Editing Johannes Kepler (section)

=== ''Harmonice Mundi'' ===
{{Main|Harmonice Mundi}}
[[File:Kepler-1619-pl-3.jpg|thumb|upright=.9|Geometrical harmonies from ''[[Harmonice Mundi]]'' (1619)]]
Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world".<ref>Quotation from Caspar, ''Kepler'', pp.&nbsp;265–266, translated from ''Harmonice Mundi''</ref> In ''Harmonice Mundi'' (1619), he attempted to explain the proportions of the natural world—particularly the astronomical and astrological aspects—in terms of music.{{NoteTag|The opening of the movie ''[[Mars et Avril]]'' by [[Martin Villeneuve]] is based on German astronomer Johannes Kepler's cosmological model from the 17th century, ''[[Harmonice Mundi]]'', in which the harmony of the universe is determined by the motion of celestial bodies. [[Benoît Charest]] also composed the score according to this theory.}} The central set of "harmonies" was the ''[[musica universalis]]'' or "music of the spheres", which had been studied by [[Pythagoras]], [[Ptolemy]] and others before Kepler; in fact, soon after publishing ''Harmonice Mundi'', Kepler was embroiled in a priority dispute with [[Robert Fludd]], who had recently published his own harmonic theory.<ref>Caspar, ''Kepler'', pp.&nbsp;264–266, 290–293</ref>

Kepler began by exploring regular polygons and [[regular solid]]s, including the figures that would come to be known as [[Kepler-Poinsot polyhedra|Kepler's solids]]. From there, he extended his harmonic analysis to music, meteorology, and astrology; harmony resulted from the tones made by the souls of heavenly bodies—and in the case of astrology, the interaction between those tones and human souls. In the final portion of the work (Book V), Kepler dealt with planetary motions, especially relationships between [[orbital speed|orbital velocity]] and orbital distance from the Sun. Similar relationships had been used by other astronomers, but Kepler—with Tycho's data and his own astronomical theories—treated them much more precisely and attached new physical significance to them.<ref>Caspar, ''Kepler'', pp.&nbsp;266–290</ref>

Among many other harmonies, Kepler articulated what came to be known as the third law of planetary motion. He tried many combinations until he discovered that (approximately) "''The square of the periodic times are to each other as the cubes of the mean distances''." Although he gives the date of this epiphany (8 March 1618), he does not give any details about how he arrived at this conclusion.<ref name="Miller2009">{{Cite book |last=Miller |first=Arthur I. |author-link=Arthur I. Miller |title=Deciphering the cosmic number: the strange friendship of Wolfgang Pauli and Carl Jung |url=https://archive.org/details/isbn_9780393065329 |url-access=registration |access-date=7 March 2011 |date=2009 |publisher=W. W. Norton & Company |isbn=978-0-393-06532-9 |page=[https://archive.org/details/isbn_9780393065329/page/80 80]}}</ref> However, the wider significance for planetary dynamics of this purely kinematical law was not realized until the 1660s. When conjoined with [[Christiaan Huygens]]' newly discovered law of centrifugal force, it enabled [[Isaac Newton]], [[Edmund Halley]], and perhaps [[Christopher Wren]] and [[Robert Hooke]] to demonstrate independently that the presumed gravitational attraction between the Sun and its planets decreased with the square of the distance between them.<ref>Westfall, ''Never at Rest'', pp.&nbsp;143, 152, 402–403; Toulmin and Goodfield, ''The Fabric of the Heavens'', p. 248; De Gandt, 'Force and Geometry in Newton's Principia', chapter 2; Wolf, ''History of Science, Technology and Philosophy'', p. 150; Westfall, ''The Construction of Modern Science'', chapters 7 and 8</ref> This refuted the traditional assumption of scholastic physics that the power of gravitational attraction remained constant with distance whenever it applied between two bodies, such as was assumed by Kepler and also by Galileo in his mistaken universal law that gravitational fall is uniformly accelerated, and also by Galileo's student Borrelli in his 1666 celestial mechanics.<ref>Koyré, ''The Astronomical Revolution'', p.&nbsp;502</ref>