The emergence of modern astronomy – a complex mosaic: Part XVI

One of the things attributed to Tycho Brahe is the geo-heliocentric model of the cosmos. In this system the Earth remains at the centre and the Moon and the Sun both orbit the Earth, whereas the other five planets orbit the Sun. This system combines most of the advantages of Copernicus’ heliocentric system without the problems caused by a moving Earth. As such, as we shall see, the Tychonic system became one of the two leading contenders later in the seventeenth century. The only problem is that although it is named after him, Tycho wasn’t the only person to suggest this model and he almost certainly wasn’t the first to think of it.


A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

The first to publish a version of the geo-heliocentric model was Nicolaus Reimers Baer (1551–1600), known as Ursus, in his Nicolai Raymari Ursi Dithmari Fundamentum astronomicum (Straßburg 1588). Ursus’ system differed from Tycho’s in that he included diurnal rotation.


Nicolaus Reimers Baer, Fundamentum Astronomicum 1588 geo-heliocentric planetary model Source: Wikimedia Commons

Ursus was a self-taught astronomer, who in his youth had worked as a pig-herd until Heinrich Rantzau (1526–1598), a humanist scholar and astrologer, recognised his talents and employed him as a mathematician.


Heinrich Rantzau Source: Wikimedia Commons

There followed a period as a private tutor and a year, 1586–87, in Kassel with Wilhelm. During his time in Kassel he translated De revolutionibus into German for Jost Bürgi, who couldn’t read Latin. In exchange Bürgi taught Ursus prosthaphaeresis, a method of using trigonometrical formulas to turn multiplications into sums to simplify calculations. From 1591 till his death, in 1600, Ursus was Imperial Mathematicus to Rudolf II in Prague.

Tycho was outraged that somebody published “his system” before he did and immediately accused Ursus of plagiarism, both of the geo-heliocentric system and of prosthaphaeresis, citing an earlier visit to Hven together with Rantzau, when Ursus was in his service. The two astronomers delivered a very unseemly public squabble through a series of publications; Tycho emphasising Ursus’ lowly birth and lack of formal qualifications and Ursus giving as good as he got in return. However, when Tycho left Hven and approached Prague, Ursus fled fearing the aristocrat’s wrath. When Kepler came to Prague to work with Tycho the first task that Tycho gave him was to write an account of the dispute, naturally expecting Kepler to find in his favour. Kepler wrote his report but didn’t ever publish it. Nicholas Jardine published a heavily annotated English translation in his The Birth of History and Philosophy of Science. Kepler’s ‘A Defence of Tycho against Ursus’ with Essays on its Provenance and Significance, CUP (2nd rev. ed. 1988)[1].

Tycho’s false accusation of theft of the trigonometrical method of prosthaphaeresis is, however, very revealing. Tycho was not the discoverer/inventor[2] of prosthaphaeresis. As far as can be ascertained, the method was originally discovered by Johannes Werner (1468–1522) but was actually taught to Tycho by the itinerant mathematician/astronomer from Breslau, Paul Wittich (c. 1546–1586). It turns out that that Wittich was probably the inspiration for both Tycho’s and Ursus’ decision to adopt a geo-heliocentric system. Wittich played around with the Capellan system, in which Mercury and Venus orbit the Sun in a geocentric system. He sketches of his thoughts are contained in his copy of De revolutionibus.


Paul Wittich’s 1578 Capellan geoheliocentric planetary model – as annotated in his copy of Copernicus’s De revolutionibus in February 1578 Source: Wikimedia Commons

Following Wittich’s, comparatively early, death Tycho went to a lot of trouble and expense to obtain both of Wittich’s copies of Copernicus’ book, suggesting he was desperately trying to cover up the origins of “his system.” Another indication of Wittich’s possible or even probable influence is the fact that David Origanus (1558–1629), who had been influenced by Wittich at the University of Frankfurt an der Oder, also “independently” invented a geo-heliocentric system but with diurnal rotation like Ursus’ system.


David Origanus Source: Wikimedia Commons

The route from a Capellan system to a full geo-heliocentric system was probably the route taken by both the physician and astrologer Helisaeus Roeslin (1545–1616) and the court mathematicus Simon Marius (1573–1625), who both claimed independent discovery of the system.


Simon Marius Source: Wikimedia Commons

Geoheliocentric cosmology, 16th century

I think it should be clear by now that a geo-heliocentric system, whether with or without diurnal rotation was seen as a logical development by several astronomers following the publication of De revolutionibus, for it combined most of the advantages of Copernicus’ system, whilst not requiring the Earth to orbit the Sun, solving as it did the problem of the missing, or better said undetectable, solar stellar parallax. Such a system also solved another perceived, empirical problem, which has been largely forgotten today, that of star size.

If the cosmos were heliocentric then the lack of detectable parallax would mean that the so-called fixed stars were absurdly distant and much worse, given the naked-eye false perception the size of the star discs, all the more absurdly immense. Tycho used this as a valid empirical argument alongside religious ones to categorically reject a heliocentric system. Because the geo-heliocentric system didn’t require stellar parallax then the distance to the fixed stars was considerably shorter and thus the star size also much smaller. The apparent star size argument would continue to play a significant role in the astronomical system debate until the end of the seventeenth century.

Tycho, naturally, hoped to use his vast quantity of freshly won, comparatively accurate celestial data to prove the empirical reality of his system. Unfortunately, he died before he could really set this project in motion. On his deathbed he extracted the promise from Johannes Kepler, his relatively new assistant, to use the data to prove the validity of his system. As is well known, Kepler did nothing of the sort but actually used Tycho’s hard won data to develop his own totally novel heliocentric system, of which more later.

However, a geo-heliocentric model of the cosmos, with or without diurnal rotation, remained, as we shall see later, one of the leading contenders amongst astronomers right up to about 1660-70. The definitive version based on Tycho’s own data was produced by Christen Sørensen, known as Longomontanus, (1562-1647),


Tycho’s longest serving and most loyal assistant, in his Astronomia Danica (1622).


Longomontanus’ system was published in direct opposition to Kepler’s heliocentric one. Unlike Tycho’s, Longomontanus’ system had diurnal rotation.

Today we tend to view the various geo-heliocentric systems, with hindsight, as more than somewhat bizarre, but they provided an important and probably necessary bridge between a pure geocentric model and a pure heliocentric one, delivering many of the perceived advantages of heliocentricity, without having to solve the problems created by an Earth flying at high speed around the Sun.

[1]A highly recommended read

[2]Chose your word according to your philosophy of mathematics


Filed under History of Astronomy, History of science, Renaissance Science

7 responses to “The emergence of modern astronomy – a complex mosaic: Part XVI

  1. Todd Timberlake

    Great summary of the complicated origins of the many geo-heliocentric theories! My understanding is that Ursus increased the size of Mars’ orbit to avoid it intersecting with the Sun’s orbit (not that the two could over collide, but he didn’t want their circles to overlap) – so in that sense Ursus’ model was worse than Tycho’s even if it was prior to, or independent of, Tycho’s, because a larger orbit for Mars would not reproduce the observed motions. But as you say there were lots of similar models in play around that time.

    One quick note: in the paragraph that begins “I think it should be clear” I believe you meant “stellar parallax” rather than “solar parallax.” I know it was just a typo but could be confusing to readers.

  2. Jim Harrison

    Johannes Werner (1468–1622), durable!

  3. Carl Vehse

    BTW, on August 1, 2019, many PBS stations in the U.S., will air Episode 2, “Finding the Center,” of the science documentary series, “Ancient Skies.”

    The episode’s description states: “Follow the efforts to give the Earth a shape and a place. From flat Earth legends to Galileo’s telescope, track major changes in scientific understanding. Ideas rise and fall as we continue to explore our ancient skies.”

    If Episode 1 was an indication, prepare to wince.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s