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title: "A Passage to Infinity"
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A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact is a 2009 book by George Gheverghese Joseph chronicling the social and mathematical origins of the Kerala school of astronomy and mathematics. The book discusses the highlights of the achievements of Kerala school and also analyses the hypotheses and conjectures on the possible transmission of Kerala mathematics to Europe.
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== An outline of the contents ==
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Introduction
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The Social Origins of the Kerala School
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The Mathematical Origins of the Kerala School
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The Highlights of Kerala Mathematics and Astronomy
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Indian Trigonometry: From Ancient Beginnings to Nilakantha
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Squaring the Circle: The Kerala Answer
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Reaching for the Stars: The Power Series for Sines and Cosines
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Changing Perspectives on Indian Mathematics
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Exploring Transmissions: A Case Study of Kerala Mathematics
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A Final Assessment
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== See also ==
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Indian astronomy
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Indian mathematics
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History of mathematics
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== References ==
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== Further references ==
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In association with the Royal Society's 350th anniversary celebrations in 2010, Asia House presented a talk based on A Passage to Infinity. See : "A Passage to Infinity: Indian Mathematics in World Mathematics". Retrieved 3 May 2010.
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For an audio-visual presentation of George Gheverghese Joseph's views on the ideas presented in the book, see : Joseph, George Gheverghese (16 September 2008). "George Gheverghese Joseph on the Transmission to Europe of Non-European Mathematics". The Mathematical Association of America. Archived from the original on 15 April 2010. Retrieved 3 May 2010.
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The Economic Times talks to George Gheverghese Joseph on The Passage to Infinity. See : Lal, Amrith (23 April 2010). "Indian mathematics loved numbers". The Economic Times.
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Review of "A PASSAGE TO INFINITY: Medieval Indian Mathematics from Kerala and its impact" by M. Ram Murty in Hardy-Ramanujan Journal, 36 (2013), 43–46.
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Nair, R. Madhavan (3 February 2011). "In search of the roots of mathematics". The Hindu. Retrieved 15 October 2014.
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title: "A Question and Answer Guide to Astronomy"
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A Question and Answer Guide to Astronomy is a book about astronomy and cosmology, and is intended for a general audience. The book was written by Pierre-Yves Bely, Carol Christian, and Jean-Rene Roy, and published in English by Cambridge University Press in 2010. It was originally written in French. The content within the book is written using a question and answer format. It contains some 250 questions, which The Science Teacher states each are answered with a "concise and well-formulated essay that is informative and readable." The Science Teacher review goes on to state that many of the answers given in the book are "little gems of science writing". The Science Teacher summarizes by stating that each question is likely to be thought of by a student, and that "the answers are informative, well constructed, and thorough".
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The book covers information about the planets, the Earth, the Universe, practical astronomy, history, and awkward questions such as astronomy in the Bible, UFOs, and aliens. Also covered are subjects such as the Big Bang, comprehension of large numbers, and the Moon illusion.
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== See also ==
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Bibliography of encyclopedias: astronomy and astronomers
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== References ==
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Additional reviews
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Wolff, Sidney (8 July 2010). "Book Review—A Question and Answer Guide to Astronomy". Astronomy Education Review. 9 (1): 010501. Bibcode:2010AEdRv...9a0501W. doi:10.3847/aer2010018.
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Mutel, R. L. "A question and answer guide to astronomy", Choice: Current Reviews for Academic Libraries; Jan2011, Vol. 48 Issue 5, p920-920
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Whitt, April S. "A Question and Answer Guide to Astronomy", Planetarian; Sep2012, Vol. 41 Issue 3, p60-60
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Mizon, Bob "A question and answer guide to astronomy", Journal of the British Astronomical Association; Jun2010, Vol. 120 Issue 3, p186-186, 1/2p
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Zetie, Ken "A Question and Answer Guide to Astronomy", Contemporary Physics; Sep/Oct2011, Vol. 52 Issue 5, p482-482, 1p
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"A Question and Answer Guide to Astronomy", MNASSA Monthly Notes of the Astronomical Society of Southern Africa; Aug2011, Vol. 70 Issue 7/8, p159-161, 3p
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== External links ==
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Cambridge University Press — A Question and Answer Guide to Astronomy
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Cosmos is a popular science book written by astronomer and Pulitzer Prize-winning author Carl Sagan. It was published in 1980 as a companion piece to the PBS mini-series Cosmos: A Personal Voyage with which it was co-developed and intended to complement. Each of the book's 13 illustrated chapters corresponds to one of the 13 episodes of the television series.
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Just a few of the ideas explored in Cosmos include the history and mutual development of science and civilization, the nature of the Universe, human and robotic space exploration, the inner workings of the cell and the DNA that controls it, and the dangers and future implications of nuclear war. One of Sagan's main purposes for both the book and the television series was to explain complex scientific ideas in a way that anyone interested in learning can understand. Sagan also believed the television was one of the greatest teaching tools ever invented, so he wished to capitalize on his chance to educate the world.
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Spurred in part by the popularity of the TV series, Cosmos spent 50 weeks on the Publishers Weekly best-sellers list and 70 weeks on the New York Times Best Seller list to become the best-selling science book ever published at the time. In 1981, it received the Hugo Award for Best Non-Fiction Book. The unprecedented success of Cosmos ushered in a dramatic increase in visibility for science-themed literature. The success of the book also served to jumpstart Sagan's literary career. The sequel to Cosmos is Pale Blue Dot: A Vision of the Human Future in Space (1994).
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In 2013, a new edition of Cosmos was published, with a foreword by Ann Druyan and an essay by Neil deGrasse Tyson.
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== Summary ==
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Cosmos has 13 chapters, corresponding to the 13 episodes of the Cosmos television series. In the original edition, each chapter is heavily illustrated. The book covers a broad range of topics, comprising Sagan's reflections on anthropological, cosmological, biological, historical, and astronomical matters from antiquity to contemporary times. Sagan reiterates his position on extraterrestrial life—that the magnitude of the universe permits the existence of thousands of alien civilizations, but no credible evidence exists to demonstrate that such life has ever visited earth. Sagan explores 15 billion years of cosmic evolution and the development of science and civilization. He traces the origins of knowledge and the scientific method, mixing science and philosophy, and speculates about the future of science. He also discusses the underlying premises of science by providing biographical anecdotes about many prominent scientists, placing their contributions in the broader context of the development of modern science.
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The book, like the television series, contains a number of Cold War undertones including subtle references to self-destruction and the futility of the arms race.
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== Popularity ==
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Shortly after release, Cosmos became the best-selling science book ever published in the English language, and was the first science book to sell more than half a million copies. Though spurred in part by the popularity of the television series, Cosmos became a best-seller by its own regard, reaching hundreds of thousands of readers. It was only surpassed in the late 1980s by Stephen Hawking's A Brief History of Time (1988). Cosmos spent 50 weeks on the Publishers Weekly best-seller's list, and 70 weeks on the New York Times Best Seller list. Cosmos sold over 900,000 copies while on these lists, and continued popularity has allowed Cosmos to sell about five million copies internationally. Shortly after Cosmos was published, Sagan received a $2 million advance for the novel Contact. This was the largest release given for an unwritten fiction book at the time. The success of Cosmos made Sagan "wealthy as well as famous." It also ushered in a dramatic increase in visibility for science books, opening up new options and readership for the previously fledgling genre. Science historian Bruce Lewenstein of Cornell University noted that among science books "Cosmos marked the moment that something different was clearly going on."
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After the success of Cosmos, Sagan turned into an early scientific celebrity. He appeared on many television programs, wrote a regular column for Parade, and worked to continually advance the popularity of the science genre.
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Lewenstein also noted the power of the book as a recruitment tool. Along with Microbe Hunters and The Double Helix, he described Cosmos as one of the "books that people cite as 'Hey, the reason I'm a scientist is because I read that book'." Particularly in astronomy and physics, he said, the book inspired many people to become scientists. Sagan has also been called the "most successful popularizing scientist of our time," for his ability to draw such a large and varied audience.
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The popularity of Sagan's Cosmos has been referenced in arguments supporting increased space exploration spending. Sagan's book was also referenced in Congress by Arthur C. Clarke in a speech promoting an end to Cold War anti-ICBM spending, instead arguing that the anti-ICBM budget would be better spent on Mars exploration.
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== Critical reception ==
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Reception for Sagan's work was generally positive. In The New York Times Book Review, novelist James Michener praised Cosmos as "a cleverly written, imaginatively illustrated summary of [Sagan's]... ruminations about our universe... His style is iridescent, with lights flashing upon unexpected juxtapositions of thought." The American astrophysicist Neil deGrasse Tyson described "Cosmos" as something "more than Carl Sagan". David Whitehouse of the British Broadcasting Corporation went so far as to say that "there is not a book on astronomy – in fact not one on science – that comes close to the eloquence and intellectual sweep of Cosmos... If we send just one book to grace the libraries of distant worlds..., let it be Cosmos." Kirkus Reviews described the book as "Sagan at his best." Cornell News Service characterized it as "an overview of how science and civilization grew up together." In 1981, Cosmos received the Hugo Award for Best Non-Fiction Book.
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The U.S. Library of Congress designated Cosmos one of eighty-eight books "that shaped America."
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== See also ==
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Kosmos by Alexander von Humboldt; like Cosmos, a book that discusses the then known universe and humankind's place in it
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== References ==
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== Further reading ==
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Shermer, Michael (August 2002). "This View of Science: Stephen Jay Gould as Historian of Science and Scientific Historian, Popular Scientist and Scientific Popularizer" (PDF). Social Studies of Science. 32 (4). London: SAGE Publications: 489–525. doi:10.1177/0306312702032004001. ISSN 0306-3127. OCLC 2242476. PMID 12503565. S2CID 220879229. Archived from the original (PDF) on 2018-09-20. Retrieved 2010-04-02.
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De Phenomenis in Orbe Lunae is a 1612 book by Collegio Romano philosophy professor Giulio Cesare la Galla that describes emission of light by a stone. La Galla's inspiration came from Galileo's debate with Vincenzo Casciarolo regarding a "lapis solaris," a stone that emitted light seemingly on its own. In De Phenomenis, de Galla asserts that the stone was only able to emit light after the stone itself had calcified. It released "a certain quantity of fire and light" that it had absorbed, just as water would be absorbed by a sponge.
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Robert Burton discusses De Phenomenis in The Anatomy of Melancholy.
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De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) is the seminal work on the heliocentric theory of the astronomer Nicolaus Copernicus (1473–1543 CE). The book, first printed in 1543 CE in Nuremberg, Holy Roman Empire, offered an alternative model of the universe to Ptolemy's geocentric system, which had been widely accepted since ancient times.
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== History ==
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Copernicus initially outlined his system in a short, untitled, anonymous manuscript that he distributed to several friends, referred to as the Commentariolus. A physician's library list dating to 1514 includes a manuscript whose description matches the Commentariolus, so Copernicus must have begun work on his new system by that time. Most historians believe that he wrote the Commentariolus after his return from Italy, possibly only after 1510. At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the perceived motions of the planets easily, with fewer motions than were necessary in the version of the Ptolemaic system current at the time. Among other techniques, the heliocentric Copernican model made use of the Urdi Lemma developed in the 13th century by the Arab astronomer Mu'ayyad al-Din al-'Urdi, the first of the Maragha astronomers to develop a geocentric but non-Ptolemaic model of planetary motion.
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Observations of Mercury by Bernhard Walther (1430–1504) of Nuremberg, a pupil of Regiomontanus, were made available to Copernicus by Johannes Schöner, 45 observations in total, 14 of them with longitude and latitude. Copernicus used three of them in De revolutionibus, giving only longitudes, and erroneously attributing them to Schöner. Copernicus' values differed slightly from the ones published by Schöner in 1544 in Observationes XXX annorum a I. Regiomontano et B. Walthero Norimbergae habitae, [4°, Norimb. 1544].
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A manuscript of De revolutionibus in Copernicus' own hand has survived. After his death, it was given to his pupil, Rheticus, who for publication had only been given a copy without annotations. Via Heidelberg, it ended up in Prague, where it was rediscovered and studied in the 19th century. Close examination of the manuscript, including the different types of paper used, helped scholars construct an approximate timetable for its composition. Apparently Copernicus began by making a few astronomical observations to provide new data to perfect his models. He may have begun writing the book while still engaged in observations. By the 1530s a substantial part of the book was complete, but Copernicus hesitated to publish. In 1536, Cardinal Nikolaus von Schönberg wrote to Copernicus and urged him to publish his manuscript.
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In 1539, Georg Joachim Rheticus, a young mathematician from Wittenberg, arrived in Frauenburg (Frombork) to study with him. Rheticus read Copernicus' manuscript and immediately wrote a non-technical summary of its main theories in the form of an open letter addressed to Schöner, his astrology teacher in Nürnberg; he published this letter as the Narratio Prima in Danzig in 1540. Rheticus' friend and mentor Achilles Gasser published a second edition of the Narratio in Basel in 1541. Due to its friendly reception, Copernicus finally agreed to publication of more of his main work—in 1542, a treatise on trigonometry, which was taken from the second book of the still unpublished De revolutionibus. Rheticus published it in Copernicus' name.
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Under strong pressure from Rheticus, and having seen that the first general reception of his work had not been unfavorable, Copernicus finally agreed to give the book to his close friend, Bishop Tiedemann Giese, to be delivered to Rheticus in Wittenberg for printing by Johannes Petreius at Nürnberg (Nuremberg). It was published just before Copernicus' death, in 1543.
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Copernicus kept a copy of his manuscript which, sometime after his death, was sent to Rheticus in the attempt to produce an authentic, unaltered version of the book. The plan failed but the copy was found during the 18th century and was published later. It is kept at the Jagiellonian University Library in Kraków, where it remains bearing the library number BJ 10 000.
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== Contents ==
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From the first edition, Copernicus' book was prefixed with an anonymous preface which argues that the following is a calculus consistent with the observations, and cannot resolve philosophical truths. Only later was this revealed to be the unauthorized interjection by Lutheran preacher Andreas Osiander, who lived in Nuremberg when the first edition was printed there. This is followed by Copernicus' own preface, where he dedicates his work to Pope Paul III and appeals to the latter's skill as a mathematician to recognize the truth of Copernicus' hypothesis.
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De revolutionibus is divided into six "books" (sections or parts), following closely the layout of Ptolemy's Almagest which it updated and replaced:
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Book I chapters 1–11 are a general vision of the heliocentric theory, and a summarized exposition of his cosmology. The world (heavens) is spherical, as is the Earth, and the land and water make a single globe. The celestial bodies, including the Earth, have regular circular and everlasting movements. The Earth rotates on its axis and around the Sun. Answers to why the ancients thought the Earth was central. The order of the planets around the Sun and their periodicity. Chapters 12–14 give theorems for chord geometry as well as a table of chords.
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Book II describes the principles of spherical astronomy as a basis for the arguments developed in the following books and gives a comprehensive catalogue of the fixed stars.
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Book III describes his work on the precession of the equinoxes and treats the apparent movements of the Sun and related phenomena.
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Book IV is a similar description of the Moon and its orbital movements.
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Book V explains how to calculate the positions of the wandering stars based on the heliocentric model and gives tables for the five planets.
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Book VI deals with the digression in latitude from the ecliptic of the five planets.
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Copernicus argued that the universe comprised eight spheres. The outermost consisted of motionless, fixed stars, with the Sun motionless at the center. The known planets revolved about the Sun, each in its own sphere, in the order: Mercury, Venus, Earth, Mars, Jupiter, Saturn. The Moon, however, revolved in its sphere around the Earth. What appeared to be the daily revolution of the Sun and fixed stars around the Earth was actually the Earth's daily rotation on its own axis.
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Copernicus adhered to one of the standard beliefs of his time, namely that the motions of celestial bodies must be composed of uniform circular motions. For this reason, he was unable to account for the observed apparent motion of the planets without retaining a complex system of epicycles similar to those of the Ptolemaic system.
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Despite Copernicus' adherence to this aspect of ancient astronomy, his radical shift from a geocentric to a heliocentric cosmology was a serious blow to Aristotle's science—and helped usher in the Scientific Revolution.
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== Ad lectorem ==
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Rheticus left Nürnberg to take up his post as professor in Leipzig. Andreas Osiander had taken over the task of supervising the printing and publication. In an effort to reduce the controversial impact of the book Osiander added his own unsigned letter Ad lectorem de hypothesibus huius operis (To the reader concerning the hypotheses of this work) printed in front of Copernicus' preface which was a dedicatory letter to Pope Paul III and which kept the title "Praefatio authoris" (to acknowledge that the unsigned letter was not by the book's author).
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Osiander's letter stated that Copernicus' system was mathematics intended to aid computation and not an attempt to declare literal truth:
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it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. Then he must conceive and devise the causes of these motions or hypotheses about them. Since he cannot in any way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly ... The present author has performed both these duties excellently. For these hypotheses need not be true nor even probable. On the contrary, if they provide a calculus consistent with the observations, that alone is enough ... For this art, it is quite clear, is completely and absolutely ignorant of the causes of the apparent [movement of the heavens]. And if any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that they are true, but merely to provide a reliable basis for computation. However, since different hypotheses are sometimes offered for one and the same ... the astronomer will take as his first choice that hypothesis which is the easiest to grasp. The philosopher will perhaps rather seek the semblance of the truth. But neither of them will understand or state anything certain, unless it has been divinely revealed to him ... Let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart this study a greater fool than when he entered. As even Osiander's defenders point out, the Ad lectorem "expresses views on the aim and nature of scientific theories at variance with Copernicus' claims for his own theory". Many view Osiander's letter as a betrayal of science and Copernicus, and an attempt to pass his own thoughts off as those of the book's author. An example of this type of claim can be seen in the Catholic Encyclopedia, which states "Fortunately for him [the dying Copernicus], he could not see what Osiander had done. This reformer, knowing the attitude of Luther and Melanchthon against the heliocentric system ... without adding his own name, replaced the preface of Copernicus by another strongly contrasting in spirit with that of Copernicus."
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While Osiander's motives behind the letter have been questioned by many, he has been defended by historian Bruce Wrightsman, who points out he was not an enemy of science. Osiander had many scientific connections including "Johannes Schoner, Rheticus's teacher, whom Osiander recommended for his post at the Nurnberg Gymnasium; Peter Apian of Ingolstadt University; Hieronymous Schreiber...Joachim Camerarius...Erasmus Reinhold...Joachim Rheticus...and finally, Hieronymous Cardan."
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The historian Wrightsman put forward that Osiander did not sign the letter because he "was such a notorious [Protestant] reformer whose name was well-known and infamous among Catholics", so that signing would have likely caused negative scrutiny of the work of Copernicus (a loyal Catholic canon and scholar). Copernicus himself had communicated to Osiander his "own fears that his work would be scrutinized and criticized by the 'peripatetics and theologians'," and he had already been in trouble with his bishop, Johannes Dantiscus, on account of his former relationship with his mistress and friendship with Dantiscus's enemy and suspected heretic, Alexander Scultetus. It was also possible that Protestant Nurnberg could fall to the forces of the Holy Roman Emperor and since "the books of hostile theologians could be burned...why not scientific works with the names of hated theologians affixed to them?" Wrightsman also holds that this is why Copernicus did not mention his top student, Rheticus (a Lutheran) in the book's dedication to the Pope. Osiander's interest in astronomy was theological, hoping for "improving the chronology of historical events and thus providing more accurate apocalyptic interpretations of the Bible... [he shared in] the general awareness that the calendar was not in agreement with astronomical movement and therefore, needed to be corrected by devising better models on which to base calculations." In an era before the telescope, Osiander (like most of the era's mathematical astronomers) attempted to bridge the "fundamental incompatibility between Ptolemaic astronomy and Aristotlian physics, and the need to preserve both", by taking an 'instrumentalist' position. Only the handful of "Philosophical purists like the Averroists... demanded physical consistency and thus sought for realist models."
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Copernicus was hampered by his insistence on preserving the idea that celestial bodies had to travel in perfect circles — he "was still attached to classical ideas of circular motion around deferents and epicycles, and spheres." This was particularly troubling concerning the Earth because he "attached the Earth's axis rigidly to a Sun-centered sphere. The unfortunate consequence was that the terrestrial rotation axis then maintained the same inclination with respect to the Sun as the sphere turned, eliminating the seasons." To explain the seasons, he had to propose a third motion, "an annual contrary conical sweep of the terrestrial axis". It was not until the Great Comet of 1577, which moved as if there were no spheres to crash through, that the idea was challenged. In 1609, Johannes Kepler modified Copernicus' theory by stating that the planets orbit the Sun not in circles, but ellipses. Only after Kepler's refinement of Copernicus' theory was the need for deferents and epicycles abolished. In his work, Copernicus "used conventional, hypothetical devices like epicycles...as all astronomers had done since antiquity. ...hypothetical constructs solely designed to 'save the phenomena' and aid computation". Ptolemy's theory contained a hypothesis about the epicycle of Venus that was viewed as absurd if seen as anything other than a geometrical device (its brightness and distance should have varied greatly, but they don't). "In spite of this defect in Ptolemy's theory, Copernicus' hypothesis predicts approximately the same variations." Because of the use of similar terms and similar deficiencies, Osiander could see "little technical or physical truth-gain" between one system and the other. It was this attitude towards technical astronomy that had allowed it to "function since antiquity, despite its inconsistencies with the principles of physics and the philosophical objections of Averroists."
|
||||
Writing Ad lectorem, Osiander was influenced by Pico della Mirandola's idea that humanity "orders [an intellectual] cosmos out of the chaos of opinions." From Pico's writings, Osiander "learned to extract and synthesize insights from many sources without becoming the slavish follower of any of them." The effect of Pico on Osiander was tempered by the influence of Nicholas of Cusa and his idea of coincidentia oppositorum. Rather than having Pico's focus on human effort, Osiander followed Cusa's idea that understanding the Universe and its Creator only came from divine inspiration rather than intellectual organization. From these influences, Osiander held that in the area of philosophical speculation and scientific hypothesis there are "no heretics of the intellect", but when one gets past speculation into truth-claims the Bible is the ultimate measure. By holding that Copernicianism was mathematical speculation, Osiander held that it would be silly to hold it up against the accounts of the Bible. Pico's influence on Osiander did not escape Rheticus, who reacted strongly against the Ad lectorem. As historian Robert S. Westman puts it, "The more profound source of Rheticus's ire however, was Osiander's view of astronomy as a disciple fundamentally incapable of knowing anything with certainty.
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:12.369663+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
For Rheticus, this extreme position surely must have resonated uncomfortably with Pico della Mirandola's attack on the foundations of divinatory astrology."
|
||||
In his Disputations, Pico had made a devastating attack on astrology. Because those who were making astrological predictions relied on astronomers to tell them where the planets were, they also became a target. Pico held that since astronomers who calculate planetary positions could not agree among themselves, how were they to be held as reliable? While Pico could bring into concordance writers like Aristotle, Plato, Plotinus, Averroes, Avicenna, and Aquinas, the lack of consensus he saw in astronomy was a proof to him of its fallibility alongside astrology. Pico pointed out that the astronomers' instruments were imprecise and any imperfection of even a degree made them worthless for astrology, people should not trust astrologists because they should not trust the numbers from astronomers. Pico pointed out that astronomers couldn't even tell where the Sun appeared in the order of the planets as they orbited the Earth (some put it close to the Moon, others among the planets). How, Pico asked, could astrologists possibly claim they could read what was going on when the astronomers they relied on could offer no precision on even basic questions? As Westman points out, to Rheticus "it would seem that Osiander now offered new grounds for endorsing Pico's conclusions: not merely was the disagreement among astronomers grounds for mistrusting the sort of knowledge that they produced, but now Osiander proclaimed that astronomers might construct a world deduced from (possibly) false premises. Thus the conflict between Piconian skepticism and secure principles for the science of the stars was built right into the complex dedicatory apparatus of De Revolutionibus itself." According to the notes of Michael Maestlin, "Rheticus...became embroiled in a very bitter wrangle with the printer [over the Ad lectorem]. Rheticus...suspected Osiander had prefaced the work; if he knew this for certain, he declared, he would rough up the fellow so violently that in future he would mind his own business."
|
||||
Objecting to the Ad lectorem, Tiedemann Giese urged the Nuremberg city council to issue a correction, but this was not done, and the matter was forgotten. Jan Broscius, a supporter of Copernicus, also despaired of the Ad lectorem, writing "Ptolemy's hypothesis is the earth rests. Copernicus' hypothesis is that the earth is in motion. Can either, therefore, be true? ... Indeed, Osiander deceives much with that preface of his ... Hence, someone may well ask: How is one to know which hypothesis is truer, the Ptolemaic or the Copernican?"
|
||||
Petreius had sent a copy to Hieronymus Schreiber, an astronomer from Nürnberg who had substituted for Rheticus as professor of mathematics in Wittenberg while Rheticus was in Nürnberg supervising the printing. Schreiber, who died in 1547, left in his copy of the book a note about Osiander's authorship. Via Michael Mästlin, this copy came to Johannes Kepler, who discovered what Osiander had done and methodically demonstrated that Osiander had indeed added the foreword. The most knowledgeable astronomers of the time had realized that the foreword was Osiander's doing. Owen Gingerich gives a slightly different version: Kepler knew of Osiander's authorship since he had read about it in one of Schreiber's annotations in his copy of De Revolutionibus; Maestlin learned of the fact from Kepler. Indeed, Maestlin perused Kepler's book, up to the point of leaving a few annotations in it. However, Maestlin already suspected Osiander, because he had bought his De revolutionibus from the widow of Philipp Apian; examining his books, he had found a note attributing the introduction to Osiander. Johannes Praetorius (1537–1616), who learned of Osiander's authorship from Rheticus during a visit to him in Kraków, wrote Osiander's name in the margin of the foreword in his copy of De revolutionibus. All three early editions of De revolutionibus included Osiander's foreword.
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:12.369663+00:00"
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||||
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|
||||
---
|
||||
|
||||
== Reception ==
|
||||
Even before the 1543 publication of De revolutionibus, rumors circulated
|
||||
about its central theses. In one of his Tischreden (Table Talks), Martin Luther is quoted as saying in 1539:
|
||||
|
||||
People gave ear to an upstart astrologer who strove to show that the earth revolves, not the heavens or the firmament, the sun and the moon ... This fool wishes to reverse the entire science of astronomy; but sacred Scripture tells us [Joshua 10:13] that Joshua commanded the sun to stand still, and not the earth.
|
||||
When the book was finally published, demand was low, with an initial print run of 400 failing to sell out. Copernicus had made the book extremely technical, unreadable to all but the most advanced astronomers of the day, allowing it to disseminate into their ranks before stirring great controversy. And, like Osiander, contemporary mathematicians and astronomers encouraged its audience to view it as a useful mathematical model without necessarily being true about causes, thereby somewhat shielding it from accusations of blasphemy.
|
||||
Among some astronomers, the book "at once took its place as a worthy successor to the Almagest of Ptolemy, which had hitherto been the Alpha and Omega of astronomers". Erasmus Reinhold hailed the work in 1542 and by 1551 had developed the Prutenic Tables ("Prussian Tables"; Latin: Tabulae prutenicae; German: Preußische Tafeln) using Copernicus' methods. The Prutenic Tables, published in 1551, were used as a basis for the calendar reform instituted in 1582 by Pope Gregory XIII. They were also used by sailors and maritime explorers, whose 15th-century predecessors had used Regiomontanus' Table of the Stars. In England, Robert Recorde, John Dee, Thomas Digges and William Gilbert were among those who adopted his position; in Germany, Christian Wurstisen, Christoph Rothmann and Michael Mästlin, the teacher of Johannes Kepler; in Italy, Giambattista Benedetti and Giordano Bruno whilst Franciscus Patricius accepted the rotation of the Earth. In Spain, rules published in 1561 for the curriculum of the University of Salamanca gave students the choice between studying Ptolemy or Copernicus. One of those students, Diego de Zúñiga, published an acceptance of Copernican theory in 1584.
|
||||
Very soon, nevertheless, Copernicus' theory was attacked with Scripture and with the common Aristotelian proofs. In 1549, Melanchthon, Luther's principal lieutenant, wrote against Copernicus, pointing to the theory's apparent conflict with Scripture and advocating that "severe measures" be taken to restrain the impiety of Copernicans.
|
||||
The works of Copernicus and Zúñiga—the latter for asserting that De revolutionibus was compatible with Catholic faith—were placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 (more than 70 years after Copernicus' publication):
|
||||
|
||||
This Holy Congregation has also learned about the spreading and acceptance by many of the false Pythagorean doctrine, altogether contrary to the Holy Scripture, that the earth moves and the sun is motionless, which is also taught by Nicholaus Copernicus' De revolutionibus orbium coelestium and by Diego de Zúñiga's In Job ... Therefore, in order that this opinion may not creep any further to the prejudice of Catholic truth, the Congregation has decided that the books by Nicolaus Copernicus [De revolutionibus] and Diego de Zúñiga [In Job] be suspended until corrected.
|
||||
De revolutionibus was not formally banned but merely withdrawn from circulation, pending "corrections" that would clarify the theory's status as hypothesis. Nine sentences that represented the heliocentric system as certain were to be omitted or changed. After these corrections were prepared and formally approved in 1620 the reading of the book was permitted. But the book was never reprinted with the changes and was available in Catholic jurisdictions only to suitably qualified scholars, by special request. It remained on the Index until 1758, when Pope Benedict XIV (1740–58) removed the uncorrected book from his revised Index.
|
||||
|
||||
== Census of copies ==
|
||||
Arthur Koestler described De revolutionibus as "The Book That Nobody Read" saying the book "was and is an all-time worst seller", despite the fact that it was reprinted four times. Owen Gingerich, an eminent astronomer and historian of science who has written on both Nicolaus Copernicus and Johannes Kepler, disproved this after a 35-year project to examine every surviving copy of the first two editions. Gingerich showed that nearly all the leading mathematicians and astronomers of the time owned and read the book; however, his analysis of the marginalia shows that almost all of them ignored the cosmology at the beginning of the book and were only interested in Copernicus' new equant-free models of planetary motion in the later chapters. Also, Nicolaus Reimers in 1587 translated the book into German.
|
||||
Gingerich's efforts and conclusions are recounted in The Book Nobody Read, published in 2004 by Walker & Co. His census included 276 copies of the first edition (by comparison, there are 228 extant copies of Shakespeare's First Folio) and 325 copies of the second. The research behind this book earned its author the Polish government's Order of Merit in 1981. Due largely to Gingerich's scholarship, De revolutionibus has been researched and catalogued better than any other first-edition historic text except for the original Gutenberg Bible.
|
||||
One of the copies now resides at the Archives of the University of Santo Tomas in the Miguel de Benavides Library. In January 2017, a second-edition copy was stolen as part of a heist of rare books from Heathrow Airport and remains unrecovered.
|
||||
|
||||
== Editions ==
|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:12.369663+00:00"
|
||||
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|
||||
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|
||||
|
||||
1543, Nuremberg, by Johannes Petreius. A copy of this is held by the University of Edinburgh; it had been owned by an astronomer, who filled the pages with scholarly annotations, and subsequently by the Scottish economist Adam Smith. Another copy is held by the Cary Graphic Arts Collection in New York, alongside astronomer Johannes de Sacrobosco's manuscript "De sphaera mundi" (On the Sphere of the World), which supports the earlier Ptolemaic model of the universe. Another 1543 copy is present in the Special Collections of Leiden University Libraries.
|
||||
1566, Basel, by Henricus Petrus. A copy of this is held by the University of Sydney; previously owned by Owen Gingerich.
|
||||
1617, Amsterdam, by Nicolaus Mulerius.
|
||||
1854, Warsaw, with Polish translation and the authentic preface by Copernicus.
|
||||
1873, Thorn; German translation sponsored by the local Coppernicus Society, with all of Copernicus' textual corrections given as footnotes.
|
||||
|
||||
== Latin texts available online ==
|
||||
1543, Nuremberg, by Johannes Petreius; online from Harvard University.
|
||||
|
||||
== English texts available online ==
|
||||
Copernicus, Nicolaus (1543) De Revolutionibus Orbium Coelestium; online from Source Library.
|
||||
|
||||
== Translations ==
|
||||
English translations of De revolutionibus have included:
|
||||
|
||||
On the Revolutions of the Heavenly Spheres, translated by C. G. Wallis, Annapolis, St John's College Bookstore, 1939. Republished in volume 16 of the Great Books of the Western World, Chicago, Encyclopædia Britannica, 1952; in the series of the same name, published by the Franklin Library, Franklin Center, Philadelphia, 1985; in volume 15 of the second edition of the Great Books, Encyclopædia Britannica, 1990; and Amherst, NY: Prometheus Books, 1995, Great Minds Series – Science, ISBN 1-57392-035-5.
|
||||
On the Revolutions of the Heavenly Spheres, translated with an introduction and notes by A. M. Duncan, Newton Abbot, David & Charles, ISBN 0-7153-6927-X; New York: Barnes and Noble, 1976, ISBN 0-06-491279-5.
|
||||
On the Revolutions; translation and commentary by Edward Rosen, Baltimore: Johns Hopkins University Press, 1992, ISBN 0-8018-4515-7. (Foundations of Natural History. Originally published in Warsaw, Poland, 1978.)
|
||||
|
||||
== See also ==
|
||||
List of most expensive books and manuscripts
|
||||
Wittenberg interpretation of Copernicus
|
||||
|
||||
== Notes ==
|
||||
|
||||
== References ==
|
||||
Copernicus, Nicolaus (1952), On the Revolutions of the Heavenly Spheres, Great Books of the Western World, vol. 16, translated by Charles Glenn Wallis, Chicago: William Benton, pp. 497–838
|
||||
Gassendi, Pierre: The Life of Copernicus, biography (1654), with notes by Olivier Thill (2002), ISBN 1-59160-193-2 ([1])
|
||||
Gingerich, Owen (2002). An annotated census of Copernicus' De revolutionibus (Nuremberg, 1543 and Basel, 1566). Leiden: Brill (Studia copernicana. Brill's series; v. 2). ISBN 90-04-11466-1.
|
||||
Gingerich, Owen (2004). The Book Nobody Read : Chasing the Revolutions of Nicolaus Copernicus. New York : Walker. ISBN 0-8027-1415-3.{{cite book}}: CS1 maint: publisher location (link)
|
||||
Hannam, James (2007). "Deconstructing Copernicus". Medieval Science and Philosophy. Retrieved 2007-08-17. Analyses the varieties of argument used by Copernicus.
|
||||
Heilbron, J.L.: The Sun in the Church: Cathedrals as Solar Observatories. Cambridge, Massachusetts, Harvard University Press, 1999 ISBN 0-674-85433-0
|
||||
Koestler, Arthur (1959). The Sleepwalkers. Hutchison.
|
||||
Sobel, D, A More Perfect Heaven - How Copernicus Revolutionised the Cosmos, Bloomsbury 2011.
|
||||
Swerdlow, N.M., O. Neugebauer: Mathematical astronomy in Copernicus' De revolutionibus. New York : Springer, 1984 ISBN 0-387-90939-7 (Studies in the history of mathematics and physical sciences; 10)
|
||||
Vermij, R.H.: The Calvinist Copernicans: The Reception of the New Astronomy in the Dutch Republic, 1575–1750 Archived 2006-09-02 at the Wayback Machine. Amsterdam : Koninklijke Nederlandse Akademie van Wetenschappen, 2002 ISBN 90-6984-340-4
|
||||
Westman, R.S., ed.: The Copernican achievement. Berkeley : University of California Press, 1975 ISBN 0-520-02877-5
|
||||
Zinner, E.: Entstehung und Ausbreitung der coppernicanischen Lehre. 2. Aufl. durchgesehen und erg. von Heribert M. Nobis und Felix Schmeidler. München : C.H. Beck, 1988 ISBN 3-406-32049-X
|
||||
|
||||
== External links ==
|
||||
Manuscript of De Revolutionibus by Nicolaus Copernicus, from Jagiellonian Library, Poland.
|
||||
|
||||
De revolutionibus orbium coelestium, from Harvard University.
|
||||
De revolutionibus orbium coelestium, from Jagiellon University, Poland.
|
||||
De Revolutionibus Orbium Coelestium Archived 2020-10-28 at the Wayback Machine, from Rare Book Room.
|
||||
On the Revolutions, from WebExhibits. English translation of part of Book I.
|
||||
On the Revolutions, Warsaw-Cracow 1978. Full English translation.
|
||||
River Campus Libraries, Book of the Month December 2005: De revolutionibus orbium coelestium
|
||||
A facsimile of De Revolutionibus Orbium Coelestium (1543) from the Rare Book and Special Collection Division at the Library of Congress
|
||||
De Revolutionibus Orbium Coelestium (1566) From the Rare Book and Special Collection Division at the Library of Congress
|
||||
De Revolutionibus Orbium Coelestium (1566) Previously owned by Owen Gingerich. Includes the third printing (previous editions 1540 and 1541) of De libris revolutionum Nicolai Copernici narratio prima. From the University of Sydney Library.
|
||||
A facsimile of De Revolutionibus Orbium Coelestium (1543) with annotations by Michael Maestlin from Stadtbibliothek Schaffhausen (Schaffhausen City Library)
|
||||
53
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|
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|
||||
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|
||||
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|
||||
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|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:13.531615+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
De sphaera mundi (Latin title meaning On the Sphere of the World, sometimes rendered The Sphere of the Cosmos; the Latin title is also given as Tractatus de sphaera, Textus de sphaera, or simply De sphaera) is a medieval introduction to the basic elements of astronomy written by Johannes de Sacrobosco (John of Holywood) c. 1230. Based heavily on Ptolemy's Almagest, and drawing additional ideas from Islamic astronomy, it was one of the most influential works of pre-Copernican astronomy in Europe.
|
||||
|
||||
|
||||
== Reception ==
|
||||
Sacrobosco's De sphaera mundi was the most successful of several competing thirteenth-century textbooks on this topic. It was used in universities for hundreds of years and the manuscript copied many times before the invention of the printing press; hundreds of manuscript copies have survived. The first printed edition appeared in 1472 in Ferrara, and at least 84 editions were printed in the next two hundred years. The work was frequently supplemented with commentaries on the original text. The number of copies and commentaries reflects its importance as a university text.
|
||||
|
||||
|
||||
== Content ==
|
||||
The 'sphere of the world' is not the earth but the heavens, and Sacrobosco quotes Theodosius saying it is a solid body. It is divided into nine parts: the "first moved" (primum mobile), the sphere of the fixed stars (the firmament), and the seven planets, Saturn, Jupiter, Mars, the sun, Venus, Mercury and the moon. There is a 'right' sphere and an oblique sphere: the right sphere is only observed by those at the equator (if there are such people), everyone else sees the oblique sphere. There are two movements: one of the heavens from east to west on its axis through the Arctic and Antarctic poles, the other of the inferior spheres at 23° in the opposite direction on their own axes.
|
||||
The world, or universe, is divided into two parts: the elementary and the ethereal. The elementary consists of four parts: the earth, about which is water, then air, then fire, reaching up to the moon. Above this is the ethereal which is immutable and called the 'fifth essence' by the philosophers. All are mobile except heavy earth which is the center of the world.
|
||||
|
||||
|
||||
=== The universe as a machine ===
|
||||
Sacrobosco spoke of the universe as the machina mundi, the machine of the world, suggesting that the reported eclipse of the Sun at the crucifixion of Jesus was a disturbance of the order of that machine. This concept is similar to the clockwork universe analogy that became very popular centuries later, during the Enlightenment.
|
||||
|
||||
|
||||
=== Spherical Earth ===
|
||||
|
||||
Though principally about the universe, De sphaera 1230 A.D. contains a clear description of the Earth as a sphere which agrees with widespread opinion in Europe during the higher Middle Ages, in contrast to statements of some 19th- and 20th-century historians that medieval scholars thought the Earth was flat. As evidence for the Earth being a sphere, in Chapter One he cites the observation that stars rise and set sooner for those in the east ("Orientals"), and lunar eclipses happen earlier; that stars near the North Pole are visible to those further north and those in the south can see different ones; that at sea one can see further by climbing up the mast; and that water seeks its natural shape which is round, as a drop.
|
||||
|
||||
|
||||
== See also ==
|
||||
Armillary sphere
|
||||
Orrery
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Sources ==
|
||||
Pedersen, Olaf (1975). Gingerich, Owen; Dobrzycki, Jerzy (eds.). "The Corpus Astronomicum and the Traditions of Medieval Latin Astronomy: A Tentative Interpretation". Colloquia Copernicana III. Wrocław: Ossolineum: 59–76.
|
||||
Thorndike, Lynn (1949). The Sphere of Sacrobosco and its Commentators. Corpus of mediaeval scientific texts sponsored jointly by the Mediaeval Academy of America and the University of Chicago; v. 2. Chicago: Univ. of Chicago Press. hdl:2027/mdp.39015025028716.
|
||||
|
||||
|
||||
== External links ==
|
||||
Media related to De sphaera mundi at Wikimedia Commons
|
||||
Summary of the contents of each chapter (Adam Mosley, Department of History and Philosophy of Science, University of Cambridge (1999))
|
||||
Sacrobosco's De Sphaera – complete treatise in English translation
|
||||
Book, The Sphere of Sacrobosco and its Commentators, by Lynn Thorndike, year 1949. Text in Latin, English translation, and commentary.
|
||||
Treasures of the RAS: The Sphere by John of Hollywood on YouTube
|
||||
Selected images from Sphaera mundi From The College of Physicians of Philadelphia Digital Library
|
||||
Digitised 1564 copy of Sphaera mundi from The University of Sydney Library
|
||||
Digitised 1485 copy of Sphaera mundi from the Delft University of Technology Library
|
||||
30
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|
||||
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|
||||
title: "Death by Black Hole"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Death_by_Black_Hole"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:14.706343+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Death by Black Hole: And Other Cosmic Quandaries is a 2007 popular science book written by Neil deGrasse Tyson. It is an anthology of several of Tyson's most popular articles, all published in Natural History magazine between 1995 and 2005, and was featured in an episode of The Daily Show with Jon Stewart.
|
||||
|
||||
|
||||
== Summary ==
|
||||
Death by Black Hole is divided into seven sections: The Nature of Knowledge, The Knowledge of Nature, Ways and Means of Nature, The Meaning of Life, When the Universe Turns Bad, Science and Culture, and Science and God.
|
||||
Section 1 comprises five chapters:
|
||||
|
||||
Chapter 1, "Coming to Our Senses", discusses how important the augmentation of our five basic senses (sight, hearing, taste, smell, touch) is for expanding scientific knowledge. Tools that convert (seemingly) latent aspects of our environment into quantities we can sense greatly ease scientific discovery. For example, night vision goggles convert the near-infrared spectrum into the visible spectrum, making it easier for biologists to observe nocturnal animal behavior.
|
||||
Chapter 2, "On Earth as in the Heavens", addresses the history of physics and how it came to be known that physical laws observed on Earth are also observed on the sun and the other planets. In short, how physics became a study of the universal rather than just the terrestrial.
|
||||
Chapter 3, "Seeing Isn't Believing", hints at the pitfalls of generalizing from too little evidence. It begins by making the point that although we know the Earth is round, it appears flat when one observes only a small, local portion of it.
|
||||
Chapter 4, "The Information Trap", observes that we can view our surroundings at many different scales, and may find different phenomena at different scales. For instance, on a macroscopic scale classical mechanics describes the physical behaviors we observe, while on a smaller scale, quantum mechanics comes into play.
|
||||
Chapter 5, "Stick-in-the-Mud Science", guides the reader through a series of experiments based primarily on watching how the shadow of a stick, stuck upright in the earth, changes as time passes. For example, one can observe that, in the northern hemisphere, over the course of a day, the shadow of the stick will trace out a semi-circle as it moves clockwise.
|
||||
|
||||
|
||||
== External links ==
|
||||
WorldCat.org record for this book
|
||||
Book TV author talk about this book
|
||||
|
||||
|
||||
== References ==
|
||||
45
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Death from the Skies!: These Are The Ways The World Will End is a book by the American astronomer Phil Plait, also known as "the Bad Astronomer". The book was published in 2008 and explores the various ways in which the human race could be rendered extinct by astronomical phenomena.
|
||||
|
||||
|
||||
== Background ==
|
||||
The author stated during an interview that one of the reasons for writing the book was that "the Universe is incredibly inhospitable, yet we have this planet that's doing OK by us. Another is that the Universe is incredibly cool and interesting. Black holes are really fun to think about. Actually, most of this is mind-stretching and fun. What happens to the Sun after 100 quadrillion years? One hundred octillion? A googol?" He also said that the reason for using doomsday scenarios was to take a scientific viewpoint, make it like a roller coaster or horror movie to make it fun and exciting. The stories were not to scare people out of their pants but make it cool to read about it.
|
||||
|
||||
|
||||
== Some of the subjects discussed in the book ==
|
||||
|
||||
|
||||
== Reviews ==
|
||||
The book has had positive reviews from Todd Dailey of Wired Magazine, Nancy Atkinson of Universe Today,
|
||||
and Rebecca Watson from Skepchick. It was also reviewed for Smithsonian magazine by Sarah Zielinski.
|
||||
|
||||
|
||||
== Appearances in other media ==
|
||||
In 2010 the Discovery Channel had a documentary called Phil Plait's Bad Universe. The show was based on a few chapters of the book.
|
||||
George Hrab and Phil Plait recorded a song called "Death from the Skies" with lyrics based on some of the events covered in the book.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
|
||||
|
||||
=== Press interviews ===
|
||||
Astronomy Cast Podcast Interview
|
||||
Paul Harris Radio Interview
|
||||
TalkingHeadTV interview
|
||||
|
||||
|
||||
=== Other ===
|
||||
Bad Astronomy, Plait's blog as of February 2017 (Syfy.com)
|
||||
Bad Astronomy, Plait's personal blog archive (Slate.com)
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||||
title: "Dictionary of Minor Planet Names"
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source: "https://en.wikipedia.org/wiki/Dictionary_of_Minor_Planet_Names"
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The Dictionary of Minor Planet Names is a reference book containing information about the discovery and naming of 12,804 asteroids (March 2006). It is published by the International Astronomical Union.
|
||||
|
||||
|
||||
== Editions ==
|
||||
Lutz D. Schmadel (1992). Dictionary of Minor Planet Names (1st ed.). Berlin Heidelberg: Springer-Verlag.
|
||||
———————— (1993). Dictionary of Minor Planet Names (2nd ed.). Berlin Heidelberg: Springer-Verlag.
|
||||
———————— (1996). Dictionary of Minor Planet Names (3rd ed.). Berlin Heidelberg: Springer-Verlag.(5,252 names, 7,041 numbered until June 1996)
|
||||
———————— (1999). Dictionary of Minor Planet Names (4th ed.). Berlin Heidelberg: Springer-Verlag.
|
||||
———————— (2003). Dictionary of Minor Planet Names (5th ed.). Berlin Heidelberg: Springer-Verlag. ISBN 3-540-00238-3. (+10,000 names)
|
||||
———————— (2005). Dictionary of Minor Planet Names Addendum to 5th edition. Berlin Heidelberg: Springer-Verlag. ISBN 3-540-34360-1.
|
||||
———————— (2008). Dictionary of Minor Planet Names Addendum to 5th edition. Berlin Heidelberg: Springer-Verlag. ISBN 978-3-642-01964-7.
|
||||
———————— (2012). Dictionary of Minor Planet Names (6th ed.). Berlin Heidelberg: Springer-Verlag. ISBN 978-3-642-29717-5. (+17,000 names)
|
||||
———————— (2014). Dictionary of Minor Planet Names Addentum to 6th edition. Berlin Heidelberg: Springer-Verlag. ISBN 978-3-642-29717-5. (22,000 names)
|
||||
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||||
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||||
title: "Divination by Astrological and Meteorological Phenomena"
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The Divination by Astrological and Meteorological Phenomena (Chinese: 天文氣象雜占; pinyin: Tiān Wén Qì Xiàng Zá Zhàn) is an ancient astronomy silk manuscript compiled by Chinese astronomers of the Western Han dynasty (202 BC – 9 AD) and found in the Mawangdui of Changsha, Hunan, China in 1973. It lists 29 comets (referred to as 彗星, huì xīng, literally broom stars) that appeared over a period of about 300 years.
|
||||
It is now exhibited in the Hunan Provincial Museum.
|
||||
|
||||
|
||||
== Contents ==
|
||||
The Divination by Astrological and Meteorological Phenomena contains what archaeologists claim is the first definitive atlas of comets. There are roughly two dozen renderings of comets, some in fold out/pop-up format. In some cases, the pages of the document roll out to be five feet long. Each comet's picture has a caption which describes an event its appearance corresponded to, such as "the death of the prince", "the coming of the plague", or "the three-year drought."
|
||||
One of the comets in the manuscript has four tails and resembles a swastika. In their 1985 book Comet, Carl Sagan and Ann Druyan argue that the appearance of a rotating comet with a four-pronged tail as early as 2,000 years BCE could explain why the swastika is found in the cultures of both the Old World and the pre-Columbian Americas.
|
||||
Bob Kobres, in a 1992 paper, contends that the swastika-like comet on the Han-dynasty manuscript was labelled a "long tailed pheasant star" (dixing) because of its resemblance to a bird's foot or footprint.
|
||||
|
||||
|
||||
== See also ==
|
||||
Chinese astrology
|
||||
Chinese astronomy
|
||||
Chu Silk Manuscript
|
||||
Mawangdui Silk Texts
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Ancient Chinese Astronomy
|
||||
Hunan Provincial Museum
|
||||
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data/en.wikipedia.org/wiki/Dresden_Codex-0.md
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The Dresden Codex is a Maya book originating from the region of Chichén Itzá in Mexico. It was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century, however in 2018 it was proven that the Maya Codex of Mexico, previously known as the Grolier Codex, is in fact older by about a century. The codex was rediscovered in the city of Dresden, Germany, hence the book's present name. It is located in the museum of the Saxon State Library. The codex contains information relating to astronomical and astrological tables, religious references, seasons of the earth, and illness and medicine. It also includes information about conjunctions of planets and moons.
|
||||
The book suffered serious water damage during World War II. The pages are made of amate, 20 centimetres (7.9 in) high, and can be folded accordion-style; when unfolded the codex is 3.7 metres (12 ft) long. It is written in Mayan hieroglyphs and refers to an original text of some three or four hundred years earlier, describing local history and astronomical tables. Like all other pre-Hispanic books from Mesoamerica, the Dresden Codex takes the form of a screenfold. The pages consist of a paper made from the pounded inner bark of a wild species of fig, Ficus cotinifolia, (hu'un in Maya—a word that became semantically equivalent to "book").
|
||||
|
||||
== Description ==
|
||||
|
||||
The Dresden Codex contains 78 pages with decorative board covers on the front and back. Most pages have writing on both sides. They have a border of red paint, although many have lost this framing due to age deterioration. The pages are generally divided into three sections; students of the codex have arbitrarily labeled these sections a, b, and c. Some pages have just two horizontal sections, while one has four and another five sections. The individual sections with their own theme are generally separated by a red vertical line. Sections are generally divided into two to four columns.
|
||||
The Dresden Codex is one of four hieroglyphic Maya codices that survived the Spanish Inquisition in the New World. Three, the Dresden, Madrid, and Paris codices, are named after the city where they were ultimately rediscovered. The fourth is the Grolier Codex, located at the Grolier Club in New York City. The Dresden Codex is held by the Saxon State and University Library Dresden (SLUB Dresden, Saxon State Library) in Dresden, Germany. The Maya codices all have about the same size pages, with a height of about 20 centimetres (7.9 in) and a width of 10 centimetres (3.9 in).
|
||||
The pictures and glyphs were painted by skilled craftsmen using thin brushes and vegetable dyes. Black and red were the main colors used for many of the pages. Some pages have detailed backgrounds in shades of yellow, green, and the Mayan blue. The codex was written by eight different scribes, who all had their own writing style, glyph designs, and subject matter.
|
||||
|
||||
== History ==
|
||||
31
data/en.wikipedia.org/wiki/Dresden_Codex-1.md
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The Dresden Codex is described by historian J. Eric S. Thompson as writings of the indigenous people of the Yucatán Peninsula in southeastern Mexico. Maya historians Peter J. Schmidt, Mercedes de la Garza, and Enrique Nalda confirm this. Thompson further narrows the probable origin of the Dresden Codex to the area of Chichen Itza, because certain picture symbols in the codex are only found on monuments in that location. He also argues that the astronomical tables would support this as the place of origin. Thompson claims that the people of the Yucatán Peninsula were known to have done such studies around 1200 A.D. Thompson also notes the similar ceramic designs in the Chichen Itza area which are known to have ceased in the early thirteenth century. British historian Clive Ruggles suggests, based on the analyses of several scholars, that the Dresden Codex is a copy and was originally written between the twelfth and fourteenth centuries. Thompson narrows the date closer to 1200 to 1250. Maya archaeologist Linton Satterthwaite puts the date when it was made as no later than 1345.
|
||||
Johann Christian Götze (1692–1749), German theologian and director of the Royal Library at Dresden, purchased the codex from a private owner in Vienna in 1739 while traveling to Italy. Thompson speculates that the codex was sent as a tribute to Charles V, Holy Roman Emperor by Hernán Cortés, governor of Mexico, since examples of local writings and other Maya items were sent to the king in 1519 when he was living in Vienna. The codex was eventually catalogued into the Royal Library of Dresden in 1744, where it remained relatively obscure until the early twentieth century.
|
||||
Alexander von Humboldt published pages 47, 48 and 50–52 from the Dresden Codex in his 1810 atlas Vues des Cordillères et Monuments des Peuples Indigènes de l'Amérique, the first reproduction of any of its pages. The first copy of the codex was published by Lord Kingsborough in his 1831 Antiquities of Mexico. In 1828 Constantine Samuel Rafinesque had identified this book as being of Maya origin based on its glyphs looking like those found at Palenque. Historian Cyrus Thomas made a connection between the codex and the 260 year cycle ("Ahau Katun") of the Maya calendar and the 365 days in a year. Ruggles shows that in the codex the Maya related their 260-day calendar to celestial bodies, especially Venus and Mars.
|
||||
The codex has played a key role in the deciphering of Mayan hieroglyphs. Dresden librarian Ernst Wilhelm Förstemann published the first complete facsimile in 1880. He deciphered the calendar section of the codex, including the Maya numerals used therein. Förstemann determined that these numbers, along with deities and day names, related to the Mayan calendar and the Mayan Long Count calendar. In the 1950s Yuri Knorozov used a phonetic approach based on the De Landa alphabet for decoding the codex, which was followed up in the 1980s by other scholars that did additional deciphering based on this concept.
|
||||
Paul Schellhas in 1897 and 1904 assigned letters to gods for specific glyphs since they had several possible names. For example God D could be Hunab Ku Itzam Na among several other names and God A could be Cizin (god of death) among others. The Schellhas system of assigning letters for the gods represented by certain glyphs as a noncommittal system was adopted by later researchers of Maya codices.
|
||||
The Dresden Codex contains accurate astronomical tables, which are recognized by students of the codex for its detailed Venus tables and lunar tables. The lunar series has intervals correlating with eclipses, while the Venus tables correlate with the movements of the planet Venus. The codex also contains astrological tables and ritual schedules. The religious references show in a cycle of a 260-day ritual calendar the important Maya royal events. The codex also includes information on the Maya new-year ceremony tradition. The rain god Chaac is represented 134 times.
|
||||
|
||||
== Image ==
|
||||
|
||||
== Deterioration and pagination ==
|
||||
|
||||
Italian artist and engraver Agostino Aglio, starting in 1826, became the first to transcribe and illustrate the codex completely for Irish antiquarian Lord Kingsborough, who published it in his nine volumes of Antiquities of Mexico in 1831–48. The codex then had some damage due to handling, sunlight, and moisture.
|
||||
It received direct water damage that was significantly destructive, from being kept in a flooded basement during the World War II bombing of Dresden in February 1945. German historian G. Zimmerman later noted that the damage was extreme on pages 2, 4, 24, 28, 34, 38, 71 and 72. Certain details of the glyph images have been lost because of this. The damage is apparent when the current codex is compared to the Kingsborough copies of 1831–48 and the Förstemann facsimile editions from 1880 and 1892.
|
||||
Today's page numbers were assigned by Aglio when he became the first to transcribe the manuscript in 1825–26. For this, he divided the original codex into two parts, labeled Codex A and Codex B. He sequenced Codex A on the front side followed by its back side, with the same order on Codex B.
|
||||
Today, historians such as Helmut Deckert and Ferdinand Anders understand that a codex reading should traverse the complete front side followed by the complete back side of the manuscript, i.e., pages 1–24 followed by 46–74 and 25–45. The librarian K. C. Falkenstein adjusted the relative position of pages for "esthetical reasons" in 1836, resulting in today's two similar length parts. While deciphering the codex, the librarian E. W. Förstemann noticed an error in Aglio's page assignment of the sheets 1/45 and 2/44, so he correctly reassigned Aglio's pages 44 and 45 to become pages 1 and 2. The reversal of the sheets 6/40, 7/39 and 8/38 is due to an error when the sheets were returned to their protective glass cabinet after drying from the water damage due to the bombing of Dresden in 1945.
|
||||
|
||||
== See also ==
|
||||
Madrid Codex (Maya)
|
||||
Paris Codex
|
||||
Maya Codex of Mexico
|
||||
Popol Vuh
|
||||
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||||
== References ==
|
||||
|
||||
== Bibliography ==
|
||||
American Anthropologist (1891). American Anthropologist. American Anthropological Association.
|
||||
Coe, S.D. (1982). Maya Hieroglyphic Codices. Institute for Mesoamerican Studies, State University of New York at Albany.
|
||||
Deckert, Helmut (1989). Die Dresdner Maya-Handschrift (in German). Akademische Druck-u. Verlagsanstalt. ISBN 978-3-201-01478-6.
|
||||
Foster, Lynn V. (2005). Handbook to Life in the Ancient Maya World. Oxford University Press. ISBN 978-0-19-518363-4.
|
||||
Grube, Nikolai K. "Dresden, Codex." In David Carraco (ed). The Oxford Encyclopedia of Mesoamerican Cultures. : Oxford University Press, 2001.
|
||||
Keane, A. H. (9 June 2011). Man: Past and Present. Cambridge University Press. ISBN 978-0-521-23410-8.
|
||||
Lyons, Martyn (2011). Books: A Living History. J. Paul Getty Museum. ISBN 978-1-60606-083-4. It dates from the eleventh or twelfth century, making it the earliest surviving book from the Americas.
|
||||
Nalda, Enrique (1998). Maya. Rizzoli. ISBN 978-0-8478-2129-7.
|
||||
Ruggles, Clive L. N. (2005). Ancient Astronomy: An Encyclopedia of Cosmologies and Myth. ABC-CLIO. ISBN 978-1-85109-477-6.
|
||||
Sharer, Robert J. (2006). The Ancient Maya. Stanford University Press. ISBN 978-0-8047-4817-9.
|
||||
Smithsonian Institution (1897). Annual Report of the Bureau of American Ethnology to the Secretary of the Smithsonian Institution. U.S. Government Printing Office.
|
||||
Taube, Karl A. (1992). The Major Gods of Ancient Yucatan. Dumbarton Oaks. ISBN 978-0-88402-204-6.
|
||||
Thomas, Cyrus (1894). The Maya Year. U.S. Government Printing Office. p. 15.
|
||||
Thompson, John Eric Sidney (1972). A Commentary on the Dresden Codex: A Maya Hieroglyphic Book. American Philosophical Society. ISBN 978-0-87169-093-7.
|
||||
|
||||
== Further reading ==
|
||||
Bricker, V.R. (2007). Literary continuities across the transformation from Maya hieroglyphic to alphabetical writing. Proceedings of the American Philosophical Society, 151(1), 27-42.
|
||||
Houston, Stephen D. (2001). The Decipherment of Ancient Maya Writing, University of Oklahoma Press, ISBN 978-0-8061-3204-4
|
||||
Schellhas, Paul. Die Göttergestalten der Maya-Handschriften: Ein mythologisches Kulturbild aus dem Alten Amerika. Dresden, 1897.
|
||||
Van Stone, Mark (2008). "It's Not the End of the World: What the Ancient Maya Tell Us About 2012." Located online at the Foundation for the Advancement of Mesoamerican Studies website.
|
||||
Villacorta C., Juan Antonio, and Carlos A. Villacorta. Códices Mayas. Reproducidos y desarrollados por J. Antonio Villacorta C. y Carlos A. Villacorta. Guatemala City, 1930. Reproduction of the three then-known codices in black-and-white line drawings.
|
||||
Facsimile: Codex Dresdensis, Akademische Druck- u. Verlagsanstalt (ADEVA) Graz 1975, Colour facsimile edition of the Maya-MS in possession of Sächsische Landesbibliothek, Dresden. 78 pp. (74 with inscriptions), size: 205 x 90 mm, total length 3,56 m, in leporello folding. Encased in box with leather spine. Commentary: With contributions by F. Anders and H. Deckert; 93 pp. introduction, 39 pp. with black-and-white reproduction of the codex, 10 colour plates. CODICES SELECTI, Vol. LIV
|
||||
|
||||
== External links ==
|
||||
|
||||
=== Video ===
|
||||
Short Deutsche Welle video on the Dresden Codex [1]
|
||||
Media related to Dresden Codex at Wikimedia Commons
|
||||
|
||||
The complete codex (high resolution PDF)
|
||||
Facsimiles of the codex at the Foundation for the Advancement of Mesoamerican Studies, Inc., with PDF downloads
|
||||
The Dresden Codex Lunar Series and Sidereal Astronomy
|
||||
Dresden Library Information on the Codex Archived 2017-09-02 at the Wayback Machine
|
||||
Dresden Library Scans Archived 2017-06-23 at the Wayback Machine High-resolution scans of the Dresden Codex (site in German, PDF link at right)
|
||||
3D reconstruction and animation of the Codex Dresden in different conditions
|
||||
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|
||||
source: "https://en.wikipedia.org/wiki/Einstein's_Unfinished_Symphony"
|
||||
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|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T06:17:40.248751+00:00"
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||||
date_saved: "2026-05-05T08:33:23.046674+00:00"
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||||
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|
||||
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|
||||
|
||||
|
||||
35
data/en.wikipedia.org/wiki/Ephemeris-0.md
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||||
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|
||||
title: "Ephemeris"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/Ephemeris"
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category: "reference"
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tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:24.329178+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
In astronomy and celestial navigation, an ephemeris (; pl. ephemerides ; from Latin ephemeris 'diary', from Ancient Greek ἐφημερίς (ephēmerís) 'diary, journal') is a book with tables that gives the trajectory of naturally occurring astronomical objects and artificial satellites in the sky, i.e., the position (and possibly velocity) over time. Historically, positions were given as printed tables of values, given at regular intervals of date and time. The calculation of these tables was one of the first applications of mechanical computers. Modern ephemerides are often provided in electronic form. However, printed ephemerides are still produced, as they are useful when computational devices are not available.
|
||||
The astronomical position calculated from an ephemeris is often given in the spherical polar coordinate system of right ascension and declination, together with the distance from the origin if applicable. Some of the astronomical phenomena of interest to astronomers are eclipses, apparent retrograde motion/planetary stations, planetary ingresses, sidereal time, positions for the mean and true nodes of the moon, the phases of the Moon, and the positions of minor celestial bodies such as Chiron.
|
||||
Ephemerides are used in celestial navigation and astronomy. They are also used by astrologers. GPS signals include ephemeris data used to calculate the position of satellites in orbit.
|
||||
|
||||
== History ==
|
||||
|
||||
1st millennium BC – Ephemerides in Babylonian astronomy.
|
||||
2nd century AD – the Almagest and the Handy Tables of Ptolemy
|
||||
8th century AD – the zīj of Ibrāhīm al-Fazārī
|
||||
9th century AD – the zīj of Muḥammad ibn Mūsā al-Khwārizmī
|
||||
11th century AD – the zīj of Ibn Yunus
|
||||
12th century AD – the Tables of Toledo – based largely on Arabic zīj sources of Islamic astronomy – were edited by Gerard of Cremona to form the standard European ephemeris until the Alfonsine Tables.
|
||||
13th century AD – the Zīj-i Īlkhānī (Ilkhanic Tables) were compiled at the Maragheh observatory in Persia.
|
||||
13th century AD – the Alfonsine Tables were compiled in Spain to correct anomalies in the Tables of Toledo, remaining the standard European ephemeris until the Prutenic Tables almost 300 years later.
|
||||
13th century AD - the Dresden Codex, an extant Mayan ephemeris
|
||||
1408 – Chinese ephemeris table (copy in Pepysian Library, Cambridge, UK (refer book '1434'); Chinese tables believed known to Regiomontanus).
|
||||
1474 – Regiomontanus publishes his day-to-day Ephemerides in Nürnberg, Germany.
|
||||
1496 – the Almanach Perpetuum of Abraão ben Samuel Zacuto (one of the first books published with a movable type and printing press in Portugal)
|
||||
1504 – While shipwrecked on the island of Jamaica, Christopher Columbus successfully predicted a lunar eclipse for the natives, using the ephemeris of the German astronomer Regiomontanus.
|
||||
1531 – Work of Johannes Stöffler is published posthumously at Tübingen, extending the ephemeris of Regiomontanus through 1551.
|
||||
1551 – the Prutenic Tables of Erasmus Reinhold were published, based on Copernicus's theories.
|
||||
1554 – Johannes Stadius published Ephemerides novae et auctae, the first major ephemeris computed according to Copernicus' heliocentric model, using parameters derived from the Prutenic Tables. Although the Copernican model provided an elegant solution to the problem of computing apparent planetary positions (it avoided the need for the equant and better explained the apparent retrograde motion of planets), it still relied on the use of epicycles, leading to some inaccuracies – for example, periodic errors in the position of Mercury of up to ten degrees. One of the users of Stadius's tables is Tycho Brahe.
|
||||
1627 – the Rudolphine Tables of Johannes Kepler based on elliptical planetary motion became the new standard.
|
||||
1679 – La Connaissance des Temps ou calendrier et éphémérides du lever & coucher du Soleil, de la Lune & des autres planètes, first published yearly by Jean Picard and still extant.
|
||||
1975 – Owen Gingerich, using modern planetary theory and digital computers, calculates the actual positions of the planets in the 16th century and graphs the errors in the planetary positions predicted by the ephemerides of Stöffler, Stadius and others. According to Gingerich, the error patterns "are as distinctive as fingerprints and reflect the characteristics of the underlying tables. That is, the error patterns for Stöffler are different from those of Stadius, but the error patterns of Stadius closely resemble those of Maestlin, Magini, Origanus, and others who followed the Copernican parameters."
|
||||
41
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||||
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|
||||
title: "Ephemeris"
|
||||
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||||
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|
||||
date_saved: "2026-05-05T08:33:24.329178+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
== Modern ephemeris ==
|
||||
For scientific uses, a modern planetary ephemeris comprises software that generates positions of planets and often of their satellites, asteroids, or comets, at virtually any time desired by the user.
|
||||
After introduction of electronic computers in the 1950s it became feasible to use numerical integration to compute ephemerides. The Jet Propulsion Laboratory Development Ephemeris is a prime example. Conventional so-called analytical ephemerides that utilize series expansions for the coordinates have also been developed, but of much increased size and accuracy as compared to the past, by making use of computers to manage the tens of thousands of terms. Ephemeride Lunaire Parisienne and VSOP are examples.
|
||||
Typically, such ephemerides cover several centuries, past and future; the future ones can be covered because the field of celestial mechanics has developed several accurate theories. Nevertheless, there are secular phenomena which cannot adequately be considered by ephemerides. The greatest uncertainties in the positions of planets are caused by the perturbations of numerous asteroids, most of whose masses and orbits are poorly known, rendering their effect uncertain. Reflecting the continuing influx of new data and observations, NASA's Jet Propulsion Laboratory (JPL) has revised its published ephemerides nearly every year since 1981.
|
||||
Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars, and galaxies.
|
||||
Scientific ephemerides for sky observers mostly contain the positions of celestial bodies in right ascension and declination, because these coordinates are the most frequently used on star maps and telescopes. The equinox of the coordinate system must be given. It is, in nearly all cases, either the actual equinox (the equinox valid for that moment, often referred to as "of date" or "current"), or that of one of the "standard" equinoxes, typically J2000.0, B1950.0, or J1900. Star maps almost always use one of the standard equinoxes.
|
||||
Scientific ephemerides often contain further useful data about the moon, planet, asteroid, or comet beyond the pure coordinates in the sky, such as elongation to the Sun, brightness, distance, velocity, apparent diameter in the sky, phase angle, times of rise, transit, and set, etc.
|
||||
Ephemerides of the planet Saturn also sometimes contain the apparent inclination of its ring.
|
||||
Celestial navigation serves as a backup to satellite navigation. Software is widely available to assist with this form of navigation; some of this software has a self-contained ephemeris. When software is used that does not contain an ephemeris, or if no software is used, position data for celestial objects may be obtained from the modern Nautical Almanac or Air Almanac.
|
||||
An ephemeris is usually only correct for a particular location on the Earth. In many cases, the differences are too small to matter. However, for nearby asteroids or the Moon, they can be quite important.
|
||||
Other modern ephemerides recently created are the EPM (Ephemerides of Planets and the Moon), from the Russian Institute for Applied Astronomy of the Russian Academy of Sciences, and the INPOP (Intégrateur numérique planétaire de l'Observatoire de Paris) by the French IMCCE.
|
||||
|
||||
== See also ==
|
||||
|
||||
== Notes ==
|
||||
|
||||
== References ==
|
||||
Duffett-Smith, Peter (1990). Astronomy With Your Personal Computer. Cambridge University Press. ISBN 0-521-38995-X.
|
||||
"ephemeris". American Heritage Dictionary of the English Language (3rd ed.). Boston: Houghton Mifflin. 1992.
|
||||
MacCraig, Hugh (1949). The 200 Year Ephemeris. Macoy Publishing Company.
|
||||
Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell. ISBN 0-943396-35-2.
|
||||
Michelsen, Neil F. (1990). Tables of Planetary Phenomena. ACS Publications, Inc. ISBN 0-935127-08-9.
|
||||
Michelsen, Neil F. (1982). The American Ephemeris for the 21st Century - 2001 to 2100 at Midnight. Astro Computing Services. ISBN 0-917086-50-3.
|
||||
Montenbruck, Oliver (1989). Practical Ephemeris Calculations. Springer-Verlag. ISBN 0-387-50704-3.
|
||||
Seidelmann, Kenneth (2006). Explanatory supplement to the astronomical almanac. University Science Books. ISBN 1-891389-45-9.
|
||||
|
||||
== External links ==
|
||||
|
||||
The JPL HORIZONS online ephemeris
|
||||
Introduction to the JPL ephemerides (archived 26 February 2005)
|
||||
"Ephemerides-IMCEE".
|
||||
@ -0,0 +1,14 @@
|
||||
---
|
||||
title: "Exploring the Earth and the Cosmos"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Exploring_the_Earth_and_the_Cosmos"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:26.693428+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Exploring the Earth and the Cosmos is a book written by Isaac Asimov in 1982.
|
||||
|
||||
|
||||
== References ==
|
||||
0
data/en.wikipedia.org/wiki/Extraterrestrial
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data/en.wikipedia.org/wiki/Extraterrestrial
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31
data/en.wikipedia.org/wiki/Feynman's_Lost_Lecture-0.md
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|
||||
---
|
||||
title: "Feynman's Lost Lecture"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Feynman's_Lost_Lecture"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:29.018768+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Feynman's Lost Lecture: The Motion of Planets Around the Sun is a book based on a lecture by Richard Feynman. Restoration of the lecture notes and conversion into book form was undertaken by Caltech physicist David L. Goodstein and archivist Judith R. Goodstein.
|
||||
Feynman had given the lecture on the motion of bodies at Caltech on March 13, 1964, but the notes and pictures were lost for a number of years and consequently not included in The Feynman Lectures on Physics series. The lecture notes were later found, but without the photographs of his illustrative chalkboard drawings. One of the editors, David L. Goodstein, stated that at first without the photographs, it was very hard to figure out what diagrams he was referring to in the audiotapes, but a later finding of his own private lecture notes made it possible to understand completely the logical framework with which Feynman delivered the lecture.
|
||||
|
||||
|
||||
== Overview ==
|
||||
|
||||
You can explain to people who don't know much of the physics, the early history... how Newton discovered... Kepler's Laws, and equal areas, and that means it's toward the sun, and all this stuff. And then the key - they always ask then, "Well, how do you see that it's an ellipse if it's the inverse square?" Well, it's God damned hard, there's no question of that. But I tried to find the simplest one I could.
|
||||
In a non-course lecture delivered to a freshman physics audience, Feynman undertakes to present an elementary, geometric demonstration of Newton's discovery of the fact that Kepler's first observation, that the planets travel in elliptical orbits, is a necessary consequence of Kepler's other two observations.
|
||||
The structure of Feynman's lecture:
|
||||
|
||||
A historical introduction to the material
|
||||
An overview of some geometric properties of an ellipse
|
||||
Newton's demonstration that equal areas in equal times is equivalent to forces toward the sun
|
||||
Feynman's demonstration that equal changes in velocity occur in equal angles in the orbit
|
||||
Feynman's demonstration, using techniques of Ugo Fano, that these velocity changes imply that the orbit is elliptical
|
||||
Discussion of Rutherford's experiments with scattering of alpha particles, and the discovery of the atomic nucleus
|
||||
The audio recording of the lectures also includes twenty minutes of informal Q&A at the blackboard with students who had attended the lecture.
|
||||
In the 1964 lecture, Feynman presents an elementary geometric proof (i.e., in the style of Isaac Newton's 1687 Philosophiæ Naturalis Principia Mathematica) of Kepler's first law. Feynman's geometric proof relies on the concept of a hodograph. Feynman reported that his motivation for presenting a proof different from Newton's was that he had failed to understand Newton's original proof in the Principia. A proof with ideas similar to Feynman's had already been published by James Clerk Maxwell in his book Matter and Motion (1877).
|
||||
|
||||
|
||||
== References ==
|
||||
54
data/en.wikipedia.org/wiki/First_Light_(Preston_book)-0.md
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|
||||
---
|
||||
title: "First Light (Preston book)"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/First_Light_(Preston_book)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:30.155532+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
First Light: The Search for the Edge of the Universe is a 1987 non-fiction book on astronomy and astronomers by Richard Preston.
|
||||
The title refers to the astronomical term first light, which is when a telescope is first used to take an astronomical image after it has been constructed. First light also refers to the moment when stars and galaxies first formed out of a dark universe.
|
||||
|
||||
|
||||
== Content ==
|
||||
The central character of First Light is the Hale Telescope on Palomar Mountain, which was the world's biggest telescope for more than three decades. Preston describes its history and technical details, and he profiles many of the people involved in astronomical research at Palomar. First Light portrays astronomers scanning the Solar System for minor planets and those seeking the outermost astronomical objects in universe. It describes historical events such as the discovery of quasars and celebrates the scientists' joy in their endeavors, their obsessions and even their thoughts.
|
||||
|
||||
|
||||
== Structure ==
|
||||
The book is structured as follows.
|
||||
|
||||
Foreword: To Readers and Teachers
|
||||
Part 1: Big Eye
|
||||
Part 2: The Shoemaker Comets
|
||||
Part 3: Gadgeteers
|
||||
Part 4: Discoveries
|
||||
(List of) Main Characters
|
||||
Glossary
|
||||
Credits
|
||||
First Light provides neither an index nor a bibliography.
|
||||
|
||||
|
||||
== Criticism ==
|
||||
As of today, some of the astronomical approaches and views are out of date. However, First Light is considered one of the best books written about astronomers.
|
||||
|
||||
|
||||
== Awards ==
|
||||
First Light won the 1988 American Institute of Physics award in science writing.
|
||||
Carolyn Shoemaker, who was a subject of First Light, named an asteroid 3792 Preston.
|
||||
|
||||
|
||||
== See also ==
|
||||
List of asteroids/3701–3800
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== References ==
|
||||
Preston, Richard. First Light. New York: Atlantic Monthly Press, ISBN 9780871132000; OCLC 16004290
|
||||
|
||||
|
||||
== External links ==
|
||||
Excerpt at richardpreston.net
|
||||
@ -0,0 +1,49 @@
|
||||
---
|
||||
title: "Five Billion Years of Solitude"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Five_Billion_Years_of_Solitude"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:31.311483+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Five Billion Years of Solitude: The Search for Life Among the Stars is a nonfiction work by the science author Lee Billings. The text was initially published on October 3, 2013 by Current. The paperback version was published on October 28, 2014.
|
||||
|
||||
|
||||
== Overview ==
|
||||
In this book, Billings explores the scientists and science behind the ever-expanding universe of exoplanets. Since the first detection of a planet orbiting another Sun-like star in 1995, scientists have discovered an increasing number of worlds beyond the Solar System through detections by telescopes and spacecraft. Billings reveals the scientists behind these discoveries and their thoughts on not only exoplanets, but also their triumphs and frustrations in their quest to solve one of the greatest mysteries of humankind: Are we alone? Billings includes interviews with Frank Drake, Geoffrey Marcy, Greg Laughlin, James Kasting, Matt Mountain, Wesley Traub, Sara Seager, and many other prominent researchers.
|
||||
|
||||
|
||||
== Topics covered ==
|
||||
The book has 10 chapters:
|
||||
|
||||
Looking for Longevity
|
||||
Drake's Orchids
|
||||
A Fractured Empire
|
||||
The Worth of a World
|
||||
After the Gold Rush
|
||||
The Big Picture
|
||||
Out of Equilibrium
|
||||
Aberrations of the Light
|
||||
The Order of the Null
|
||||
Into the Barren Lands
|
||||
|
||||
|
||||
== Reviews ==
|
||||
Overbye, Dennis (8 November 2013). "Lonely Planet". Sunday Book Review. The New York Times. Retrieved 23 November 2013.
|
||||
Brown, Mike (15 November 2013). "Five Billion Years of Solitude: The Search for Life Among the Stars by Lee Billings". The Washington Post. Retrieved 23 November 2013.
|
||||
Henderson, Caspar (21 November 2013). "Five Billion Years of Solitude: The Search for Life Among the Stars – review". The Guardian. Retrieved 23 November 2013.
|
||||
Teitel, Amy Shira (14 October 2013). "Lee Billings' Five Billion Years of Solitude (Review)". Discovery News Book Reviews. Discovery News. Retrieved 23 November 2013.
|
||||
Kuchner, Marc (12 December 2014). "Five Billion Years of Solitude: The Search for Life Among the Stars". Physics Today. 67 (12): 59. Bibcode:2014PhT....67l..59K. doi:10.1063/PT.3.2626. Retrieved 18 December 2014.
|
||||
|
||||
|
||||
== See also ==
|
||||
The Science of Interstellar
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
for Five Billion Years of Solitude — Penguin Books website
|
||||
20
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|
||||
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|
||||
title: "Ganitagannadi"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Ganitagannadi"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:32.502568+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Gaṇitagannaḍi (Mirror of Mathematics) is a commentary in Kannada on Viddṇācārya's Vārșikatantra composed by Śaṅkaranārāyaṇa Joisāru in 1604. Viddṇācārya's Vārșikatantra is a karaṇa text written before 1370 CE.
|
||||
The book, written in Nandinagari script, is a karaṇa text, that is, a book which explain the various computations in astronomy especially with regard to those related to the preparation of Panchangam-s (calendar). Even though manuscripts of Kannada commentaries of several Sanskrit texts on astronomy like Sūryasiddhānta have been identified, Gaṇitagannaḍi is the first such commentary ever to be translated into English, printed and published. Gaṇitagannaḍi was translated into English by B. S. Shylaja, a scientist associated with Jawaharlal Nehru Planetarium, Bengaluru and Seetharama Javagal and was published in 2021. It was Seetharama Javagal who brought to light the palm leaf manuscript of Gaṇitagannaḍi in his grandfather's collection.
|
||||
The most important specialty of the book from an astronomical point of view is that, "in the third chapter (Chāyāddhāya). all the computations are based on a single parameter, namely the shadow length. Other quantities are based on Dyu-nishardha-Karna, to be obtained daily. This includes vishuvat-karna and vishuvatchaya. This clearly demonstrates the importance of actual observations. These traditional astronomers always advocated drig-ganita-aikya (that is, the concordance between observation and computation)."
|
||||
|
||||
|
||||
== Outline of the book ==
|
||||
The first chapter of the book deals with the procedure for getting kalidina, starting from the kalivarsa count, and the method for getting the mean positions for planets. The second chapter provides the method for deriving the true positions of all planets, perigees and the nodes. The third chapter describes the procedures of tripraśnādhikāra in Sūryasiddhānta. The fourth chapter is devoted to eclipses. The fifth chapter describes a graphical method for obtaining the timings, magnitudes, and points of ingress. The next three chapters are very brief. The last chapter describes the determination of the elevation of the cusps of the crescent moon.
|
||||
|
||||
|
||||
== References ==
|
||||
123
data/en.wikipedia.org/wiki/Grahalaghava-0.md
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123
data/en.wikipedia.org/wiki/Grahalaghava-0.md
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|
||||
---
|
||||
title: "Grahalaghava"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Grahalaghava"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:33.688671+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Grahalāghavaṃ is a Sanskrit treatise on astronomy composed by Gaṇeśa Daivajna (c. 1507–1554), a sixteenth century astronomer, astrologer, and mathematician from western India, probably from the Indian state of Maharashtra. It is a work in the genre of the karaṇa text in the sense that it is in the form of a handbook or manual for the computation of the positions of the planets. Of all the ancient and medieval karaṇa texts on astronomy, Grahalāghavaṃ is the most popular among the pañcāṅgaṃ makers of most parts of India.It is also considered to be the most comprehensive, exhaustive and easy to use karaṇa text on astronomy. The popularity of this work is attested by the large number of commentaries (at least 14 in number) on it and also by the large number of modern editions (at least 23 in number) of the book. The work is divided into sixteen chapters and covers all the commonly discussed topics in such texts including planetary positions, timekeeping and calendar construction, eclipses, heliacal rising and settings, planetary conjunctions, and the mahāpāta-s.
|
||||
The most striking features of the work that made it highly popular include its use of an ingenious method to reduce the traditional method of computations involving 'astronomical numbers' to smaller numbers and its meticulous and careful avoidance of the use of the trigonometrical sines by replacing them with simpler, still acceptably accurate, algebraic expressions. The former is effected by introducing the concept of a new cycle called a cakra, a period consisting of 4016 days which is approximately 11 years. Traditional computations make use the concept of ahargaṇa which is the number of civil days elapsed since the kali epoch which falls on 17/18 February 3102 BCE. The traditional ahargaṇa is a huge number. For example, the ahargaṇa corresponding to 1 January 2025 is 1872211. The ahargaṇa as modified in Grahalāghavaṃ is the remainder number of days after completing full cakra-s of 4016 days each since the beginning of the epoch. Thus the modified ahargaṇa corresponding to 1 January 2025 would be 755, a number less than 4016. To avoid the use of trigonometrical sines, Grahalāghavaṃ uses several approximations to the sine function. For example, in the context of computing the true longitudes of celestial objects, approximation formulas based on the following approximation to the sine function (known as the Bhāskara I's sine approximation formula) is used:
|
||||
|
||||
|
||||
|
||||
|
||||
sin
|
||||
|
||||
|
||||
x
|
||||
|
||||
∘
|
||||
|
||||
|
||||
≈
|
||||
|
||||
|
||||
|
||||
4
|
||||
x
|
||||
(
|
||||
180
|
||||
−
|
||||
x
|
||||
)
|
||||
|
||||
|
||||
40500
|
||||
−
|
||||
x
|
||||
(
|
||||
180
|
||||
−
|
||||
x
|
||||
)
|
||||
|
||||
|
||||
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle \sin x^{\circ }\approx {\frac {4x(180-x)}{40500-x(180-x)}}.}
|
||||
|
||||
|
||||
In the context of the computation of eclipses, the following approximation is used:
|
||||
|
||||
When
|
||||
|
||||
|
||||
|
||||
x
|
||||
|
||||
|
||||
{\displaystyle x}
|
||||
|
||||
is small,
|
||||
|
||||
|
||||
|
||||
sin
|
||||
|
||||
|
||||
x
|
||||
|
||||
∘
|
||||
|
||||
|
||||
≈
|
||||
|
||||
|
||||
3
|
||||
175
|
||||
|
||||
|
||||
x
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle \sin x^{\circ }\approx {\frac {3}{175}}x.}
|
||||
|
||||
It may be noted that this is an approximation to the well known result
|
||||
|
||||
|
||||
|
||||
sin
|
||||
|
||||
θ
|
||||
≈
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \sin \theta \approx \theta }
|
||||
|
||||
when
|
||||
|
||||
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \theta }
|
||||
|
||||
is in radians and is small.
|
||||
|
||||
|
||||
== Full texts ==
|
||||
Full text of the work with commentaries in Sanskrit and with English translation are available at the following sources:
|
||||
|
||||
Kapilesvara Sasthri (1948). The Grahalaghava of Ganesa Daivajnja with Sanskrit Commentary by Visvanatha Daivajnja. Benares City: Jayakrishna das Haridas Gupta. Retrieved 12 January 2025.
|
||||
For an English translation of the full text of Grahalāghavaṃ see: Rao, S. Balachandra & S. K. Uma, Grahalaghavam of Ganesa Daivajna – an English Exposition, Mathematical Explanation and Notes, IJHS 41.1 (2006) Supplement pp. S1-88; 41.2 (2006) Supplement pp. S89-183; 41.3 (2006) Supplement pp. S185-315; 41.4 (2006) Supplement pp. S317-415.
|
||||
|
||||
|
||||
== References ==
|
||||
16
data/en.wikipedia.org/wiki/Guinness_Book_of_Astronomy-0.md
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16
data/en.wikipedia.org/wiki/Guinness_Book_of_Astronomy-0.md
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@ -0,0 +1,16 @@
|
||||
---
|
||||
title: "Guinness Book of Astronomy"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Guinness_Book_of_Astronomy"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:36.059550+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Guinness Book of Astronomy is a book (ISBN 0-85112-375-9) by the British astronomer Patrick Moore, first published in 1979, and running to seven editions.
|
||||
The first part of the book is written like a Guinness Book of Records, with paragraphs like "the most luminous star", "the farthest star", and so on. Solar System objects are explained in detail.
|
||||
The second part is a detailed sky atlas for amateur astronomy observations: for each constellation, a list of bright and dim stars, deep sky, and other notable objects is given to the reader. The object tables are so complete that this book alone is enough for months of observations with small telescopes.
|
||||
|
||||
|
||||
== Notes ==
|
||||
24
data/en.wikipedia.org/wiki/Habitable_Planets_for_Man-0.md
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24
data/en.wikipedia.org/wiki/Habitable_Planets_for_Man-0.md
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@ -0,0 +1,24 @@
|
||||
---
|
||||
title: "Habitable Planets for Man"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Habitable_Planets_for_Man"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:37.225643+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Habitable Planets For Man is a work by Stephen Dole, first edition published by Blaisdell Publishing Company, A division of Ginn and Company, copyright 1964 by The RAND Corporation. Originally 158 pages, it was republished in a posthumous second edition in 2007, as Planets for Man.
|
||||
The revised edition, 174 pages, contains a detailed scientific study on the nature of worlds that may support life in the universe, the probability of their existence, and ways of finding them. It includes assessments of 14 stars within 22 light years with a relatively high probability of having habitable planets (a collective probability of 43%). Writing in a Scientific American blog in 2011, Caleb Scharf called it "extraordinarily detailed and prescient".
|
||||
|
||||
|
||||
== Publication data ==
|
||||
ISBN 0833042270
|
||||
ISBN 978-0833042279
|
||||
|
||||
|
||||
== External links ==
|
||||
Official RAND Corporation Site
|
||||
|
||||
|
||||
== References ==
|
||||
43
data/en.wikipedia.org/wiki/Harmonia_Macrocosmica-0.md
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43
data/en.wikipedia.org/wiki/Harmonia_Macrocosmica-0.md
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@ -0,0 +1,43 @@
|
||||
---
|
||||
title: "Harmonia Macrocosmica"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Harmonia_Macrocosmica"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:38.322123+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Harmonia Macrocosmica is a celestial atlas written by Andreas Cellarius and published in 1660 in Amsterdam by the cartographic publisher Johannes Janssonius. It is regarded as an important work in the history of celestial cartography and was produced during the Golden Age of Netherlandish cartography.
|
||||
The atlas contains engraved diagrams illustrating several cosmological systems discussed in early modern astronomy, including those associated with Claudius Ptolemy, Nicolaus Copernicus, and Tycho Brahe. It also includes star charts depicting the constellations of the northern and southern skies.
|
||||
Cellarius intended Harmonia Macrocosmica to serve as the introductory astronomical volume of a larger work on cosmography. A planned second volume was never published.
|
||||
|
||||
|
||||
== History ==
|
||||
The celestial atlas Harmonia Macrocosmica was published in Amsterdam in 1660 by the map publisher Johannes Janssonius. It was created by the German–Dutch cosmographer Andreas Cellarius as part of a larger cosmographical project.
|
||||
The volume contains diagrams illustrating several cosmological systems, including those associated with Claudius Ptolemy, Nicolaus Copernicus, and Tycho Brahe. It also includes celestial charts depicting the constellations, some of which follow the Christianized constellation system introduced by Julius Schiller in Coelum stellatum christianum (1627).
|
||||
Cellarius intended the atlas to serve as the introductory historical and astronomical volume of a planned two-part work on cosmography. The second volume was never published.
|
||||
|
||||
|
||||
== Description ==
|
||||
The atlas is divided into two main parts. The first contains a series of copper-engraved plates illustrating different models of the universe that were discussed in early modern astronomy. These include the geocentric system associated with Claudius Ptolemy, the heliocentric system proposed by Nicolaus Copernicus, and the geo-heliocentric system developed by Tycho Brahe. The diagrams show how each system explained the motions of the Sun, Moon, and planets.
|
||||
The later plates contain star charts showing the constellations of the northern and southern skies. These include the traditional constellations known from classical astronomy, as well as constellations introduced by the German scholar Julius Schiller. In his work Coelum stellatum christianum (1627), Schiller replaced many of the classical constellation figures with Christian and biblical figures. Cellarius included these alternative constellations alongside the traditional ones in the atlas.
|
||||
|
||||
|
||||
=== Origins of the engravings ===
|
||||
Of the various engravers and artists who worked on the plates of the atlas, only two signed their work. The frontispiece was created by the Dutch engraver Frederik Hendrik van den Hove, while ten of the plates were engraved by Johannes van Loon.
|
||||
The figures used for the classical constellations were not newly designed for the atlas. Instead, they were based on earlier constellation images created by the Dutch engraver Jan Pieterszoon Saenredam, whose work influenced later celestial atlases of the seventeenth century.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
Van Gent, Robert H. (2006), Andreas Cellarius, Harmonia Macrocosmica of 1660, TASCHEN, ISBN 978-3-8228-5290-3
|
||||
Bio-bibliography of Andreas Cellarius
|
||||
|
||||
|
||||
== External links ==
|
||||
Media related to Cellarius Harmonia Macrocosmica at Wikimedia Commons
|
||||
|
||||
rarebookroom.org
|
||||
Harmonia Macrocosmica
|
||||
Digitized example of the 1661 Harmonia Macrocosmica at RareMaps.com
|
||||
27
data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md
Normal file
27
data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md
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@ -0,0 +1,27 @@
|
||||
---
|
||||
title: "Harmonice Mundi"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/Harmonice_Mundi"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:39.488056+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Harmonice Mundi (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.
|
||||
The full title is Harmonices mundi libri V (The Five Books of The Harmony of the World), which is commonly but ungrammatically shortened to Harmonices mundi.
|
||||
|
||||
== Background and history ==
|
||||
Kepler began working on Harmonice Mundi around 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 adoption of elliptic orbits in the Copernican system) allowed him to explore new theorems. Another important development that allowed Kepler to establish his celestial-harmonic relationships was the abandonment of the Pythagorean tuning as the basis for musical consonance and the adoption of geometrically supported musical ratios; this would eventually be what allowed Kepler to relate musical consonance and the angular velocities of the planets. Thus, Kepler could reason that his relationships gave evidence for God acting as a grand geometer, rather than a Pythagorean numerologist.
|
||||
The concept of musical harmonies intrinsically existing within the spacing of the planets existed in medieval philosophy prior to Kepler. Musica universalis was a traditional philosophical metaphor that was taught in the quadrivium, and was often called the "music of the spheres." Kepler was intrigued by this idea while he sought explanation for a rational arrangement of the heavenly bodies. When Kepler uses the term "harmony" it is not strictly referring to the musical definition, but rather a broader definition encompassing congruence in Nature and the workings of both the celestial and terrestrial bodies. He notes musical harmony as being a product of man, derived from angles, in contrast to a harmony that he refers to as being a phenomenon that interacts with the human soul. In turn, this allowed Kepler to claim the Earth has a soul because it is subjected to astrological harmony.
|
||||
While writing the book, Kepler had to defend his mother in court after she had been accused of witchcraft.
|
||||
|
||||
== Content ==
|
||||
Kepler divides The Harmony of the World into five long chapters: the first is on regular polygons; the second is on the congruence of figures; the third is on the origin of harmonic proportions in music; the fourth is on harmonic configurations in astrology; the fifth is on the harmony of the motions of the planets.
|
||||
|
||||
=== Chapter 1 and 2 ===
|
||||
Chapters 1 and 2 of The Harmony of the World contain most of Kepler's contributions concerning polyhedra. He is primarily interested with how polygons, which he defines as either regular or semiregular, can come to be fixed together around a central point on a plane to form congruence. His primary objective was to be able to rank polygons based on a measure of sociability, or rather, their ability to form partial congruence when combined with other polyhedra. He returns to this concept later in Harmonice Mundi with relation to astronomical explanations. In the second chapter is the earliest mathematical understanding of two types of regular star polyhedra, the small and great stellated dodecahedron; they would later be called Kepler's solids or Kepler Polyhedra and, together with two regular polyhedra discovered by Louis Poinsot, as the Kepler–Poinsot polyhedra. He describes polyhedra in terms of their faces, which is similar to the model used in Plato's Timaeus to describe the formation of Platonic solids in terms of basic triangles. The book features illustrations of solids and tiling patterns, some of which are related to the golden ratio.
|
||||
While medieval philosophers spoke metaphorically of the "music of the spheres", Kepler discovered physical harmonies in planetary motion. He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms). Kepler explains the reason for the Earth's small harmonic range:
|
||||
|
||||
The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway.
|
||||
The celestial choir Kepler formed was made up of a tenor (Mars), two bass (Saturn and Jupiter), a soprano (Mercury), and two altos (Venus and Earth). Mercury, with its large elliptical orbit, was determined to be able to produce the greatest number of notes, while Venus was found to be capable of only a single note because its orbit is nearly a circle. At very rare intervals all of the planets would sing together in "perfect concord": Kepler proposed that this may have happened only once in history, perhaps at the time of creation. Kepler reminds us that harmonic order is only mimicked by man, but has origin in the alignment of the heavenly bodies:
|
||||
46
data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md
Normal file
46
data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md
Normal file
@ -0,0 +1,46 @@
|
||||
---
|
||||
title: "Harmonice Mundi"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/Harmonice_Mundi"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:39.488056+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Accordingly you won't wonder any more that a very excellent order of sounds or pitches in a musical system or scale has been set up by men, since you see that they are doing nothing else in this business except to play the apes of God the Creator and to act out, as it were, a certain drama of the ordination of the celestial movements.
|
||||
Kepler discovers that all but one of the ratios of the maximum and minimum speeds of planets on neighboring orbits approximate musical harmonies within a margin of error of less than a diesis (a 25:24 interval). The orbits of Mars and Jupiter produce the one exception to this rule, creating the inharmonic ratio of 18:19.
|
||||
|
||||
=== Chapter 5 ===
|
||||
Chapter 5 includes a long digression on astrology. This is immediately followed by Kepler's third law of planetary motion, which shows a constant proportionality between the cube of the semi-major axis of a planet's orbit and the square of the time of its orbital period. Kepler's previous book, Astronomia nova, related the discovery of the first two principles now known as Kepler's laws.
|
||||
|
||||
== Recent history ==
|
||||
A copy of the 1619 edition was stolen from the National Library of Sweden in the 1990s.
|
||||
|
||||
== Use in recent music ==
|
||||
A small number of recent compositions either make reference to or are based on the concepts of Harmonice Mundi or Harmony of the Spheres. The most notable of these are:
|
||||
|
||||
Laurie Spiegel: Kepler's Harmony of the Worlds (1977). An excerpt of the piece was selected by Carl Sagan for inclusion on the Voyager Golden Record, launched aboard the Voyager spacecraft.
|
||||
Mike Oldfield, (English musician and composer, born 1953), Music of the Spheres (album released in 2008 by Mercury Records).
|
||||
Joep Franssens (Dutch composer, born 1955), Harmony of the Spheres (cycle in five movements for mixed choir and string orchestra), composed 2001.
|
||||
Philip Glass, American composer, Kepler opera (2009), homage to Johannes Kepler, commissioned by the city of Linz, where the astronomer lived.
|
||||
Tim Watts, (English composer, born 1979), Kepler's Trial (2016–2017), premiered at St John's College, Cambridge (2016); revised version performed at the Victoria and Albert Museum, 9 November 2017
|
||||
Paul Hindemith, German composer, Die Harmonie der Welt Symphony (originally entitled Symphonie „Die Harmonie der Welt“ in German), IPH 50, is a symphony composed in 1951, and which served as the basis for the 1957 opera Die Harmonie der Welt.
|
||||
Miriam Monaghan (British recorder player and composer) Kepler’s Planets (2019), written for Palisander Recorder Quartet. Extracts were premiered live on BBC Radio 3 In Tune (October 2019) with full concert premiere at London International Festival of Early Music (November 2019).
|
||||
Dave Soldier, American composer, wrote Motet: Harmony of the World (2022), closely hewing to Kepler's instructions in the book for a future composer to write a motet, including the use of a specific six-voice choir (recorded by the microtonal choir Ekmeles), the particular just intonation intervals, and the harmonies allowed in Kepler's diagrams. The text sets the Prayer to the Sun by Proclus in ancient Greek, a poet heavily quoted in Kepler's text.
|
||||
|
||||
== See also ==
|
||||
Pythagoreanism
|
||||
Mysterium Cosmographicum
|
||||
|
||||
== References ==
|
||||
|
||||
== Further reading ==
|
||||
Johannes Kepler, The Harmony of the World. Tr. Charles Glenn Wallis. Chicago: Encyclopædia Britannica, 1952.
|
||||
"Johannes Kepler," in The New Grove Dictionary of Music and Musicians. Ed. Stanley Sadie. 20 vol. London, Macmillan Publishers, 1980. ISBN 1-56159-174-2.
|
||||
|
||||
== External links ==
|
||||
|
||||
Harmonice mundi ("The Harmony of the Worlds") in fulltext facsimile; Carnegie-Mellon University
|
||||
Harmonice Mundi at Archive.org in Latin
|
||||
Harmonies of the World excerpt from Harmonice Mundi translated by Charles Glenn Wallis
|
||||
0
data/en.wikipedia.org/wiki/Horizons
Normal file
0
data/en.wikipedia.org/wiki/Horizons
Normal file
@ -0,0 +1,45 @@
|
||||
---
|
||||
title: "How I Killed Pluto and Why It Had It Coming"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/How_I_Killed_Pluto_and_Why_It_Had_It_Coming"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:42.284969+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
How I Killed Pluto and Why It Had It Coming is a 2010 memoir by Mike Brown, the American astronomer most responsible for the reclassification of Pluto from planet to dwarf planet.
|
||||
|
||||
|
||||
== Summary ==
|
||||
The memoir is an account of the events surrounding the redefinition of the term planet that eventually changed the status of Pluto.
|
||||
Brown recounts his professional career as a faculty member at the California Institute of Technology leading a team which examined large patches of the sky in an attempt to identify and track Trans-Neptunian objects.
|
||||
|
||||
In the mid to late 1990's, the team utilizes analog plates (in the same way as Clyde Tombaugh discovered Pluto in 1930), a painstaking process, which did not yield good results.
|
||||
The team progresses to computer software and digital scanning technology, writing code to automatically identify patches of sky with moving stars. Initial iterations of the software identified many false positives due to smudges and light artifacts.
|
||||
Into the early 2000's, the team is successful in finding a series of Kuiper belt objects.
|
||||
The first, dubbed "Object X" (Quaoar) is discovered in 2002. A year later, Brown's team finds more objects, which the team dubs "Santa" (Haumea) and "Easter Bunny" (Makemake) as they were discovered close to the holidays.
|
||||
|
||||
Brown's team intends to keep the discoveries a secret until they have surveyed them for several months and are able to write a formal scientific paper on each of them. This is in order to avoid misleading the public about the materials and size of the planets, as each one they have found up to now was thought to be larger than Pluto at first - only for size measurements to be refined down due to brighter-than-expected surface materials.
|
||||
However, NASA researchers (who had to be contacted in order to arrange for Hubble operation time) plan to announce the discoveries at an upcoming conference.
|
||||
A team of astronomers at the Sierra Nevada Observatory in Spain led by José Luis Ortiz Moreno, finds NASA's conference agenda, track down the object using a publicly available repository of the sky pictures used by Brown's team, and publish the discovery as their own. Brown initially allows them to take credit for it but swiftly changes his mind.
|
||||
Against his original desire, Brown and his team schedule public press conferences and interviews about their work, releasing information about Makemake, Haumea, and a new discovery, Xena (Eris).
|
||||
Brown also recounts his personal life, speaking about his wife Diane's role in consoling and advising him, along with the birth of his daughter Lilah in 2005, at the same time his team was rushing to complete reports on Eris.
|
||||
Eris was mistakenly thought to be larger than Pluto, causing many to suggest that it may be the 10th planet. However, Brown himself dismisses this notion, stating that neither Pluto nor Eris should be considered planets due to their size difference with the rest of the Solar System objects. He also notes that shortly after Ceres and Vesta were discovered in the 1800s, those were also considered planets until they were reclassified as asteroids.
|
||||
|
||||
In 2006, after protracted argument over the definition of the term planet, the International Astronomical Union schedules a vote that removes Pluto from the list of Solar System planets. Pluto, Eris and all the objects that Brown's team discovered are renamed dwarf planets.
|
||||
|
||||
|
||||
== Reviews ==
|
||||
Reviews of the book have been generally positive, with James Kennedy of The Wall Street Journal calling the book a "brisk" and "enjoyable ... chronicle" of the tale of the search for new planets and the eventual demotion of Pluto from planetary status. Janet Maslin of The New York Times called it a "short, eager-to-please research memoir".
|
||||
|
||||
|
||||
== See also ==
|
||||
List of former planets
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Bibliography ==
|
||||
Brown, Michael E. (2010). How I Killed Pluto and Why It Had It Coming. ISBN 978-0-385-53108-5.
|
||||
32
data/en.wikipedia.org/wiki/How_It_Began-0.md
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|
||||
---
|
||||
title: "How It Began"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/How_It_Began"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:43.457736+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
How It Began: A Time Traveler's Guide to the Universe is a non-fiction book by the astronomer Chris Impey that discusses the history of the universe, with chapters ranging from the proximate universe to within an iota of the Big Bang. It was published as a hardcover by W. W. Norton & Company in 2012 and as a paperback in 2013. It is actually the prequel to his 2010 book How it Ends: From You to the Universe, which talks about how everything, from individual humans, to the human species, to the Earth, and finally, the universe, might one day end in the future.
|
||||
|
||||
|
||||
== Summary ==
|
||||
How It Began: A Time Traveler's Guide to the Universe is a non-fiction book by astronomy professor Chris Impey on the origins of everything from the Moon to the universe. The finite speed of light and the vastness of space turn modern large telescopes into time machines and astronomers into armchair time travelers. Looking out in space is looking back in time. Each chapter has vignettes that place the reader in increasingly unfamiliar physical situations that are increasingly unfamiliar. How It Began has an associated web site containing source material on each major topic.
|
||||
The first third of the book deals with the proximate universe. The journey starts with the Moon and its formation from an impact with the infant Earth. Next stop is the outer Solar System and the process by particles of dust growing into planets. The nearest star is the place where star formation is considered, followed by the Orion Nebula, where young stars are forming at a furious rate. The last stop in the nearby universe is the Galactic Center, the center of the Milky Way galaxy, site of a black hole four million times the mass of the Sun.
|
||||
The second third of the book examines the remote universe. Andromeda is seen as it was before humans evolved on the plains of Africa, and galaxies are all seen over time spans that dwarf our existence. The next stop is the massive Coma Cluster of galaxies, a swarm of thousands of galaxies bound by invisible dark matter. This section continues with a visit to galaxies that created their stars long before the Earth formed and it finished with the time when stars first congealed out of gas in the expanding universe, 200 million years after the Big Bang.
|
||||
The last third of the book ventures into the alien universe. The microwave background radiation is a relic of time when stable atoms first formed and the "fog lifted" in the infant universe. Reaching back to the time when the universe was as hot as the core of a star, the Big Bang is manifested in the creation of helium. The last chapters of the book cross into the realm of speculation, with descriptions the tiny asymmetry in the forces of nature that led to a tiny excess of matter over antimatter, the early exponential expansion that flattened space-time, and the idea of the universe as one quantum event among many.
|
||||
|
||||
|
||||
== Reception ==
|
||||
How It Began received strong reviews. Writing in the Wall Street Journal, Manjit Kumar wrote "In clear, enthusiastic and occasionally lyrical prose, Mr. Impey takes the reader on a mind-blowing tour back through eons, stopping along the way to explain the formation of the solar system, the birth and death of stars, white dwarfs, supernovas, spiral galaxies, cosmic inflation, string theory, black holes and M-theory". Maclean's magazine notes "With Impey flexing his creative writing muscles, How It Began could almost be a science fiction novel. But when he describes what we really do know about the universe—and questions we're grappling with—it's even more incredible than anything a science fiction writer could dream up". Science fiction author Ben Bova said "Chris Impey has achieved the near-impossible: an accurate, up-to-date account of 'the state of the universe' that is told in gripping human terms. A great achievement and a 'must-read' book." Kirkus Reviews concluded its review with "An astute tour of the cosmos by a skillful teacher."
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Official website
|
||||
W. W. Norton
|
||||
Amazon Author Page
|
||||
Chris Impey's Website
|
||||
0
data/en.wikipedia.org/wiki/Interstellar
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0
data/en.wikipedia.org/wiki/Interstellar
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38
data/en.wikipedia.org/wiki/Irish_Astronomical_Tract-0.md
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38
data/en.wikipedia.org/wiki/Irish_Astronomical_Tract-0.md
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|
||||
---
|
||||
title: "Irish Astronomical Tract"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Irish_Astronomical_Tract"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:45.786045+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Irish Astronomical Tract is an Irish text that was created in the first half of the 14th century. It was written in Early Modern Irish and is based on a Latin translation of an Arabic work De Scientia Motus Orbis by Masha'allah ibn Atharī (c.740–815 AD). Of its 40 chapters, 27 correspond to chapters in Masha'allah's work and the rest to various classical authors.
|
||||
The name of its author and place of composition is unknown, but it is dated by its reference to the use of spectacles.
|
||||
|
||||
|
||||
== See also ==
|
||||
Ranna an aeir
|
||||
|
||||
|
||||
== Manuscripts ==
|
||||
Stowe, B II 1; Royal Irish Academy, Dublin. Electronically available, with cataloguing information, on the ISOS Project (http://www.isos.dcu.ie).
|
||||
Z 2. 2. 1. (olim V. 3. 1. 38); Marsh's Library, Dublin.
|
||||
23 F 13; Royal Irish Academy, Dublin.
|
||||
British Library L 3. B. 32 (transcript of 'De Scientia Motus Orbis').
|
||||
|
||||
|
||||
== Editions ==
|
||||
J. J. O'Farrelly, Irish Cosmographical Tract: Transcription of the Irish Text with contractions retained [From Stowe B II 1]. Unpublished handwritten manuscript, MS 3A7, 852, Royal Irish Academy Library, 1893.
|
||||
J. J. O'Farrelly, Irish Cosmographical Tract Transcription of the Irish Text, with contractions in Irish extended with reference to Marsh copy and to RIA copy 2. Unpublished handwritten manuscript, MS 3A10, 855, Royal Irish Academy Library, 1893.
|
||||
J. E. Gore, 'An Irish Astronomical Tract', in: 'Knowledge & Scientific News'; February, 1909.
|
||||
Maura Power, Chapters 8, 39, and a portion of chapter 9, with another small fragment of the text, were published with the same English translation of the 1914 edition in Celtia, a pan-Celtic monthly magazine, 11 (London, The Celtic Association) 54–6; 90–92; 101–03.
|
||||
Tomás Ó Concheanainn, The Scribe of the Irish Astronomical Tract in the Royal Irish Academy, B II 1, Celtica 11 (1976) 158–67.
|
||||
Bartholomei Anglici, De proprietatibus rerum liber octavus, Leagan Gaeilge ó thús na 15ú aoise. Ed. by Gearóid Mac Niocaill, Celtica 8 (1968) 201–42; 9 (1971) 266–315.
|
||||
An Irish Corpus Astronomiae (being Manus O'Donnell's seventeenth century version of the Lunario of Geronymo Cortès), ed. by F. W. O'Connell and R. M. Henry, London 1915.
|
||||
John A. Williams, The Irish Astronomical Tract: a case study of scientific terminology in 14th century Irish, M.Phil. Thesis, University of Sydney, 2002. Contains a revised translation. Electronically available at: http://hdl.handle.net/2123/515
|
||||
|
||||
|
||||
== External links ==
|
||||
http://www.ucc.ie/celt/published/G600030/index.html
|
||||
@ -0,0 +1,13 @@
|
||||
---
|
||||
title: "Isaac Asimov's Guide to Earth and Space"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Isaac_Asimov's_Guide_to_Earth_and_Space"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:46.892486+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Guide to Earth and Space (ISBN 0-449-22059-1) is a non-fiction work by American writer Isaac Asimov and published by Random House in 1991. The book differs somewhat in structure from typical literature by presenting its information in the form of answers to a series of questions, presumably posed by the reader. Like many of Asimov's non-fiction pieces, this "Guide" starts with the basics, answering relatively simple (to the modern reader) questions about the Earth - is it flat, does it spin, is it the center of the universe, etc...
|
||||
From there, the questions progress roughly through the evolution of astronomy and discovery to introduce more complex topics, from the orbits of the planets to the formation of stars and the characteristics of quasars and black holes.
|
||||
Many of the concepts discussed in the latter sections of the books can be compared with those presented in Asimov's 1966 work The Universe: From Flat Earth to Quasar; furthermore, they serve in several cases to update the state of the art from the intervening 25 years between publications.
|
||||
63
data/en.wikipedia.org/wiki/Karanapaddhati-0.md
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63
data/en.wikipedia.org/wiki/Karanapaddhati-0.md
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|
||||
---
|
||||
title: "Karanapaddhati"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Karanapaddhati"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:49.309331+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Karanapaddhati is an astronomical treatise in Sanskrit attributed to Puthumana Somayaji, an astronomer-mathematician of the Kerala school of astronomy and mathematics. The period of composition of the work is uncertain. C.M. Whish, a civil servant of the East India Company, brought this work to the attention of European scholars for the first time in a paper published in 1834. The book is divided into ten chapters and is in the form of verses in Sanskrit. The sixth chapter contains series expansions for the value of the mathematical constant π, and expansions for the trigonometric sine, cosine and inverse tangent functions.
|
||||
|
||||
|
||||
== Author and date of Karanapaddhati ==
|
||||
Nothing definite is known about the author of Karanapaddhati. The last verse of the tenth chapter of Karanapaddhati describes the author as a Brahamin residing in a village named Sivapura. Sivapura is an area surrounding the present day Thrissur in Kerala, India.
|
||||
The period in which Somayaji lived is also uncertain. There are several theories in this regard.
|
||||
|
||||
C.M. Whish, the first westerner to write about Karanapaddhati, based on his interpretation that certain words appearing in the final verse of Karanapaddhati denote in katapayadi system the number of days in the Kali Yuga, concluded that the book was completed in 1733 CE. Whish had also claimed that the grandson of the author of the Karanapaddhati was alive and was in his seventieth year at the time of writing his paper.
|
||||
Based on reference to Puthumana Somayaji in a verse in Ganita Sucika Grantha by Govindabhatta, Raja Raja Varma placed the author of Karanapaddhati between 1375 and 1475 CE.
|
||||
An internal study of Karanapaddhati suggests that the work is contemporaneous with or even antedates the Tantrasangraha of Nilakantha Somayaji (1465–1545 CE).
|
||||
|
||||
|
||||
== Synopsis of the book ==
|
||||
A brief account of the contents of the various chapters of the book is presented below.
|
||||
|
||||
Chapter 1 : Rotation and revolutions of the planets in one mahayuga; the number of civil days in a mahayuga; the solar months, lunar months, intercalary months; kalpa and the four yugas and their durations, the details of Kali Yuga, calculation of the Kali era from the Malayalam Era, calculation of Kali days; the true and mean position of planets; simple methods for numerical calculations; computation of the true and mean positions of planets; the details of the orbits of planets; constants to be used for the calculation of various parameters of the different planets.
|
||||
Chapter 2 : Parameters connected with Kali era, the positions of the planets, their angular motions, various parameters connected with Moon.
|
||||
Chapter 3 : Mean center of Moon and various parameters of Moon based on its latitude and longitude, the constants connected with Moon.
|
||||
Chapter 4 : Perigee and apogee of the Mars, corrections to be given at different occasions for the Mars, constants for Mars, Mercury, Jupiter, Venus, Saturn in the respective order, the perigee and apogee of all these planets, their conjunction, their conjunctions possibilities.
|
||||
Chapter 5 : Division of the kalpa based on the revolution of the planets, the number of revolutions during the course of this kalpa, the number of civil and solar days of earth since the beginning of this kalpa, the number and other details of the manvantaras for this kalpa, further details on the four yugas.
|
||||
Chapter 6 : Calculation of the circumference of a circle using variety of methods; the division of the circumference and diameters; calculation of various parameters of a circle and their relations; a circle, the arc, the chord, the arrow, the angles, their relations among a variety of parameters; methods to memorize all these factors using the katapayadi system.
|
||||
Chapter 7 : Epicycles of the Moon and the Sun, the apogee and perigee of the planets; sign calculation based on the zodiacal sign in which the planets are present; the chord connected with rising, setting, the apogee and the perigee; the method for determining the end-time of a month; the chords of the epicycles and apogee for all the planets, their hypotenuse.
|
||||
Chapter 8 : Methods for the determination of the latitude and longitude for various places on the earth; the R-sine and R-cosine of the latitude and longitude, their arc, chord and variety of constants.
|
||||
Chapter 9 : Details of the Alpha aeries sign; calculation of the positions of the planets in correct angular values; calculation of the position of the stars, the parallax connected with latitude and longitude for various planets, Sun, Moon and others stars.
|
||||
Chapter 10 : Shadows of the planets and calculation of various parameters connected with the shadows; calculation of the precision of the planetary positions.
|
||||
|
||||
|
||||
== Infinite series expressions ==
|
||||
The sixth chapter of Karanapaddhati is mathematically very interesting. It contains infinite series expressions for the constant π and infinite series expansions for the trigonometric functions. These series also appear in Tantrasangraha and their proofs are found in Yuktibhāṣā.
|
||||
|
||||
|
||||
=== Series expressions for π ===
|
||||
Series 1
|
||||
|
||||
Series 2
|
||||
|
||||
Series 3
|
||||
|
||||
|
||||
=== Series expansions of trigonometric functions ===
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
Venketeswara Pai R, K Ramasubramanian, M S Sriram and M D Srinivas, Karanapaddhati of Putumana Somayaji, Translation with detailed Mathematical notes, Jointly Published by HBA (2017) and Springer (2018).
|
||||
|
||||
|
||||
== Further references ==
|
||||
Open Library reference to Karana-paddhati with two commentaries.[1]
|
||||
Bag, Amulya Kumar (1976). "Madhava's sine and cosine series" (PDF). Indian Journal of History of Science. 11 (1). Indian National Academy of Science: 54–57. Archived from the original (PDF) on 14 February 2010. Retrieved 17 December 2009.
|
||||
Bag, Amulya Kumar (1975). "The method of integral solutions of indeterminate equations of the type BY=AX ± C in ancient and medieval India" (PDF). Indian Journal of History of Science. 12 (1). Indian National Academy of Science: 1–16. Retrieved 12 January 2010.
|
||||
P.K. Koru, ed. (1953). Karanapaddhati of Puthumana Somayaji. Cherpu, Kerala, India: Astro Printing and Publishing Company.
|
||||
Indian National Science Academy has started a project in 2007–08 titled "A Critical Study of Karana-paddhati of Putumana Somayaji and Preparation of English Translation with Mathematical Notes" by Dr. K Ramasubramanian, Assistant Professor, Dept. of History, Indian Institute of Technology, Powai, Mumbai 400076.[2] (Retrieved on 13 January 2010)
|
||||
16
data/en.wikipedia.org/wiki/Khandakhadyaka-0.md
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16
data/en.wikipedia.org/wiki/Khandakhadyaka-0.md
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|
||||
---
|
||||
title: "Khandakhadyaka"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Khandakhadyaka"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:50.539050+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Khaṇḍakhādyaka (meaning "edible bite; morsel of food") is a Sanskrit-language astronomical treatise written by Indian mathematician and astronomer Brahmagupta in 665 CE. The treatise contains eight chapters covering such topics as the longitudes of the planets, diurnal rotation, lunar and solar eclipses, risings and settings, the moon's crescent and conjunctions of the planets. The treatise also includes an appendix which in some versions has only one chapter, and in other has three.
|
||||
The treatise was written as a response to Aryabhata's Ardharatrikapaksa.
|
||||
Ama-raja alias Ama-sharman (c. 1200) of Anandapura wrote a commentary titled Vasana-bhashya (IAST: Vāsanābhāṣya) on Khanda-khadyaka during the Chaulukya period. This work refers to earlier commentaries on Bhaskara's text, including those by Lalla (c. 748 CE), Prthudaka-svamin (c. 864), Utpala, and Someshvara (c. 1040). Khandakhadyaka was known to al-Biruni.
|
||||
|
||||
|
||||
== References ==
|
||||
63
data/en.wikipedia.org/wiki/Kriyakramakari-0.md
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63
data/en.wikipedia.org/wiki/Kriyakramakari-0.md
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|
||||
---
|
||||
title: "Kriyakramakari"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Kriyakramakari"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:51.711586+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Kriyakramakari (Kriyā-kramakarī) is an elaborate commentary in Sanskrit written by Sankara Variar and Narayana, two astronomer-mathematicians belonging to the Kerala school of astronomy and mathematics, on Bhaskara II's well-known textbook on mathematics Lilavati. Kriyakramakari ('Operational Techniques'), along with Yuktibhasa of Jyeshthadeva, is one of the main sources of information about the work and contributions of Sangamagrama Madhava, the founder of Kerala school of astronomy and mathematics. Also the quotations given in this treatise throw much light on the contributions of several mathematicians and astronomers who had flourished in an earlier era. There are several quotations ascribed to Govindasvami a 9th-century astronomer from Kerala.
|
||||
Sankara Variar (c. 1500 - 1560), the first author of Kriyakramakari, was a pupil of Nilakantha Somayaji and a temple-assistant by profession. He was a prominent member of the Kerala school of astronomy and mathematics. His works include Yukti-dipika an extensive commentary on Tantrasangraha by Nilakantha Somayaji. Narayana (c. 1540–1610), the second author, was a Namputiri Brahmin belonging to the Mahishamangalam family in Puruvanagrama (Peruvanam in modern-day Thrissur District in Kerala).
|
||||
Sankara Variar wrote his commentary of Lilavati up to stanza 199. Variar completed this by about 1540 when he stopped writing due to other preoccupations. Sometimes after his death, Narayana completed the commentary on the remaining stanzas in Lilavati.
|
||||
|
||||
|
||||
== On the computation of π ==
|
||||
As per K.V. Sarma's critical edition of Lilavati based on Kriyakramakari, stanza 199 of Lilavati reads as follows (Harvard-Kyoto convention is used for the transcription of the Indian characters):
|
||||
|
||||
vyAse bha-nanda-agni-hate vibhakte kha-bANa-sUryais paridhis sas sUkSmas/
|
||||
dvAviMzati-ghne vihRte atha zailais sthUlas atha-vA syAt vyavahAra-yogyas//
|
||||
This could be translated as follows;
|
||||
|
||||
"Multiply the diameter by 3927 and divide the product by 1250; this gives the more precise circumference. Or, multiply the diameter by 22 and divide the product by 7; this gives the approximate circumference which answers for common operations."
|
||||
Taking this verse as a starting point and commenting on it, Sanakara Variar in his Kriyakrakari explicated the full details of the contributions of Sangamagrama Madhava towards obtaining accurate values of π. Sankara Variar commented like this:
|
||||
|
||||
"The teacher Madhava also mentioned a value of the circumference closer [to the true value] than that: "Gods [thirty-three], eyes [two], elephants [eight], serpents [eight], fires [three], three, qualities [three], Vedas [four], naksatras [twentyseven], elephants [eight], arms [two] (2,827,433,388,233)—the wise said that this is the measure of the circumference when the diameter of a circle is nine nikharva [10^11]." Sankara Variar says here that Madhava's value 2,827,433,388,233 / 900,000,000,000 is more accurate than "that", that is, more accurate than the traditional value for π."
|
||||
Sankara Variar then cites a set of four verses by Madhava that prescribe a geometric method for computing the value of the circumference of a circle. This technique involves calculating the perimeters of successive regular circumscribed polygons, beginning with a square.
|
||||
|
||||
|
||||
=== An infinite series for π ===
|
||||
Sankara Variar then describes an easier method due to Madhava to compute the value of π.
|
||||
|
||||
"An easier way to get the circumference is mentioned by him (Madhava). That is to say:
|
||||
Add or subtract alternately the diameter multiplied by four and divided in order by the odd numbers like three, five, etc., to or from the diameter multiplied by four and divided by one.
|
||||
Assuming that division is completed by dividing by an odd number, whatever is the even number above [next to] that [odd number], half of that is the multiplier of the last [term].
|
||||
The square of that [even number] increased by 1 is the divisor of the diameter multiplied by 4 as before. The result from these two (the multiplier and the divisor) is added when [the previous term is] negative, when positive subtracted.
|
||||
The result is an accurate circumference. If division is repeated many times, it will become very accurate."
|
||||
To translate these verses into modern mathematical notations, let C be the circumference and D the diameter of a circle. Then Madhava's easier method to find C reduces to the following expression for C:
|
||||
|
||||
C = 4D/1 - 4D/3 + 4D/5 - 4D/7 + ...
|
||||
This is essentially the series known as the Gregory-Leibniz series for π. After stating this series, Sankara Variar follows it up with a description of an elaborate geometrical rationale for the derivation of the series.
|
||||
|
||||
|
||||
=== An infinite series for arctangent ===
|
||||
The theory is further developed in Kriyakramakari. It takes up the problem of deriving a similar series for the computation of an arbitrary arc of a circle. This yields the infinite series expansion of the arctangent function. This result is also ascribed to Madhava.
|
||||
|
||||
"Now, by just the same argument, the determination of the arc of a desired Sine can be [made]. That is as [follows]:
|
||||
The first result is the product of the desired Sine and the radius divided by the Cosine. When one has made the square of the Sine the multiplier and the square of the Cosine the divisor,
|
||||
now a group of results is to be determined from the [previous] results beginning with the first. When these are divided in order by the odd numbers 1, 3, and so forth,
|
||||
and when one has subtracted the sum of the even[-numbered results] from the sum of the odd ones, [that] should be the arc. Here, the smaller of the Sine and Cosine is required to be considered as the desired [Sine].
|
||||
Otherwise there would be no termination of the results even if repeatedly [computed]."
|
||||
The above formulas state that if for an arbitrary arc θ of a circle of radius R the sine and cosine are known and if we assume that sin θ < cos θ, then we have:
|
||||
|
||||
θ = (R sin θ)/(1 cos θ) − (R sin3 θ)/(3 cos3 θ) + (R sin5 θ)/(5 cos5 θ) − (R sin7 θ)/(7 cos7 θ)+ . . .
|
||||
|
||||
|
||||
== See also ==
|
||||
Kerala school of astronomy and mathematics
|
||||
Lilavati
|
||||
Sankara Variar
|
||||
|
||||
|
||||
== References ==
|
||||
@ -4,7 +4,7 @@ chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/List_of_Indian_astronomical_treatises"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T07:53:27.657837+00:00"
|
||||
date_saved: "2026-05-05T08:33:52.919488+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
|
||||
37
data/en.wikipedia.org/wiki/Mad_About_Physics-0.md
Normal file
37
data/en.wikipedia.org/wiki/Mad_About_Physics-0.md
Normal file
@ -0,0 +1,37 @@
|
||||
---
|
||||
title: "Mad About Physics"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Mad_About_Physics"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:55.250372+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Mad about Physics: Brainteasers, Paradoxes, and Curiosities is a book revolving around physics puzzles first released in 2001 and published by Wiley.
|
||||
It covers mechanics, electricity, magnetism and optics, as well as the physics of sports, space exploration and astronomy. It has been translated into seven languages, including German, Greek, Japanese and Chinese. The book is in its 10th reprinting as of 2013.
|
||||
|
||||
|
||||
== Content ==
|
||||
The book contains around 400 questions, along with many marginalia, jokes, anecdotes, and scientific facts. It also contains some quotations from Albert Einstein and the cartoon character Bugs Bunny congruent to the theme of the book.
|
||||
|
||||
|
||||
== Reception and Reviews ==
|
||||
Peter Ford, a physicist at the University of Bath in the UK, called Mad about Physics "an interesting new book." He wrote that "many of its problems will be useful for teachers, both at senior level in schools and at universities, for discussion with students in small groups. Such tutorials should be used to encourage students to start talking about physics and 'thinking like a physicist.'"
|
||||
Carol Ryback wrote, "Here's a quick fix for those brain-teasing inquiries that stick in your mind like an old song. While not limited to astronomy-related trivia, 'Mad about Physics"—like a top-40 countdown on the radio – has an allure that makes you want more."
|
||||
|
||||
|
||||
== Awards ==
|
||||
In 2002, Mad about Physics was selected by the New York Public Library as "one of the best" titles of the year 2001 in the teen books and media category.
|
||||
|
||||
|
||||
== See also ==
|
||||
Cognitive dissonance
|
||||
Paradox
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
New York Public Library (link to NYPL's list of best 2001 titles in teen books and media)
|
||||
27
data/en.wikipedia.org/wiki/Man_and_the_Planets-0.md
Normal file
27
data/en.wikipedia.org/wiki/Man_and_the_Planets-0.md
Normal file
@ -0,0 +1,27 @@
|
||||
---
|
||||
title: "Man and the Planets"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Man_and_the_Planets"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:56.410348+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Man and the Planets: The Resources of the Solar System is a book written by Duncan Lunan.
|
||||
|
||||
|
||||
== Contents ==
|
||||
Man and the Planets is a book published in 1983 which studies the resources of each planet in the Solar System.
|
||||
|
||||
|
||||
== Reception ==
|
||||
Dave Langford reviewed Man and the Planets for White Dwarf #41, and stated that "Lunan's enthusiasm is infectious, his research exhaustive; he's absolutely committed to the Dream of Space and has no time for the many equally learned people who fear that the expense of opening up this new frontier would wreck our world economy long before producing tangible benefits."
|
||||
|
||||
|
||||
== Reviews ==
|
||||
Review by Tom Easton (1983) in Analog Science Fiction/Science Fact, November 1983
|
||||
Space Voyager
|
||||
|
||||
|
||||
== References ==
|
||||
28
data/en.wikipedia.org/wiki/Mars_and_the_Mind_of_Man-0.md
Normal file
28
data/en.wikipedia.org/wiki/Mars_and_the_Mind_of_Man-0.md
Normal file
@ -0,0 +1,28 @@
|
||||
---
|
||||
title: "Mars and the Mind of Man"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Mars_and_the_Mind_of_Man"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:57.631828+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Mars and the Mind of Man is a non-fiction book chronicling a public symposium at the California Institute of Technology on November 12, 1971. The panel consisted of five luminaries of science, literature, and journalism: Ray Bradbury; Arthur C. Clarke; Bruce C. Murray; Carl Sagan and Walter Sullivan. These five are the authors of this book. The symposium occurred shortly before the Mariner 9 space probe entered orbit around Mars. The book was published in 1973 by Harper and Row of New York.
|
||||
|
||||
|
||||
== About the book ==
|
||||
The book is record of the November 1971 discussion undertaken by the five distinguished panel members mentioned above. This conversation earmarked Mariner 9's Martian arrival as an important moment. Also, the symposium hailed a remarkable milestone. Mariner 9 was to be the first earth spacecraft to be inserted into the orbit of another distinct planet. As noted, "...Caltech Planetary Science professor Bruce Murray summoned [the] formidable panel of thinkers to discuss the implications of this historic event." The discussion's moderator was Walter Sullivan, the New York Times science editor. Varied perspectives were offered on the Mariner 9 mission; the red planet itself; the interrelationship of humans and the Cosmos; prioritizing the exploration of space; and contemplating civilization's future. Also included in the book are the first photos sent to Earth by the Mariner 9 space probe and "...a selection of 'afterthoughts' by the panelists, looking back on the historic achievement."
|
||||
|
||||
|
||||
== Bradbury's poem ==
|
||||
On several minutes of archived footage released by NASA, Bradbury is shown engaging in witty banter with other panel members at the November 1971 panel discussion. The film segment was issued in 2012 to honor a newly named site on the red planet,"Bradbury Landing". Also the released footage shows Bradbury reading his poem "If Only We Had Taller Been" (poem begins at 2:20) At the time, this was "...one of several unpublished poems he shared at the event." Before reading the poem, Bradbury is recorded saying "I don’t know what in the hell I’m doing here. I’m the least scientific of all the people up on the platform here today...I was hoping, that during the last few days, as we got closer to Mars and the dust cleared, that we’d see a lot of Martians standing there with huge signs saying, ‘Bradbury was right,’”
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
ISBN 978-0-06-010443-6
|
||||
Wilford, John Noble (30 August 2013). "Bruce C. Murray, Who Helped Earth Learn of Mars, Dies at 81". The New York Times.
|
||||
Exploration of the Planets. A short 1971 NASA film. US National Archives. YouTube.
|
||||
32
data/en.wikipedia.org/wiki/Mirror_Earth-0.md
Normal file
32
data/en.wikipedia.org/wiki/Mirror_Earth-0.md
Normal file
@ -0,0 +1,32 @@
|
||||
---
|
||||
title: "Mirror Earth"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Mirror_Earth"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:58.824393+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Mirror Earth: The Search for Our Planet's Twin is a 2012 non-fiction book by Michael D. Lemonick. It discusses the work of "exoplaneteers"—defining the term as a group of scientists looking through various other planetary systems to detect alternate planets that are suitable for possible life.
|
||||
Lemonick has served as a science journalist for Time as well as an author of multiple other books such as Echo of the Big Bang. Positive reviews for his latest book appeared in publications such as Kirkus Reviews, Publishers Weekly, and The Wall Street Journal.
|
||||
|
||||
|
||||
== Contents ==
|
||||
Lemonick describes the diverse methods with which astronomers work to try to find Earth-like planets. Some evaluate images of clumps of stars, tens of thousands of them together, in order to pick up slight reductions in brightness caused by planets passing in front of their host stars, some examine individual stars for planetary gravitation influences, and others focus on stars considerably smaller than the Earth's sun to pick up more easily detectable planetary information.
|
||||
|
||||
|
||||
== Reviews ==
|
||||
The Wall Street Journal ran a supportive review by Mike Brown, a professor of planetary astronomy at Caltech. He commented that "Lemonick's interactions with these scientists is the overwhelming strength of this very human story". Brown also wrote, "By the end of this engaging book, the discovery of such a twin feels so close that you can almost taste the slightly alien water on the tip of your tongue."
|
||||
Publishers Weekly praised the book, stating that it "offers readers an informal and accessible view into the work" of the 'exoplaneteers'. Kirkus Reviews ran a positive review as well. The publication described the book as a "solid overview of the cutting edge of astronomy and of the new breed of astronomers who are exploring it."
|
||||
|
||||
|
||||
== See also ==
|
||||
|
||||
2012 in literature
|
||||
Extrasolar planet
|
||||
List of nearest terrestrial exoplanet candidates
|
||||
Planetary habitability
|
||||
|
||||
|
||||
== References ==
|
||||
22
data/en.wikipedia.org/wiki/Mysterium_Cosmographicum-0.md
Normal file
22
data/en.wikipedia.org/wiki/Mysterium_Cosmographicum-0.md
Normal file
@ -0,0 +1,22 @@
|
||||
---
|
||||
title: "Mysterium Cosmographicum"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/Mysterium_Cosmographicum"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:59.923834+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
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, published at Tübingen in late 1596 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 solids, enclosed within a sphere that represented the orbit of Saturn.
|
||||
This book explains Kepler's cosmological theory, based on the Copernican system, in which the five Platonic solids dictate the structure of the universe and reflect God's plan through geometry. This was virtually the first attempt since Copernicus to say that the theory of heliocentrism is physically true. Thomas Digges 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.
|
||||
|
||||
== Shapes and the planets ==
|
||||
|
||||
Johannes Kepler's first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery), was a defence of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac: he realized that regular polygons 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. 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, Earth, Mars, Jupiter, and Saturn. By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, and cube—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: 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’s geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of the Trinity, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between to the Holy Spirit. 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, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible exegesis and the addition of a simpler, more understandable description of the Copernican system (the Narratio prima 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.
|
||||
35
data/en.wikipedia.org/wiki/Mysterium_Cosmographicum-1.md
Normal file
35
data/en.wikipedia.org/wiki/Mysterium_Cosmographicum-1.md
Normal file
@ -0,0 +1,35 @@
|
||||
---
|
||||
title: "Mysterium Cosmographicum"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/Mysterium_Cosmographicum"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:59.923834+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
== 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 ==
|
||||
Kepler corresponded with and provided courtesy book copies to a number of astronomers around the time of publication, including Galileo Galilei, Tycho Brahe, Reimarus Ursus, and Georg Limnaeus. In response to Mysterium Cosmographicum, the Danish astronomer Tycho Brahe (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 Austrian 10 euro Johannes Kepler silver commemorative coin minted in 2002.
|
||||
|
||||
== See also ==
|
||||
Golden ratio § History
|
||||
Titius–Bode law
|
||||
|
||||
== Notes ==
|
||||
|
||||
== References ==
|
||||
Citations
|
||||
|
||||
== Further reading ==
|
||||
|
||||
== External links ==
|
||||
Media related to Mysterium Cosmographicum at Wikimedia Commons
|
||||
Mysterium cosmographicum by Johannes Kepler, 1596 edition, in Latin, full text scan, 181 pp.
|
||||
George W. Hart, "Johannes Kepler's polyhedra"
|
||||
38
data/en.wikipedia.org/wiki/Narratio_Prima-0.md
Normal file
38
data/en.wikipedia.org/wiki/Narratio_Prima-0.md
Normal file
@ -0,0 +1,38 @@
|
||||
---
|
||||
title: "Narratio Prima"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Narratio_Prima"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:01.073879+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
De libris revolutionum Copernici narratio prima, usually referred to as Narratio Prima (Latin: First Account), is an abstract of Nicolaus Copernicus' heliocentric theory, written by Georg Joachim Rheticus in 1540. It is an introduction to Copernicus's major work, De revolutionibus orbium coelestium, published in 1543, largely due to Rheticus's instigation. Narratio Prima is the first printed publication of Copernicus's theory.
|
||||
|
||||
|
||||
== History ==
|
||||
Copernicus, born in 1473 and already well over 60 years old, had never published any astronomical work, as his only publication had been his translation of poems of Theophylact Simocatta, printed in 1509 by Johann Haller. At the same time, he had distributed his ideas among friends, with manuscripts called Commentariolus. In the 1530s, he was urged to publish by many, yet still hesitated when in 1539, Rheticus arrived in Frauenburg (Frombork) to become Copernicus' first and only pupil. Philipp Melanchthon had arranged for Rheticus to visit several astronomers and study with them.
|
||||
In September 1539 Rheticus went to Danzig (Gdańsk) to visit the mayor who gave Rheticus some financial assistance to publish the Narratio Prima. This Narratio Prima, published by Franz Rhode in Danzig in 1540, is still considered to be the best introduction to Copernicus' De revolutionibus orbium coelestium. As the full title states, the Narratio was published as an open letter to Johannes Schöner of Nuremberg (Nürnberg). It was bundled together with the Encomium Prussiae which praised the spirit of humanism in Prussia.
|
||||
During his two-year stay in Prussia, Rheticus published works of his own, and in cooperation with Copernicus, in 1542 a treatise on trigonometry which was a preview to the second book of De revolutionibus. Under strong pressure from Rheticus, and having seen the favorable first general reception of the Narratio Prima, Copernicus finally agreed to give the book to his close friend, bishop Tiedemann Giese, to be delivered to Nuremberg for printing by Johannes Petreius under Rheticus's supervision.
|
||||
Later editions of Narratio Prima were printed in Basel, in 1541 by Robert Winter, and in 1566 by Henricus Petrus in connection with the second edition of De revolutionibus. In 1597 when Johannes Kepler's first book Mysterium Cosmographicum was prepared for publication in Tübingen, his advisor Michael Maestlin decided to include Rheticus' Narratio Prima following Kepler's text, as a supplementary explanation of heliocentric theory.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Bibliography ==
|
||||
Rheticus: Narratio prima de libris revolutionum Copernici, Danzig 1540
|
||||
Richard S. Westfall, Indiana University. Rheticus, George Joachim. "Catalog of the Scientific Community of the 16th and 17th Centuries," The Galileo Project.
|
||||
Dennis Danielson (2006). The First Copernican: Georg Joachim Rheticus and the Rise of the Copernican Revolution. Walker & Company, New York. ISBN 0-8027-1530-3
|
||||
Karl Heinz Burmeister: Georg Joachim Rhetikus 1514–1574. Bd. I–III. Guido Pressler Verlag, Wiesbaden 1967.
|
||||
Stefan Deschauer: Die Arithmetik-Vorlesung des Georg Joachim Rheticus, Wittenberg 1536: eine kommentierte Edition der Handschrift X-278 (8) der Estnischen Akademischen Bibliothek; Augsburg: Rauner, 2003; ISBN 3-936905-00-2
|
||||
R. Hooykaas: G. J. Rheticus’ Treatise on holy scripture and the motion of the earth / with transl., annotations, commentary and additional chapters on Ramus-Rheticus and the development of the problem before 1650; Amsterdam: North-Holland, 1984
|
||||
|
||||
|
||||
== External links ==
|
||||
|
||||
O'Connor, John J.; Robertson, Edmund F., "Narratio Prima", MacTutor History of Mathematics Archive, University of St Andrews
|
||||
Scienceworld article on Rheticus
|
||||
Narratio Prima (1540) – scanned edition at Linda Hall Library
|
||||
in English
|
||||
56
data/en.wikipedia.org/wiki/Newcomb's_Tables_of_the_Sun-0.md
Normal file
56
data/en.wikipedia.org/wiki/Newcomb's_Tables_of_the_Sun-0.md
Normal file
@ -0,0 +1,56 @@
|
||||
---
|
||||
title: "Newcomb's Tables of the Sun"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Newcomb's_Tables_of_the_Sun"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:02.228981+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Newcomb's Tables of the Sun (full title Tables of the Motion of the Earth on its Axis and Around the Sun) is a work by the American astronomer and mathematician Simon Newcomb, published in volume VI of the serial publication Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac. The work contains Newcomb's mathematical development of the position of the Earth in the Solar System, which is constructed from classical celestial mechanics as well as centuries of astronomical measurements. The bulk of the work, however, is a collection of tabulated precomputed values that provide the position of the sun at any point in time.
|
||||
Newcomb's Tables were the basis for practically all ephemerides of the Sun published from 1900 through 1983, including the annual almanacs of the U.S. Naval Observatory and the Royal Greenwich Observatory. The physical tables themselves were used by the ephemerides from 1900 to 1959, computerized versions were used from 1960 to 1980, and evaluations of the Newcomb's theories were used from 1981 to 1983. The tables are seldom used now; since the Astronomical Almanac for 1984 they have been superseded by more accurate numerically-integrated ephemerides developed at the Jet Propulsion Laboratory, based on much more accurate observations than were available to Newcomb. Also, the tables did not account for the effects of general relativity which was unknown at the time. Nevertheless, his tabulated values remain accurate to within a few seconds of arc to this day.
|
||||
He developed similar formulas and tables for the planets Mercury, Venus, Mars, Uranus and Neptune; those of the inner planets have proved to be the most accurate.
|
||||
|
||||
|
||||
== Expressions ==
|
||||
Certain expressions have been cited in a number of other works over a long period, and are listed below. Newcomb assigns the symbol T to the time since "1900, Jan. 0, Greenwich Mean noon", measured in Julian centuries of 36,525 days.
|
||||
|
||||
|
||||
=== Sun's geometric mean longitude ===
|
||||
The Sun's geometric mean longitude, freed from aberration is given as
|
||||
|
||||
L = 279° 41' 48.04" + 129 602 768.13" T + 1.089" T2
|
||||
Authors citing this expression include Borkowski (p. 12) and the Nautical Almanac Offices of the United Kingdom and United States (p. 98).
|
||||
|
||||
|
||||
=== Fictitious mean Sun ===
|
||||
Newcomb gives the Right ascension of the fictitious mean Sun, affected by aberration (which is used in finding mean solar time) as
|
||||
|
||||
τ = 18h 38m 45.836s + 8640184.542s T + 0.0929s T2
|
||||
Authors citing this expression include McCarthy & Seidelmann (p. 13) and the Nautical Almanac Offices of the United Kingdom and United States (p. 73).
|
||||
|
||||
|
||||
== Discontinuance ==
|
||||
By 1970 the astronomical community recognized the need for improved ephemerides, which are used to prepare national almanacs. The changes required were
|
||||
|
||||
a new fundamental catalog of stars to replace FK4
|
||||
the use of improved values of astronomical constants that had been discovered
|
||||
a better definition and practical realization of ephemeris time which would take advantage of atomic time
|
||||
a new epoch to replace 1950.0
|
||||
It was decided to introduce as many changes as possible at one time in a consistent system, and the new system would go into effect for the 1984 edition of the ephemerides. "The majority of the resolutions were prepared and adopted by the General Assembly of the IAU at the 1976 and 1979 meetings."
|
||||
The new fundamental ephemeris was prepared by the Jet Propulsion Laboratory and named DE200/LE200. It uses numerical integration.
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Works cited ==
|
||||
Borkowski, K. M. "The Tropical Year and Solar Calendar". Journal of the Royal Astronomical Society of Canada 85 no. 3 (1990): 121–130.
|
||||
McCarthy, D. D. & Seidelmann, P. K. TIME from Earth Rotation to Atomic Physics. (Weinheim: Wiley-VCH, 2009).
|
||||
[U.S.] Nautical Almanac Office and HM Nautical Almanac Office. "The Improved IAU System", a supplement bound with The Astronomical Almanac for the Year 1984. (Washington and London: U.S. Government Printing Office and Her Majesty's Stationery Office, 1983).
|
||||
Nautical Almanac Offices of the United Kingdom and United States of America. Explanatory Supplement to the Ephemeris. (London: Her Majesty's Stationery Office, 1961).
|
||||
Newcomb, Simon. Tables of the Four Inner Planets, 2nd ed. (Washington: Bureau of Equipment, Navy Dept., 1898).
|
||||
@ -0,0 +1,96 @@
|
||||
---
|
||||
title: "On Sizes and Distances (Hipparchus)"
|
||||
chunk: 1/3
|
||||
source: "https://en.wikipedia.org/wiki/On_Sizes_and_Distances_(Hipparchus)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:03.519801+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
On Sizes and Distances (of the Sun and Moon) (Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Peri megethon kai apostematon) is a text by the ancient Greek astronomer Hipparchus (c. 190 – c. 120 BC) in which approximations are made for the radii of the Sun and the Moon as well as their distances from the Earth. It is not extant, but some of its contents have been preserved in the works of Ptolemy and his commentator Pappus of Alexandria. Several modern historians have attempted to reconstruct the methods of Hipparchus using the available texts.
|
||||
|
||||
== Sources ==
|
||||
Most of what is known about Hipparchus' text comes from two ancient sources: Ptolemy and Pappus. The work is also mentioned by Theon of Smyrna and others, but their accounts have proven less useful in reconstructing the procedures of Hipparchus.
|
||||
|
||||
=== Ptolemy ===
|
||||
In Almagest V, 11, Ptolemy writes:
|
||||
|
||||
Now Hipparchus made such an examination principally from the sun. Since from other properties of the sun and moon (of which a study will be made below) it follows that if the distance of one of the two luminaries is given, the distance of the other is also given, he tries by conjecturing the distance of the sun to demonstrate the distance of the moon. First, he assumes the sun to show the least perceptible parallax to find its distance. After this, he makes use of the solar eclipse adduced by him, first as if the sun shows no perceptible parallax, and for exactly that reason the ratios of the moon's distances appeared different to him for each of the hypotheses he set out. But with respect to the sun, not only the amount of its parallax, but also whether it shows any parallax at all is altogether doubtful.
|
||||
This passage gives a general outline of what Hipparchus did, but provides no details. Ptolemy clearly did not agree with the methods employed by Hipparchus, and thus did not go into any detail.
|
||||
|
||||
=== Pappus of Alexandria ===
|
||||
The works of Hipparchus were still extant when Pappus wrote his commentary on the Almagest in the 4th century. He fills in some of the details that Ptolemy omits:
|
||||
|
||||
Now, Hipparchus made such an examination principally from the sun, and not accurately. For since the moon in the syzygies and near greatest distance appears equal to the sun, and since the size of the diameters of the sun and moon is given (of which a study will be made below), it follows that if the distance of one of the two luminaries is given, the distance of the other is also given, as in Theorem 12, if the distance of the moon is given and the diameters of the sun and moon, the distance of the sun is given. Hipparchus tries by conjecturing the parallax and the distance of the sun to demonstrate the distance of the moon, but with respect to the sun, not only the amount of its parallax, but also whether it shows any parallax at all is altogether doubtful. For in this way Hipparchus was in doubt about the sun, not only about the amount of its parallax but also about whether it shows any parallax at all. In the first book "On Sizes and Distances" it is assumed that the earth has the ratio of a point and center to the sun. And by means of the eclipse adduced by him...
|
||||
Then later,
|
||||
|
||||
For in Book 1 of "On Sizes and Distances" he takes the following observation: an eclipse of the sun, which in the regions around the Hellespont was an exact eclipse of the whole solar disc, such that no part of it was visible, but at Alexandria by Egypt approximately four-fifths of it was eclipsed. By means of this he shows in Book 1 that, in units of which the radius of the earth is one, the least distance of the moon is 71, and the greatest 83. Hence the mean is 77... Then again he himself in Book 2 of "On Sizes and Distances" shows from many considerations that, in units of which the radius of the earth is one, the least distance of the moon is 62, and the mean 671⁄3, and the distance of the sun 490. It is clear that the greatest distance of the moon is 722⁄3.
|
||||
This passage provides enough details to make a reconstruction feasible. In particular, it makes clear that there were two separate procedures, and it gives the precise results of each. It provides clues with which to identify the eclipse, and says that Hipparchus used a formula "as in Theorem 12," a theorem of Ptolemy's which is extant.
|
||||
|
||||
== Modern reconstructions ==
|
||||
Several historians of science have attempted to reconstruct the calculations involved in On Sizes and Distances. The first attempt was made by Friedrich Hultsch in 1900, but it was later rejected by Noel Swerdlow in 1969. G. J. Toomer expanded on his efforts in 1974.
|
||||
|
||||
=== Hultsch ===
|
||||
Friedrich Hultsch determined in a 1900 paper that the Pappus source had been miscopied, and that the actual distance to the Sun, as calculated by Hipparchus, had been 2490 Earth radii (not 490). As in English, there is only a single character difference between these two results in Greek.
|
||||
His analysis was based on a text by Theon of Smyrna which states that Hipparchus found the Sun to be 1880 times the size of the Earth, and the Earth 27 times the size of the Moon. Assuming that this refers to volumes, it follows that
|
||||
|
||||
|
||||
|
||||
|
||||
s
|
||||
=
|
||||
|
||||
|
||||
1880
|
||||
|
||||
3
|
||||
|
||||
|
||||
|
||||
≈
|
||||
12
|
||||
+
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
|
||||
|
||||
{\displaystyle s={\sqrt[{3}]{1880}}\approx 12+1/3}
|
||||
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
=
|
||||
|
||||
|
||||
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
27
|
||||
|
||||
|
||||
3
|
||||
|
||||
|
||||
|
||||
=
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
|
||||
|
||||
{\displaystyle \ell ={\sqrt[{3}]{1/27}}=1/3}
|
||||
|
||||
|
||||
Assuming that the Sun and Moon have the same apparent size in the sky, and that the Moon is 671⁄3 Earth radii distant, it follows that
|
||||
@ -0,0 +1,662 @@
|
||||
---
|
||||
title: "On Sizes and Distances (Hipparchus)"
|
||||
chunk: 2/3
|
||||
source: "https://en.wikipedia.org/wiki/On_Sizes_and_Distances_(Hipparchus)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:03.519801+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
|
||||
|
||||
|
||||
S
|
||||
=
|
||||
|
||||
|
||||
s
|
||||
ℓ
|
||||
|
||||
|
||||
L
|
||||
≈
|
||||
|
||||
|
||||
|
||||
12
|
||||
+
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
|
||||
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
|
||||
|
||||
|
||||
(
|
||||
67
|
||||
+
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
)
|
||||
=
|
||||
2491
|
||||
+
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
3
|
||||
≈
|
||||
2490
|
||||
|
||||
|
||||
{\displaystyle S={\frac {s}{\ell }}L\approx {\frac {12+1/3}{1/3}}(67+1/3)=2491+1/3\approx 2490}
|
||||
|
||||
|
||||
This result was generally accepted for the next seventy years, until Noel Swerdlow reinvestigated the case.
|
||||
|
||||
=== Book 2 reconstruction (Swerdlow) ===
|
||||
|
||||
Swerdlow determined that Hipparchus relates the distances to the Sun and Moon using a construction found in Ptolemy. It would not be surprising if this calculation had been originally developed by Hipparchus himself, as he was a primary source for the Almagest.
|
||||
Using this calculation, Swerdlow was able to relate the two results of Hipparchus (671⁄3 for the Moon and 490 for the Sun). Obtaining this relationship exactly requires following a very precise set of approximations.
|
||||
Using simple trigonometric identities gives
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
=
|
||||
L
|
||||
tan
|
||||
|
||||
θ
|
||||
≈
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \ell =L\tan \theta \approx L\sin \theta }
|
||||
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
h
|
||||
=
|
||||
|
||||
|
||||
|
||||
tan
|
||||
|
||||
φ
|
||||
|
||||
|
||||
tan
|
||||
|
||||
θ
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
≈
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
ℓ
|
||||
≈
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle h={\frac {\tan \varphi }{\tan \theta }}\ell \approx {\frac {\varphi }{\theta }}\ell \approx {\frac {\varphi }{\theta }}L\sin \theta }
|
||||
|
||||
|
||||
By parallel lines and taking t = 1, we get
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
+
|
||||
x
|
||||
=
|
||||
t
|
||||
+
|
||||
(
|
||||
t
|
||||
−
|
||||
h
|
||||
)
|
||||
=
|
||||
2
|
||||
t
|
||||
−
|
||||
h
|
||||
⇒
|
||||
x
|
||||
≈
|
||||
2
|
||||
−
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \ell +x=t+(t-h)=2t-h\Rightarrow x\approx 2-\left({\frac {\varphi }{\theta }}+1\right)L\sin \theta }
|
||||
|
||||
|
||||
By similarity of triangles,
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
t
|
||||
x
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
S
|
||||
|
||||
S
|
||||
−
|
||||
L
|
||||
|
||||
|
||||
|
||||
⇒
|
||||
S
|
||||
=
|
||||
|
||||
|
||||
L
|
||||
|
||||
1
|
||||
−
|
||||
x
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {t}{x}}={\frac {S}{S-L}}\Rightarrow S={\frac {L}{1-x}}}
|
||||
|
||||
|
||||
Combining these equations gives
|
||||
|
||||
|
||||
|
||||
|
||||
S
|
||||
≈
|
||||
|
||||
|
||||
L
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
−
|
||||
1
|
||||
|
||||
|
||||
|
||||
=
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
(
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
sin
|
||||
|
||||
θ
|
||||
−
|
||||
|
||||
|
||||
1
|
||||
L
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle S\approx {\frac {L}{\left({\frac {\varphi }{\theta }}+1\right)L\sin \theta -1}}=1\left/\left(\left({\frac {\varphi }{\theta }}+1\right)\sin \theta -{\frac {1}{L}}\right)\right.}
|
||||
|
||||
|
||||
The values which Hipparchus took for these variables can be found in Ptolemy's Almagest IV, 9. He says Hipparchus found that the Moon measured its own circle close to 650 times, and that the angular diameter of Earth's shadow is 2.5 times that of the Moon. Pappus tells us that Hipparchus took the mean distance to the Moon to be 671⁄3. This gives:
|
||||
|
||||
According to Swerdlow, Hipparchus now evaluated this expression with the following roundings (the values are in sexagesimal):
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
≈
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
≈
|
||||
0
|
||||
;
|
||||
19
|
||||
,
|
||||
30
|
||||
|
||||
|
||||
{\displaystyle \ell \approx L\sin \theta \approx 0;19,30}
|
||||
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
h
|
||||
≈
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
ℓ
|
||||
≈
|
||||
0
|
||||
;
|
||||
48
|
||||
,
|
||||
45
|
||||
|
||||
|
||||
{\displaystyle h\approx {\frac {\varphi }{\theta }}\ell \approx 0;48,45}
|
||||
|
||||
|
||||
Then, because
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
+
|
||||
h
|
||||
≈
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
+
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
=
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
L
|
||||
sin
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \ell +h\approx {\frac {\varphi }{\theta }}L\sin \theta +L\sin \theta =\left({\frac {\varphi }{\theta }}+1\right)L\sin \theta }
|
||||
|
||||
|
||||
it follows that
|
||||
|
||||
|
||||
|
||||
|
||||
S
|
||||
≈
|
||||
L
|
||||
|
||||
/
|
||||
|
||||
(
|
||||
ℓ
|
||||
+
|
||||
h
|
||||
−
|
||||
1
|
||||
)
|
||||
≈
|
||||
67
|
||||
;
|
||||
20
|
||||
|
||||
/
|
||||
|
||||
0
|
||||
;
|
||||
8
|
||||
,
|
||||
15
|
||||
≈
|
||||
489.70
|
||||
≈
|
||||
490
|
||||
|
||||
|
||||
{\displaystyle S\approx L/(\ell +h-1)\approx 67;20/0;8,15\approx 489.70\approx 490}
|
||||
|
||||
|
||||
Swerdlow used this result to argue that 490 was the correct reading of the Pappus text, thus invalidating Hultsch' interpretation. While this result is highly dependent on the particular approximations and roundings used, it has generally been accepted. It leaves open, however, the question of where the lunar distance 671⁄3 came from.
|
||||
Following Pappus and Ptolemy, Swerdlow suggested that Hipparchus had estimated 490 Earth radii as a minimum possible distance to the Sun. This distance corresponds to a solar parallax of 7', which may have been the maximum that he thought would have gone unnoticed (the typical resolution of the human eye is 2'). The formula obtained above for the distance to the Sun can be inverted to determine the distance to the Moon:
|
||||
|
||||
|
||||
|
||||
|
||||
L
|
||||
≈
|
||||
|
||||
|
||||
S
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
S
|
||||
sin
|
||||
|
||||
θ
|
||||
−
|
||||
1
|
||||
|
||||
|
||||
|
||||
=
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
(
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
φ
|
||||
θ
|
||||
|
||||
|
||||
+
|
||||
1
|
||||
|
||||
)
|
||||
|
||||
sin
|
||||
|
||||
θ
|
||||
−
|
||||
|
||||
|
||||
1
|
||||
S
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle L\approx {\frac {S}{\left({\frac {\varphi }{\theta }}+1\right)S\sin \theta -1}}=1\left/\left(\left({\frac {\varphi }{\theta }}+1\right)\sin \theta -{\frac {1}{S}}\right)\right.}
|
||||
|
||||
|
||||
Using the same values as above for each angle, and using 490 Earth radii as the minimum solar distance, it follows that the maximum mean lunar distance is
|
||||
|
||||
|
||||
|
||||
|
||||
L
|
||||
≈
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
(
|
||||
|
||||
(
|
||||
2.5
|
||||
+
|
||||
1
|
||||
)
|
||||
sin
|
||||
|
||||
|
||||
0.277
|
||||
|
||||
∘
|
||||
|
||||
|
||||
−
|
||||
|
||||
|
||||
1
|
||||
490
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
≈
|
||||
67.203
|
||||
≈
|
||||
67
|
||||
|
||||
|
||||
|
||||
1
|
||||
3
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle L\approx 1\left/\left((2.5+1)\sin 0.277^{\circ }-{\frac {1}{490}}\right)\right.\approx 67.203\approx 67{\tfrac {1}{3}}}
|
||||
|
||||
|
||||
Toomer expanded on this by observing that as the distance to the Sun increases without bound, the formula approaches a minimum mean lunar distance:
|
||||
|
||||
|
||||
|
||||
|
||||
L
|
||||
≈
|
||||
1
|
||||
|
||||
/
|
||||
|
||||
(
|
||||
|
||||
(
|
||||
2.5
|
||||
+
|
||||
1
|
||||
)
|
||||
sin
|
||||
|
||||
|
||||
0.277
|
||||
|
||||
∘
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
≈
|
||||
59.10
|
||||
|
||||
|
||||
{\displaystyle L\approx 1\left/\left((2.5+1)\sin 0.277^{\circ }\right)\right.\approx 59.10}
|
||||
|
||||
|
||||
This is close to the value later claimed by Ptolemy.
|
||||
|
||||
=== Book 1 reconstruction (Toomer) ===
|
||||
In addition to explaining the minimum lunar distance that Hipparchus achieved, Toomer was able to explain the method of the first book, which employed a solar eclipse. Pappus states that this eclipse was total in the region of the Hellespont, but was observed to be 4/5 of total in Alexandria.
|
||||
|
||||
If Hipparchus assumed that the Sun was infinitely distant (i.e. that "the earth has the ratio of a point and center to the sun"), then the difference in magnitude of the solar eclipse must be due entirely to the parallax of the Moon. By using observational data, he would be able to determine this parallax, and hence the distance of the Moon.
|
||||
Hipparchus would have known
|
||||
|
||||
|
||||
|
||||
|
||||
φ
|
||||
|
||||
A
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle \varphi _{A}}
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle \varphi _{H}}
|
||||
|
||||
, the latitudes of Alexandria and the Hellespontine region, respectively. He also would have known
|
||||
|
||||
|
||||
|
||||
δ
|
||||
|
||||
|
||||
{\displaystyle \delta }
|
||||
|
||||
, the declination of the Moon during the eclipse, and
|
||||
|
||||
|
||||
|
||||
μ
|
||||
|
||||
|
||||
{\displaystyle \mu }
|
||||
|
||||
, which is related to the difference in totality of the eclipse between the two regions.
|
||||
@ -0,0 +1,645 @@
|
||||
---
|
||||
title: "On Sizes and Distances (Hipparchus)"
|
||||
chunk: 3/3
|
||||
source: "https://en.wikipedia.org/wiki/On_Sizes_and_Distances_(Hipparchus)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:03.519801+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
|
||||
|
||||
|
||||
A
|
||||
H
|
||||
=
|
||||
|
||||
|
||||
|
||||
t
|
||||
Crd
|
||||
|
||||
∠
|
||||
A
|
||||
O
|
||||
H
|
||||
|
||||
R
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
t
|
||||
Crd
|
||||
|
||||
(
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
−
|
||||
|
||||
φ
|
||||
|
||||
A
|
||||
|
||||
|
||||
)
|
||||
|
||||
R
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle AH={\frac {t\operatorname {Crd} \angle AOH}{R}}={\frac {t\operatorname {Crd} (\varphi _{H}-\varphi _{A})}{R}}}
|
||||
|
||||
|
||||
Crd here refers to the chord function, which maps an angle in degrees to the corresponding length of a chord of a circle of unit diameter. Also, R is the radius of the base circle that Hipparchus used to compute the chord function and t is the radius of the Earth. Since the Moon is very distant, it follows that
|
||||
|
||||
|
||||
|
||||
|
||||
ζ
|
||||
′
|
||||
|
||||
≈
|
||||
ζ
|
||||
|
||||
|
||||
{\displaystyle \zeta '\approx \zeta }
|
||||
|
||||
. Using this approximation gives
|
||||
|
||||
|
||||
|
||||
|
||||
ζ
|
||||
=
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
−
|
||||
δ
|
||||
|
||||
|
||||
{\displaystyle \zeta =\varphi _{H}-\delta }
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
∠
|
||||
Z
|
||||
H
|
||||
A
|
||||
=
|
||||
|
||||
180
|
||||
|
||||
∘
|
||||
|
||||
|
||||
−
|
||||
∠
|
||||
O
|
||||
H
|
||||
A
|
||||
|
||||
|
||||
{\displaystyle \angle ZHA=180^{\circ }-\angle OHA}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
∠
|
||||
O
|
||||
H
|
||||
A
|
||||
=
|
||||
|
||||
|
||||
|
||||
|
||||
180
|
||||
|
||||
∘
|
||||
|
||||
|
||||
−
|
||||
∠
|
||||
A
|
||||
O
|
||||
H
|
||||
|
||||
2
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
|
||||
180
|
||||
|
||||
∘
|
||||
|
||||
|
||||
−
|
||||
(
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
−
|
||||
|
||||
φ
|
||||
|
||||
A
|
||||
|
||||
|
||||
)
|
||||
|
||||
2
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle \angle OHA={\frac {180^{\circ }-\angle AOH}{2}}={\frac {180^{\circ }-(\varphi _{H}-\varphi _{A})}{2}}}
|
||||
|
||||
|
||||
Hence,
|
||||
|
||||
|
||||
|
||||
|
||||
∠
|
||||
Z
|
||||
H
|
||||
A
|
||||
=
|
||||
|
||||
90
|
||||
|
||||
∘
|
||||
|
||||
|
||||
+
|
||||
|
||||
|
||||
1
|
||||
2
|
||||
|
||||
|
||||
(
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
−
|
||||
|
||||
φ
|
||||
|
||||
A
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
{\displaystyle \angle ZHA=90^{\circ }+{\frac {1}{2}}(\varphi _{H}-\varphi _{A})}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
∠
|
||||
M
|
||||
H
|
||||
A
|
||||
=
|
||||
θ
|
||||
=
|
||||
∠
|
||||
Z
|
||||
H
|
||||
A
|
||||
−
|
||||
|
||||
ζ
|
||||
′
|
||||
|
||||
≈
|
||||
∠
|
||||
Z
|
||||
H
|
||||
A
|
||||
−
|
||||
ζ
|
||||
=
|
||||
|
||||
90
|
||||
|
||||
∘
|
||||
|
||||
|
||||
−
|
||||
|
||||
|
||||
1
|
||||
2
|
||||
|
||||
|
||||
(
|
||||
|
||||
φ
|
||||
|
||||
H
|
||||
|
||||
|
||||
+
|
||||
|
||||
φ
|
||||
|
||||
A
|
||||
|
||||
|
||||
)
|
||||
+
|
||||
δ
|
||||
|
||||
|
||||
{\displaystyle \angle MHA=\theta =\angle ZHA-\zeta '\approx \angle ZHA-\zeta =90^{\circ }-{\frac {1}{2}}(\varphi _{H}+\varphi _{A})+\delta }
|
||||
|
||||
|
||||
With
|
||||
|
||||
|
||||
|
||||
A
|
||||
H
|
||||
|
||||
|
||||
{\displaystyle AH}
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
θ
|
||||
|
||||
|
||||
{\displaystyle \theta }
|
||||
|
||||
, we only need
|
||||
|
||||
|
||||
|
||||
μ
|
||||
|
||||
|
||||
{\displaystyle \mu }
|
||||
|
||||
to get
|
||||
|
||||
|
||||
|
||||
|
||||
D
|
||||
′
|
||||
|
||||
|
||||
|
||||
{\displaystyle D'}
|
||||
|
||||
. Because the eclipse was total at H, and 4/5 total at A, it follows that
|
||||
|
||||
|
||||
|
||||
μ
|
||||
|
||||
|
||||
{\displaystyle \mu }
|
||||
|
||||
is 1/5 of the apparent diameter of the Sun. This quantity was well known by Hipparchus—he took it to be 1/650 of a full circle. The distance from the center of the Earth to the Moon then follows from
|
||||
|
||||
|
||||
|
||||
D
|
||||
≈
|
||||
|
||||
D
|
||||
′
|
||||
|
||||
+
|
||||
t
|
||||
|
||||
|
||||
{\displaystyle D\approx D'+t}
|
||||
|
||||
.
|
||||
Toomer determined how Hipparchus determined the chord for small angles (see Chord (geometry)). His values for the latitudes of the Hellespont (41 degrees) and Alexandria (31 degrees) are known from Strabo's work on Geography. To determine the declination, it is necessary to know which eclipse Hipparchus used.
|
||||
Because he knew the value which Hipparchus eventually gave for the distance to the Moon (71 Earth radii) and the rough region of the eclipse, Toomer was able to determine that Hipparchus used the solar eclipse of March 14, 190 BC. This eclipse fits all the mathematical parameters very well, and also makes sense from a historical point of view. The eclipse was total in Nicaea, Hipparchus' birthplace, so he may have heard stories of it. There is also an account of it in Strabo's Ab Urbe Condita VIII.2. The declination of the Moon at this time was
|
||||
|
||||
|
||||
|
||||
δ
|
||||
=
|
||||
−
|
||||
|
||||
3
|
||||
|
||||
∘
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle \delta =-3^{\circ }}
|
||||
|
||||
. Hence, using chord trigonometry, gives
|
||||
|
||||
|
||||
|
||||
|
||||
θ
|
||||
=
|
||||
|
||||
54
|
||||
|
||||
∘
|
||||
|
||||
|
||||
+
|
||||
δ
|
||||
|
||||
|
||||
{\displaystyle \theta =54^{\circ }+\delta }
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
A
|
||||
H
|
||||
=
|
||||
|
||||
|
||||
|
||||
t
|
||||
Crd
|
||||
|
||||
|
||||
10
|
||||
|
||||
∘
|
||||
|
||||
|
||||
|
||||
R
|
||||
|
||||
|
||||
≈
|
||||
t
|
||||
|
||||
|
||||
|
||||
600
|
||||
3438
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle AH={\frac {t\operatorname {Crd} 10^{\circ }}{R}}\approx t\ {\frac {600}{3438}}}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
μ
|
||||
=
|
||||
|
||||
|
||||
|
||||
360
|
||||
⋅
|
||||
60
|
||||
|
||||
|
||||
5
|
||||
⋅
|
||||
650
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle \mu ={\frac {360\cdot 60}{5\cdot 650}}}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
D
|
||||
′
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
Crd
|
||||
|
||||
2
|
||||
θ
|
||||
⋅
|
||||
A
|
||||
H
|
||||
|
||||
|
||||
Crd
|
||||
|
||||
μ
|
||||
⋅
|
||||
2
|
||||
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
Crd
|
||||
|
||||
(
|
||||
|
||||
108
|
||||
|
||||
∘
|
||||
|
||||
|
||||
+
|
||||
2
|
||||
δ
|
||||
)
|
||||
⋅
|
||||
600
|
||||
⋅
|
||||
5
|
||||
⋅
|
||||
650
|
||||
|
||||
|
||||
21600
|
||||
⋅
|
||||
2
|
||||
⋅
|
||||
3438
|
||||
|
||||
|
||||
|
||||
t
|
||||
|
||||
|
||||
{\displaystyle D'={\frac {\operatorname {Crd} 2\theta \cdot AH}{\operatorname {Crd} \mu \cdot 2}}={\frac {\operatorname {Crd} (108^{\circ }+2\delta )\cdot 600\cdot 5\cdot 650}{21600\cdot 2\cdot 3438}}t}
|
||||
|
||||
|
||||
Now using Hipparchus' chord tables,
|
||||
|
||||
|
||||
|
||||
|
||||
Crd
|
||||
|
||||
(
|
||||
|
||||
108
|
||||
|
||||
∘
|
||||
|
||||
|
||||
+
|
||||
2
|
||||
(
|
||||
−
|
||||
|
||||
3
|
||||
|
||||
∘
|
||||
|
||||
|
||||
)
|
||||
)
|
||||
=
|
||||
Crd
|
||||
|
||||
|
||||
102
|
||||
|
||||
∘
|
||||
|
||||
|
||||
≈
|
||||
2
|
||||
⋅
|
||||
3438
|
||||
sin
|
||||
|
||||
|
||||
51
|
||||
|
||||
∘
|
||||
|
||||
|
||||
≈
|
||||
5340
|
||||
|
||||
|
||||
{\displaystyle \operatorname {Crd} (108^{\circ }+2(-3^{\circ }))=\operatorname {Crd} 102^{\circ }\approx 2\cdot 3438\sin 51^{\circ }\approx 5340}
|
||||
|
||||
|
||||
and hence
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
D
|
||||
′
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
5340
|
||||
⋅
|
||||
600
|
||||
⋅
|
||||
5
|
||||
⋅
|
||||
650
|
||||
|
||||
|
||||
21600
|
||||
⋅
|
||||
2
|
||||
⋅
|
||||
3438
|
||||
|
||||
|
||||
|
||||
t
|
||||
≈
|
||||
70.1
|
||||
t
|
||||
⇒
|
||||
D
|
||||
≈
|
||||
|
||||
D
|
||||
′
|
||||
|
||||
+
|
||||
t
|
||||
≈
|
||||
71.1
|
||||
t
|
||||
|
||||
|
||||
{\displaystyle D'={\frac {5340\cdot 600\cdot 5\cdot 650}{21600\cdot 2\cdot 3438}}t\approx 70.1t\Rightarrow D\approx D'+t\approx 71.1t}
|
||||
|
||||
|
||||
This agrees well with the value of 71 Earth radii that Pappus reports.
|
||||
|
||||
== Conclusion ==
|
||||
Assuming that these reconstructions accurately reflect what Hipparchus wrote in On Sizes and Distances, then this work was a remarkable accomplishment. This approach of setting limits on an unknown physical quantity was not new to Hipparchus (see Aristarchus of Samos. Archimedes also did the same with pi), but in those cases, the bounds reflected the inability to determine a mathematical constant to an arbitrary precision, not uncertainty in physical observations.
|
||||
Hipparchus appears to have eventually resolved the contradiction between his two results. His aim in calculating the distance to the Moon was to obtain an accurate value for the lunar parallax, so that he might predict eclipses with more precision. To this, he had to settle on a particular value for the distance/parallax, not a range of values.
|
||||
There is some evidence that he did this. Combining the calculations of Book 2 and the account of Theon of Smyrna yields a lunar distance of 60.5 Earth radii. Doing the same with the account of Cleomedes yields a distance of 61 Earth radii. These are remarkably close to both Ptolemy's value and the modern one.
|
||||
According to Toomer,
|
||||
|
||||
This procedure, if I have constructed it correctly, is very remarkable... What is astonishing is the sophistication of approaching the problem by two quite different methods, and also the complete honesty with which Hipparchus reveals his discrepant results... which are nevertheless of the same order of magnitude and (for the first time in the history of astronomy) in the right region.
|
||||
|
||||
== See also ==
|
||||
Aristarchus of Samos (c. 310 – c. 230 BC), a Greek mathematician who calculated the distance from the Earth to the Sun.
|
||||
Axial precession
|
||||
Eratosthenes (c. 276 – c. 194/195 BC), a Greek mathematician who calculated the circumference of the Earth and also the distance from the Earth to the Sun.
|
||||
Greek mathematics
|
||||
Hipparchus (c. 190 – c. 120 BC)
|
||||
Posidonius (c. 135 – c. 51 BC), a Greek astronomer and mathematician who calculated the circumference of the Earth.
|
||||
|
||||
== References ==
|
||||
|
||||
F. Hultsch, "Hipparchos über die Grösse und Entfernung der Sonne", Sächsische Akademie der Wissenschaften, 52, 169–200 (1900).
|
||||
N. M. Swerdlow, "Hipparchus on the distance of the sun", Centaurus, 14 (1969), 287–305.
|
||||
G. J. Toomer, "Hipparchus on the distances of the sun and moon", Archive for History of Exact Sciences, 14 (1974), 126–142.
|
||||
G. Hon, "Is there a concept of experimental error in Greek astronomy?" The British Journal for the History of Science, 22.02 (1989): 129–150. (Available online at https://www.researchgate.net/profile/Giora_Hon/publication/231844424_Is_There_a_Concept_of_Experimental_Error_in_Greek_Astronomy/links/564fa57b08ae4988a7a858bd.pdf)
|
||||
64
data/en.wikipedia.org/wiki/On_the_Heavens-0.md
Normal file
64
data/en.wikipedia.org/wiki/On_the_Heavens-0.md
Normal file
@ -0,0 +1,64 @@
|
||||
---
|
||||
title: "On the Heavens"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/On_the_Heavens"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:04.703836+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
On the Heavens (Greek: Περὶ οὐρανοῦ; Latin: De Caelo or De Caelo et Mundo) is Aristotle's chief cosmological treatise: written in 350 BCE, it contains his astronomical theory and his ideas on the concrete workings of the terrestrial world. It should not be confused with the spurious work On the Universe (De Mundo, also known as On the Cosmos).
|
||||
This work is significant as one of the defining pillars of the Aristotelian worldview, a school of philosophy that dominated intellectual thinking for almost two millennia. Similarly, this work and others by Aristotle were important seminal works from which much of scholasticism was derived.
|
||||
|
||||
|
||||
== Argument ==
|
||||
According to Aristotle in On the Heavens, the heavenly bodies are the most perfect realities, (or "substances"), whose motions are ruled by principles other than those of bodies in the sublunary sphere. The latter are composed of one or all of the four classical elements (earth, water, air, fire) and are perishable; but the matter of which the heavens are made is imperishable aether, so they are not subject to generation and corruption. Hence their motions are eternal and perfect, and the perfect motion is the circular one, which, unlike the earthly up-and down-ward locomotions, can last eternally selfsame – an early predecessor to Newton's first law of motion. Aristotle theorized that aether did not exist anywhere on Earth, but that it was an element exclusive to the heavens. As substances, celestial bodies have matter (aether) and form (a given period of uniform rotation). Sometimes Aristotle seems to regard them as living beings with a rational soul as their form (see also Metaphysics, book XII).
|
||||
Aristotle proposed a geocentric model of the universe in On the Heavens. The Earth is the center of motion of the universe, with circular motion being perfect because Earth was at the center of it. There can be only one center of the universe, and as a result there are no other inhabited worlds within it besides Earth. As such the Earth is unique and alone in this regard. Aristotle theorized that beyond the sublunary sphere and the heavens is an external spiritual space that mankind cannot fathom directly.
|
||||
Aristotle also argued for the view that the following six directions exist as human-independent realities, not just relative to us: left, right, up, down, front, and back. This is an important part of his theory that the heavens move always in one direction and with no irregularities.
|
||||
Much of On the Heavens is concerned with refuting the views of his predecessors. For example, Aristotle sets his eyes multiple times on the analyses of weight given by the Pythagoreans and Plato in the Timaeus.
|
||||
|
||||
|
||||
== Historical connections ==
|
||||
Aristotelian philosophy and cosmology were influential in the Islamic world, where his ideas were taken up by the Falsafa school of philosophy throughout the later half of the first millennium AD. Of these, philosophers Averroes and Avicenna are especially notable. Averroes in particular wrote extensively about On the Heavens, trying for some time to reconcile the various themes of Aristotelian philosophy, such as natural movement of the elements and the concept of planetary spheres centered on the Earth, with the mathematics of Ptolemy. These ideas would remain central to philosophical thought in the Islamic world well into the pre-modern period, and its influences can be found in both the theological and mystical tradition, including in the writings of al-Ghazali and Fakhr al-Din al-Razi.
|
||||
|
||||
European philosophers had a similarly complex relationship with On the Heavens, attempting to reconcile church doctrine with the mathematics of Ptolemy and the structure of Aristotle. A particularly cogent example of this is in the work of Thomas Aquinas, theologian, philosopher and writer of the 13th century. Thomas worked to synthesize Aristotle's cosmology as presented in On the Heavens with Christian doctrine, an endeavor that led him to reclassify Aristotle's unmoved movers as angels and attributing the 'first cause' of motion in the celestial spheres to them. Otherwise, Thomas accepted Aristotle's explanation of the physical world, including his cosmology and physics.
|
||||
The 14th-century French philosopher Nicole Oresme translated and commented on On the Heavens in his role as adviser to King Charles V of France, on two occasions, once early on in life, and again near the end of it. These versions were a traditional Latin transcription and a more comprehensive French version that synthesized his views on cosmological philosophy in its entirety, Questiones Super de Celo and Livre du ciel et du monde respectively. Livre du ciel et du monde was written at the command of King Charles V, though for what purpose remains of some debate. Some speculate that, having already had Oresme translate Aristotelian works on ethics and politics in the hope of educating his courtiers, doing the same with On the Heavens may be of some value to the king.
|
||||
Francis Bacon was critical of Aristotelian thought. Jürgen Klein explains that "he does not repudiate Aristotle completely", but he saw that Aristotle's cosmology and his theory of science had become obsolete, and so felt that "many of the medieval thinkers who followed his lead" were misguided.
|
||||
|
||||
|
||||
== Translations ==
|
||||
(In reverse chronological order)
|
||||
|
||||
C. D. C. Reeve, De Caelo (Indianapolis: Hackett, 2020). ISBN 978-1-62466-881-4.
|
||||
Stuart Leggatt, On the Heavens: Books I & II (Oxbow Books, 1995). ISBN 978-0-85668-663-4.
|
||||
William Keith Chambers Guthrie, Aristotle On the Heavens (Cambridge, Mass.: Harvard University Press "Loeb Classical Library", 1939).
|
||||
John Leofric Stocks, On the Heavens (Oxford: Clarendon Press, 1922).
|
||||
Adelaide Etexts
|
||||
Sacred Texts
|
||||
InfoMotions
|
||||
MIT (incomplete)
|
||||
Internet Archive (Scanned Version of Printed Text)
|
||||
Free Audiobook (Translated by John Leofric Stocks)
|
||||
Thomas Taylor, The Treatises of Aristotle, On the Heavens, On Generation & Corruption, and On Meteors (Somerset, England: The Prometheus Trust, 2004, 1807). ISBN 1-898910-24-3.
|
||||
|
||||
|
||||
== See also ==
|
||||
Physics (Aristotle)
|
||||
Aristotelian physics
|
||||
Dynamics of the celestial spheres
|
||||
Celestial spheres
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Further reading ==
|
||||
Elders, L., Aristotle’s Cosmology: A Commentary on the De Caelo (Assen, Netherlands: Van Gorcum, 1966).
|
||||
|
||||
|
||||
== External links ==
|
||||
|
||||
On the Heavens in Greek is found in the 2nd volume of the 11-volume 1837 Bekker edition of Aristotle's Works in Greek (PDF Archived 2022-11-24 at the Wayback Machine · DJVU)
|
||||
On the Heavens in The Internet Classics Archive.
|
||||
On the Heavens public domain audiobook at LibriVox
|
||||
@ -0,0 +1,606 @@
|
||||
---
|
||||
title: "On the Sizes and Distances (Aristarchus)"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:05.903361+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
On the Sizes and Distances (of the Sun and Moon) (Ancient Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Perì megethôn kaì apostēmátōn [hēlíou kaì selḗnēs]) is widely accepted as the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa 310–230 BCE. This work calculates the sizes of the Sun and Moon, as well as their distances from the Earth in terms of Earth's radius.
|
||||
The book was possibly preserved by students of Pappus of Alexandria's course in mathematics, although the evidence for this is sparse. The editio princeps was published by John Wallis in 1688, using several medieval manuscripts compiled by Sir Henry Savile. The earliest Latin translation was made by Giorgio Valla in 1488. There is also a 1572 Latin translation and commentary by Frederico Commandino.
|
||||
|
||||
== Symbols ==
|
||||
The work's method relied on several observations:
|
||||
|
||||
The apparent size of the Sun and the Moon in the sky.
|
||||
The size of the Earth's shadow in relation to the Moon during a lunar eclipse
|
||||
The angle between the Sun and Moon during a half moon is 90°.
|
||||
The rest of the article details a reconstruction of Aristarchus' method and results. The reconstruction uses the following variables:
|
||||
|
||||
== Half Moon ==
|
||||
Aristarchus began with the premise that, during a half moon, the moon forms a right triangle with the Sun and Earth. By observing the angle between the Sun and Moon, φ, the ratio of the distances to the Sun and Moon could be deduced using a form of trigonometry.
|
||||
|
||||
From the diagram and trigonometry, we can calculate that
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
S
|
||||
L
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
1
|
||||
|
||||
cos
|
||||
|
||||
φ
|
||||
|
||||
|
||||
|
||||
=
|
||||
sec
|
||||
|
||||
φ
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle {\frac {S}{L}}={\frac {1}{\cos \varphi }}=\sec \varphi .}
|
||||
|
||||
|
||||
The diagram is greatly exaggerated, because in reality, S = 390 L, and φ is extremely close to 90°. Aristarchus determined φ to be a thirtieth of a quadrant (in modern terms, 3°) less than a right angle: in current terminology, 87°. Trigonometric functions had not yet been invented, but using geometrical analysis in the style of Euclid, Aristarchus determined that
|
||||
|
||||
|
||||
|
||||
|
||||
18
|
||||
<
|
||||
|
||||
|
||||
S
|
||||
L
|
||||
|
||||
|
||||
<
|
||||
20.
|
||||
|
||||
|
||||
{\displaystyle 18<{\frac {S}{L}}<20.}
|
||||
|
||||
|
||||
In other words, the distance to the Sun was somewhere between 18 and 20 times greater than the distance to the Moon. This value (or values close to it) was accepted by astronomers for the next two thousand years, until the invention of the telescope permitted a more precise estimate of solar parallax.
|
||||
Aristarchus also reasoned that as the angular size of the Sun and the Moon were the same, but the distance to the Sun was between 18 and 20 times further than the Moon, the Sun must therefore be 18–20 times larger.
|
||||
|
||||
== Lunar eclipse ==
|
||||
Aristarchus then used another construction based on a lunar eclipse:
|
||||
|
||||
By similarity of the triangles,
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
D
|
||||
L
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
t
|
||||
|
||||
t
|
||||
−
|
||||
d
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {D}{L}}={\frac {t}{t-d}}\quad }
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
D
|
||||
S
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
t
|
||||
|
||||
s
|
||||
−
|
||||
t
|
||||
|
||||
|
||||
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle \quad {\frac {D}{S}}={\frac {t}{s-t}}.}
|
||||
|
||||
|
||||
Dividing these two equations and using the observation that the Sun and Moon appear the same size to people on Earth,
|
||||
|
||||
|
||||
|
||||
s
|
||||
|
||||
/
|
||||
|
||||
S
|
||||
=
|
||||
ℓ
|
||||
|
||||
/
|
||||
|
||||
L
|
||||
|
||||
|
||||
{\displaystyle s/S=\ell /L}
|
||||
|
||||
, yields
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
s
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
t
|
||||
−
|
||||
d
|
||||
|
||||
|
||||
s
|
||||
−
|
||||
t
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
⟹
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
s
|
||||
−
|
||||
t
|
||||
|
||||
s
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
t
|
||||
−
|
||||
d
|
||||
|
||||
ℓ
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
⟹
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
t
|
||||
ℓ
|
||||
|
||||
|
||||
+
|
||||
|
||||
|
||||
t
|
||||
s
|
||||
|
||||
|
||||
=
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
d
|
||||
ℓ
|
||||
|
||||
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle {\frac {\ell }{s}}={\frac {t-d}{s-t}}\ \ \implies \ \ {\frac {s-t}{s}}={\frac {t-d}{\ell }}\ \ \implies \ \ {\frac {t}{\ell }}+{\frac {t}{s}}=1+{\frac {d}{\ell }}.}
|
||||
|
||||
|
||||
The rightmost equation can either be solved for
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
|
||||
/
|
||||
|
||||
t
|
||||
|
||||
|
||||
{\displaystyle \ell /t}
|
||||
|
||||
or
|
||||
|
||||
|
||||
|
||||
s
|
||||
|
||||
/
|
||||
|
||||
t
|
||||
|
||||
|
||||
{\displaystyle s/t}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
s
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
d
|
||||
ℓ
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
,
|
||||
|
||||
|
||||
|
||||
s
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
s
|
||||
ℓ
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
d
|
||||
ℓ
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle {\frac {\ell }{t}}={\frac {1+{\dfrac {\ell }{s}}}{1+{\dfrac {d}{\ell }}}},\qquad {\frac {s}{t}}={\frac {1+{\dfrac {s}{\ell }}}{1+{\dfrac {d}{\ell }}}}.}
|
||||
|
||||
|
||||
These equations can be made to appear simpler by expressing the lengths
|
||||
|
||||
|
||||
|
||||
d
|
||||
|
||||
|
||||
{\displaystyle d}
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
s
|
||||
|
||||
|
||||
{\displaystyle s}
|
||||
|
||||
in terms of the moon's radius
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
|
||||
|
||||
{\displaystyle \ell }
|
||||
|
||||
as a unit, defining
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
d
|
||||
^
|
||||
|
||||
|
||||
|
||||
=
|
||||
d
|
||||
|
||||
/
|
||||
|
||||
ℓ
|
||||
|
||||
|
||||
{\displaystyle {\hat {d}}=d/\ell }
|
||||
|
||||
and
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
s
|
||||
^
|
||||
|
||||
|
||||
|
||||
=
|
||||
s
|
||||
|
||||
/
|
||||
|
||||
ℓ
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle {\hat {s}}=s/\ell .}
|
||||
|
||||
Then
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
ℓ
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
s
|
||||
^
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
s
|
||||
^
|
||||
|
||||
|
||||
|
||||
(
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
d
|
||||
^
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
,
|
||||
|
||||
|
||||
|
||||
s
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
s
|
||||
^
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
1
|
||||
+
|
||||
|
||||
|
||||
|
||||
d
|
||||
^
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {\ell }{t}}={\frac {1+{\hat {s}}}{{\hat {s}}(1+{\hat {d}})}},\qquad {\frac {s}{t}}={\frac {1+{\hat {s}}}{1+{\hat {d}}}}}
|
||||
|
||||
|
||||
The above equations give the radii of the Moon and Sun entirely in terms of observable quantities.
|
||||
The following formulae give the distances to the Sun and Moon in terrestrial units:
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
L
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
(
|
||||
|
||||
|
||||
ℓ
|
||||
t
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
180
|
||||
|
||||
π
|
||||
θ
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {L}{t}}=\left({\frac {\ell }{t}}\right)\left({\frac {180}{\pi \theta }}\right)}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
S
|
||||
t
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
|
||||
|
||||
s
|
||||
t
|
||||
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
180
|
||||
|
||||
π
|
||||
θ
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {S}{t}}={\biggl (}{\frac {s}{t}}{\biggr )}\left({\frac {180}{\pi \theta }}\right)}
|
||||
|
||||
|
||||
where θ is the apparent radius of the Moon and Sun measured in degrees.
|
||||
Aristarchus did not use these exact formulae, yet these formulae are likely a good approximation for those of Aristarchus.
|
||||
|
||||
== Results ==
|
||||
The above formulae can be used to reconstruct the results of Aristarchus. The following table shows the results of a long-standing (but dubious) reconstruction using n = 2, x = 19.1 (φ = 87°) and θ = 1°, alongside the modern day accepted values.
|
||||
@ -0,0 +1,44 @@
|
||||
---
|
||||
title: "On the Sizes and Distances (Aristarchus)"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:05.903361+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The error in this calculation comes primarily from the poor values for x and θ. The poor value for θ is especially surprising, since Archimedes writes that Aristarchus was the first to determine that the Sun and Moon had an apparent diameter of half a degree. This would give a value of θ = 0.25, and a corresponding distance to the Moon of 80 Earth radii, a much better estimate. The disagreement of the work with Archimedes seems to be due to its taking an Aristarchus statement that the lunisolar diameter is 1/15 of a "meros" of the zodiac to mean 1/15 of a zodiacal sign (30°), unaware that the Greek word "meros" meant either "portion" or 7°1/2; and 1/15 of the latter amount is 1°/2, in agreement with Archimedes' testimony.
|
||||
A similar procedure was later used by Hipparchus, who estimated the mean distance to the Moon as 67 Earth radii, and Ptolemy, who took 59 Earth radii for this value.
|
||||
|
||||
== Illustrations ==
|
||||
Some interactive illustrations of the propositions in On Sizes can be found here:
|
||||
|
||||
Hypothesis 4 states that when the Moon appears to us halved, its distance from the Sun is then less than a quadrant by one-thirtieth of a quadrant [that is, it is less than 90° by 1/30th of 90° or 3°, and is therefore equal to 87°] (Heath 1913:353).
|
||||
Proposition 1 states that two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or of the cone, touches the spheres (Heath 1913:354).
|
||||
Proposition 2 states that if a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere (Heath 1913:358).
|
||||
Proposition 3 states that the circle in the Moon which divides the dark and the bright portions is least when the cone comprehending both the Sun and the Moon has its vertex at our eye (Heath 1913:362).
|
||||
Proposition 4 states that the circle which divides the dark and the bright portions in the Moon is not perceptibly different from a great circle in the Moon (Heath 1913:365).
|
||||
Proposition 6 states that the Moon moves [in an orbit] lower than [that of] the Sun, and, when it is halved, is distant less than a quadrant from the Sun (Heath 1913:372).
|
||||
Proposition 7 states that the distance of the Sun from the Earth is greater than 18 times, but less than 20 times, the distance of the Moon from the Earth (Heath 1913:377). In other words, the Sun is 18 to 20 times farther away and wider than the Moon.
|
||||
Proposition 13 states that the straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the Moon move is less than double of the diameter of the Moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the Sun, but has to it a ratio greater than that which 21 has to 225. But it has to the straight line drawn from the centre of the Sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10 125 (Heath 1913:394).
|
||||
Proposition 14 states that the straight line joined from the centre of the Earth to the centre of the Moon has to the straight line cut off from the axis towards the centre of the Moon by the straight line subtending the [circumference] within the Earth's shadow a ratio greater than that which 675 has to 1 (Heath 1913:400).
|
||||
Proposition 15 states that the diameter of the Sun has to the diameter of the Earth a ratio greater than 19/3, but less than 43/6 (Heath 1913:403). This means that the Sun is (a mean of) 6+3⁄4 times wider than the Earth, or that the Sun is 13+1⁄2 Earth-radii wide. The Moon and Sun must then be 20+1⁄4 and 387 Earth-radii away from us in order to subtend an angular size of 2º.
|
||||
Proposition 17a in al-Tusi's medieval Arabic version of the book On Sizes states that the ratio of the distance of the vertex of the shadow cone from the center of the Moon (when the Moon is on the axis [that is, at the middle of an eclipse] of the cone containing the Earth and the Sun) to the distance of the center of the Moon from the center of the Earth is greater than the ratio 71 to 37 and less than the ratio 3 to one (Berggren & Sidoli 2007:218). In other words, that the tip of the Earth's shadow cone is between 108/37 and four times farther away than the Moon.
|
||||
|
||||
== Known copies ==
|
||||
Library of Congress Vatican Exhibit.
|
||||
|
||||
== See also ==
|
||||
Aristarchus of Samos
|
||||
Eratosthenes (c. 276 – c. 194/195 BC), a Greek mathematician who calculated the circumference of the Earth and also the distance from the Earth to the Sun.
|
||||
Hipparchus (c. 190 – c. 120 BC), a Greek mathematician who measured the radii of the Sun and the Moon as well as their distances from the Earth.
|
||||
On the Sizes and Distances (Hipparchus)
|
||||
Posidonius (c. 135 – c. 51 BC), a Greek astronomer and mathematician who calculated the circumference of the Earth.
|
||||
|
||||
== Notes ==
|
||||
|
||||
== Bibliography ==
|
||||
Gomez, Alberto (2023). Decoding Aristarchus. Berlin: Peter Lang Verlag. ISBN 9783631892619.
|
||||
Heath, Thomas (1913). Aristarchus of Samos, the Ancient Copernicus. Oxford: Clarendon. This was later reprinted, see (ISBN 0-486-43886-4).
|
||||
van Helden, A. Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley. Chicago: Univ. of Chicago Pr., 1985. ISBN 0-226-84882-5.
|
||||
41
data/en.wikipedia.org/wiki/Pale_Blue_Dot_(book)-0.md
Normal file
41
data/en.wikipedia.org/wiki/Pale_Blue_Dot_(book)-0.md
Normal file
@ -0,0 +1,41 @@
|
||||
---
|
||||
title: "Pale Blue Dot (book)"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Pale_Blue_Dot_(book)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:07.111673+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Pale Blue Dot: A Vision of the Human Future in Space is a 1994 book by the astronomer Carl Sagan. It is the sequel to Sagan's 1980 book Cosmos and was inspired by the famous 1990 Pale Blue Dot photograph, for which Sagan provides a poignant description. In the book, Sagan mixes philosophy about the human place in the universe with a description of the current knowledge about the Solar System. He also details a human vision for the future.
|
||||
In 2023, the audiobook of Pale Blue Dot, read by Sagan, was selected by the Library of Congress for preservation in the United States National Recording Registry as being "culturally, historically, or aesthetically significant."
|
||||
|
||||
|
||||
== Summary ==
|
||||
The first part of the book examines the claims made throughout history that Earth and the human species are unique. Sagan proposes two reasons for the persistence of the idea of a geocentric, or Earth-centered universe: human pride in our existence, and the threat of torturing those who dissented from it, particularly during the time of the Roman Inquisition. However, he also admits that the scientific tools to prove the Earth orbited the Sun were (until the last few hundred years) not accurate enough to measure effects such as parallax, making it difficult for astronomers to prove that the geocentric theory was false.
|
||||
|
||||
After saying that we have gained humility from understanding that we are not literally the center of the universe, Sagan embarks on an exploration of the entire Solar System. He begins with an account of the Voyager program, in which he was a participating scientist. He describes the difficulty of working with the low light levels at distant planets, and the mechanical and computer problems which beset the twin spacecraft as they aged, and which could not always be diagnosed and fixed remotely. Sagan then examines each one of the major planets, as well as some of the moons—including Titan, Triton, and Miranda—focusing on whether life is possible at the frontiers of the Solar System.
|
||||
Sagan argues that studying other planets provides context for understanding the Earth—and protecting humanity's only home planet from environmental catastrophe. He believes that NASA's decision to cut back exploration of the Moon after the Apollo program was a short-sighted decision, despite its expense and declining popularity among the American public. Sagan says future exploration of space should focus on ways to protect Earth and to extend human habitation beyond it. The book was published the same year comet Shoemaker-Levy 9 crashed into Jupiter, an event Sagan uses to highlight the danger Earth faces from the occasional asteroid or comet large enough to cause substantial damage if it were to hit Earth. He says we need the political will to track large extraterrestrial objects, or we risk losing everything. Sagan argues that in order to save the human race, space colonization and terraforming should be utilized.
|
||||
Later in the book, Sagan's wife, Ann Druyan, challenges readers to pick one of the other planetary dots photographed and featured in the book, and imagine that there are inhabitants on that world who believe that the universe was created solely for themselves. She shared Sagan's belief that humans are not as important as they think they are.
|
||||
The first edition of the book includes an extensive list of illustrations and photographs, much of it taken from public archives of information released by NASA.
|
||||
|
||||
|
||||
== See also ==
|
||||
|
||||
Anthropocentrism
|
||||
Earthrise, 1968 Apollo 8 photograph
|
||||
The Blue Marble, 1972 Apollo 17 photograph
|
||||
Wanderers (2014 film)
|
||||
|
||||
|
||||
== References ==
|
||||
Sagan, Carl (1994). Pale Blue Dot: A Vision of the Human Future in Space (1st ed.). New York: Random House. ISBN 0-679-43841-6.
|
||||
|
||||
|
||||
== External links ==
|
||||
Sagan's rationale for human spaceflight Article about Carl Sagan and Pale Blue Dot
|
||||
Short audio recording of Carl Sagan describing the primary concept of his book The Pale Blue Dot at the United States Library of Congress Seth MacFarlane Collection of the Carl Sagan and Ann Druyan Archive
|
||||
A new picture of Earth taken through the rings of Saturn by the Cassini spacecraft on September 15, 2006. More information about photo.
|
||||
We Are Here: The Pale Blue Dot. A short, fan-made film on The Pale Blue Dot, released a decade after Sagan's death. The posthumous narration is from Sagan himself, taken from one version of the audiobook version of Pale Blue Dot.
|
||||
A partial video tour of the Sagan Planet Walk monument in Ithaca, NY
|
||||
34
data/en.wikipedia.org/wiki/Planisphaerium-0.md
Normal file
34
data/en.wikipedia.org/wiki/Planisphaerium-0.md
Normal file
@ -0,0 +1,34 @@
|
||||
---
|
||||
title: "Planisphaerium"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Planisphaerium"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:09.423503+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Planisphaerium is a work by Ptolemy. The title can be translated as "celestial plane" or "star chart". In this work Ptolemy explored the mathematics of mapping figures inscribed in the celestial sphere onto a plane by what is now known as stereographic projection. This method of projection preserves the properties of circles.
|
||||
|
||||
|
||||
== Publication ==
|
||||
|
||||
Originally written in Ancient Greek, Planisphaerium was one of many scientific works which survived from antiquity in Arabic translation. One reason why Planisphaerium attracted interest was that stereographic projection was the mathematical basis of the plane astrolabe, an instrument which was widely used in the medieval Islamic world. The Suda lists a work of Ptolemy titled Simplification of the Sphere (Ancient Greek: Ἅπλωσις ἐπιφανείας σφαίρας) which is presumed to be Planisphaerium. In 1143 the work was translated from Arabic into Latin by Herman of Carinthia, who also translated commentaries by Maslamah Ibn Ahmad al-Majriti. The oldest known translation is in Arabic done by an unknown scholar as part of the Translation Movement in Baghdad.
|
||||
|
||||
|
||||
== Planisphere ==
|
||||
|
||||
The word planisphere (Latin planisphaerium) was originally used in the second century by Ptolemy to describe the representation of a spherical Earth by a map drawn in the plane.
|
||||
|
||||
Planisphere
|
||||
|
||||
|
||||
== Editions and translations ==
|
||||
Commandino, Federico, ed. (1558). Ptolemaei Planisphaerium. Iordani Planisphaerium. Federici Commandini Vrbinatis in Ptolemaei Planisphaerium commentarius (in Latin). Venice: Paulus Manutius.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
"Ptolemy on Astrolabes"
|
||||
31
data/en.wikipedia.org/wiki/Poor_Richard's_Almanack-0.md
Normal file
31
data/en.wikipedia.org/wiki/Poor_Richard's_Almanack-0.md
Normal file
@ -0,0 +1,31 @@
|
||||
---
|
||||
title: "Poor Richard's Almanack"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/Poor_Richard's_Almanack"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:11.787915+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Poor Richard's Almanack (sometimes Almanac) was a yearly almanac published by Benjamin Franklin, who adopted the pseudonym of "Poor Richard" or "Richard Saunders" for this purpose. The publication appeared continually from 1732 to 1758. It sold exceptionally well for a pamphlet published in the Thirteen Colonies; print runs reached 10,000 per year.
|
||||
Franklin, the American inventor, statesman, and accomplished publisher and printer, achieved success with Poor Richard's Almanack. Almanacks were very popular books in colonial America, offering a mixture of seasonal weather forecasts, practical household hints, puzzles, and other amusements. Poor Richard's Almanack was also popular for its extensive use of wordplay, and some of the witty phrases coined in the work survive in the contemporary American vernacular.
|
||||
|
||||
== History ==
|
||||
|
||||
On December 28, 1732, Benjamin Franklin announced in The Pennsylvania Gazette that he had just printed and published the first edition of The Poor Richard, by Richard Saunders, Philomath. Franklin published the first Poor Richard's Almanack on December 28, 1732, and continued to publish new editions for 25 years, bringing him much economic success and popularity. The almanack sold as many as 10,000 copies a year. In 1735, upon the death of Franklin's brother, James, Franklin sent 500 copies of Poor Richard's to his widow for free, so that she could make money selling them.
|
||||
|
||||
== Contents ==
|
||||
The Almanack contained the calendar, weather, poems, sayings, and astronomical and astrological information that a typical almanac of the period would contain. Franklin also included the occasional mathematical exercise, and the Almanack from 1750 features an early example of demographics. It is chiefly remembered, however, for being a repository of Franklin's proverbs, many of which live on in American English. These maxims typically counsel thrift and courtesy, with a dash of cynicism.
|
||||
In the spaces that occurred between noted calendar days, Franklin included proverbial sentences about industry and frugality. Several of these sayings were borrowed from an earlier writer, Lord Halifax, many of whose aphorisms sprang from a "basic skepticism directed against the motives of men, manners, and the age." In 1757, Franklin made a selection of these and prefixed them to the almanac as the address of an old man to the people attending an auction. This was later published as The Way to Wealth, and was popular in both America and England.
|
||||
Jill Lepore points out that "Franklin didn't write most of Poor Richard's proverbs. By his own guess, he wrote perhaps one out of every ten; the rest he found in books, especially anthologies like Thomas Fuller's 1732 Gnomologia: Adagies and Proverbs; Wise Sentences and Witty Sayings Ancient and Modern, Foreign and British. She adds that Franklin was adept at modifying and sharpening the proverbs he found, for example, Fuller had written, "A Man in Passion rides a horse that runs away with him", whereas Franklin converted it to, "A Man in a Passion rides a mad Horse."
|
||||
|
||||
== Poor Richard ==
|
||||
Franklin borrowed the name "Richard Saunders" from the seventeenth-century author of Rider's British Merlin, a popular London almanac which continued to be published throughout the eighteenth century. Franklin created the Poor Richard persona based in part on Jonathan Swift's pseudonymous character, "Isaac Bickerstaff". In a series of three letters in 1708 and 1709, known as the Bickerstaff papers, "Bickerstaff" predicted the imminent death of astrologer and almanac maker John Partridge. Franklin's Poor Richard, like Bickerstaff, claimed to be a philomath and astrologer and, like Bickerstaff, predicted the deaths of actual astrologers who wrote traditional almanacs. In the early editions of Poor Richard's Almanack, predicting and falsely reporting the deaths of these astrologers—much to their dismay—was something of a running joke. However, Franklin's endearing character of "Poor" Richard Saunders, along with his wife Bridget, was ultimately used to frame (if comically) what was intended as a serious resource that people would buy year after year. To that end, the satirical edge of Swift's character is largely absent in Poor Richard. Richard was presented as distinct from Franklin himself, occasionally referring to the latter as his printer.
|
||||
In later editions, the original Richard Saunders character gradually disappeared, replaced by a Poor Richard, who largely stood in for Franklin and his own practical scientific and business perspectives. By 1758, the original character was even more distant from the practical advice and proverbs of the almanac, which Franklin presented as coming from "Father Abraham," who in turn got his sayings from Poor Richard.
|
||||
|
||||
== Serialization ==
|
||||
One of the appeals of the Almanack was that it contained various "news stories" in serial format, so that readers would purchase it year after year to find out what happened to the protagonists. One of the earliest of these was the "prediction" that the author's "good Friend and Fellow-Student, Mr. Titan Leeds" would die on October 17 of that year, followed by the rebuttal of Mr. Leeds himself that he would die, not on the 17th, but on October 26. Appealing to his readers, Franklin urged them to purchase the next year or two or three or four editions to show their support for his prediction. The following year, Franklin expressed his regret that he was too ill to learn whether he or Leeds was correct. Nevertheless, the ruse had its desired effect: people purchased the Almanack to find out who was correct. (Later editions of the Almanack would claim that Leeds had died and that the person claiming to be Leeds was an impostor; Leeds, in fact, died in 1738, which prompted Franklin to applaud the supposed impostor for ending his ruse.)
|
||||
|
||||
== Criticism ==
|
||||
For some writers the content of the Almanack became inextricably linked with Franklin's character—and not always to favorable effect. Both Nathaniel Hawthorne and Herman Melville caricatured the Almanack—and Franklin by extension—in their writings, while James Russell Lowell, reflecting on the public unveiling in Boston of a statue to honor Franklin, wrote:
|
||||
34
data/en.wikipedia.org/wiki/Poor_Richard's_Almanack-1.md
Normal file
34
data/en.wikipedia.org/wiki/Poor_Richard's_Almanack-1.md
Normal file
@ -0,0 +1,34 @@
|
||||
---
|
||||
title: "Poor Richard's Almanack"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/Poor_Richard's_Almanack"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:11.787915+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
... we shall find out that Franklin was born in Boston, and invented being struck with lightning and printing and the Franklin medal, and that he had to move to Philadelphia because great men were so plenty in Boston that he had no chance, and that he revenged himself on his native town by saddling it with the Franklin stove, and that he discovered the almanac, and that a penny saved is a penny lost, or something of the kind.
|
||||
The Almanack was also a reflection of the social norms and social mores of his times, rather than a philosophical document setting a path for new-freedoms, as the works of Franklin's contemporaries, Thomas Jefferson, John Adams, and Thomas Paine were. Historian Howard Zinn offers, as an example, the adage "Let thy maidservant be faithful, strong, and homely" as indication of Franklin's belief in the legitimacy of controlling the sexual lives of servants for the economic benefit of their masters.
|
||||
At least one modern biographer has published the claim that Franklin "stole", not borrowed, the name of Richard Saunders from the deceased astrologer-doctor. Franklin also "borrowed—apparently without asking—and adapted the title of an almanac his brother James Franklin was publishing at Newport: Poor Robin's Almanack (itself appropriated from a seventeenth-century almanac published under the same title in London)".
|
||||
|
||||
== Cultural impact ==
|
||||
King Louis XVI of France gave a ship to John Paul Jones who renamed it after the Almanack's author—Bonhomme Richard, or "Goodman (that is, a polite title of address for a commoner who is not a member of the gentry) Richard" (the first of several US warships so named). The Almanack was translated into Italian, along with the Pennsylvania State Constitution (which Franklin helped draft) at the establishment of the Cisalpine Republic. It was also twice translated into French, reprinted in Great Britain in broadside for ease of posting, and was distributed by members of the clergy to poor parishioners. It was the first work of English literature to be translated into Slovene, translated in 1812 by Janez Nepomuk Primic (1785–1823).
|
||||
The Almanack also had a strong cultural and economic impact in the years following publication. In Pennsylvania, changes in monetary policy in regard to foreign expenses were evident for years after the issuing of the Almanack. Later writers such as Noah Webster were inspired by the almanac, and it went on to influence other publications of this type such as the Old Farmer's Almanac.
|
||||
Sociologist Max Weber considered Poor Richard's Almanack and Franklin to reflect the "spirit of capitalism" in a form of "classical" purity. This is why he filled the pages of Chapter 2 of his 1905 book The Protestant Ethic and the Spirit of Capitalism with illustrative quotations from Franklin's almanacks.
|
||||
Numerous farmer's almanacs trace their format and tradition to Poor Richard's Almanack; the Old Farmer's Almanac, for instance, has included a picture of Franklin on its cover since 1851.
|
||||
In 1958, the United States mobilized its naval forces in response to an attack on Vice President Richard Nixon in Caracas, Venezuela. The operation was code-named "Poor Richard".
|
||||
|
||||
== See also ==
|
||||
The Papers of Benjamin Franklin
|
||||
|
||||
== Citations ==
|
||||
|
||||
== Bibliography ==
|
||||
|
||||
== External links ==
|
||||
|
||||
Poor Richard's Almanack public domain audiobook at LibriVox
|
||||
|
||||
"High-Quality Scanned Images of several pages of Poor Richard's Almanack". flickr.com. 14 February 2006.
|
||||
"Rare Book Room Titles – Benjamin Franklin". Rare Book Room. Archived from the original on February 22, 2020.
|
||||
@ -0,0 +1,25 @@
|
||||
---
|
||||
title: "Practical Astronomy with Your Calculator"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Practical_Astronomy_with_Your_Calculator"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:12.941893+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Practical Astronomy with your Calculator is a book written by Peter Duffett-Smith, a University Lecturer and a Fellow of Downing College. It was first published in 1979 and has been in publication for over 30 years. The book teaches how to solve astronomical calculations with a pocket calculator. The book covers topics such as time, coordinate systems, the Sun, planetary systems, binary stars, the Moon and eclipses. The third edition features new sections on generalised coordinate transformations, nutation, aberration, and selenographic coordinates. The fourth edition, coauthored by Jonathan Zwart, adds "or Spreadsheet" to the end of the title.
|
||||
The book has been used by amateur astronomers and those studying introductory astronomy. It was written because of a suggestion by Dr. Anthony Winter.
|
||||
|
||||
|
||||
== Modern use ==
|
||||
The mathematical operations used in the book are subtraction, addition, multiplication, division and trigonometric functions. Angles are illustrated in degrees and not radians. The calculations are carried out on a calculator. The book "explains in simpler terms the equations used to calculate almanac data."
|
||||
|
||||
|
||||
== Critical reception ==
|
||||
The Cambridge Guide to Astronomical Discovery states that Practical Astronomy with your Calculator is a "must"-have book if one has no personal computer for astronomical calculations.
|
||||
New Scientist magazine gave a favourable review of the book, although stating that there were small errors in some calculations.
|
||||
Archaeoastronomy states "the book is recommended as easy to use and reliable."
|
||||
|
||||
|
||||
== References ==
|
||||
@ -0,0 +1,29 @@
|
||||
---
|
||||
title: "Quasars, Redshifts and Controversies"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Quasars,_Redshifts_and_Controversies"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:14.137332+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Quasars, Redshifts and Controversies is a 1987 book by Halton Arp, an astronomer famous for his Atlas of Peculiar Galaxies (1966). Arp argued that many quasars with otherwise high redshift are somehow linked to close objects such as nearby galaxies. Arp also argued that some galaxies showed unusual redshifts, and that redshifts themselves could be quantized.
|
||||
These are controversial views which do not accord with the standard model of physical cosmology. It also contradicts the accepted model that quasars are bright nuclei of very distant galaxies. Most astronomers reject Arp's interpretation of the data since the anomalous observations could be explained by perspective effects. Reportedly, some of Arp's calculations seem to be simply "bad mathematics". Arp asserted that many questions he posed to the scientific establishment are still unanswered and that his requests for more observation time had been systematically rejected.
|
||||
Halton Arp's proposal was an idea based on analyses done before the sky surveys increased the number of measured redshifts by several orders of magnitude. The idea was that the cosmological redshift might be showing evidence of periodicity which would be difficult to explain in a Hubble's law universe that had the feature of continuous expansion. However, most astronomers agree that the analysis suffers from poor methodology and small number statistics.
|
||||
Halton Arp continued to report the existence of apparently connected objects with very different redshifts. Arp has interpreted these connections to mean that these objects are in fact physically connected. He further hypothesized that the higher redshift objects are ejected from the lower redshift objects - which are usually active galactic nuclei (AGN)- and that the large observed redshifts of these "ejected" objects is dominated by a non-cosmological (intrinsic) component. The rest of the community regards these as chance alignments and Arp's hypothesis has very few supporters.
|
||||
The book has been translated into Italian and Spanish, as of 1998.
|
||||
His work is updated in his last book, Catalogue of Discordant Redshift Associations, C. Roy Keys Inc. (February, 2003), ISBN 978-0968368992.
|
||||
|
||||
|
||||
== See also ==
|
||||
Non-standard cosmology
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== External links and references ==
|
||||
Arp, Halton C., Quasars, Redshifts and Controversies. September 1988. ISBN 0-521-36314-4
|
||||
Arp, Halton C., Seeing Red: Redshifts, Cosmology and Academic Science, Aperion (August, 1998), ISBN 0-9683689-0-5
|
||||
Rowan-Robinson, Michael, Arp's astronomical exotica, Nature vol. 336, (November 17, 1988)
|
||||
26
data/en.wikipedia.org/wiki/Ranna_an_aeir-0.md
Normal file
26
data/en.wikipedia.org/wiki/Ranna_an_aeir-0.md
Normal file
@ -0,0 +1,26 @@
|
||||
---
|
||||
title: "Ranna an aeir"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Ranna_an_aeir"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:16.368335+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Ranna an aeir ("The Constellations") is the title of a medieval Irish astronomical tract, thought to date from c.1500–1550? It was written in Early Modern Irish, with some words in English and Latin.
|
||||
|
||||
|
||||
== See also ==
|
||||
An Irish Astronomical Tract
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
=== Manuscript Sources ===
|
||||
National Library of Scotland; Advocates 72.1.2 olim Gaelic II (The National Library of Ireland holds a microfilm copy (n. 307, p. 452).)
|
||||
|
||||
|
||||
=== Edition ===
|
||||
A. O. Anderson, Ranna an aeir [The Constellations] in Revue Celtique, Ed. Henri d'Arbois de Jubainville, Volume 30, Paris, F. Vieweg (1909) page 404–417
|
||||
28
data/en.wikipedia.org/wiki/Rider's_British_Merlin-0.md
Normal file
28
data/en.wikipedia.org/wiki/Rider's_British_Merlin-0.md
Normal file
@ -0,0 +1,28 @@
|
||||
---
|
||||
title: "Rider's British Merlin"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Rider's_British_Merlin"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:18.671687+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Rider's British Merlin was one of the earliest almanacs to be published, issued from 1656 until at least 1837.
|
||||
|
||||
|
||||
== Content ==
|
||||
The almanac contained the calendar, weather, and astronomical and astrological information that a typical almanac of the period would contain. The pages for each month of the year were accompanied by advice on what, and what not to eat and drink, and otherwise how to keep in good health. There were horticultural notes with abundant attention paid to herbs, fruit and vegetables.
|
||||
The lengthiest sections of this little book listed annual fairs in England and Wales of fixed and moveable date. The first would generally be associated with a saint's day, while the second would be of the type "second Monday in October". This list of town names and dates represented important information in the days before Agricultural Advisers, Trade Fairs and Job Offices, when the fairs played an important role not only in buying and selling, but also in exhibiting innovations in husbandry, in information exchange and in the hiring of labour.
|
||||
|
||||
|
||||
== "Rider" ==
|
||||
It is generally held that Cardanus Rider is a pseudonym, and near-anagram: the letters rearrange as Ric_ard Saunder_. Richard Saunders was an English physician and astrologer, born in 1613, and who died (sources differ) either in 1675, 1687, or 1692.
|
||||
The National Archives in London hold a book by Saunders on palmistry, with horoscopes; also attributed to him is The Astrological Judgment and Practice of Physick, published in 1677, although the fact that it includes charts from as early as 1616 to 1618 has led doubts to be cast on the actual authorship. Be that as it may, its subject matter was dear to the heart of "Cardanus Rider"; it stands as one of the earliest astro-medical treatises in the English language. Using the terminology of his day, the writer speaks of humours and winds, of conditions hot, cold or dry, of the cholerick and melancholy, of illnesses produced by the planets in the various signs of the zodiac, when to administer medicines based on planetary hours, and much more.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Rider's British Merlin - Special collections - University of Glasgow
|
||||
39
data/en.wikipedia.org/wiki/Rocket_Men_(book)-0.md
Normal file
39
data/en.wikipedia.org/wiki/Rocket_Men_(book)-0.md
Normal file
@ -0,0 +1,39 @@
|
||||
---
|
||||
title: "Rocket Men (book)"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Rocket_Men_(book)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:19.833869+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Rocket Men: The Daring Odyssey of Apollo 8 and the Astronauts Who Made Man's First Journey to the Moon is a 2018 nonfiction book by Robert Kurson recounting NASA's 1968 Apollo 8 mission, which was the first crewed spacecraft to reach the Moon and return safely to Earth. The book is Kurson's fourth, and it debuted on the New York Times bestseller list.
|
||||
|
||||
|
||||
== Background ==
|
||||
Kurson drew on hundreds of hours of one-on-one interviews with NASA staff, industry experts, astronauts (including all three Apollo 8 astronauts) and their families as source material for the book.
|
||||
|
||||
|
||||
== Synopsis ==
|
||||
Rocket Men is an account of the Apollo 8 mission with focus on Frank Borman, Jim Lovell and William Anders, the three astronauts who flew the mission. The book also places an emphasis on the astronauts' families during the mission.
|
||||
From The Washington Post:
|
||||
|
||||
"'Rocket Men' opens in summer 1968, with the space race in high gear. The Soviet Union had already put the world’s first satellite, Sputnik, as well as the first human, Yuri Gagarin, into Earth’s orbit. The Soviets were projected to reach the moon by the end of the year, months ahead of the United States."
|
||||
The book includes chapters dedicated to each astronaut, the Space Race itself, and background and chronological progress of the mission including critical maneuvers and mission setbacks. It is set against the backdrop of 1968, considered by many to be among the most divisive and violent years in American history.
|
||||
|
||||
|
||||
== Reception ==
|
||||
The book reached #7 on the New York Times bestseller list and has received positive reviews from critics. The USA Today called Rocket Men a "first-rate account of this remarkable spaceflight" and added, "There are many pieces to the Apollo 8 story, but Kurson brings them together effortlessly." The New York Times called the book "gripping" and "a riveting introduction to the [Apollo 8] flight" in which "Kurson details the mission in crisp, suspenseful scenes." Writing for The Washington Post, Mary Roach compared the book to Alfred Lansing's 1959 book Endurance and Jon Krakauer's 1997 Into Thin Air, and called Kurson's writing style "as close to a movie as writing gets."
|
||||
The film rights to Rocket Men were secured by Makeready prior to the book's publication.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Official website
|
||||
Discussion on Rocket Men with Kurson and astronauts Frank Borman, Jim Lovell, and Bill Anders, April 5, 2018, C-SPAN
|
||||
Q&A interview with Kurson on Rocket Men, May 6, 2018, C-SPAN
|
||||
Presentation by Kurson on Rocket Men, June 10, 2018, C-SPAN
|
||||
Washington Journal interview with Kurson on Rocket Men, December 16, 2018, C-SPAN
|
||||
36
data/en.wikipedia.org/wiki/Romaka_Siddhanta-0.md
Normal file
36
data/en.wikipedia.org/wiki/Romaka_Siddhanta-0.md
Normal file
@ -0,0 +1,36 @@
|
||||
---
|
||||
title: "Romaka Siddhanta"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Romaka_Siddhanta"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:20.967337+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Romaka Siddhanta (Sanskrit: रोमकसिद्धान्त, romanized: Romaka Siddhānta), literally "The Doctrine of the Romans", is one of the five siddhantas (doctrine or tradition) mentioned in Varahamihira's Panchasiddhantika which is an Indian astronomical treatise.
|
||||
Romaka Siddhanta is based on the astronomical learning of the Byzantine Empire, also referred to as the Eastern Roman Empire.
|
||||
|
||||
|
||||
== Content ==
|
||||
It is the only one of all Indian astronomical works which is based on the tropical system. It was considered one of "The Five Astronomical Canons" in India in the 5th century.
|
||||
|
||||
|
||||
== See also ==
|
||||
Paulisa Siddhanta
|
||||
Indian science and technology
|
||||
Indian mathematics
|
||||
Indian astronomy
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== References ==
|
||||
McEvilley, Thomas (November 2001). The Shape of Ancient Thought: Comparative Studies in Greek and Indian Philosophies. Allworth Press. ISBN 978-1-58115-203-6.
|
||||
Sarma, Nataraja (2000), "Diffusion of Astronomy in the Ancient World", Endeavour, 24 (2000): 157-164.
|
||||
|
||||
|
||||
== External links ==
|
||||
Indian astronomy and Western influences
|
||||
a
|
||||
32
data/en.wikipedia.org/wiki/Sadratnamala-0.md
Normal file
32
data/en.wikipedia.org/wiki/Sadratnamala-0.md
Normal file
@ -0,0 +1,32 @@
|
||||
---
|
||||
title: "Sadratnamala"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Sadratnamala"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:22.165175+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Sadratnamala is an astronomical-mathematical treatise in Sanskrit written by Sankara Varman, an astronomer-mathematician of the Kerala school of mathematics, in 1819. Even though the book has been written at a time when western mathematics and astronomy had been introduced in India, it is composed purely in the traditional style followed by the mathematicians of the Kerala school. Sankara Varman has also written a detailed commentary on the book in Malayalam.
|
||||
Sadratnamala is one of the books cited in C. M. Whish's paper on the achievements of the Kerala school of mathematics. This paper published in the Transactions of the Royal Asiatic Society of Great Britain and Ireland in 1834, was the first ever attempt to bring the accomplishments of Keralese mathematicians to the attention of Western mathematical scholarship.
|
||||
Whish wrote in his paper thus: "The author of Sadratnamalah is SANCARA VARMA, the younger brother of the present Raja of Cadattanada near Tellicherry, a very intelligent man and acute mathematician. This work, which is a complete system of Hindu astronomy, is comprehended in two hundred and eleven verses of different measures, and abounds with fluxional forms and series, to be found in no work of foreign or other Indian countries."
|
||||
|
||||
|
||||
== Synopsis of the book ==
|
||||
The book contains 212 verses divided into six chapters, called prakarana-s.
|
||||
|
||||
Chapter 1: Gives the names of numerals; defines the eight operations of addition, subtraction, multiplication, division, squaring, extracting square root, cubing, and extracting cube root.
|
||||
Chapter 2: Lists the different measures, namely, the measures of time, angles, lunar days, planets and stars, almanacs, length, grain weight, money and the directions.
|
||||
Chapter 3: Defines the rule of three and syllabic enumeration; explains methods for the computation of the elements of the almanac, namely, mean and true sun, moon and planets, lunar day, yoga and karana; gives methods for determining the time elapsed after sunrise and after sunset.
|
||||
Chapter 4: Deals with arcs and sines and its application in astronomical measurements and computations.
|
||||
Chapter 5: Deals with computations relating to the shadow, eclipse, vyatipata, retrograde motion of the planets and apses of the moon.
|
||||
Chapter 6: Explains the necessity of periodic revision of astronomical constants; gives a full description of parahita-karana.
|
||||
|
||||
|
||||
== Sankara Varman (1774–1839) ==
|
||||
|
||||
Sankara Varman, author of Sadratnamala, was born as a younger prince in the principality of Katathanad in the North Malabar in Kerala. To the local people he was known as Appu Thampuran. The date of birth of Sankara Varman is still uncertain. There are some strong arguments in favour of the year 1774 CE. Sankara Varman died in 1839 CE.
|
||||
|
||||
|
||||
== References ==
|
||||
@ -0,0 +1,26 @@
|
||||
---
|
||||
title: "Selenographia, sive Lunae descriptio"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Selenographia,_sive_Lunae_descriptio"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:24.491165+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Selenographia, sive Lunae descriptio (Selenography, or A Description of The Moon) was printed in 1647 and is a milestone work by the astronomer and lunar topographer Johannes Hevelius, the mayor of Danzig (Gdańsk). It includes the first detailed map of the Moon, created from Hevelius's personal observations.
|
||||
|
||||
|
||||
== Contents and criticism of Galileo Galilei's previous efforts ==
|
||||
In his treatise, Hevelius reflected on the difference between his own work and that of Galileo Galilei. Hevelius remarked that the quality of Galileo's representations of the Moon in Sidereus nuncius (1610) left something to be desired. Selenography was dedicated to King Ladislaus IV of Poland and along with Riccioli/Grimaldi's Almagestum Novum became the standard work on the Moon for over a century.
|
||||
|
||||
|
||||
== Surviving copies ==
|
||||
There are many copies that have survived, including those in Bibliothèque nationale de France, in the library of Polish Academy of Sciences, in the Stillman Drake Collection at the Thomas Fisher Rare Books Library at the University of Toronto, and in the Gunnerus Library at the Norwegian University of Science and Technology in Trondheim.
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Selenographia, sive Lunae descriptio
|
||||
16
data/en.wikipedia.org/wiki/Shrouds_of_the_Night-0.md
Normal file
16
data/en.wikipedia.org/wiki/Shrouds_of_the_Night-0.md
Normal file
@ -0,0 +1,16 @@
|
||||
---
|
||||
title: "Shrouds of the Night"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Shrouds_of_the_Night"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:25.662999+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Shrouds of the Night is a book from the astronomy genre.
|
||||
The book was written at the Mount Stromlo Observatory in 2007 by David Block and Ken Freeman. It is a timetable of astronomical photography from 1826 to the present day.
|
||||
Much of the content of this book is published here for the first time. Two examples of this are: one from Arizona's Lowell Observatory and another from the Royal Astronomical Society of London.
|
||||
|
||||
|
||||
== Notes ==
|
||||
33
data/en.wikipedia.org/wiki/Sidereus_Nuncius-0.md
Normal file
33
data/en.wikipedia.org/wiki/Sidereus_Nuncius-0.md
Normal file
@ -0,0 +1,33 @@
|
||||
---
|
||||
title: "Sidereus Nuncius"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/Sidereus_Nuncius"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:26.902865+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Sidereus Nuncius (usually Sidereal Messenger, also Starry Messenger or Sidereal Message) is a short astronomical treatise (or pamphlet) published in Neo-Latin by Galileo Galilei on March 13, 1610. It was the first published scientific work based on observations made through a telescope, and it contains the results of Galileo's early observations of the imperfect and mountainous Moon, of hundreds of stars not visible to the naked eye in the Milky Way and in certain constellations, and of the Medicean Stars (Galilean moons) that appeared to be circling Jupiter.
|
||||
The Latin word nuncius was typically used during this time period to denote messenger; however, it was also (though less frequently) rendered as message. Though the title Sidereus Nuncius is usually translated into English as Sidereal Messenger, many of Galileo's early drafts of the book and later related writings indicate that the intended purpose of the book was "simply to report the news about recent developments in astronomy, not to pass himself off solemnly as an ambassador from heaven."
|
||||
|
||||
== Telescope ==
|
||||
The first telescopes appeared in the Netherlands in 1608, when Middelburg spectacle-maker Hans Lippershey tried to obtain a patent on one. By 1609 Galileo had learned of this and built his own improved version. He was not the first person to aim the new invention at the night sky but his was the first published study of celestial bodies using one. One of Galileo's first telescopes had 8x to 10x linear magnification and was made out of lenses that he had ground himself. This was increased to 20x linear magnification in the improved telescope he used to make the observations in Sidereus Nuncius.
|
||||
|
||||
== Content ==
|
||||
|
||||
Sidereus Nuncius contains more than seventy drawings and diagrams of the Moon, certain constellations such as Orion, the Pleiades, and Taurus, and the Medicean Stars of Jupiter. Galileo's text also includes descriptions, explanations, and theories of his observations.
|
||||
|
||||
=== Moon ===
|
||||
In observing the Moon, Galileo saw that the line separating lunar day from night (the terminator) was smooth where it crossed the darker regions of the Moon but quite irregular where it crossed the brighter areas. From this he deduced that the darker regions are flat, low-lying areas, and the brighter regions rough and mountainous. Basing his estimate on the distance of sunlit mountaintops from the terminator, he judged, quite accurately, that the lunar mountains were at least four miles high. Galileo's engravings of the lunar surface provided a new form of visual representation, besides shaping the field of selenography, the study of physical features on the Moon.
|
||||
|
||||
=== Stars ===
|
||||
Galileo reported that he saw at least ten times more stars through the telescope than are visible to the naked eye, and he published star charts of the belt of Orion and the star cluster Pleiades showing some of the newly observed stars. With the naked eye observers could see only six stars in the Pleiades; through his telescope, however, Galileo was capable of seeing thirty-five – almost six times as many. When he turned his telescope on Orion, he was capable of seeing eighty stars, rather than the previously observed nine – almost nine times more. In Sidereus Nuncius, Galileo revised and reproduced these two star groups by distinguishing between the stars seen without the telescope and those seen with it. Also, when he observed some of the "nebulous" stars in the Ptolemaic star catalogue, he saw that rather than being cloudy, they were made of many small stars. From this he deduced that the nebulae and the Milky Way were "congeries of innumerable stars grouped together in clusters" too small and distant to be resolved into individual stars by the naked eye.
|
||||
|
||||
=== Medicean Stars (Moons of Jupiter) ===
|
||||
|
||||
In the last part of Sidereus Nuncius, Galileo reported his discovery of four objects that appeared to form a straight line of stars near Jupiter. On the first night he detected a line of three little stars close to Jupiter parallel to the ecliptic; the following nights brought different arrangements and another star into his view, totalling four stars around Jupiter. Throughout the text, Galileo gave illustrations of the relative positions of Jupiter and its apparent companion stars as they appeared nightly from late January through early March 1610. That they changed their positions relative to Jupiter from night to night and yet always appeared in the same straight line near it, persuaded Galileo that they were orbiting Jupiter. On January 11 after four nights of observation he wrote:
|
||||
|
||||
I therefore concluded and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury round the Sun; which at length was established as clear as daylight by numerous subsequent observations. These observations also established that there are not only three, but four, erratic sidereal bodies performing their revolutions round Jupiter...the revolutions are so swift that an observer may generally get differences of position every hour.
|
||||
In his drawings, Galileo used an open circle to represent Jupiter and asterisks to represent the four stars. He made this distinction to show that there was in fact a difference between these two types of celestial bodies. Galileo used the terms planet and star interchangeably, and "both words were correct usage within the prevailing Aristotelian terminology."
|
||||
At the time of Sidereus Nuncius' publication, Galileo was a mathematician at the University of Padua and had recently received a lifetime contract for his work in building more powerful telescopes. He desired to return to Florence, and in hopes of gaining patronage there, he dedicated Sidereus Nuncius to his former pupil, now the Grand Duke of Tuscany, Cosimo II de' Medici. In addition, he named his discovered four moons of Jupiter the "Medicean Stars," in honor of the four royal Medici brothers. This helped him receive the position of Chief Mathematician and Philosopher to the Medici at the University of Pisa. Ultimately, his effort at naming the moons failed, for they are now referred to as the "Galilean moons".
|
||||
58
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|
||||
title: "Sidereus Nuncius"
|
||||
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|
||||
source: "https://en.wikipedia.org/wiki/Sidereus_Nuncius"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:26.902865+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
== Reception ==
|
||||
The reactions to Sidereus Nuncius, ranging from appraisal and hostility to disbelief, soon spread throughout Italy and England. Many poems and texts were published expressing love for the new form of astronomical science. Three works of art were even created in response to Galileo's book: Adam Elsheimer's The Flight into Egypt (1610; contested by Keith Andrews), Lodovico Cigoli's Assumption of the Virgin (1612), and Andrea Sacchi's Divine Wisdom (1631). In addition, the discovery of the Medicean Stars fascinated other astronomers, and they wanted to view the moons for themselves. Their efforts "set the stage for the modern scientific requirement of experimental reproducibility by independent researchers. Verification versus falsifiability…saw their origins in the announcement of Sidereus Nuncius."
|
||||
But many individuals and communities were sceptical. A common response to the Medicean Stars was simply to say that the telescope had a lens defect and was producing illusory points of light and images; those saying this completely denied the existence of the moons. That only a few could initially see and verify what Galileo had observed supported the supposition that the optical theory during this period "could not clearly demonstrate that the instrument was not deceiving the senses". By naming the four moons after the Medici brothers and convincing the Grand Duke Cosimo II of his discoveries, the defence of Galileo's reports became a matter of State. Moran notes, "the court itself became actively involved in pursuing the confirmation of Galileo's observations by paying Galileo out of its treasury to manufacture spyglasses that could be sent through ambassadorial channels to the major courts of Europe". The secretary to Giovanni Antonio Magini, a Bohemian astronomer named Martin Horký, published an incendiary pamphlet criticizing the Sidereus Nuncius, alleging in it that Galileo's observations were the result of poor lenses and influenced by personal ambitions. After gaining some traction in Italy, however, Horky's work was ultimately strongly rebutted.
|
||||
The first astronomer to publicly support Galileo's findings was Johannes Kepler, who published an open letter in April 1610, enthusiastically endorsing Galileo's credibility. It was not until August 1610 that Kepler was able to publish his independent confirmation of Galileo's findings, due to the scarcity of sufficiently powerful telescopes.
|
||||
Several astronomers, such as Thomas Harriot, Joseph Gaultier de la Vatelle, Nicolas-Claude Fabri de Peiresc, and Simon Marius, published their confirmation of the Medicean Stars after Jupiter became visible again in the autumn of 1610. Marius, a German astronomer who had studied with Tycho Brahe, was the first to publish a book of his observations. Marius attacked Galileo in Mundus Jovialis (published in 1614) by insisting that he had found Jupiter's four moons before Galileo and had been observing them since 1609. Marius believed that he therefore had the right to name them, which he did: he named them after Jupiter's love conquests: Io, Europa, Ganymede, and Callisto. But Galileo was not confounded; he pointed out that being outside the Church, Marius had not yet accepted the Gregorian calendar and was still using the Julian calendar. Therefore, the night Galileo first observed Jupiter's moons was January 7, 1610 on the Gregorian calendar—December 28, 1609 on the Julian calendar (Marius claimed to have first observed Jupiter's moons on December 29, 1609). Although Galileo did indeed discover Jupiter's four moons before Marius, Io, Europa, Ganymede, and Callisto are now the names by which Galileo's four moons are known.
|
||||
By 1626 knowledge of the telescope had spread to China when German Jesuit and astronomer Johann Adam Schall von Bell published Yuan jing shuo, (Explanation of the Telescope) in Chinese and Latin.
|
||||
|
||||
== Controversy with the Catholic Church ==
|
||||
Galileo's drawings of an imperfect Moon directly contradicted Ptolemy's and Aristotle's cosmological descriptions of perfect and unchanging heavenly bodies made of quintessence (the fifth element in ancient and medieval philosophy of which the celestial bodies are composed).
|
||||
Before the publication of Sidereus Nuncius, the Catholic Church accepted the Copernican heliocentric system as strictly mathematical and hypothetical. However, once Galileo began to speak of the Copernican system as fact rather than theory, it introduced "a more chaotic system, a less-than-godly lack of organization." In fact, the Copernican system that Galileo believed to be real was interpreted by the Catholic leadership as a challenge to the Scriptures, "which referred to the sun 'rising' and the earth as 'unmoving.'"
|
||||
The conflict ended in 1633 with Galileo being sentenced to a form of house arrest by the Catholic Church. However, by 1633, Galileo had published other works in support of the Copernican view, and these were largely what caused his sentencing.
|
||||
|
||||
== Translations ==
|
||||
|
||||
=== English ===
|
||||
Edward Stafford Carlos; translations with introduction and notes. The Sidereal messenger of Galileo Galilei, and a part of the preface to Kepler's Dioptrics. Waterloo Place, London: Oxford and Cambridge, January 1880. 148 pp. ISBN 9781151499646.
|
||||
Stillman Drake. Discoveries and Opinions of Galileo, includes translation of Galileo's Sidereus Nuncius. Doubleday: Anchor, 1957. 320 pp. ISBN 978-0385092395.
|
||||
Stillman Drake. Telescopes, Tides, and Tactics: A Galilean Dialogue about The Starry Messenger and Systems of the World, including translation of Galileo's Sidereus Nuncius. London: University Of Chicago Press, 1983. 256 pp. ISBN 978-0226162317.
|
||||
Albert Van Helden (Professor Emeritus of History at Rice University); translation with introduction, conclusion and notes. Galileo Galilei, Sidereus Nuncius, or The Sidereal Messenger. Chicago and London: The University of Chicago Press, 1989. xiii + 127 pp. ISBN 978-0226279039.
|
||||
William R. Shea and Tiziana Bascelli; translated from the Latin by William R. Shea, introduction and notes by William R. Shea and Tiziana Bascelli. Galileo's Sidereus Nuncius or Sidereal Message. Sagamore Beach, MA: Science History Publications/USA, 2009. viii + 115 pp. ISBN 978-0-88135-375-4.
|
||||
|
||||
=== French ===
|
||||
Isabelle Pantin. Sidereus Nuncius: Le Messager Céleste. Paris: Belles Lettres, 1992. ASIN B0028S7JLK.
|
||||
Fernand Hallyn. Le messager des étoiles. France: Points, 1992. ISBN 978-2757812259.
|
||||
|
||||
=== German ===
|
||||
Anna Mudry. Sternenbotschaft, in Galilei Galilei: Schriften, Briefe, Dokumente, Band 1, pp. 94–144. Berlin: Rütten & Loening, 1987. ISBN 978-3-352-00122-2
|
||||
Hans Blumenberg. Sidereus Nuncius. Nachricht von neuen Sternen. Frankfurt: Suhrkamp, 1980. ISBN 978-3-51827937-3
|
||||
|
||||
=== Italian ===
|
||||
Maria Timpanaro Cardini. Sidereus nuncius. Firenze: Sansoni, 1948.
|
||||
|
||||
== See also ==
|
||||
Discourse on Comets
|
||||
Letters on Sunspots
|
||||
Nuncius (journal)
|
||||
Selenographia, sive Lunae descriptio
|
||||
|
||||
== References ==
|
||||
|
||||
== External links ==
|
||||
|
||||
Sidereus Nuncius 1610. From Rare Book Room. Photographed first edition.
|
||||
Sidereus Nuncius, in Latin in HTML format, or in Italian in pdf format or odt format. From LiberLiber.
|
||||
Linda Hall Library has a scanned first edition, as well as a scanned pirated edition from Frankfurt, also from 1610.
|
||||
Sidereus nuncius (Adams.5.61.1) Full digital edition in Cambridge Digital Library.
|
||||
The Sidereal Messenger of Galileo Galilei in English at Project Gutenberg.
|
||||
Sidereus nuncius Full digital edition in the Stanford Libraries.
|
||||
0
data/en.wikipedia.org/wiki/Space_Atlas
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data/en.wikipedia.org/wiki/Space_Atlas
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data/en.wikipedia.org/wiki/Star_Names-0.md
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|
||||
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|
||||
title: "Star Names"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/Star_Names"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:30.370164+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
Star-Names and Their Meanings (retitled Star Names: Their Lore and Meaning in some later reprints) is an 1899 book by Richard Hinckley Allen, that discusses the names of stars, constellations, and their histories.
|
||||
|
||||
|
||||
== Background and authorship ==
|
||||
|
||||
Richard Hinckley Allen (1838, near Buffalo, New York – 1908, Northampton, Massachusetts) was a youthful polymath with interests in "nature, astronomy, ornithology, and literature" whom his classmates described as "the walking encyclopedia"; after a college year spent at Yale, a pursuit abandoned because of problems with his eyesight, he traveled and then "joined his father’s export trade business". Allen's interest in astronomy, and in star names in particular, may have been stimulated by his coming across such a name with which he was unfamiliar, after which "[h]e spent many years researching astronomical nomenclature... primarily for personal enjoyment". With the encouragement of professors from Yale and Princeton, and from personal friends, Allen proceeded to publish the information he had gathered—as Star-Names and Their Meanings in 1899.
|
||||
|
||||
|
||||
== Content ==
|
||||
|
||||
First published in 1899 as Star-Names and Their Meanings, this work collected the origins of the names of stars and constellations from a panoply of sources, some primary but most secondary. It also briefly retells the various myths and folklore connected with stars in the Greco-Roman tradition, as well as in the Arabic, Babylonian, Indian and Chinese traditions (for which, however, some modern criticism having taken it to task, claiming it to be largely superseded).
|
||||
The book also provides some cursory details about astronomy, at the knowledge level of the end of the 19th century. Similarly, astrology and its history are dealt with briefly in the introduction, and some other basic astrological references (although downplayed) are scattered throughout the book.
|
||||
|
||||
|
||||
== Reception ==
|
||||
|
||||
Late historian of astronomy Paul Kunitzsch notes that the "book may be taken as a handbook summing up the state of knowledge arrived at by his time," but that to standards current to his 1979 publication, it was generally unreliable with regard to star names and their derivations. Science fiction writers/editors Algis Budrys and Frederik Pohl called Star Names "a fine book (but hardly 'hammock reading')", in a 1965 review. In an assessment by amateur classicist Bill Thayer, the book was presented as mostly accurate in its explanations of Greek and Latin star names, although containing minor historical errors, and overestimates of the age of some Greek temples. It was also criticised with regard to star names by Gary D. Thompson, an amateur astronomer who maintains its discussion of Arabic, Mesopotamian, and Egyptian constellations and star names are likewise especially unreliable.
|
||||
|
||||
|
||||
== Further reading ==
|
||||
Kunitzsch, Paul; Smart, Tim (1986). Short Guide to Modern Star Names. Wiesbaden, Germany: O. Harrassowitz. ISBN 9783447025805. Retrieved March 14, 2025.
|
||||
Kunitzsch, Paul; Smart, Tim (2006). A Dictionary of Modern Star Names: A Short Guide to 254 Star Names and Their Derivations (2nd ed.). Cambridge, MA: AAS Sky Publishing Corporation. ISBN 9781931559447. Retrieved March 14, 2025.
|
||||
Ridpath, Ian (2018). Star Tales (Revised, expanded ed.). Cambridge, England: Lutterworth Press. ISBN 9780718847814. Retrieved March 14, 2025. This book's subject area is described as literary criticism.
|
||||
|
||||
|
||||
== See also ==
|
||||
History of the constellations
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Allen's Star Names at LacusCurtius
|
||||
@ -0,0 +1,38 @@
|
||||
---
|
||||
title: "The Equatorie of the Planetis"
|
||||
chunk: 1/2
|
||||
source: "https://en.wikipedia.org/wiki/The_Equatorie_of_the_Planetis"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:25.529318+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Equatorie of the Planetis is a 14th-century scientific work which describes the construction and use of an equatorium. It was first studied in the early 1950s by Derek J. Price, and was formerly attributed to Geoffrey Chaucer. However, in 2014 it was shown to be written in the hand of the St Albans monk John Westwyk. It is largely written in Middle English, with some additions in Latin. It is accompanied by extensive astronomical tables, with Latin headings and annotations.
|
||||
|
||||
== Manuscript ==
|
||||
Peterhouse MS 75 was a composite manuscript. In the early 1950s, after Price discovered the Equatorie in it, the manuscript was split into two parts (and both parts rebound): MS 75.I, containing the Equatorie, and MS 75.II, containing works by Nicholas Trivet and Vegetius.
|
||||
MS 75.I has two parts: fol. 1r-71r contains largely astronomical tables, and some astrological material, in two hands; 71v-78v contains the text of the Equatorie treatise. The parchment is of varying quality, with ten quires of pages measuring 365x260mm (except for the last quires). The ink is brown; there are signs of dampness on the upper edge, especially in the first quire, with some blurring in the fourth quire on the top of the pages. According to Rand Schmidt, the dampness and the wear and tear on some of the quires is evidence that the quires spent some time unbound.
|
||||
The text contains references to 31 December 1392, and this is used as a baseline date for many of the tables. John North showed that the text was written during the first nine months of 1393. How it came to Peterhouse is not known, but it probably happened during the 15th century; around 1538 it is entered in Peterhouse catalog, as Tab. aequ. planetarum autore Simon Bredon. The Equatorie occupies eight leaves of the manuscript; the phrase Radix chaucer appears on fol. 5v.
|
||||
The manuscript has been digitised for the Cambridge University Digital Library website, together with a virtual model of the equatorium.
|
||||
|
||||
=== "Radix chaucer" ===
|
||||
On f. 5v, in a note on a page full of tables, the manuscript has the number "1392", followed by that number in sexagesimal notation, and the text "deffea xpi & Rxa chaucer". Price, and following him other scholars, expanded this as "differentia Christi et radix Chaucer"—or "the difference (in number of days) between (the year of Christ) and the (year of the) radix of Chaucer"—the radix in question then being the year 1392. F.N. Robinson was not convinced that this (third-person) reference indicated Chaucer's authorship. However, John North argued that the attachment of a name to a relatively "trivial" piece of data made it likely that this was a case of self-citation.
|
||||
|
||||
== Discovery and authorship ==
|
||||
The manuscript was in the library of Peterhouse, Cambridge by 1538, and probably by 1472. It was discovered there by the historian Derek de Solla Price in December 1951. Although the 19th-century manuscript catalogue stated that the manuscript contained "directions for making an astrolabe (?)", Price identified the instrument as a planetary equatorium. He argued that the manuscript was authored by, and written in the hand of, Geoffrey Chaucer. This was a controversial claim, and was treated with some scepticism by Chaucer scholars, though it received influential backing from the historian of astronomy John North. The manuscript was shown to be in the hand of John Westwyk by Kari Anne Rand in 2014. Further evidence for Westwyk's authorship was revealed by Seb Falk in a book published in 2020.
|
||||
|
||||
=== Debate ===
|
||||
Price published an abstract in 1953, and the whole text (facsimile, transcription, and studies of the manuscript) in 1955. He maintained the possibility that Chaucer authored the Equatorie, possibly as the missing part of his A Treatise on the Astrolabe, which describes the astrolabe; the Equatorie makes direct reference to it. He argued that the manuscript was a holograph draft, written in the hand of its author, as shown by the many additions and corrections in the manuscript.
|
||||
Price offered five points as indicators of Chaucer's authorship:
|
||||
|
||||
Style and scientific treatment of the material are similar to A Treatise on the Astrolabe;
|
||||
The text mentions that the year 1392 is the "Radix" (or "root") of Chaucer;
|
||||
The main hand (including that of the "Radix" note) resembled, Price thought, a document likely written in Chaucer's hand;
|
||||
Linguistic similarities between the Equatorie and Chaucer's work, including "verbal echoes of the Astrolabe;
|
||||
The author is influenced by Merton's school of astronomy but lives in London, and the writing is that of an amateur, not a professional astronomer; in addition, the writer is familiar with "the diplomatic cipher methods of his time"—all elements that correspond with Chaucer's biography.
|
||||
Following the publication of the facsimile and transcription, G. Herdan published an article in which he concluded, based upon the percentage of words in the Equatorie of "Romance vocabulary" (which includes words from Old French, Anglo-Norman French, and Latin), that Chaucer was indeed the author: "The agreement between observation and expectation, or between fact and theory, is so striking that without going further into the question of statistical significance we may conclude that by the token of Romance vocabulary the Equatorie is to be regarded as a work by Chaucer".
|
||||
However, Price's arguments were challenged in various ways. His claim that the manuscript was a draft in the hand of its author was disputed, though ultimately the evidence does seem to support it. More significantly, Price's claim that the handwriting was that of Geoffrey Chaucer was disproved by analysis by Kari Anne Rand Schmidt.
|
||||
In 2014 Kari Anne Rand identified the hand as belonging to John Westwyk.
|
||||
|
||||
== Content ==
|
||||
@ -0,0 +1,31 @@
|
||||
---
|
||||
title: "The Equatorie of the Planetis"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/The_Equatorie_of_the_Planetis"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:25.529318+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The text describes the construction of an equatorium, an instrument comparable to the astrolabe – but where an astrolabe shows the positions of the stars, an equatorium computes them for the planets, according to the Geocentric model of Ptolemy. The instrument is constructed from two discs, six feet in diameter. One of them is solid, and is marked with characteristics of the orbits of the various planets: their apogee, their equants, and other centres. The other disc consists of "a ring, a diametral bar, and a rule pivoted at the centre of the bar". The two discs are joined and simulate the motions of each of the planets. A divided circle around the rims of the two discs allow for the transferral of information from sets of tables (the Alfonsine tables, from a Parisian document) that contain the data for each planet.
|
||||
The design was based on earlier equatoria, but refined for greater ease of manufacture and use. It permits the user to find the longitudes of any classical planet (including the Sun and Moon, as well as the lunar latitude).
|
||||
|
||||
=== Cipher ===
|
||||
A cipher is used for some comments on the tables, and Price gave the key. He could not, however, discern what the rationale of or the ordering behind the key was – whether it was perhaps based on some medieval version of the Greek alphabet, or whether there was "some key-phrase or sentence such as a name or family motto" behind it.
|
||||
|
||||
== References ==
|
||||
|
||||
=== Notes ===
|
||||
|
||||
=== Bibliography ===
|
||||
Falk, Seb (2020). The Light Ages: A Medieval Journey of Discovery. London: Penguin. ISBN 978-0241374252.
|
||||
North, J.D. (1988). Chaucer's Universe. Oxford: Clarendon Press. ISBN 0-19-812668-9.
|
||||
Price, Derek de Solla (1975). Science Since Babylon. Yale University Press. ISBN 0-300-01798-7.
|
||||
Price, Derek J. (1955). The Equatorie of the Planetis. Cambridge University Press. p. 3. ISBN 9781107404274. {{cite book}}: ISBN / Date incompatibility (help)
|
||||
Rand, Kari Anne (2015). "The Authorship of The Equatorie of the Planetis Revisited". Studia Neophilologica. 87 (1): 15–35. doi:10.1080/00393274.2014.982355. S2CID 161392650.
|
||||
Rand Schmidt, Kari Anne (1993). The Authorship of the Equatorie of the Planetis. D.S. Brewer. ISBN 0-85991-370-8.
|
||||
|
||||
== External links ==
|
||||
Cambridge Digital Library: Equatorie of the Planetis Digitised images, transcription, translation & virtual model of Peterhouse MS 75.I.
|
||||
Seb Falk: What's the difference between an astrolabe and an equatorium Blog post.
|
||||
26
data/en.wikipedia.org/wiki/The_Grand_Design_(book)-0.md
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||||
---
|
||||
title: "The Grand Design (book)"
|
||||
chunk: 1/4
|
||||
source: "https://en.wikipedia.org/wiki/The_Grand_Design_(book)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:34.876413+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Grand Design is a popular-science book written by physicists Stephen Hawking and Leonard Mlodinow and published by Bantam Books in 2010. The book examines the history of scientific knowledge about the universe and explains eleven-dimensional M-theory. The authors of the book point out that a Unified Field Theory (a theory, based on an early model of the universe, proposed by Albert Einstein and other physicists) may not exist.
|
||||
It argues that invoking God is not necessary to explain the origins of the universe, and that the Big Bang is a consequence of the laws of physics alone. In response to criticism, Hawking said: "One can't prove that God doesn't exist, but science makes God unnecessary." When pressed on his own religious views by the 2010 Channel 4 documentary Genius of Britain, he clarified that he did not believe in a personal God.
|
||||
Published in the United States on September 7, 2010, the book became the number one bestseller on Amazon.com just a few days after publication.
|
||||
It was published in the United Kingdom on September 9, 2010, and became the number two bestseller on Amazon.co.uk on the same day. It topped the list of adult non-fiction books of The New York Times Non-fiction Best Seller list in September–October 2010.
|
||||
|
||||
== Synopsis ==
|
||||
The book examines the history of scientific knowledge about the universe. It starts with the Ionian Greeks, who claimed that nature works by laws, and not by the will of the gods. It later presents the work of Nicolaus Copernicus, who advocated the concept that the Earth is not located in the center of the universe.
|
||||
The book attempts to explain topics in a easier-to-understand way. Many examples related from daily life, mythology and history have been taken to explain, such as Viking Mythology about Skoll and Hati, movies like The Matrix, and the geocentric model of the universe.
|
||||
The authors then describe the theory of quantum mechanics using, as an example, the probable movement of an electron around a room. The presentation has been described as easy to understand by some reviewers, but also as sometimes "impenetrable," by others.
|
||||
The central claim of the book is that the theory of quantum mechanics and the theory of relativity together help us understand how universes could have formed out of nothing.
|
||||
|
||||
The authors write: Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.
|
||||
The authors explain, in a manner consistent with M-theory, that as the Earth is only one of several planets in the Solar System, and as the Milky Way galaxy is only one of many galaxies, the same may apply to our universe itself: that is, the universe may be one of a huge number of universes.
|
||||
The book concludes with the statement that only some universes of the multiple universes (or multiverse) support life forms and that we are located in one of those universes. The laws of nature that are required for life forms to exist appear in some universes by pure chance , Hawking and Mlodinow explain (see Anthropic principle).
|
||||
|
||||
== Reactions ==
|
||||
19
data/en.wikipedia.org/wiki/The_Grand_Design_(book)-1.md
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19
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||||
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|
||||
title: "The Grand Design (book)"
|
||||
chunk: 2/4
|
||||
source: "https://en.wikipedia.org/wiki/The_Grand_Design_(book)"
|
||||
category: "reference"
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tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:34.876413+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
=== Positive reactions ===
|
||||
Evolutionary biologist and advocate for atheism Richard Dawkins welcomed Hawking's position and said that "Darwinism kicked God out of biology but physics remained more uncertain. Hawking is now administering the coup de grace."
|
||||
Theoretical physicist Sean M. Carroll, writing in The Wall Street Journal, described the book as speculative but ambitious: "The important lesson of The Grand Design is not so much the particular theory being advocated but the sense that science may be able to answer the deep 'Why?' questions that are part of fundamental human curiosity."
|
||||
Cosmologist Lawrence Krauss, in his article "Our Spontaneous Universe", wrote that "there are remarkable, testable arguments that provide firmer empirical evidence of the possibility that our universe arose from nothing. ... If our universe arose spontaneously from nothing at all, one might predict that its total energy should be zero. And when we measure the total energy of the universe, which could have been anything, the answer turns out to be the only one consistent with this possibility. Coincidence? Maybe. But data like this coming in from our revolutionary new tools promise to turn much of what is now metaphysics into physics. Whether God survives is anyone's guess."
|
||||
James Trefil, a professor of physics at George Mason University, said in his Washington Post review: "I've waited a long time for this book. It gets into the deepest questions of modern cosmology without a single equation. The reader will be able to get through it without bogging down in a lot of technical detail and will, I hope, have his or her appetite whetted for books with a deeper technical content. And who knows? Maybe in the end the whole multiverse idea will actually turn out to be right!"
|
||||
Canada Press journalist Carl Hartman said: "Cosmologists, the people who study the entire cosmos, will want to read British physicist and mathematician Stephen Hawking's new book. The Grand Design may sharpen appetites for answers to questions like 'Why is there something rather than nothing?' and 'Why do we exist?' – questions that have troubled thinking people at least as far back as the ancient Greeks."
|
||||
Writing in the Los Angeles Times, Michael Moorcock praised the authors: "their arguments do indeed bring us closer to seeing our world, universe and multiverse in terms that a previous generation might easily have dismissed as supernatural. This succinct, easily digested book could perhaps do with fewer dry, academic groaners, but Hawking and Mlodinow pack in a wealth of ideas and leave us with a clearer understanding of modern physics in all its invigorating complexity."
|
||||
German daily Süddeutsche Zeitung devoted the whole opening page of its culture section to The Grand Design. CERN physicist and novelist Ralf Bönt reviews the history of the theory of everything from the 18th century to M-theory, and takes Hawking's conclusion on God's existence as a very good joke which he obviously welcomes very much.
|
||||
Best selling author Deepak Chopra in an interview with CNN said: "We have to congratulate Leonard and Stephen for finally, finally contributing to the climatic overthrow of the superstition of materialism. Because everything that we call matter comes from this domain which is invisible, which is beyond space and time. All religious experience is based on just three basic fundamental ideas...And nothing in the book invalidates any of these three ideas".
|
||||
22
data/en.wikipedia.org/wiki/The_Grand_Design_(book)-2.md
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22
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|
||||
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|
||||
title: "The Grand Design (book)"
|
||||
chunk: 3/4
|
||||
source: "https://en.wikipedia.org/wiki/The_Grand_Design_(book)"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:34.876413+00:00"
|
||||
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|
||||
---
|
||||
|
||||
=== Critical reactions ===
|
||||
John Lennox, Professor of Mathematics at Oxford University, declared "nonsense remains nonsense, even when talked by world-famous scientists." He points to several self-contradictory elements within the central claim of the text, as well as many logical errors made throughout the book which claims "philosophy is dead."
|
||||
Roger Penrose in the FT doubts that adequate understandings can come from this approach, and points out that "unlike quantum mechanics, M-theory enjoys no observational support whatsoever". Joe Silk in Science suggests that "Some humbleness would be welcome here...A century or two hence...I expect that M-theory will seem as naïve to cosmologists of the future as we now find Pythagoras's cosmology of the harmony of the spheres". Gerald Schroeder in "The Big Bang Creation: God or the Laws of Nature" explains that "The Grand Design breaks the news, bitter to some, that … to create a universe from absolute nothing God is not necessary. All that is needed are the laws of nature. … [That is,] there can have been a big bang creation without the help of God, provided the laws of nature pre-date the universe. Our concept of time begins with the creation of the universe. Therefore if the laws of nature created the universe, these laws must have existed prior to time; that is the laws of nature would be outside of time. What we have then is totally non-physical laws, outside of time, creating a universe. Now that description might sound somewhat familiar. Very much like the biblical concept of God: not physical, outside of time, able to create a universe."
|
||||
Dwight Garner in The New York Times was critical of the book, saying: "The real news about The Grand Design is how disappointingly tinny and inelegant it is. The spare and earnest voice that Mr. Hawking employed with such appeal in A Brief History of Time has been replaced here by one that is alternately condescending, as if he were Mr. Rogers explaining rain clouds to toddlers, and impenetrable."
|
||||
Craig Callender, in the New Scientist, was not convinced by the theory promoted in the book: "M-theory ... is far from complete. But that doesn't stop the authors from asserting that it explains the mysteries of existence ... In the absence of theory, though, this is nothing more than a hunch doomed – until we start watching universes come into being – to remain untested. The lesson isn't that we face a dilemma between God and the multiverse, but that we shouldn't go off the rails at the first sign of coincidences."
|
||||
Paul Davies in The Guardian wrote: "The multiverse comes with a lot of baggage, such as an overarching space and time to host all those bangs, a universe-generating mechanism to trigger them, physical fields to populate the universes with material stuff, and a selection of forces to make things happen. Cosmologists embrace these features by envisaging sweeping "meta-laws" that pervade the multiverse and spawn specific bylaws on a universe-by-universe basis. The meta-laws themselves remain unexplained – eternal, immutable transcendent entities that just happen to exist and must simply be accepted as given. In that respect the meta-laws have a similar status to an unexplained transcendent god." Davies concludes "there is no compelling need for a supernatural being or prime mover to start the universe off. But when it comes to the laws that explain the big bang, we are in murkier waters."
|
||||
Dr. Marcelo Gleiser, in his article "Hawking And God: An Intimate Relationship", stated that "contemplating a final theory is inconsistent with the very essence of physics, an empirical science based on the gradual collection of data. Because we don’t have instruments capable of measuring all of Nature, we cannot ever be certain that we have a final theory. There’ll always be room for surprises, as the history of physics has shown again and again. In fact, I find it quite pretentious to imagine that we humans can achieve such a thing. ... Maybe Hawking should leave God alone."
|
||||
Physicist Peter Woit, of Columbia University, has criticized the book: "One thing that is sure to generate sales for a book of this kind is to somehow drag in religion. The book's rather conventional claim that "God is unnecessary" for explaining physics and early universe cosmology has provided a lot of publicity for the book. I'm in favor of naturalism and leaving God out of physics as much as the next person, but if you're the sort who wants to go to battle in the science/religion wars, why you would choose to take up such a dubious weapon as M-theory mystifies me."
|
||||
In Scientific American, John Horgan is not sympathetic to the book:
|
||||
"M-theory, theorists now realize, comes in an almost infinite number of versions, which "predict" an almost infinite number of possible universes. Critics call this the "Alice's Restaurant problem," a reference to the refrain of the old Arlo Guthrie folk song: "You can get anything you want at Alice's Restaurant." Of course, a theory that predicts everything really doesn't predict anything... The anthropic principle has always struck me as so dumb that I can't understand why anyone takes it seriously. It's cosmology's version of creationism. ... The physicist Tony Rothman, with whom I worked at Scientific American in the 1990s, liked to say that the anthropic principle in any form is completely ridiculous and hence should be called CRAP. ... Hawking is telling us that unconfirmable M-theory plus the anthropic tautology represents the end of that quest. If we believe him, the joke's on us."
|
||||
The Economist is also critical of the book: Hawking and Mlodinow "...say that these surprising ideas have passed every experimental test to which they have been put, but that is misleading in a way that is unfortunately typical of the authors. It is the bare bones of quantum mechanics that have proved to be consistent with what is presently known of the subatomic world. The authors' interpretations and extrapolations of it have not been subjected to any decisive tests, and it is not clear that they ever could be. Once upon a time it was the province of philosophy to propose ambitious and outlandish theories in advance of any concrete evidence for them. Perhaps science, as Professor Hawking and Mr Mlodinow practice it in their airier moments, has indeed changed places with philosophy, though probably not quite in the way that they think."
|
||||
The Bishop of Swindon, Dr. Lee Rayfield, said, "Science can never prove the non-existence of God, just as it can never prove the existence of God." Anglican priest, Cambridge theologian and psychologist Rev. Dr. Fraser N. Watts said "a creator God provides a reasonable and credible explanation of why there is a universe, and ... it is somewhat more likely that there is a God than that there is not.
|
||||
21
data/en.wikipedia.org/wiki/The_Grand_Design_(book)-3.md
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21
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|
||||
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|
||||
title: "The Grand Design (book)"
|
||||
chunk: 4/4
|
||||
source: "https://en.wikipedia.org/wiki/The_Grand_Design_(book)"
|
||||
category: "reference"
|
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tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:34.876413+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
That view is not undermined by what Hawking has said."
|
||||
British scientist Baroness Greenfield also criticized the book in an interview with BBC Radio: "Of course they can make whatever comments they like, but when they assume, rather in a Taliban-like way, that they have all the answers, then I do feel uncomfortable." She later claimed her Taliban remarks were "not intended to be personal", saying she "admired Stephen Hawking greatly" and "had no wish to compare him in particular to the Taliban". Denis Alexander responded to Stephen Hawking's The Grand Design by stating that "the 'god' that Stephen Hawking is trying to debunk is not the creator God of the Abrahamic faiths who really is the ultimate explanation for why there is something rather than nothing", adding that "Hawking's god is a god-of-the-gaps used to plug present gaps in our scientific knowledge." "Science provides us with a wonderful narrative as to how [existence] may happen, but theology addresses the meaning of the narrative". Mathematician and philosopher of science Wolfgang Smith wrote a chapter-by-chapter summary and critique of the book, first published in Sophia: The Journal of Traditional Studies, and subsequently published as "From Physics to Science Fiction: Response to Stephen Hawking" in the 2012 edition of his collection of essays, Science & Myth.
|
||||
|
||||
== See also ==
|
||||
A Brief History of Time – 1988 book by Stephen Hawking
|
||||
A Briefer History of Time – 2005 popular science book by Stephen Hawking
|
||||
Brief Answers to the Big Questions – 2018 popular science book by Stephen Hawking
|
||||
Model-dependent realism – View of scientific inquiry that focuses on the role of scientific models of phenomena
|
||||
A Question and Answer Guide to Astronomy
|
||||
|
||||
== References ==
|
||||
36
data/en.wikipedia.org/wiki/The_Jupiter_Effect-0.md
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36
data/en.wikipedia.org/wiki/The_Jupiter_Effect-0.md
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|
||||
---
|
||||
title: "The Jupiter Effect"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/The_Jupiter_Effect"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:48.058108+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Jupiter Effect is a 1974 book by John Gribbin and Stephen Plagemann, in which the authors predicted that an alignment of the planets of the Solar System would create a number of catastrophes, including a great earthquake on the San Andreas Fault, on March 10, 1982. The book became a best-seller. The predicted catastrophes did not occur.
|
||||
|
||||
|
||||
== History ==
|
||||
Astronomers had long been aware that there would be an alignment of the planets on that date, when Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto would be on the same side of the Sun, within an arc 95 degrees wide. But no effect could be expected as the tidal forces of the other planets affecting the Earth's crust are negligible even at the planets' closest approach. In this book, the authors sought to partially sidestep these objections by considering the effect of the alignment on the Sun, and hence on the solar wind, which in turn is known to affect weather on the Earth. Atmospheric conditions on the Earth can alter the speed of its rotation. The effect on the Sun would also be quite small, however, and in fact there had been an even closer alignment in the year 1128 without any incident.
|
||||
As a result of the book's popularity, the alignment received widespread media attention around the world when it occurred on March 10, 1982. While some took the predictions seriously, others marked the date with "end of the world"-themed parties. By the time the alignment happened, Gribbin already disavowed the theory, telling the New York Times in February 1982 that his key prediction of increased solar activity had failed to materialize.
|
||||
In April 1982, Gribbin and Plagemann published a lesser-selling book, The Jupiter Effect Reconsidered. In it they theorized that the effect had actually taken place in 1980, despite the lack of planetary alignment then, and that it had triggered the volcanic eruption of Mount St. Helens.
|
||||
In his book, The Little Book of Science (pub. 1999), Gribbin admitted about his "Jupiter Effect" theory "...I don't like it, and I'm sorry I ever had anything to do with it."
|
||||
|
||||
|
||||
== References to the Jupiter Effect ==
|
||||
In his novel Goodbye California, (Fontana, 1980) Alistair Maclean makes a reference to the Jupiter Effect in the author's preface.
|
||||
The novel Syzygy, by Frederik Pohl, published in 1981, uses the Jupiter Effect as a source of panic whipped up by religious fanatics, politicians and land speculators in Los Angeles around the time of the alignment. The narrative makes detailed references to the book's arguments and places them in the context of science, the politics of scientific funding, and social reactions.
|
||||
A film version titled The Jupiter Menace was released in 1982, directed by Lee Auerbach and Peter Matulavich, and hosted by George Kennedy. The documentary features interviews with Stephen Plagemann, Jeffrey Goodman and John White (author of Pole Shift), It also includes Biblical prophecy, planetary alignments and survivalism. These topics are covered by interviews with CSA leader James Ellison, psychics Clarissa Bernhardt and Alex Tanous, and members of the Stelle community. The film's soundtrack was composed and produced by Larry Fast, under the name Synergy.
|
||||
Jeff Johnson and Sandy Simpson released a song called "The Jupiter Effect" on their 1982 album, Through the Door.
|
||||
In the 1984 film Blood Simple, the Jupiter Effect is mentioned on a car radio.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
The Jupiter Menace at IMDb
|
||||
Watch The Jupiter Menace on the Internet Archive
|
||||
Review on Planet Neukoln, 2016
|
||||
Review on The Internet is in America, 2013
|
||||
33
data/en.wikipedia.org/wiki/The_Living_Cosmos-0.md
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33
data/en.wikipedia.org/wiki/The_Living_Cosmos-0.md
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|
||||
---
|
||||
title: "The Living Cosmos"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/The_Living_Cosmos"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:33:54.122320+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Living Cosmos: Our Search for Life in the Universe is a non-fiction book by the astronomer Chris Impey that discusses the subject of astrobiology and efforts to discover life beyond Earth. It was published as a hardcover by Random House in 2007 and as a paperback by Cambridge University Press in 2011.
|
||||
|
||||
|
||||
== Summary ==
|
||||
The Living Cosmos is a non-fiction book by University of Arizona professor of astronomy Chris Impey on the status of astrobiology. It summarizes the state of research as scientists trying to address one of the most profound questions we can ask about nature: Is there life in the universe beyond the Earth? The author interviewed dozens of leading researchers, and he includes material from the interviews and vignettes of the researchers in the book. The companion web site to the book contains articles and video clips on astrobiology produced by the author, as well as a glossary and links to other relevant sites.
|
||||
The book begins with a review of the cosmic setting for life and reviews the insights of astronomy since Copernicus. The discovery that we live in a "biological universe" would be a continuation of the progression where there is nothing exceptional about the setting of the Earth and the events that have occurred on this planet.
|
||||
Subsequent chapters consider the origin of life on Earth, and the physical extremes to which life as adapted. In astrobiology, it pays to think "outside the box" and imagine how strange life might be or whether post-biological evolution is possible, where the basis is mechanical or computational. A chapter on evolution shows how it is affected by the cosmic environment.
|
||||
Possibilities of life in the Solar System are considered next, with emphasis on Mars, Titan, and outer moons harboring liquid water. Next is a summary of the rapidly changing state of play in the search for extrasolar planets or exoplanets. After centuries of speculation and decades of futile searching, planets around other stars were first discovered in 1995 and the number is now over 850, with several thousand more candidates from the Kepler mission. The book ends with the search for extraterrestrial intelligence (SETI) and the use of the Drake equation to frame discussions of cosmic companionship.
|
||||
The web site for the book features images of a set of seven mixed media, boxed construction art pieces by Heather Green, commissioned specially for the book. The art is on permanent display in the BIO5 Institute at the University of Arizona. An article on the collaboration between Heather Green and Chris Impey and the artistic and scientific themes of the work was published in the Leonardo Journal online.
|
||||
|
||||
|
||||
== Reception ==
|
||||
The Living Cosmos was generally very well received. It received a starred review from Kirkus Reviews, referring to the book as a "Lively, clear, and up-to-date overview of astronomy, cosmology, biology, and evolution, specifically as related to the search for extraterrestrial life". Popular magazine Entertainment Weekly gave the book a grade of B+, saying it was "not an easy read" but calling it a "live, elegant overview". It was reviewed by Nature, Physics Today, and New Scientist, with the latter commenting on occasional digressions, but declaring the book "beautifully written". Reader reviews are 85% five stars on Amazon and over 90% like the book on Goodreads. The 2011 paperback edition has updates to help keep up with the accelerating pace of exoplanet discovery.
|
||||
|
||||
|
||||
== Notes ==
|
||||
|
||||
|
||||
== External links ==
|
||||
Official website
|
||||
Cambridge University Press
|
||||
Amazon Author Page
|
||||
Chris Impey's Website
|
||||
21
data/en.wikipedia.org/wiki/The_Pluto_Files-0.md
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21
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|
||||
---
|
||||
title: "The Pluto Files"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/The_Pluto_Files"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:10.568696+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Pluto Files: The Rise and Fall of America's Favorite Planet is a book written by the astrophysicist and Hayden Planetarium director Neil deGrasse Tyson. The book is about Pluto, which was demoted to the status of dwarf planet in August 2006 by the International Astronomical Union, thereby depriving it of its planet-hood. The book also focuses on the fact that many Americans rallied their support for this icy dwarf on the edge of the Solar System because it was discovered by an American.
|
||||
The book was given a good review by Jon Stewart in a guest segment with Tyson on The Daily Show. During the interview, Stewart humorously lauded the book as "the most exciting book about Pluto you will ever read in your life," as well as "the compelling story of how [Tyson] destroyed Pluto's life."
|
||||
The book explains in full detail the journey of Pluto's life from its days as Planet X, to its discovery in the early 20th century and all the way to its current title as a Trans-Neptunian object.
|
||||
The book appeared on the extended hardcover nonfiction bestseller list in The New York Times in February 2009.
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== External links ==
|
||||
The Pluto Files at the publisher's site
|
||||
@ -0,0 +1,53 @@
|
||||
---
|
||||
title: "The Revelation in Storm and Thunder"
|
||||
chunk: 1/1
|
||||
source: "https://en.wikipedia.org/wiki/The_Revelation_in_Storm_and_Thunder"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:17.513364+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
In March 1907 the Russian astronomer Nikolai Alexandrovich Morozov published the book Revelation In Thunderstorm And Tempest. History of the Apocalypses Origin. (Russian: «Откровение в грозе и буре»; German title Die Offenbarung Johannis – Eine astronomisch-historische Untersuchung, meaning in English: The Revelation to John: An Astronomic Historical Investigation). After intervention by the Orthodox clergy, the book was added to the index of prohibited books the next year. In his book Morozov makes the case that the Book of Revelation is describing the astronomical constellation over the island of Patmos on Sunday, September 30, 395 (Julian date). Morozov presumes that the educated John was able to calculate the Saros cycle and, therefore, did observe the sky on this day in attendance of a solar eclipse. (This eclipse did occur indeed—over South America, however.)
|
||||
|
||||
|
||||
== Morozov's claims ==
|
||||
1. The weekday of the event is named explicitly:
|
||||
|
||||
Rev. 1,10: "I was in the Spirit on the Lords Day" (believed to be Sunday).
|
||||
2. The description of the skies starts systematically at the Pole with a constellation named Throne (presently Ursa Minor):
|
||||
|
||||
Rev. 4,2: And a throne was set in heaven...
|
||||
3. The text continues mentioning the Milky Way and the signs of the zodiac denoting the four seasons: Lion, Taurus, Sagittarius and Eagle (presently Aquarius):
|
||||
|
||||
Rev. 4,6-7: And before the throne there was a sea of glass like unto crystal: and in the midst of the throne, and round about the throne, were four beasts full of eyes before and behind. And the first beast was like a lion, and the second beast like a calf, and the third beast had a face as a man, and the fourth beast was like a flying eagle.
|
||||
4. The four horses were interpreted by Morozov as traditional metaphors for the planets Jupiter, Mars, Mercury and Saturn. The constellations Sagittarius, Perseus, Libra and Scorpion were sitting on them:
|
||||
|
||||
Rev. 6,2: And I saw, and behold a white horse: and he that sat on him had a bow;
|
||||
Rev. 6,4: And there went out another horse that was red: and power was given to him that sat thereon to take peace from the earth, and that they should kill one another: and there was given unto him a great sword.
|
||||
Rev. 6,5: And I beheld, and lo a black horse; and he that sat on him had a pair of balances in his hand.
|
||||
Rev. 6,8: And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him.
|
||||
5. Sun and Moon were named explicitly. The only female character of the zodiac is Virgo:
|
||||
|
||||
Rev. 12,1: A woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars.
|
||||
6. The planet Venus , used as a symbol of female eroticism and harlotry, united with the red star Antares (Anti-Mars) within the constellation Scorpion:
|
||||
|
||||
Rev. 17,3-4: and I saw a woman sit upon a scarlet colored beast, full of names of blasphemy, having seven heads and ten horns. And the woman was arrayed in purple and scarlet color, and decked with gold and precious stones and pearls, having a golden cup in her hand full of abominations and filthiness of her fornication.
|
||||
The description within the Book of Revelation matches exactly the Constellation for the Julian date 30-9-395.
|
||||
|
||||
Right ascension and Declination for the island of Patmos at 15:00 UTC on this day were calculated using the program Yoursky. (Due to precession R.A. of the stars has been shifted since 395).
|
||||
Sun, Moon and the 3 outer and 2 inner planets will produce 3.732.480 combinations within the 12 signs of the zodiac (125 × 5 × 3).
|
||||
Therefore, an accidental match is quite unlikely.
|
||||
At this point criticism of Chronology begins: Common understanding says, referring to Irenaeus (Haer. V,30,3), that the Revelation to John was written near the end of the reign of the Roman emperor Domitian (81-96). Consequently, either the Revelation has been dated some three centuries too old, or the reign of Domitian has. Unless of course real prophecy was occurring and the constellations of 30th Sept 395 were predicted in it. Such confirmation by astronomy may have contributed to its acceptance as canonical.
|
||||
|
||||
|
||||
== Literature ==
|
||||
Nikolai A. Morozov: "The Revelation to John - An astronomic historical Investigation" (Die Offenbarung Johannis – Eine astronomisch-historische Untersuchung, 223 pages, Stuttgart 1912.)
|
||||
Nikolai A. Morozov: "Revelation within Thunderstorm and Tempest. History of the Apocalypses Origin." (Откровение в грозе и буре. История возникновения Апокалипсиса. СПб.: Былое, 1907.)
|
||||
|
||||
|
||||
== References ==
|
||||
|
||||
|
||||
== Notes ==
|
||||
This article is a translation from the German Wikipedia.
|
||||
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---
|
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title: "The Sand Reckoner"
|
||||
chunk: 1/2
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source: "https://en.wikipedia.org/wiki/The_Sand_Reckoner"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:23.314778+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, Archimedes had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers.
|
||||
The work, also known in Latin as Arenarius, is about eight pages long in translation and is addressed to the Syracusan king Gelo II (son of Hiero II). It is considered the most accessible work of Archimedes.
|
||||
|
||||
== Naming large numbers ==
|
||||
|
||||
First, Archimedes had to invent a system of naming large numbers. The number system in use at that time could express numbers up to a myriad (μυριάς — 10,000), and by utilizing the word myriad itself, one can immediately extend this to naming all numbers up to a myriad myriads (108). Archimedes called the numbers up to 108 "first order" and called 108 itself the "unit of the second order". Multiples of this unit then became the second order, up to this unit taken a myriad-myriad times, 108·108=1016. This became the "unit of the third order", whose multiples were the third order, and so on. Archimedes continued naming numbers in this way up to a myriad-myriad times the unit of the 108-th order, i.e., (108)^(108)
|
||||
After having done this, Archimedes called the orders he had defined the "orders of the first period", and called the last one,
|
||||
|
||||
|
||||
|
||||
(
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
|
||||
|
||||
|
||||
)
|
||||
|
||||
(
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle (10^{8})^{(10^{8})}}
|
||||
|
||||
, the "unit of the second period". He then constructed the orders of the second period by taking multiples of this unit in a way analogous to the way in which the orders of the first period were constructed. Continuing in this manner, he eventually arrived at the orders of the myriad-myriadth period. The largest number named by Archimedes was the last number in this period, which is
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
(
|
||||
|
||||
|
||||
(
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
(
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
(
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
|
||||
|
||||
)
|
||||
|
||||
|
||||
=
|
||||
|
||||
10
|
||||
|
||||
8
|
||||
⋅
|
||||
|
||||
10
|
||||
|
||||
16
|
||||
|
||||
|
||||
|
||||
|
||||
.
|
||||
|
||||
|
||||
{\displaystyle \left(\left(10^{8}\right)^{(10^{8})}\right)^{(10^{8})}=10^{8\cdot 10^{16}}.}
|
||||
|
||||
|
||||
Another way of describing this number is a one followed by (short scale) eighty quadrillion (80·1015) zeroes.
|
||||
Archimedes' system is reminiscent of a positional numeral system with base 108, which is remarkable because the ancient Greeks used a very simple system for writing numbers, which employs 27 different letters of the alphabet for the units 1 through 9, the tens 10 through 90 and the hundreds 100 through 900.
|
||||
|
||||
=== Law of exponents ===
|
||||
Archimedes also discovered and proved the law of exponents,
|
||||
|
||||
|
||||
|
||||
|
||||
b
|
||||
|
||||
m
|
||||
|
||||
|
||||
|
||||
b
|
||||
|
||||
n
|
||||
|
||||
|
||||
=
|
||||
|
||||
b
|
||||
|
||||
m
|
||||
+
|
||||
n
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle b^{m}b^{n}=b^{m+n}}
|
||||
|
||||
, necessary to manipulate powers of some base
|
||||
|
||||
|
||||
|
||||
b
|
||||
|
||||
|
||||
{\displaystyle b}
|
||||
|
||||
. (Specifically, for this case,
|
||||
|
||||
|
||||
|
||||
b
|
||||
=
|
||||
10
|
||||
|
||||
|
||||
{\displaystyle b=10}
|
||||
|
||||
for powers of 10.)
|
||||
|
||||
== Estimation of the size of the universe ==
|
||||
Archimedes then estimated an upper bound for the number of grains of sand required to fill the Universe. To do this, he used the heliocentric model of Aristarchus of Samos. The original work by Aristarchus has been lost. This work by Archimedes however is one of the few surviving references to his theory, whereby the Sun remains unmoved while the Earth orbits the Sun. In Archimedes's own words:
|
||||
|
||||
His [Aristarchus'] hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.
|
||||
The reason for the large size of this model is that the Greeks were unable to observe stellar parallax with available techniques, which implies that any parallax is extremely small and so the stars must be placed at great distances from the Earth (assuming heliocentrism to be true).
|
||||
According to Archimedes, Aristarchus did not state how far the stars were from the Earth. Archimedes therefore had to make the following assumptions:
|
||||
|
||||
The Universe was spherical
|
||||
The ratio of the diameter of the Universe to the diameter of the orbit of the Earth around the Sun equalled the ratio of the diameter of the orbit of the Earth around the Sun to the diameter of the Earth.
|
||||
This assumption can also be expressed by saying that the stellar parallax caused by the motion of the Earth around its orbit equals the solar parallax caused by motion around the Earth. Put in a ratio:
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Diameter of Universe
|
||||
Diameter of Earth orbit around the Sun
|
||||
|
||||
|
||||
=
|
||||
|
||||
|
||||
Diameter of Earth orbit around the Sun
|
||||
Diameter of Earth
|
||||
|
||||
|
||||
|
||||
|
||||
{\displaystyle {\frac {\text{Diameter of Universe}}{\text{Diameter of Earth orbit around the Sun}}}={\frac {\text{Diameter of Earth orbit around the Sun}}{\text{ Diameter of Earth}}}}
|
||||
|
||||
|
||||
In order to obtain an upper bound, Archimedes made the following assumptions of their dimensions:
|
||||
43
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|
||||
---
|
||||
title: "The Sand Reckoner"
|
||||
chunk: 2/2
|
||||
source: "https://en.wikipedia.org/wiki/The_Sand_Reckoner"
|
||||
category: "reference"
|
||||
tags: "science, encyclopedia"
|
||||
date_saved: "2026-05-05T08:34:23.314778+00:00"
|
||||
instance: "kb-cron"
|
||||
---
|
||||
|
||||
that the circumference of the Earth was no bigger than 300 myriad stadia (5.55·105 km, an over estimate by roughly a factor of 40).
|
||||
that the Moon was no larger than the Earth, and that the Sun was no more than thirty times larger than the Moon (1.65·107 km, an over estimate by roughly a factor of 10)
|
||||
that the angular diameter of the Sun, as seen from the Earth, was greater than 1/200 of a right angle (π/400 radians = 0.45° degrees, an over estimate, but accurate to within 20% of the true value).
|
||||
Archimedes then concluded that the diameter of the Universe was no more than 1014 stadia (in modern units, about 2 light years), and that it would require no more than 1063 grains of sand to fill it. With these measurements, each grain of sand in Archimedes's thought-experiment would have been approximately 19 μm (0.019 mm) in diameter.
|
||||
|
||||
=== Calculation of the number of grains of sand in the Aristarchian Universe ===
|
||||
Archimedes claims that forty poppy-seeds laid side by side would equal one Greek daktylos (finger-width) which was approximately 19 mm (3/4 inch) in length. Since volume proceeds as the cube of a linear dimension ("For it has been proved that spheres have the triplicate ratio to one another of their diameters") then a sphere one dactyl in diameter would contain (using our current number system) 403, or 64,000 poppy seeds.
|
||||
He then claimed (without evidence) that each poppy seed could contain a myriad (10,000) grains of sand. Multiplying the two figures together he proposed 640,000,000 as the number of hypothetical grains of sand in a sphere one dactyl in diameter.
|
||||
To make further calculations easier, he rounded up 640 million to one billion, noting only that the first number is smaller than the second, and that therefore the number of grains of sand calculated subsequently will exceed the actual number of grains. Recall that Archimedes's meta-goal with this essay was to show how to calculate with what were previously considered impossibly large numbers, not simply to accurately calculate the number of grains of sand that would fit in the universe.
|
||||
A Greek stadium had a length of 600 Greek feet, and each foot was 16 dactyls long, so there were 9,600 dactyls in a stadium. Archimedes rounded this number up to 10,000 (a myriad) to make calculations easier, again, noting that the resulting number will exceed the actual number of grains of sand.
|
||||
The cube of 10,000 is a trillion (1012); and multiplying a billion (the number of grains of sand in a dactyl-sphere) by a trillion (number of dactyl-spheres in a stadium-sphere) yields 1021, the number of grains of sand in a stadium-sphere.
|
||||
Archimedes had estimated that the Aristarchian Universe was 1014 stadia in diameter, so there would accordingly be (1014)3 stadium-spheres in the universe, or 1042. Multiplying 1021 by 1042 yields 1063, the number of grains of sand in the Aristarchian Universe.
|
||||
Following Archimedes's estimate of a myriad (10,000) grains of sand in a poppy seed; 64,000 poppy seeds in a dactyl-sphere; the length of a stadium as 10,000 dactyls; and accepting 19mm as the width of a dactyl, the diameter of Archimedes's typical sand grain would be 18.3 μm, which today we would call a grain of silt. Currently, the smallest grain of sand would be defined as 50 μm in diameter.
|
||||
|
||||
=== Additional calculations ===
|
||||
Archimedes made some interesting experiments and computations along the way. One experiment was to estimate the angular size of the Sun, as seen from the Earth. Archimedes's method is especially interesting as it takes into account the finite size of the eye's pupil, and therefore may be the first known example of experimentation in psychophysics, the branch of psychology dealing with the mechanics of human perception, whose development is generally attributed to Hermann von Helmholtz. Another interesting computation accounts for solar parallax and the different distances between the viewer and the Sun, whether viewed from the center of the Earth or from the surface of the Earth at sunrise. This may be the first known computation dealing with solar parallax.
|
||||
|
||||
== Quote ==
|
||||
|
||||
There are some, king Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its magnitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the Earth, including in it all the seas and the hollows of the Earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken.
|
||||
|
||||
But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the Earth filled up in the way described, but also that of the mass equal in magnitude to the universe.
|
||||
|
||||
== References ==
|
||||
|
||||
== Further reading ==
|
||||
The Sand-Reckoner, by Gillian Bradshaw. Forge (2000), 348pp, ISBN 0-312-87581-9. This is a historical novel about the life and work of Archimedes.
|
||||
|
||||
== External links ==
|
||||
Original Greek text
|
||||
The Sand Reckoner (annotated)
|
||||
The Sand Reckoner (Arenario) Italian annotated translation, with notes about Archimedes and Greek mathematical notation and unit of measure. Source file of the Arenarius Greek text (for LaTeX).
|
||||
Archimedes, The Sand Reckoner, by Ilan Vardi; includes a literal English version of the original Greek text
|
||||
0
data/en.wikipedia.org/wiki/The_Sleepwalkers
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0
data/en.wikipedia.org/wiki/The_Sleepwalkers
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0
data/en.wikipedia.org/wiki/The_Stars
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0
data/en.wikipedia.org/wiki/The_Stars
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