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''Mysterium Cosmographicum'' (lit. ''The Cosmographic Mystery'', alternately translated as ''Cosmic Mystery'', ''The Secret of the World'', or some variation) is an astronomy book by the German astronomer
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
, published at
Tübingen Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in three ...
in 1597 and in a second edition in 1621. Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five
Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all e ...
s, enclosed within a sphere that represented the orbit of
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
. This book explains Kepler's cosmological theory, based on the Copernican system, in which the five
Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all e ...
s dictate the structure of the universe and reflect God's plan through geometry. This was virtually the first attempt since
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated ...
to say that the theory of heliocentrism is physically true.
Thomas Digges Thomas Digges (; c. 1546 – 24 August 1595) was an English mathematician and astronomer. He was the first to expound the Copernican system in English but discarded the notion of a fixed shell of immoveable stars to postulate infinitely many s ...
had published a defense of Copernicus in an appendix in 1576. According to Kepler's account, he discovered the basis of the model while demonstrating the geometrical relationship between two circles. From this he realized that he had stumbled on a similar ratio to the one between the orbits of Saturn and Jupiter. He wrote, "I believe it was by divine ordinance that I obtained by chance that which previously I could not reach by any pains." But after doing further calculations he realized he could not use two-dimensional polygons to represent all the planets, and instead had to use the five
Platonic solids In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
.


Shapes and the planets

Johannes Kepler's first major astronomical work, ''Mysterium Cosmographicum'' (''The Cosmographic Mystery''), was the second published defence of the Copernican system. Kepler claimed to have had an
epiphany Epiphany may refer to: * Epiphany (feeling), an experience of sudden and striking insight Religion * Epiphany (holiday), a Christian holiday celebrating the revelation of God the Son as a human being in Jesus Christ ** Epiphany season, or Epiph ...
on July 19, 1595, while teaching in
Graz Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the popul ...
, demonstrating the periodic
conjunction Conjunction may refer to: * Conjunction (grammar), a part of speech * Logical conjunction, a mathematical operator ** Conjunction introduction, a rule of inference of propositional logic * Conjunction (astronomy), in which two astronomical bodies ...
of
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
and
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
in the
zodiac The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the Sun path, apparent path of the Sun across the celestial sphere over the course of the year. ...
: he realized that
regular polygon In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either convex p ...
s bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional
polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...
. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets— Mercury,
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...
,
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
,
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
,
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
, and
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
. By ordering the solids correctly—
octahedron In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
, icosahedron,
dodecahedron In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
,
tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all th ...
, and
cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...
—Kepler found that the spheres correspond to the relative sizes of each planet's path around the Sun, generally varying from astronomical observations by less than 10%. He attributed most of the variances to inaccuracies in measurement. Kepler also found a formula relating the size of each planet's orbit to the length of its
orbital period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula because it was not precise enough.


Theological and philosophical foundation

As he indicated in the title, Kepler thought he had revealed
God In monotheism, monotheistic thought, God is usually viewed as the supreme being, creator deity, creator, and principal object of Faith#Religious views, faith.Richard Swinburne, Swinburne, R.G. "God" in Ted Honderich, Honderich, Ted. (ed)''The Ox ...
’s geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his
theological Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the ...
convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
corresponding to the Father, the stellar sphere to the
Son A son is a male offspring; a boy or a man in relation to his parents. The female counterpart is a daughter. From a biological perspective, a son constitutes a first degree relative. Social issues In pre-industrial societies and some current c ...
, and the intervening space between to the
Holy Spirit In Judaism, the Holy Spirit is the divine force, quality, and influence of God over the Universe or over his creatures. In Nicene Christianity, the Holy Spirit or Holy Ghost is the third person of the Trinity. In Islam, the Holy Spirit acts as ...
. His first manuscript of ''Mysterium'' contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. With the support of his mentor
Michael Maestlin Michael Maestlin (also Mästlin, Möstlin, or Moestlin) (30 September 1550 – 26 October 1631) 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 tea ...
, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible
exegesis Exegesis ( ; from the Ancient Greek, Greek , from , "to lead out") is a critical explanation or interpretation (logic), interpretation of a text. The term is traditionally applied to the interpretation of Bible, Biblical works. In modern usage, ...
and the addition of a simpler, more understandable description of the Copernican system (the ''
Narratio prima ''De libris revolutionum Copernici narratio prima'', usually referred to as ''Narratio Prima'' ( la, First Account), is an abstract of Nicolaus Copernicus' heliocentric theory, written by Georg Joachim Rheticus in 1540. It is an introduction to ...
'' by Rheticus) as an appendix. ''Mysterium'' was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system. Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherical cosmology of ''Mysterium Cosmographicum''. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it. In 1621, Kepler published an expanded second edition of ''Mysterium'', half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication.


Epistemology and philosophy of sciences

Many of Kepler's thoughts about epistemology can be found in his ''Defense of Tycho against Ursus'' or ''Contra Ursum'' (CU), a work which emerged from a polemical framework, the plagiarism conflict between Nicolaus Raimarus Ursus (1551–1600) and Tycho Brahe: causality and physicalization of astronomical theories, the concept and status of astronomical hypotheses, the polemic “realism-instrumentalism”, his criticism of scepticism in general, the epistemological role of history, etc. Jardine has pointed out that it would be sounder to read Kepler's CU more as a work against scepticism than in the context of the modern realism/instrumentalism debate. On the one hand, "causality" is a notion implying the most general idea of "actual scientific knowledge" which guides and stimulates each investigation. In this sense, Kepler already embarked in his MC on a causal investigation by asking for the cause of the number, the sizes and the "motions" (the speeds) of the heavenly spheres. On the other hand, "causality" implies in Kepler, according to the Aristotelian conception of physical science, the concrete "physical cause", the efficient cause which produces a motion or is responsible for keeping the body in motion. Original to Kepler, however, and typical of his approach is the resoluteness with which he was convinced that the problem of equipollence of the astronomical hypotheses can be resolved and the consequent introduction of the concept of causality into astronomy—traditionally a mathematical science. This approach is already present in his MC, where he, for instance, relates for the first time the distances of the planets to a power which emerges from the Sun and decreases in proportion to the distance of each planet, up to the sphere of the fixed stars.


Reception

In response to ''Mysterium Cosmographicum'', the Danish astronomer
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was k ...
(whom Kepler had sent a copy) said that the ideas were intriguing but could only be verified through the observations Brahe himself had been making over the past 30 years. Because he was promised use of these observations by Brahe, Kepler sought him out in the beginning of 1600. Brahe only gave him the data on Mars, but this meeting helped Kepler formulate his laws of planetary motion.


In popular culture

The ''Mysterium Cosmographicum'' was featured on the
Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
n 10
euro The euro ( symbol: €; code: EUR) is the official currency of 19 out of the member states of the European Union (EU). This group of states is known as the eurozone or, officially, the euro area, and includes about 340 million citizens . ...
Johannes Kepler silver commemorative coin minted in 2002.coin-database.com, ''10 euro: Eggenberg Palace''.
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See also

*
Titius–Bode law The Titius–Bode law (sometimes termed just Bode's law) is a formulaic prediction of spacing between planets in any given solar system. The formula suggests that, extending outward, each planet should be approximately twice as far from the Sun as ...
* Golden ratio#History


Notes


References

; Citations


Further reading

* Dreyer, J. L. E., ''A History of Astronomy from Thales to Kepler'', Dover Publications, 1953, pp. 331, 377–379.


External links

*
''Mysterium cosmographicum''
by Johannes Kepler, 1596 edition, in Latin, full text scan, 181 pp.

{{Authority control 16th-century Latin books 1596 books Astronomy books Astrological texts Astrological aspects Astronomical hypotheses Pythagorean philosophy Works by Johannes Kepler