When Johannes Kepler (1571–1630) rewrote our conception of how heavenly bodies move by replacing the ideal and eternal circles of classical philosophy with elliptical orbits along which planets move with variable velocities, he did so in part by harnessing the power of a hot piece of mathematical technology fresh off the presses, the logarithm. Originating in 1614 in John Napier’s *Mirifici Logarithmorum Canonis Descriptio*, the logarithm was recognised by some as a powerful tool for discovering new connections between the measurable quantities of nature, and an even more useful widget for simplifying the pain-staking computations that were the ruin of mathematical astronomers in the early modern era.

For others, however, logarithms were little more than new-fangled mathematical interlopers, parlor tricks employed by weak-willed scientists trying to avoid good honest computational work. Mathematical conservatives such as these distrusted logarithms and, by extension, didn’t entirely embrace scientific work that employed them. What was needed was a volume that showed the validity of Kepler’s conception of the universe, but that employed mathematics that the entire scientific community, and the larger world of scientific enthusiasts, felt comfortable with. It took a couple of decades, but that task was eventually accomplished in a little-known but important text authored in 1650 by the Silesian polymath, Maria Cunitz (1610–1664).

*Photo by Piotrus*

Cunitz was likely born in 1610 in the currently Polish town of Wolow, which had by that point been passed back and forth between Bohemia, Poland, and Austria for centuries in a game of central European hot potato that would only continue in the years to come. Her father was a prosperous doctor and her mother was the daughter of Anton von Scholtz, who was a sixteenth century mathematician. Cunitz (sometimes rendered as Cunitia or Kunic) therefore had the resources and the family background to carve out a path for herself denied to most women of her time. Her father ensured that she had a private education that encompassed mathematics, music, poetry, medicine, history, and languages (by the end of her life she was fluent in seven tongues: Polish, German, French, Italian, Latin, Greek and Hebrew.)

All that education, however, nearly came to naught at the hands of her century’s predilection for early marriage. Cunitz was married in 1623, at the likely age of thirteen, to the attorney David von Gerstmann, whose death in 1626 freed her to form a much more congenial match with the physician and amateur astronomer Elias von Löwen. Together, they observed Venus and Jupiter in the late 1620s and married in 1630, at the height of the continent-wide catastrophe known as the Thirty Years War (1618–1648). While hiding out from the devastation of that conflict at the Cistercian convent of Olobok, Cunitz carried out a correspondence with some of Europe’s most eminent astronomers, and gathered material for her masterpiece, *Urania Propitia*.

That work’s full title, *Urania Propitia Sive Tabulae Astronomicae Mire Faciles, Vim Hypothesium Physicarum A Kepplero Proditarum Complexae; Facillimo Calculandi Compendio, Sine Ulla Logarithmorum Mentione Phenomenis Satisfacietes; Quarum usum pro tempore praesente, exacto et futuro communicat Maria Cunitia. Das ist: Neue und Langgewunschete/leichte Astronomische Tabelln durch derer Vermittelung auss eine sonders behene Arth aller Planeten Bewegung nach der länge [indec] under andern Zufallen auss alle vergangene, gegenwertige, und kunssstige Zeiespuncten furgestellet wird*, tells us a few things about the full importance of this work. Firstly, the fact that the title is half in Latin and half in German points to an important aspect of the book, namely that it is written in both what was the academic language of the time, Latin, and in a language regular people could actually understand, German. It was, in fact, one of the first scientific texts written in German, and so we could place Maria Cunitz as a pioneer of the SciComm movement to make specialised technical information accessible and available to the general public.

Secondly, the phrase ‘Sine Ulla Logarithmorum’ which translates as ‘without any logarithms,’’ testifies to just how tendentious logarithmic calculations still were in 1650. For some, as we mentioned above, they were considered too easy, almost like cheating (the 17th century equivalent of a person today using a graphing calculator to factor a quadratic equation or calculate 14 times 5), whereas to others they just seemed odd and forbidding new mathematical objects that were difficult to conceptualise. (I personally see this centuries old terror reenacted every year in students coming into my calculus course from Algebra 2 or PreCalculus whose eyes gloss over and mouths gape open in a mute scream every time the word Log is so much as mentioned). Cunitz’s book, then, promises that there will be None Of That in *her *calculations, a labour which, had her volume been more widely published, could have gone far in making Kepler’s thought more accessible, sooner.

Thirdly, we see in the phrase ‘Langgewunschete/leichte Astronomische Tabelln,’’ or ‘Long Desired and Simple Astronomical Tables’ another Selling Point of *Urania Propitia*. Kepler had published his Rudolphine Tables in 1627, a monumental effort that occupied much of Kepler’s time after the publication of *Harmonices Mundi *in 1619. The creation of the tables, grounded in the data he had inherited from Tycho Brahe’s legendary observatory in 1601, was a neck-breaking process, though one made simpler by the use of logarithms, which allowed multiplication and division problems (such as occur regularly with the trigonometric quantities involved in spherical geometry) to be reduced to much easier and more accurate addition and subtraction problems. The tables predicted star and planet positions based on a heliocentric model that were accurate to within one arc minute for most objects, and even those who were skeptical about his Three Laws of Planetary Motion saw the great value in the Tables.

They were, however, complicated, not only in their use of logarithms, but in the solution of Kepler’s Equation, M = E – e sin E. In this equation, M is equal to 2 pi t/P, where t is the time elapsed since the planet was closest to the sun (its periapsis), and P is the period (how long the planet takes to complete one revolution around the sun). E, meanwhile, is an indicator of the position of the planet, measured as an angle from the segment connecting the centre of the planet’s elliptical orbit to the sun. In other words, it is an equation relating time to position for an ellipse of eccentricity e (higher e values mean that you have a less circular shape to your orbit). This is a tricky equation to solve, if you are looking for E and know M. Enter Cunitz. She vastly simplified the process of knowing a planet’s position at a given time by cutting straight to the chase, and looking at the angle between the planet, the Sun, and the periapsis, instead of Kepler’s E, the angle between the planet, the centre of the ellipse, and the periapsis. That angle, called the True Anomaly, could by Cunitz’s method be accurately calculated directly from M, without needing to go through the difficult process to find E, making calculating future planet positions in the Keplerian heliocentric system much simpler in theory.

Cunitz’s system wasn’t perfect, as some of the coefficients she bypassed turned out to be sufficiently significant as to produce observable errors in her tables, but by and large the increase in ease of use and prediction, combined with the accessibility to a more general audience, represented an important advance in bringing heliocentrism to a wider appreciation. Unfortunately, the small original print run of *Urania Propitia *prevented it from attaining the significance that was its due, and soon a disaster would befall Cunitz that prevented her from building on the impressive foundations she had established.

In 1656, a fire destroyed most of the city of Pitisch, where Maria and Elias had settled after the Thirty Years War, and their home was among those destroyed. All of her astronomical observations, instruments, and notes were consumed in the blaze, and as far as we know she did not attempt to rebuild her work from the ashes. Her husband died in 1661, and she followed him in 1664, though her name will continue for as long as our solar system is remembered in the form of the Cunitz crater, a 49 km wide impact crater on Venus that was named after Maria by the International Astronomical Union in 1991.

__FURTHER READING: __

Though it now exists in only 9 remaining physical copies, *Urania Propitia *has been entirely scanned into an online digital version that is free to leaf through, and which can be found online. For her life, Gabriella Bernardi’s *The Unforgotten Sisters *(2016) is a good starting point, while for the larger context of Kepler’s Rudolphine Tables I don’t have a book I’m wildly in love with. After the big hermetic turn in interpreting the early astronomers, books about Kepler really grooved on his mystical side as sort of the central case of the Hermetic Hypothesis, to the detriment of the more technical aspects of How his calculations worked and why his methods did or did not catch on from a mathematical point of view. If I haaaaad to choose one though, I’d say the Oxford Portraits in Science volume is an accessible work that keeps the sensationalism to a minimum.

If you'd like to read more about women astronomers like this one, check out my History of Women in Astronomy and Space Exploration, which you can order from __Amazon__, or from Pen and Sword __US__ or __UK__.

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