Tycho's original work, and questions on his knowledge before his departure

Hello everyone,

I am sorry if something similar has been already posted in the forum.

I was viewing the origional work of Tycho Brahe Astronomiae instauratae progymnasmata, available on the following link (unfortunately in Latin): https://www.loc.gov/resource/rbc0001.2013gen94777/?sp=1&st=gallery

The pages can be viewed as gallery and PDF as well. I cannot confirm whether it is the complete work.

I was curiously navigating the sketches in the book whether Tycho Brahe had recognised that the planets’ traces proposed by him align with the observations from Earth and work as expected.
To be specific, did Tycho convert his numerical records of the planets into a small scale orbits (as seen in the image that shows Mars trace over 16 years)? or was this done after his departure?.

If he could convert them into a scaled simulation sketches he would promptly recognise that the model works, and would not need to hand anything to Kepler (or this was maybe the task of Kepler?). I can imagine it was not easy to create a simulation in their times, especially that those orbits despite perfect in motion, it is not easy to plot them without the aid of a computer and have a comperhensive visualization.

My subquestion is do we know what was the exact task that was given by Tycho to Kepler? like was there something baffling Tycho specifically about Mars to ask Kepler’s help? if yes, could i please ask what was that. I learned about the deviation in its orbit, but in which form does this deviation appear in their perspective? Only in the catalogues? Or did he detect the deviation after sketching the traces?

My two primary questions are in bold text, and sorry in advance if something is not clear I appreciate your patience. My major point is about the capacity of Tycho’s knowledge on the validity of his discovered model before his death (in fact before publishing his third volume of the book).

Thank you for your time reading


Hello CuriosityX - and welcome to the forum

I fully understand and appreciate your (good and pertinent) questions, so let me try and address them to the best of my explanatory capacity. :slight_smile:

Re: your 1st question: did Tycho convert his numerical records of the planets into a small scale orbits (as seen in the image that shows Mars trace over 16 years)? or was this done after his departure? .

The image you mention is the diagram attributed to Kepler titled “De Motibus Stellae Martis” (“Of the Motion of the Star Mars”) - and was published in the first chapter of his “master treatise” Astronomia Nova (1609). Here’s what we can read about it at the University of Chicago Press website :

“In the first chapter of his Astronomia Nova , Kepler introduced a diagram that, he claimed, represents the path of Mars between 1580 and 1596, assuming a resting Earth. In the words of William H. Donahue, “the appearance of this diagram is a dramatic moment in the history of thought. Nothing like it had ever been published before.” It is unique mainly because it is the first diagram that offers what is explicitly asserted to be an accurate representation of the trajectory of a planet, the first diagram in which the path of a planet appeared clearly separated from the geometrical devices that produced it. This essay aims to offer an analysis of the accuracy of this diagram. The authors try to determine what tables, ephemerides, observations, or models are behind its construction and how accurately the diagram reflects the different elements of the trajectory of Mars. The outcome of this analysis raises the question of whether the diagram was made for the role it ultimately played in the Astronomia Nova or for some other purpose.”

Here’s an image from Chapter 5 of my book which shows just how precisely the Tychosium 3D simulator matches Kepler’s (or Brahe’s?) ‘geocentric’ diagram of the motions of Mars between 1580 and 1596 :

Astronomia Nova was published about 8 years after Tycho Brahe’s death - and we know that Kepler stole all of Brahe’s papers and drawings, so we simply don’t know whether Brahe was aware of this diagram - or if he (possibly) even was the original author of it!

Re: your 2nd question: Do we know what was the exact task that was given by Tycho to Kepler?Like was there something baffling Tycho specifically about Mars to ask Kepler’s help?

Well, Brahe was obviously aware of what we call today the General Precession, i.e. the constant eastward drift of the entire star firmament, currently reckoned to amount to about 50.3" arcseconds per year. (Incidentally, and quite interestingly, Brahe’s estimate of the GP was 51" arcseconds, which compares well with my own estimate of 51.136" arcseconds in the TYCHOS model).

But here’s the thing: since Brahe believed that the Earth was immobile, he would have either attributed the observed general Precession to:

  • A general precession of all the stars - all of them drifting eastwards in unison by 51"
  • The infamous Copernican idea of a slow “wobble” of the Earth’s axis

Being a very smart fellow, he probably didn’t like the 1st option (a general drift of all the stars). This left him with the Copernican idea of the Earth’s “lunisolar wobble”. Yet, since this wobble would also have affected Mars, making it drift eastwards by 51" every year (which it does NOT), he would have been deeply baffled about this - since his wondrous observational instruments (reputedly capable of a 2" precision) certainly would have allowed him to notice this discrepancy - over the many decades of observations that he made in Hven.

In short, Brahe was probably ‘stuck’ with this problematic affair - and thus allowed Kepler to ‘give it a go’ with his mathematical skills (although the two never liked each other and kept arguing & bickering - as widely reported in history books).

All in all, it all comes down to the fact that Brahe was not aware of the Earth’s translational motion around its PVP orbit amounting to an annual ‘westward’ / annual displacement of about 14036km. Now, Mars returns “in opposition” - as it passes closest to Earth - every 15 or 17 years, during which the Earth will move ‘westwards’ by a good 210450km or 238612km. Tycho Brahe’s fine instruments would surely have ‘detected’ these earthly displacements (which would have upset any calculations and predictions that Brahe would have made of Mars’s motions), yet the poor man would not have known what to make of it all !

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Thank you very much for the detailed answers mr. Simon. I have no further inquries in this regard. And indeed, I have read your book (Chapters Stellar Parallax, Mars, PVP…) and watched the youtube discussions.

Again thanks for your time and detailed illustration!

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Omitting the truth in this lamentation, since this fatal calamity of Astronomy has befallen; that which we now consider to be our duty, who is advised to Posterity, whose account is first of all ours; We beseech Your Majesty, through the immortal God and the Sacred Urania, not to neglect the palm, placed in the midst of eternal praise, among these warlike tumults, but to urge, by his authority and the wealth of those tables, the perfection of those tables, a matter worthy of the Emperor’s majesty. Let them be Moecenates, they will not be wanting, Flacce, Marones, he said. Let them be Alphonsus, Albertus, Frederickus, Charlesus; those who are to take up this Province with a zealous spirit (since the main foundations of this matter have already been laid) are not dead or wanting; and the remainder, whatever there is, which is very little, will be discharged within a few years. If any perishable fruit of such a thing can or should be proposed, surely we will pledge the name and glory to the Stars themselves as a coeval reward of Your Majesty’s restored Astronomy, and as much as is in our power, we will gladly and zealously procure it. What is left, we humbly commend to Your Sacred Imperial Majesty God’s best, greatest protection for the most gracious government of the Empire, and we Brahe’s Imperial heirs and our parent’s promised clientele, at Prague on the day before the Calendar of August of the Christian Year 1602

Your majesty’s Sacred House

The most loyal customers

Tycho of Brahe

Last page of the dedication p.13 (Kepler?)

From Library of Congress page

    • The 1st volume of a projected work on recent astronomical phenomena. The 2nd volume had been printed and privately distributed at Uraniborg in 1588 under title: De mundi aetherei recentioribus phaenomenis liber secundus. The 3rd and final volume was never written. Cf. Tycho Brahe / J.L.E. Dreyer. 1890. p. 162-163.
    • Prepared for publication after the author’s death by Johannes Kepler, who also wrote the Appendix (p. 817-822). Cf. Dreyer, p. 368-369.