, however he believed many of the observations and calculations were correct. He even defended Tycho in a book he wrote and said he was very accurate.[7] Both men were Protestants that had moved to a Catholic ruled city in order to produce and publish scientific data, which was ultimately an inventory of the stars and recording of the new stars. Tycho died a year after working on the tables and Kepler was assigned to finish the tables. It took him eleven years to complete the tables with all of Tycho's data and his original work. The tables were anticipated for many years, with pleas for its publication reaching as far as India and Jesuit missionaries in China.[8] 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".[9] They were finally completed near the end of 1623. During the production of the tables, he had to do the role of the astronomical advisor as well, because he was the successor of Tycho. These duties included predicting events and horoscopes of the noblemen.


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.[10] 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.[11] 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.[12] 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,[13] and included corrective factors for atmospheric refraction.[14] 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.[15]

The cover of the book had a very detailed drawing with each individual piece having a meaning behind it being included. There were religious and academic reasons behind this, such as the pillars and columns. Each of the twelve columns represent a different zodiac sign. The woman at the top is the muse of astronomy, Urania, who is surrounded by six other muses. There is another astronomer from a different civilization making observations to pay homage to some of the earliest astronomers. There are two names, Meton and Aratus, each of them Greek. Meton used geometry to make a calendar and came up with a system for a lunar calendar. Aratus was a poet that Eudoxus used to describe stars and planets, then with him is an armillary sphere. This sphere belongs to Hipparchus to display the stars. Hipparchus was an astronomer and the founder of trigonometry. Ptolemy is sitting at a table, writing his book and holding an instrument. The book was an accurate depiction of what he was writing with his theorems of planetary motion, and the instrument is an astrolabe. One of the biggest illustrations on the page is Copernicus, Tycho did not agree completely with him, but he did use some of his ideas, and Kepler was more of a Copernican than Tycho making Copernicus’ ideas an integral part of Kepler’s theorems. Tycho is also in the picture asking Copernicus what something is, but the whole background setting is in Tycho’s observatory with most of his art and works. Copernicus and Tycho are portrayed as very large and powerful, with their work and instruments around while Kepler is small and to the side, but some of his works also with him. Using Tycho's observations of Mars, he was also able to create a law of planetary motion.[1]

See also


  1. Rågstedt, Mikael (2013-06-10). "About the cover: Kepler and the Rudolphine Tables". Bulletin of the American Mathematical Society. 50 (4): 629–639. doi:10.1090/s0273-0979-2013-01416-2. ISSN 0273-0979.
  2. Blair, Ann (1990). "Tycho Brahe's Critique of Copernicus and the Copernican System". Journal of the History of Ideas. 51 (3): 355–377. doi:10.2307/2709620. ISSN 0022-5037.
  3. Håkansson, Håkan (2006). Att låta själen flyga mellan himlens tinnar: Tycho Brahe och Renässansen (in Swedish). Stockholm: Atlantis. ISBN 978-91-7353-104-7. OCLC 184982721.
  4. Brahe, Tycho (1590). "Tycho Brahe note acknowledging receipt of money". Retrieved 2019-12-03.
  5. Thoren, Victor E; Christianson, J. R (1990). The Lord of Uraniborg: a biography of Tycho Brahe. Cambridge [England]; New York: Cambridge University Press. ISBN 978-0-521-35158-4. OCLC 21116731.
  6. Håkansson, Håkan (2007), Killeen, Kevin; Forshaw, Peter J. (eds.), "Tycho the Prophet: History, Astrology and the Apocalypse in Early Modern Science", The Word and the World: Biblical Exegesis and Early Modern Science, Palgrave Macmillan UK, pp. 137–156, doi:10.1057/9780230206472_8, ISBN 978-0-230-20647-2, retrieved 2019-12-03
  7. Christianson, J. R (2008). On Tycho's island: Tycho Brahe and his assistants, 1570-1601. Cambridge: Cambridge University Press. ISBN 978-0-521-10106-6. OCLC 502278009.
  8. Koestler, p. 376
  9. Koestler, p. 376
  10. Koestler, p. 377-379
  11. Hannam, James (2011). The Genesis of Science: How the Christian Middle Ages launched the scientific revolution (1st American ed.). Washington, DC: Regnery. p. 294. ISBN 1596981555.
  12. Kusukawa, Sachiko (1999). "Kepler and Astronomical Tables".
  13. Tirion, Wil; Barry Rappaport; George Lovi (1992). Uranometria 2000.0 (1988 ed.). Richmond, Va.: Willmann-Bell. p. xvii. ISBN 0-943396-15-8.
  14. The New Encyclopædia Britannica, 1988, Volume 10, pg. 232
  15. Athreya, A.; Gingerich, O. (December 1996). "An Analysis of Kepler's Rudolphine Tables and Implications for the Reception of His Physical Astronomy". Bulletin of the American Astronomical Society. 28 (4): 1305. Bibcode:1996AAS...189.2404A.


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