The Origin of the Idea of Material and Life Cycles in the Ancient Cosmos of Concentric Spheres
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The Ptolemaic System Claudius Ptolemy
Putting it All Together: The Ptolemaic System Claudius Ptolemy (c. 90 - c. 168 CE) • Librarian at Alexandria • “The Great Treatise” & “The Almagest” (to the 12th Century) The Ptolemaic System: Objectives Wanted: A Model to explain the observed apparent motions of the Sun, Moon, Planets, and the Celestial Sphere. The Model should explain related phenomena such as the lunar phases, eclipses, and planetary brightness variation. The Model should be capable of accurately predicting these phenomena. (When? Where? Details?) The Model is geostatic, geocentric, and uses only uniform circular motions. (cf., the Aristotelian doctrines and the Aristarchian heresy.) The Ptolemaic System Observations • The apparent rotation of the Celestial Sphere • The annual motion of the Sun along the ecliptic • The monthly motion of the Moon The lunar phases and the synodic month Lunar and Solar Eclipses • The motions of the planets on the celestial sphere Direct and retrograde motions Planetary brightness variations Periodicities: The synodic periods Assumptions • A Geostatic cosmology (The Earth does not move.) • Uniform Circular motions (It is a “perfect” universe.) Approaches • The offsets and epicycles introduced by Hipparchus The Ptolemaic System For Inferior Planets (Mercury Venus) Deferent Period is 1 Year; Epicyclic period is the Synodic Period For Superior Planets (Mars, Jupiter, Saturn) Deferent Period is the Synodic period; Epicyclic Period is 1 year The Ptolemaic System (“To Scale”) Note: Indicated motions are with respect to the Celestial Sphere AGAIN: Problems with the Ptolemaic System Recollect the assumptions • The Earth doesn’t move (“geostatic”) • The Earth is at the center of the universe (“geocentric”) • All motions are circular (... or combinations thereof) • All motions are uniform (.. -
Thinking Outside the Sphere Views of the Stars from Aristotle to Herschel Thinking Outside the Sphere
Thinking Outside the Sphere Views of the Stars from Aristotle to Herschel Thinking Outside the Sphere A Constellation of Rare Books from the History of Science Collection The exhibition was made possible by generous support from Mr. & Mrs. James B. Hebenstreit and Mrs. Lathrop M. Gates. CATALOG OF THE EXHIBITION Linda Hall Library Linda Hall Library of Science, Engineering and Technology Cynthia J. Rogers, Curator 5109 Cherry Street Kansas City MO 64110 1 Thinking Outside the Sphere is held in copyright by the Linda Hall Library, 2010, and any reproduction of text or images requires permission. The Linda Hall Library is an independently funded library devoted to science, engineering and technology which is used extensively by The exhibition opened at the Linda Hall Library April 22 and closed companies, academic institutions and individuals throughout the world. September 18, 2010. The Library was established by the wills of Herbert and Linda Hall and opened in 1946. It is located on a 14 acre arboretum in Kansas City, Missouri, the site of the former home of Herbert and Linda Hall. Sources of images on preliminary pages: Page 1, cover left: Peter Apian. Cosmographia, 1550. We invite you to visit the Library or our website at www.lindahlll.org. Page 1, right: Camille Flammarion. L'atmosphère météorologie populaire, 1888. Page 3, Table of contents: Leonhard Euler. Theoria motuum planetarum et cometarum, 1744. 2 Table of Contents Introduction Section1 The Ancient Universe Section2 The Enduring Earth-Centered System Section3 The Sun Takes -
Nicolaus Copernicus: the Loss of Centrality
I Nicolaus Copernicus: The Loss of Centrality The mathematician who studies the motions of the stars is surely like a blind man who, with only a staff to guide him, must make a great, endless, hazardous journey that winds through innumerable desolate places. [Rheticus, Narratio Prima (1540), 163] 1 Ptolemy and Copernicus The German playwright Bertold Brecht wrote his play Life of Galileo in exile in 1938–9. It was first performed in Zurich in 1943. In Brecht’s play two worldviews collide. There is the geocentric worldview, which holds that the Earth is at the center of a closed universe. Among its many proponents were Aristotle (384–322 BC), Ptolemy (AD 85–165), and Martin Luther (1483–1546). Opposed to geocentrism is the heliocentric worldview. Heliocentrism teaches that the sun occupies the center of an open universe. Among its many proponents were Copernicus (1473–1543), Kepler (1571–1630), Galileo (1564–1642), and Newton (1643–1727). In Act One the Italian mathematician and physicist Galileo Galilei shows his assistant Andrea a model of the Ptolemaic system. In the middle sits the Earth, sur- rounded by eight rings. The rings represent the crystal spheres, which carry the planets and the fixed stars. Galileo scowls at this model. “Yes, walls and spheres and immobility,” he complains. “For two thousand years people have believed that the sun and all the stars of heaven rotate around mankind.” And everybody believed that “they were sitting motionless inside this crystal sphere.” The Earth was motionless, everything else rotated around it. “But now we are breaking out of it,” Galileo assures his assistant. -
OR GREAT BOOK. Figure 10 Explains the Cosmographic System of The
36 THE "ALMAGEST" OR GREAT BOOK. Figure 10 explains the cosmographic system of the same astronomer. In the centre we see the Earth, externally surrounded by fire [which is precisely opposite to the truth, according to the fundamental principles of modern geology; but the reader will understand that we are not attempting here to expose the errors of Ptolemaus; we confine ourselves to a description of his system]. Above the Earth spreads the first crystalline heaven, which carries and conveys the Moon. In the second and third crystal heavens the planets Mercury and Venus respectively describe their epicycles. The fourth heaven belongs to the Sun ; wherein it traverses the circle known as the ecliptic. The three last celestial spheres include Mars, Jupiter, and Saturn. Beyond these planets shines the heaven of the fixed stars. It rotates upon itself from east to west, with an inconceivable rapidity and an incalculable force of impulsion, for it is this which sets in motion all the fabulous machine. Ptolemaus places on the extreme confines of his vast Whole the eternal abode of the blessed. Thrice happy they in having no further cause to concern themselves %I c r ~NT about so terrible a system ; a system far from transparent, notwithstand ing all its crystal! S The treatise in which the Greek SU N X astronomer summed up his labours r _N_U remained for generations in high ( favour with the learned, and especi r F; r ally with the Arabs, whose privilegp and renown it is to have preserved intact the precious deposit of the sciences, when the Europe of the N - twelfth and thirteenth centuries was plunged in the night-shadows of the profoundest ignorance. -
The Planetary Increase of Brightness During Retrograde Motion: an Explanandum Constructed Ad Explanantem
Studies in History and Philosophy of Science 54 (2015) 90e101 Contents lists available at ScienceDirect Studies in History and Philosophy of Science journal homepage: www.elsevier.com/locate/shpsa The planetary increase of brightness during retrograde motion: An explanandum constructed ad explanantem Christián Carlos Carman National University of Quilmes/CONICET, Roque Sáenz Peña 352, B1876BXD Bernal, Buenos Aires, Argentina article info abstract Article history: In Ancient Greek two models were proposed for explaining the planetary motion: the homocentric Received 5 May 2015 spheres of Eudoxus and the Epicycle and Deferent System. At least in a qualitative way, both models Received in revised form could explain the retrograde motion, the most challenging phenomenon to be explained using circular 17 September 2015 motions. Nevertheless, there is another explanandum: during retrograde motion the planets increase their brightness. It is natural to interpret a change of brightness, i.e., of apparent size, as a change in Keywords: distance. Now, while according to the Eudoxian model the planet is always equidistant from the earth, Epicycle; according to the epicycle and deferent system, the planet changes its distance from the earth, Deferent; fi Homocentric spheres; approaching to it during retrograde motion, just as observed. So, it is usually af rmed that the main ’ Brightness change reason for the rejection of Eudoxus homocentric spheres in favor of the epicycle and deferent system was that the first cannot explain the manifest planetary increase of brightness during retrograde motion, while the second can. In this paper I will show that this historical hypothesis is not as firmly founded as it is usually believed to be. -
Historical Astronomy
Historical Astronomy (Neolithic record of Moon Phases) Introduction Arguably the history of astronomy IS the history of science. Many cultures carried out astronomical observations. However, very few formed mathematical or physical models based on their observations. It is those that did that we will focus on here, primarily the Babylonians and Greeks. Other Examples At the same time, that focus should not cause us to forget the impressive accomplishments of other cultures. Other Examples ∼ 2300 year old Chankillo Big Horn Medicine Wheel, Observatory, near Lima, Wyoming Peru Other Examples Chinese Star Map - Chinese records go back over 4000 Stonehenge, England years Babylonian Astronomy The story we will follow in more detail begins with the Babylonians / Mesopotamians / Sumerians, the cultures that inhabited the “fertile crescent.” Babylonian Astronomy Their observations and mathematics was instrumental to the development of Greek astronomy and continues to influence science today. They were the first to provide a mathematical description of astronomical events, recognize that astronomical events were periodic, and to devise a theory of the planets. Babylonian Astronomy Some accomplishments: • The accurate prediction of solar and lunar eclipses. • They developed mathematical models to predict the motions of the planets. • Accurate star charts. • Recognized the changing apparent speed of the Sun’s motion. • Developed models to account for the changing speed of the Sun and Moon. • Gave us the idea of 360◦ in a circle, 600 in a degree, 6000 in a minute. Alas, only very fragmentary records of their work survives. Early Greek The conquests of Alexander the Great are oen credited with bringing knowl- edge of the Babylonians science and mathematics to the Greeks. -
“Point at Infinity Hape of the World
“Point at Infinity hape of the World Last week, we began a series of posts dedicated to thinking about immortality. If we want to even pretend to think precisely about immortality, we will have to consider some fundamental questions. What does it mean to be immortal? What does it mean to live forever? Are these the same thing? And since immortality is inextricably tied up in one’s relationship with time, we must think about the nature of time itself. Is there a difference between external time and personal time? What is the shape of time? Is time linear? Circular? Finite? Infinite? Of course, we exist not just across time but across space as well, so the same questions become relevant when asked about space. What is the shape of space? Is it finite? Infinite? It is not hard to see how this question would have a significant bearing on our thinking about immortality. In a finite universe (or, more precisely, a universe in which only finitely many different configurations of maer are possible), an immortal being would encounter the same situations over and over again, would think the same thoughts over and over again, would have the same conversations over and over again. Would such a life be desirable? (It is not clear that this repetition would be avoidable even in an infinite universe, but more on that later.) Today, we are going to take a lile historical detour to look at the shape of the universe, a trip that will take us from Ptolemy to Dante to Einstein, a trip that will uncover a remarkable confluence of poetry and physics. -
Proof of Geocentric Theory E
Proof of geocentric theory E. A. Abdo Abstract: Rejected by modern science, the geocentric theory (in Greek, ge means earth), which maintained that Earth was the center of the universe, dominated ancient and medieval science. It seemed evident to early astronomers that the rest of the universe moved about a stable, motionless Earth. The Sun, Moon, planets, and stars could be seen moving about Earth along circular paths day after day. It appeared reasonable to assume that Earth was stationary, for nothing seemed to make it move. Furthermore, the fact that objects fall toward Earth provided what was perceived as support for the geocentric theory. Finally, geocentrism was in accordance with the theocentric (God-centered) world view, dominant in in the Middle Ages, when science was a subfield of theology. Introduction: The geocentric model created by Greek astronomers assumed that the celestial bodies moving about the Earth followed perfectly circular paths. This was not a random assumption: the circle was regarded by Greek mathematicians and philosophers as the perfect geometric figure and consequently the only one appropriate for celestial motion. However, as astronomers observed, the patterns of celestial motion were not constant. The Moon rose about an hour later from one day to the next, and its path across the sky changed from month to month. The Sun's path, too, changed with time, and even the configuration of constellations changed from season to season. These changes could be explained by the varying rates at which the celestial bodies revolved around the Earth. However, the planets (which got their name from the Greek word planetes, meaning wanderer and subject of error), behaved in ways that were difficult to explain. -
The Arithmetic of the Spheres
The Arithmetic of the Spheres Je↵ Lagarias, University of Michigan Ann Arbor, MI, USA MAA Mathfest (Washington, D. C.) August 6, 2015 Topics Covered Part 1. The Harmony of the Spheres • Part 2. Lester Ford and Ford Circles • Part 3. The Farey Tree and Minkowski ?-Function • Part 4. Farey Fractions • Part 5. Products of Farey Fractions • 1 Part I. The Harmony of the Spheres Pythagoras (c. 570–c. 495 BCE) To Pythagoras and followers is attributed: pitch of note of • vibrating string related to length and tension of string producing the tone. Small integer ratios give pleasing harmonics. Pythagoras or his mentor Thales had the idea to explain • phenomena by mathematical relationships. “All is number.” A fly in the ointment: Irrational numbers, for example p2. • 2 Harmony of the Spheres-2 Q. “Why did the Gods create us?” • A. “To study the heavens.”. Celestial Sphere: The universe is spherical: Celestial • spheres. There are concentric spheres of objects in the sky; some move, some do not. Harmony of the Spheres. Each planet emits its own unique • (musical) tone based on the period of its orbital revolution. Also: These tones, imperceptible to our hearing, a↵ect the quality of life on earth. 3 Democritus (c. 460–c. 370 BCE) Democritus was a pre-Socratic philosopher, some say a disciple of Leucippus. Born in Abdera, Thrace. Everything consists of moving atoms. These are geometrically• indivisible and indestructible. Between lies empty space: the void. • Evidence for the void: Irreversible decay of things over a long time,• things get mixed up. (But other processes purify things!) “By convention hot, by convention cold, but in reality atoms and• void, and also in reality we know nothing, since the truth is at bottom.” Summary: everything is a dynamical system! • 4 Democritus-2 The earth is round (spherical). -
Hestia: the Indo-European Goddess of the Cosmic Central Fire
Hestia: The Indo-European Goddess of the Cosmic Central Fire Marcello De Martino Abstract: The Pythagorean Philolaus of Croton (470-390 BCE) created a unique model of the Universe and he placed at its centre a ‘fire’, around which the spheres of the Earth, the Counter-Earth, the five planets, the Sun, the Moon and the outermost sphere of fixed stars, also viewed as fire but of an ‘aethereal’ kind, were revolving. This system has been considered as a step towards the heliocentric model of Aristarchus of Samos (310-230 BCE), the astronomical theory opposed to the geocentric system, which already was the communis opinio at that time and would be so for many centuries to come: but is that really so? In fact, comparing the Greek data with those of other ancient peoples of Indo-European language, it can be assumed that the ‘pyrocentric’ system is the last embodiment of a theological tradition going back to ancient times: Hestia, the central fire, was the descendant of an Indo-European goddess of Hearth placed at the centre of the religious and mythological view of a deified Cosmos where the gods were essentially personifications of atmospheric phenomena and of celestial bodies. In 1960, an article came out in a scientific journal which specialised in topics which were a bit more eccentric that those of traditional research studies on the history of religions, especially the classical ones. Its title was On the Relation between Early Greek Scientific Thought and Mysticism: Is Hestia, the Central Fire, an Abstract Astronomical Concept?.1 The author was Rudolph E. -
To Save the Phenomena
To Save the Phenomena Prof. David Kaiser Thursday, June 23, 2011, STS.003 Heavens unit Overarching questions: Are representations of astronomical phenomena true or merely useful? How does scientific knowledge travel? I. Ptolemy and the Planets II. Medieval Islamic Astronomy III. Copernican Revolutions Readings: Ptolemy, The Almagest, 5-14, 86-93; Al-Tusi, Memoir on Astronomy, 194-222; Lindberg, Beginnings of Western Science, 85-105. Timeline Ancient Medieval 500 BCE 500 CE 1450 Renaissance Enlightenment 1450 1700 1850 Modern 1850 today Thursday, June 23, 2011, STS.003 Puzzle of the Planets ―planet‖ = ―wanderer‖ 1. Planets roughly follow the path of the sun (within 5˚of the ecliptic). 2. They tend to move W to E over the year, but with varying speeds. 3. They sometimes display retrograde motion. 4. They appear brightest during retrograde. Plato‘s challenge: ―to save the phenomena.‖ ―By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?‖ Retrograde Motion Illustration explaining retrograde motion removed due to copyright restrictions. Mars, 2003 Geocentrism Nearly all of the ancient scholars assumed geocentrism: that the Earth sits at rest in the middle of the cosmos, while the sun, planets, and stars revolve around it. Aristotle, ca. 330 BCE ―[Some people think] there is nothing against their supposing the heavens immobile and the earth as turning on the same axis from west to east very nearly one revolution a day. But it has escaped their notice in the light of what happens around us in the air that such a notion would seem altogether absurd.‖ “That the Earth does not in any way move Aristotle, De Caelo locally” – Ptolemy, Almagest, 1:7 Flat Earth? No! Nearly all Greek scholars assumed that the Earth was a perfect sphere. -
Astronomical & Astrophysical Transactions
This article was downloaded by:[Bochkarev, N.] On: 7 December 2007 Access Details: [subscription number 746126554] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Astronomical & Astrophysical Transactions The Journal of the Eurasian Astronomical Society Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713453505 Comparison and historical evolution of ancient Greek cosmological ideas and mathematical models Antonios D. Pinotsis a a Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Athens, Greece Online Publication Date: 01 December 2005 To cite this Article: Pinotsis, Antonios D. (2005) 'Comparison and historical evolution of ancient Greek cosmological ideas and mathematical models', Astronomical & Astrophysical Transactions, 24:6, 463 - 483 To link to this article: DOI: 10.1080/10556790600603859 URL: http://dx.doi.org/10.1080/10556790600603859 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.