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Michael Maestlin

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"Maestlin" redirects here. For the impact crater on the Moon, see Maestlin (crater).

Michael Maestlin (also Mästlin, Möstlin, or Moestlin; 30 September 1550 – 26 October 1631)[1] was a German astronomer and mathematician, known for being the mentor of Johannes Kepler. He was a student of Philipp Apian and was known as the teacher who most influenced Kepler. Maestlin was considered to be one of the most significant astronomers between the time of Copernicus and Kepler.[2]

Michael Maestlin
Born30 September 1550
Göppingen, Duchy of Württemberg, Holy Roman Empire
Died26 October 1631
(aged 81)
Tübingen, Duchy of Württemberg, Holy Roman Empire
EducationTübinger Stift
Known forMentor of Johannes Kepler
First known decimal approximation of the (inverse) golden ratio

Early life and family

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Maestlin was born on 30 September 1550, in Göppingen, a small town in Southern Germany about 50 kilometers east of Tübingen. The son of Jakob Maestlin and Dorothea Simon, Michael Maestlin was born into a Protestant family.[3] Maestlin had an older sister named Elisabeth and a younger brother named Matthäus. His family's original surname was Leckher or Legecker, and they lived in the village of Boll, just a few kilometers south of Göppingen.[4] In his autobiography, Maestlin recounts how the family name of Legecker became Mästlin.[4] He claims that one of his ancestors was given this as a nickname when an old blind woman touched him and exclaimed "Wie bist du doch so mast und feist! Du bist ein rechter Mästlin!" This roughly translates to "How are you so large and plump? You rightly are a fatso!"[4]

Maestlin married Margarete Grüniger on 9 April 1577.[3] There is little information on his children from this marriage. However, it is known that he had at least three sons, Ludwig, Michael, and Johann Georg, and at least three daughters, Margareta, Dorothea Ursula and Anna Maria. In 1588, Margarete died at the age of 37, potentially due to complications from childbirth.[3] This untimely death left several children under Maestlin's care and could have influenced his decision to remarry the following year. In 1589, Maestlin married Margarete Burkhardt. Maestlin and Burkhardt had eight children together. In a 1589 letter to Johannes Kepler, Maestlin recounts how the death of his month-old son, August, deeply troubled him.[3]

Education

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In 1565, when Maestlin was around 15 years old, he was sent to the nearby Klosterschule in Königsbronn.[3] In 1567, Maestlin transferred to a similar school in Herrenalb.[5] Upon finishing his education in Herrenalb, Maestlin enrolled in university, matriculating on 3 December 1568 at the University of Tübingen.[6][3] When Maestlin entered the university in 1569, he did so as one of the beneficiaries of a scholarship from the Duke of Württemberg.[7]

He studied theology at the Tübinger Stift, which was founded in 1536 by Duke Ulrich von Württemberg, and was regarded as an elite institution of education.[8] He obtained his Baccalaureate in 1569 and his master's degree in 1571.[3] After receiving his master's degree, Maestlin remained at the university as a theology student and as a tutor in the theological seminary church located in Württemberg.[7] In letters sent to Maestlin regarding his qualifications, it was revealed that he graduated summa cum laude and ranked third in his graduating class of twenty.[3] During the time he spent earning his master's degree, Maestlin studied under Philipp Apian.[9] It is not certain, but it is believed that Apian taught courses on Frisius's Arithmetic, Euclid's Elements, Proclus's Sphera, Peurbach's Theoricae Novae Planetarus, and the proper use of geodetic instruments.[3] Apian's teachings evidently influenced Maestlin's paper on sundials, as the contents of this essay involve elements of structured celestial globes and maps.[3]

In 1584, Maestlin was named Professor of Mathematics at Tübingen. He was elected Dean of the Arts Faculty for the following terms: 1588–89, 1594–95, 1600–01, 1607–09, 1610–11, 1615, 1623, and 1629.[3] Maestlin taught trigonometry and astronomy. It was very likely that he used his book Epitome Astronomiae in his lectures.[citation needed]

In 1576, Maestlin was sent to be a deacon at the Lutheran church in Backnang, a town about 30 kilometers northwest of Göppingen. While there, he observed a comet that appeared in 1577. Tycho Brahe in Denmark observed the same comet, and from observations of its parallax, both Tycho and Maestlin were able to determine that the comet must be above the Moon, contrary to the astronomical theories of both Aristotle and Ptolemy. Maestlin concluded that, in the Copernican system, the comet must lie in a region between the sphere of Venus and that of the Earth and Moon.[10] Maestlin served as the Duke's chief scientific adviser from 1577 to 1580.[3]

Career

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In 1580, Maestlin became a professor of mathematics, first at the University of Heidelberg, then at the University of Tübingen, where he taught for 47 years beginning in 1583. In 1582, Maestlin wrote a popular introduction to astronomy.[citation needed] While teaching at the university, Maetslin taught traditional Ptolemaic astronomy in his courses. However, he did present Copernican's heliocentric astronomy to his advanced students.[11]

While Maestlin had many interests like calendar reform and mathematics, he was above all, an astronomer. He spent much time researching the Sun, Moon, and eclipses. His 1596 work, Disputatio de Eclipsibus is almost entirely about the Sun and the Moon and is often referenced in Kepler's 1604 work, Astronomiae pars optica.[3] In 1587, Maestlin published a manuscript entitled Tabula Motus Horarii in which he gives the daily motion of the Sun in hours and minutes with its positions in two-minute intervals. Other tables he published give equivalent information but in degrees, minutes, and seconds.[3]

Among his students was Johannes Kepler (1571–1630), who considered Maestlin not only a teacher but also a lifelong mentor.[12] Although he primarily taught the traditional geocentric Ptolemaic view of the Solar System, Maestlin was also one of the first to accept and teach the heliocentric Copernican view.[12] Maestlin corresponded with Kepler frequently and played a sizable role in the latter's adoption of the Copernican system. Galileo Galilei's adoption of heliocentrism was also attributed to Maestlin.[13]

The first known calculation[14] of the (inverse) golden ratio as a decimal of "about 0.6180340" was written in 1597 by Maestlin on a letter he got from to Kepler about the Kepler triangle.[15]

Maestlin was one of the very few astronomers of the 16th century to fully adopt the Copernican hypothesis, which proposed that the Earth was a planet that moved around the Sun. In 1570, he acquired an edition of Copernicus' seminal work, De revolutionibus orbium coelestium (Maestlin's personal copy containing his handwritten notes in the margins is held in the municipal library of Schaffhausen).[16] Maestlin reacted to the thought of distant stars spinning around a fixed Earth every 24 hours in his notes and taught everything that he could about Copernicus to Kepler.[17]

In accepting the Copernican view of the Solar System, Maestlin believed that the "movement of commutation" (or "parallactic motion") of the superior planets (those farther from the Sun compared to the Earth) and the lack of parallactic motion in the supernova meant that the supernova must have occurred outside the planetary rings and in the ring of fixed stars. This contradicted the previous understandings of Ptolemaic and Aristotelian models. Maestlin also concluded that the nova helped to prove the heliocentric Solar System as he said unless people concede that comets can be placed in the stellar orb, whose altitude is immense and whose extension we do not know, to which also the distance between the Sun and the Earth is incomparable, as witnessed by Copernicus.[18]

In 1589, Maestlin published a dissertation on the fundamental principles of astronomy and the first edition of his book Epitome Astronomiae (Epitome of Astronomy).[3] Epitome Astonomiae consisted of six editions and used works like Ptolemy's famous geocentric model to create descriptions of astronomy.[citation needed]

The preface in the 1596 republication of Georg Joachim Rheticus' Narratio Prima was written by Maestlin. This preface was an introduction to the work of Copernicus.

In 1613, Maestlin obtained his first set of telescopes. In a letter to Kepler, Maestlin says he was unable to view the satellites of Saturn or the phases of Venus, however, he was able to see the moons of Jupiter.[3]

SN 1572 supernova

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In November 1572, Maestlin and many others around the world witnessed a strange light in the sky that we now know was a galactic supernova.[18] This Type Ia supernova, known as SN 1572, took place in the constellation of Cassiopeia and was the first galactic supernova to be observed in Europe.[18] Maestlin attempted to explain this phenomenon in his tract entitled Demonstratio astronomica loci stellae novae, tum respectu centri mundi, tum respectu signiferi & aequinoctialis. This tract was a short mathematical and astronomical appendix detailing the supernova, and it was published in Tübingen in March or April of 1573.[18] Maestlin's treatise attracted the attention of Tycho Brahe, who reproduced it in its entirety, accompanied by his own criticisms, in one of the best-known publications on the subject, his posthumously printed Astronomiae instauratae progymnasmata.[18] Maestlin's treatise is available in manuscript format in Stuttgart and in Marburg.[18]

Maestlin's treatise on the nova of 1572 featured many aspects extremely similar to Tycho de Brahe's much longer treatise on the same nova titled De Stella Nova. Both were published the same year, 1602, even though Maestlin's was thought to be written much earlier. In this treatise, Maestlin focused extensively on the mathematics behind the new star's exact location.[18][19]

Great comet of 1577

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In accordance with the Copernican view of the heavens, Johannes Kepler calculated there to be empty spaces between the planetary orbs of the heavens, and Maestlin suggested that these empty spaces might be where comets frequently occur.[10] This sort of revelation was only possible under the assumption of a heliocentric universal organization. Maestlin is believed to have come to this heliocentric view after observing the path of the Great Comet of 1577.[10] When that comet appeared, Maestlin, along with the Danish astronomer Tycho Brahe were the first people who actively tried to calculate its path in a more complex way than simply tracking its path across the sky.[10] Tycho Brahe and Maestlin deduced that the comet was not only travelling across the sky, but was traversing Aristotle's and Ptolemy's solid geocentric orbs, suggesting that the spheres of planets were not solid as previous astronomers believed.[11] In 1589, he shared his conclusions about the appearance of the comet with his friend, the astrologer Helisaeus Roeslin, who believed that the Great Comet of 1577 was located beyond the moon.[20]

 
Tycho Brahe's depiction of the comet of 1577 traveling across the sky.

Role in Kepler's Mysterium Cosmographicum

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Maestlin also supervised and made many contributions to tables and diagrams in Kepler's Mysterium Cosmographicum, published in 1596. Maestlin and Kepler communicated through letters about the book, and some of those letters form the foundation of Maestlin's appendix to the publication, which focused on Copernican planetary theory, using the values given in Erasmus Reinhold's Prutenic Tables to give a set of planetary distances.[21] The appendix was entitled "On the Dimensions of the Heavenly Circles and Spheres, according to the Prutenic tables after the theory of Nicolaus Copernicus" and was intended to both address "the needs of a hypothetical educated reader" and answer some of the questions Kepler had raised in the book.[21] Maestlin also discusses Kepler and the quality of his findings and knowledge on the subject of astronomy.[22]

In addition to his appendix, Maestlin also added his own understanding of Nicolaus Copernicus' geometry to Kepler's book, and in their correspondence they discussed such topics such as the inaccuracy of the values that Copernicus used when calculating the spheres of the cosmos.[21]

Kepler believed that he had discovered the distances between the Sun and the planets in 1595. He assumed equal velocity of each planet and observed that the planets did not revolve just according to the length of their radii. Kepler observed that the Sun exerted a force that was progressively attenuated the farther away a planet was from the Sun. Maestlin provided the geometry to help visualize Kepler's theory of the Sun's force and its effects of the other planets, which was included in Mysterium Cosmographicum.[21] Maestlin added diagrams of his views on the order of the planets and the spacing between them. This was the first time such a thing had been done.[23] These diagrams caused a misunderstanding that lasted centuries as Maestlin did not make it clear whether the planets were supposed to be moving along the lines of the circles that were supposed to represent his planetary system, or whether they were meant to be moving within the spaces drawn by him.[23] This led to many people believing that the planetary system suggested by Copernicus included a smaller number of modifications (such as epicycles) than that of Ptolemy, when the very opposite was the case.[21] Despite the confusion these diagrams caused, Maestlin is still credited with having greatly contributed greatly to Kepler's Mysterium; Kepler even acknowledged his co-authoring of the book in a letter to Maestlin.[24]

Kepler's Supernova

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In 1604, Maestlin was one of the first astronomers able to observe the 1604 Supernova (later dubbed Kepler's Supernova) on 9 October 1604. He made his observations visually, without instruments, but did not immediately publish them. Instead, he began working on a treatise, entitled Consideratio Astronomica inusitatae Novae et prodigiosae Stellae, superiori 1604 anno, sub initium Octobris, iuxta Eclipticam in signo Sagittarii vesperi exortae, et adhuc nunc eodem loco lumine corusco lucentis (Astronomical consideration of the extraordinary and prodigious new star that appeared near the ecliptic in the sign of Sagittarius one evening in early October in the preceding year 1604, and continues to shine in the same place with a tremulous light) with the intent to publish it in the coming years. He began seriously working on the treatise in 1606; however, it was never fully completed.[2]

While frequently in communication with Kepler between 1594 and 1600, Maestlin stopped responding to Kepler between 1600 and 1605. Kepler, eager to keep the conversation alive, wrote many letters to which he would receive no response. One theory posits that Maestlin's period of silence ensued due to his fear that Kepler would publish their letters of correspondence, while another suggests that it was the result of a personal crisis on Maestlin's behalf in reaction to rumors of his own suicide.[2] Kepler, frustrated with his teacher's refusal to continue their written communication, complained to Maestlin in a letter dated 14 December 1604. He implored him to respond with his thoughts on the recently discovered and highly discussed 1604 Supernova. To not write about this event would make Maestlin guilty of the "crime of deserting astronomy," according to Kepler.[2] Maestlin finally responded at the end of January 1605. He justified his silence by claiming that, concerning the questions Kepler had addressed to him, he had nothing more of use to add to the prior explanations. In regard to the nova, he deduced that it was in fact just a star that had previously not been discovered or noticed.[2]

Maestlin did begin writing a treatise on Kepler's supernova, though it was never finished. This work, written completely in Latin, was titled "Consideratio Astronomica inusitatae Novae et prodigiosae Stellae, superiori 1604 anno, sub initium Octobris, iuxta Eclipticam in signo Sagittarii vesperi exortae, et adhuc nunc eodem loco lumine corusco lucentis" ("Astronomical consideration of the extraordinary and prodigious new star that appeared near the ecliptic in the sign of Sagittarius one evening in early October in the preceding year 1604, and continues to shine in the same place with a tremulous light"). The work is just over 12 pages and unfinished, which has led scholars to believe that either Maestlin failed to finish writing it or the final pages were lost over the centuries. It is estimated he wrote the treatise in April 1605, as Maestlin describes the months of February or March, when the supernova showed signs of decreasing intensity and brightness. He estimated its expiration or disappearance in May of the same year. His reasoning for this estimation came from the fact that the Sun would be in opposition with the nova at this point in time. He discusses extensively the intensity and magnitude of the nova and how it differs from the patterns seen in previous novas, such as that of 1572, which was first seen at a certain magnitude and then like others before and after it, experienced a constant decreasing throughout its visibility. The 1604 Supernova however, maintained a large magnitude for some time, as a first-magnitude star like that of Venus and the other brightest stars.[2]

Christianity

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During the days of Maestlin and Kepler, it could be considered dangerous to question God's responsibility for creating the world and all the creatures in it, because one might be accused of blasphemy. Maestlin saw things in a different light, however. He was a follower of the Lutheran church, and as such, he believed that studying the natural world and unraveling the laws that embody it will bring humanity closer to God. In Maestlin's opinion, understanding God's creations will enable his children to be closer to him and his divine plan. He further believed that finding out more about the natural world we live in will enrich the knowledge we have of God.[25] Maestlin at one time had even been a Lutheran pastor.[26]

Michael Maestlin used his notability to project his religious and political views. In 1582, Maestlin voiced his view in treaties on the new Gregorian calendar and its creation.[27] His arguments focused on mathematics perceptive and political perceptive. He agreed that Julian calendar was inaccurate and that it states a year to be 365 days and 6 hours long, but as Maestiling said, the year is "365 days, five hours, forty-nine minutes and 46 thirds long".[27] Also, he discusses that the golden numbers are calculated wrong.[27] While his argument with mathematics mostly supports the replacement of the Julian calendar, his argument for political reasons differ. Maestlin was against the adoption of the Gregorian calendar even though he believed there was a need for a new accurate calendar.[27] He argues that the need for a new calendar was known for two hundred years, but nothing was done.[27] He suggested that the reason that calendar was being adopted now was because the Catholic Church lost power, and the Pope wanted "to further his dominion".[28] This stems from Maestlin's dislike of the position of the Pope, which is shown by his statement, the Pope does not direct "the movements of the sun and moon".[27] Maestlin believed that the Pope was trying to project power into countries that rather recently rid the Pope's powers.[27] Then he suggested that only educated people would notice the problems with the calendar.[27] He believed the judgment day in the year 2000, which with the Julian calendar is an inaccuracy of three days.[27] So he does not believe the correction is worth it.[27]

Notable astronomical observations

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  • Catalogued the Pleiades cluster on 24 December 1579. Eleven stars in the cluster were recorded by Maestlin, and possibly as many as fourteen were observed.[29]
  • Occultation of Mars by Venus on 13 October 1590, seen by Maestlin at Heidelberg.[30]
  • Observed Kepler's Supernova on 9 October 1604 but did not begin to publicly record the observation until 1606[31]

Legacy

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In Jules Verne's Cinq semaines en ballon (Five Weeks in a Balloon) the character of Joe, the manservant, is described as enjoying, "in common with Moestlin, Kepler's professor, the rare faculty of distinguishing the satellites of Jupiter with the naked eye, and of counting fourteen of the stars in the group of Pleiades, the remotest of them being only of the ninth magnitude."

Michael Maestlin has more than one piece of art made in memoriam to him. The first is a woodcut portrait that was solely made for Maestlin. The second one is part of a monument that was made for Johannes Kepler in Weil-der-Stadt, which was Kepler's hometown. Kepler's monument has four statues of those who deeply influenced his work in astronomy, and needless to say, one of them is of Michael Maestlin. The third artwork of Maestlin is a plaque, which is also on Kepler's monument, that shows Maestlin teaching Kepler and his other students.[32]

In 2000, a conference was held in Tubingen (where Maestlin was a professor at the university) on Maestlin and his life and works. From these, Gerhard Betsch produced a collective volume on their findings, and a breakdown of his works as well as a summary of Maestlin's nachlass. His nachlass had been kept and preserved among different library archives in both Germany and Austria. Betsch discussed many things in his dissertation including a treatise composed by Maestlin on the Comet of 1618–1619 written completely in German.

See also

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References

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  1. ^ Volker Bialas (1987), "Mästlin, Michael", Neue Deutsche Biographie (in German), vol. 15, Berlin: Duncker & Humblot, pp. 644–645
  2. ^ a b c d e f Granada, Miguel A (February 2014). "Michael Maestlin and his Unpublished Treatise on the Nova of 1604". Universitat de Barcelona. 45 (1): 91–122. Bibcode:2014JHA....45...91G. doi:10.1177/002182861404500106. S2CID 120423355.
  3. ^ a b c d e f g h i j k l m n o p Jarrell, Richard A. (1972). The life and scientific work of the Tübingen astronomer Michael Mästlin 1550–1631 (Thesis).[page needed]
  4. ^ a b c Decker, Martin (1939). Blatter für Württembergische Familienkunde. pp. 102–104.
  5. ^ Steiff, Karl (1892). Der Tuebingen Professor der Mathematik und Astronomie Michael Maestlin. pp. 49–64.
  6. ^ Die Matrikeln der Universitat Tübingen 1477-1817. 1906. p. 487.
  7. ^ a b Methuen, Charlotte (1996). "Maestlin's Teaching of Copernicus: The Evidence of His University Textbook and Disputations". Isis. 87 (2): 230–247. doi:10.1086/357482. JSTOR 236062. S2CID 144999540.
  8. ^ Michael Mästlin. (n.d.). Retrieved from https://www.uni-online.de/personen/michael-maestlin/ Archived 23 October 2020 at the Wayback Machine.
  9. ^ Rössler, Hellmuth (1953). Biographisches Wörterbuch zur deutschen Geschichte. Munich. p. 457.{{cite book}}: CS1 maint: location missing publisher (link)
  10. ^ a b c d Barker, Peter (June 2002). "Constructing Copernicus". Perspectives on Science. 10 (2): 208–227. doi:10.1162/106361402321147531. S2CID 57563317. Project MUSE 39052.
  11. ^ a b Barker, Peter; Goldstein, Bernard R. (2001). "Theological Foundations of Kepler's Astronomy". Osiris. 16: 88–113. doi:10.1086/649340. JSTOR 301981. S2CID 145170215.
  12. ^ a b Kuhn, Thomas (1985) [1957]. The Copernican Revolution. Harvard University Press. p. 187. ISBN 978-0-674-17103-9.
  13. ^ Smolka, Josef (2002). "Michael Mästlin und Galileo Galilei". Acta Historica Astronomiae. 17: 122–140. Bibcode:2002AcHA...17..122S.
  14. ^ J J O'Connor and E F Robertson, The Golden ratio, 2001, The first known calculation of the golden ratio as a decimal was given in a letter written in 1597 by Michael Maestlin, at the University of Tübingen, to his former student Kepler. He gives "about 0.6180340" for the length of the longer segment of a line of length 1 divided in the golden ratio. The correct value is 0.61803398874989484821... The mystical feeling for the golden ratio was of course attractive to Kepler, as was its relation to the regular solids. History.mcs.st-andrews.ac.uk
  15. ^ Caspar, Johannes Kepler Gesammelte Werke, Kepler digital, vol. 13, Brief 75, page 144, Randbemerkung. See also Brief 80, page 152.
  16. ^ Kopernikus, Nikolaus (1543). De revolutionibus orbium coelestium, Libri VI. apud Ioh. Petreium. doi:10.3931/e-rara-79844 – via e-rara.ch.
  17. ^ Calinger, Ronald (2000). "Review of Kepler's Tübingen: Stimulus to a Theological Mathematics". The Catholic Historical Review. 86 (1): 128–129. doi:10.1353/cat.2000.0127. JSTOR 25025682. S2CID 125186100.
  18. ^ a b c d e f g Granada, Miguel A. (2007). "Michael Maestlin and the New Star of 1572". Journal for the History of Astronomy. 38 (130): 99–124. Bibcode:2007JHA....38...99G. doi:10.1177/002182860703800105. S2CID 117171271.
  19. ^ Barker, Peter; Goldstein, Bernard R (2001). "Theological Foundations of Kepler's Astronomy". The University of Chicago Press on Behalf of the History of Science Society. 16: 88–113. Bibcode:2001Osir...16...88B.
  20. ^ Hellman, C. D. (1971). The Comet of 1577. AMS Press. pp. 159–161. ISBN 978-5-88224-384-4.
  21. ^ a b c d e Grafton, Anthony (1973). "Michael Maestlin's Account of Copernican Planetary Theory". Proceedings of the American Philosophical Society. 117 (6): 523–550. Bibcode:1973PAPhS.117..523G. JSTOR 986463.
  22. ^ Grafton, Anthony (31 December 1973). "Michael Maestlin's Account of Copernican Planetary Theory". Proceedings of the American Philosophical Society. 117 (6): 523–550. Bibcode:1973PAPhS.117..523G. JSTOR 986463.
  23. ^ a b Grasshoff, G. (2012). Michael Maestlins mystery: Theory building with diagrams. Cambridge, Eng.
  24. ^ Grasshoff, Gerd (2012). "Michael Maestlin's Mystery: Theory Building with Diagrams". Journal for the History of Astronomy. 43 (1): 57–73. Bibcode:2012JHA....43...57G. doi:10.1177/002182861204300104. S2CID 117056401.
  25. ^ Barker, P., & Goldstein, B. R. (2001). Theological foundations of Keplers astronomy. Ithaca, NY.
  26. ^ "Johannes Kepler - Kepler's social world". Encyclopedia Britannica. Retrieved 2 December 2019.
  27. ^ a b c d e f g h i j Methuen, Charlotte (March 2001). "Time Human or Time Divine? Theological Aspects in the Opposition to Gregorian Calendar Reform". Reformation & Renaissance Review. 3 (1): 36–50. doi:10.1558/rrr.v3i1.36. S2CID 159708565.
  28. ^ McNutt, Jennifer Powell (September 2006). "Hesitant Steps: Acceptance of the Gregorian Calendar in Eighteenth-Century Geneva". Church History. 75 (3): 544–564. doi:10.1017/s0009640700098620. S2CID 154764575.
  29. ^ Winnecke (December 1878). "On the Visibility of Stars in the Pleiades with the Naked Eye". Monthly Notices of the Royal Astronomical Society. XXXIX. #2 (2): 146–148. Bibcode:1878MNRAS..39..146W. doi:10.1093/mnras/39.2.146.
  30. ^ Albers, Steven C. (March 1979). "Mutual Occultations of Planets: 1557 to 2230". Sky and Telescope. 57: 220. Bibcode:1979S&T....57..220A.
  31. ^ Burke-Gaffney, W. (1937). "Kepler and the Star of Bethlehem". Journal of the Royal Astronomical Society of Canada. 31: 417. Bibcode:1937JRASC..31..417B.
  32. ^ "Michael Maestlin - Scientist of the Day". Linda Hall Library. 30 September 2015. Retrieved 8 December 2021.

Further reading

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