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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 of planetary motion, and his books '' Astronomia nova'', ''Harmonice Mundi'', and ''Epitome Astronomiae Copernicanae''. These works also provided one of the foundations for Newton's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and ...
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Kepler's Laws Of Planetary Motion
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. The three laws state that: # The orbit of a planet is an ellipse with the Sun at one of the two foci. # A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. # The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law helps to establish that when a planet is closer to the Sun, it travels faster. The thi ...
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Astronomia Nova
''Astronomia nova'' (English: ''New Astronomy'', full title in original Latin: ) is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year-long investigation of the motion of Mars. One of the most significant books in the history of astronomy, the ''Astronomia nova'' provided strong arguments for heliocentrism and contributed valuable insight into the movement of the planets. This included the first mention of the planets' elliptical paths and the change of their movement to the movement of free floating bodies as opposed to objects on rotating spheres. It is recognized as one of the most important works of the Scientific Revolution. Background Prior to Kepler, Nicolaus Copernicus proposed in 1543 that the Earth and other planets orbit the Sun. The Copernican model of the Solar System was regarded as a device to explain the observed positions of the planets rather than a physical description. Kepler sought for and proposed physica ...
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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 teacher who most influenced Kepler. Maestlin was considered to be one of the most significant astronomers between the time of Copernicus and Kepler. Early life and family Maestlin was born on September 30, 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. Maestlin had an older sister named Elisabeth and a younger brother named Matthäus. The original family name of the Maestlin was Leckher or Legecker and they lived in the village of Boll, just a few kilometers south of Göppingen (Decker 103). In his autobiography, Maestlin recounts how the family name of Legecker became Mästlin. He claims that one o ...
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Harmonice Mundi
''Harmonice Mundi (Harmonices mundi libri V)''The full title is ''Ioannis Keppleri Harmonices mundi libri V'' (''The Five Books of Johannes Kepler's The Harmony of the World''). (Latin: ''The Harmony of the World'', 1619) is a book by Johannes Kepler. In the work, written entirely in Latin, Kepler discusses harmony and congruence in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called "third law of planetary motion". Background and history Kepler began working on ''Harmonice Mundi'' sometime near 1599, which was the year Kepler sent a letter to Michael Maestlin detailing the mathematical data and proofs that he intended to use for his upcoming text, which he originally planned to name ''De harmonia mundi.'' Kepler was aware that the content of ''Harmonice Mundi'' closely resembled that of the subject matter for Ptolemy's ''Harmonica,'' but was not concerned. The new astronomy Kepler would use-most notably the adoptio ...
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Kepler Conjecture
The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is around 74.05%. In 1998, Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof, and the Kepler conjecture was accepted as a theorem. In 2014, the Flyspeck project team, headed by Hales, announced the completion of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistan ...
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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 known during his lifetime as an astronomer, astrologer, and alchemist. He was the last major astronomer before the invention of the telescope. An heir to several noble families, Tycho was well-educated. He took an interest in astronomy and in the creation of more accurate instruments of measurement. He worked to combine what he saw as the geometrical benefits of Copernican heliocentrism with the philosophical benefits of the Ptolemaic system, and devised the Tychonic system, his own version of a model of the universe, with the Sun orbiting the Earth, and the planets as orbiting the Sun. In ''De nova stella'' (1573), he refuted the Aristotelian belief in an unchanging celestial realm. His measurements indicated that "new stars" (''stel ...
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Rudolphine Tables
The ''Rudolphine Tables'' ( la, Tabulae Rudolphinae) consist of a star catalogue and planetary tables published by Johannes Kepler in 1627, using observational data collected by Tycho Brahe (1546–1601). The tables are named in memory of Rudolf II, Holy Roman Emperor, in whose employ Brahe and Kepler had begun work on the tables. The main purpose of the Rudolphine tables was to allow the computation of the positions of the then known planets of the Solar System, and they were considerably more precise than earlier such tables. Previous tables Star tables had been produced for many centuries and were used to establish the position of the planets relative to the fixed stars (particularly the twelve constellations used in astrology) on a specific date in order to construct horoscopes. Until the end of the 16th century, the most widely used had been the '' Alphonsine tables'', first produced in the 13th century and regularly updated thereafter. These were based on a Ptolemaic, geo ...
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Scientific Revolution
The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transformed the views of society about nature.Galilei, Galileo (1974) ''Two New Sciences'', trans. Stillman Drake, (Madison: Univ. of Wisconsin Pr. pp. 217, 225, 296–67.Clagett, Marshall (1961) ''The Science of Mechanics in the Middle Ages''. Madison, Univ. of Wisconsin Pr. pp. 218–19, 252–55, 346, 409–16, 547, 576–78, 673–82 Hannam, p. 342 The Scientific Revolution took place in Europe starting towards the second half of the Renaissance period, with the 1543 Nicolaus Copernicus publication '' De revolutionibus orbium coelestium'' (''On the Revolutions of the Heavenly Spheres'') often cited as its beginning. The era of the Scientific Renaissance focused to some degree on recovering the knowledge of the ancients, and is considered to h ...
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Epitome Astronomiae Copernicanae
The ''Epitome Astronomiae Copernicanae'' was an astronomy book on the heliocentric system published by Johannes Kepler in the period 1618 to 1621. The first volume (books I–III) was printed in 1618, the second (book IV) in 1620, and the third (books V–VII) in 1621. Content The book contained in particular the first version in print of his third law of planetary motion. The work was intended as a textbook, and the first part was written by 1615. Divided into seven books, the ''Epitome'' covers much of Kepler's earlier thinking, as well as his later positions on physics, metaphysics and archetypes. In Book IV he supported the Copernican cosmology. Book V provided mathematics underpinning Kepler's views. Kepler wrote and published this work in parallel with his '' Harmonices Mundi'' (1619), the last Books V to VII appearing in 1621. Kepler introduced the idea that the physical laws determining the motion of planets around the Sun were the same governing the motion of moons a ...
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Nicolaus 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 a model of the universe that placed the Sun rather than Earth at its center. In all likelihood, Copernicus developed his model independently of Aristarchus of Samos, an ancient Greek astronomer who had formulated such a model some eighteen centuries earlier. The publication of Copernicus's model in his book ' (''On the Revolutions of the Celestial Spheres''), just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region that had been part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematic ...
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Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism. The ...
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Regensburg
Regensburg or is a city in eastern Bavaria, at the confluence of the Danube, Naab and Regen rivers. It is capital of the Upper Palatinate subregion of the state in the south of Germany. With more than 150,000 inhabitants, Regensburg is the fourth-largest city in the State of Bavaria after Munich, Nuremberg and Augsburg. From its foundation as an imperial Roman river fort, the city has been the political, economic and cultural centre of the surrounding region; it is still known in the Romance languages by a cognate of its Latin name of "Ratisbona" (the version "Ratisbon" was long current in English). Later, under the rule of the Holy Roman Empire, it housed the Perpetual Diet of Regensburg. The medieval centre of the city was made a UNESCO World Heritage Site in 2006 because of its well-preserved architecture and the city's historical importance for assemblies during the Holy Roman Empire. In 2014, Regensburg was among the top sights and travel attractions in Germany. Hist ...
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