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Topic: Epicycles

	The Universe of Aristotle and Ptolemy
		Then, the centers of the epicycles executed uniform circular motion as they went around the deferent at uniform angular velocity, and at the same time the epicyles (to which the planets were attached) executed their own uniform circular motion.
		As the center of the epicycle moves around the deferent at constant angular velocity, the planet moves around the epicycle, also at constant angular velocity.
		In actual models, the center of the epicycle moved with uniform circular motion, not around the center of the deferent, but around a point that was displaced by some distance from the center of the deferent.
	csep10.phys.utk.edu /astr161/lect/retrograde/aristotle.html (757 words)

	Deferent and epicycle - Wikipedia, the free encyclopedia
		The rate at which the planet moved on the epicycle was fixed such that the angle between the center of the of epicycle and the planet was the same as the angle between the earth and the sun.
		The addition of epicycles, a gradual process of going from a simple model to a complex model is sometimes used as an allegory for some modern technical boondoggles.
		Epicycles were finally eliminated in Europe in the 17th century, when Johannes Kepler's model of elliptical orbits gradually replaced Copernicus' model based on perfect circles.
	en.wikipedia.org /wiki/Epicycle (1085 words)

	Solar System Models (Site not responding. Last check: 2007-10-11)
		However, when the detailed observations of the planets in the skies is examined, the planets undergo motion which is impossible to explain in the geocentric model, a backward track for the outer planets.
		Kepler (1600's) a student of Tycho who used Brahe's database to formulate the Laws of Planetary Motion which corrects the problems of epicycles in the heliocentric theory by using ellipses instead of circles for orbits of the planets.
		The orbital motion of a planet is completely described by six elements: the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the argument of the perihelion and the time of the perihelion.
	zebu.uoregon.edu /~js/ast221/lectures/lec06.html (1751 words)

	Epicycle and Deferent Demo (Site not responding. Last check: 2007-10-11)
		This is the ratio of the angular velocity of the deferent to that of the epicycle.
		To set the epicycle in motion around the deferent, increase the rotation ratio (the ratio of the angular velocities of the deferent to epicycle) from 0, and adjust the rate ("fast","medium" or "slow"), which governs how fast the planet's positions are drawn.
		To change the size of the epicycle, adjust "Size ratio", which is the ratio of the diameters of the deferent to the epicycle.
	physics.syr.edu /courses/java/demos/kennett/Epicycle/Epicycle.html (274 words)

	The Ptolemaic Model
		The Ptolemaic model accounted for the apparent motions of the planets in a very direct way, by assuming that each planet moved on a small sphere or circle, called an epicycle, that moved on a larger sphere or circle, called a deferent.
		The stars, it was assumed, moved on a celestial sphere around the outside of the planetary spheres.
		While the fact that we base planetarium projectors on the Ptolemaic model of the universe that was developed almost 2,000 years ago may seem impressive, a better test of the model is how long the model was accepted by society.
	www.polaris.iastate.edu /EveningStar/Unit2/unit2_sub1.htm (458 words)

	Adding Epicycles
		You have to admit, though, that epicycles are a pretty clever approximation.
		Epicycles and the like were not necessarily seen to be a problem.
		Yes, the epicycle models clung to circles too tightly, but we may be doing the same thing but don't know it yet.
	c2.com /cgi/wiki?AddingEpicycles (1092 words)

	Moses Maimonides (1135-1204): the Reality of Epicycles and Eccentrics Denied
		But if an epicycle existed, its motion would be neither from that point nor toward it nor around it.
		Now if epicycles exist, theirs would be a circular motion that would not revolve round an immobile thing.
		The extreme predilection that I have for investigating the truth is evidenced by the fact that I have explicitly stated and reported my perplexity regarding these matters as well as by the fact that I have not heard nor do I know a demonstration as to anything concerning them.
	homepages.wmich.edu /~mcgrew/maimonides.htm (1837 words)

	Ptolemy (Site not responding. Last check: 2007-10-11)
		The planets moved on small circular paths, called epicycles.
		The centers of these epicycles move around the earth of other circular paths, called deferents.
		The combination of the planetary motions along the epicycles and deferents produces the observed wandering of the planets among the stars, including the retrograde motion.
	astrosun2.astro.cornell.edu /academics/courses/astro201/ptolemy.htm (139 words)

	Webjay - "The changelings - epicycles + astronomica" by yoshipp (Site not responding. Last check: 2007-10-11)
		The changelings - Epicycles - 02 - Eclipse
		The changelings - Epicycles - 05 - The young merlins
		The changelings - Epicycles - 04 - Dulcinea
	webjay.org /by/yoshipp/epicycles (224 words)

	Parabola Magazine - Epicycles - Myth, Tradition, and the Search for Meaning (Site not responding. Last check: 2007-10-11)
		We call these tales "Epicycles." In geometry, an epicycle is a small circle which moves on the circumference of a larger circle--in this case, the theme of the issue.
		Parabola does not accept as Epicycles recountings of dreams or visionary experiences, or "invented" mythology of any kind.
		The tradition from which the tale comes (Navajo, Greek, Christian, etc.) must be noted on the manuscript; if possible, please mention the source of the story (the Mahabharata, the Iliad, traditional storyteller, etc.) in your cover letter.
	www.parabola.org /magazine/submissions/epicycle.php4 (418 words)

	Lecture 5
		So astronomers added epicycle upon epicycle (up to 28 in Ptolemy's system) to try to get predicted positions that would agree with the observations.
		Moreover, some of the epicycles were not centered on previous orbital paths (the "deferent") but were offset.
		Copernicus re-introduced this idea in the 16th century in order to reduce the number of epicycles needed in the calculations.
	www.astrobio.nau.edu /~koerner/ast180/lectures/lec5.html (851 words)

	black-holes.org—Relativity and the Center of the Universe
		When the Greek astronomer Ptolemy approached this issue, he believed that the Earth ought to hold a privileged place in the cosmos, so he put it at the center of his system, and had the heavenly bodies move basically on circles centered on the Earth.
		An epicycle is a secondary circle with its center moving along the main circle.
		Eventually, though planets were supposed to be following epicycles upon epicycles upon epicycles, and the system became very complicated and awkward.
	www.black-holes.org /relativity1.html (680 words)

	History and Philosophy of Western Astronomy
		During the years between Ptolemy and Copernicus, many small epicycles had been added to the main epicycles to make Ptolemy's model agree with the observations.
		His model still used small epicycles to get the details of the retrograde loops correct, though they were only a minor feature.
		He used trigonometry to describe the distances of the planets from the Sun relative to the astronomical unit (average Earth-Sun distance), but he did not know the numerical value of the astronomical unit.
	www.astronomynotes.com /history/s4.htm (1106 words)

	Geocentric model (Site not responding. Last check: 2007-10-11)
		The following animation shows a simplified geocentric model with three objects: the Earth (blue) in the centre with the Sun (yellow) and Mars (red) in circular orbits around it.
		Mars travels on an epicycle which is centred on its deferent.
		The phenomenon of ``retrograde motion'' occurs while Mars is at opposition.
	www.astro.utoronto.ca /~zhu/ast210/geocentric.html (128 words)

	Myths about the Copernican Revolution
		The reason why some Arab astronomers introduced epicycles on epicycles, was to avoid using an equant point.
		One essential assumptions in Ptolemy's Almagest is that the center of the epicycles of Mercury and Venus are collinear with the Earth and the Sun.
		With hindsight this is of course true, but his contemporaries were most impressed by the way he had removed the equant point and his use of eccentrics with compound, small epicycles and Tusi couple.
	www.math.nus.edu.sg /aslaksen/teaching/copernicus.html (817 words)

	fractalus gallery: copyright
		All of the images in this gallery, including "Epicycles", are protected by copyright.
		You are welcome to download the image using the links below, provided it is for personal use only.
		If you would like to comment on this image, please use this feedback form.
	www.fractalus.com /gallery/copyright/epicycles/?page=1 (66 words)

	Clavius, Sphaera, Ch. 4
		Observations supporting epicycles I: Variations in apparent magnitude at apogee
		Observations supporting epicycles II: Variations in proper motion at apogee
		Observations supporting epicycles III: Variability of lunar eclipses
	www.sal.wisc.edu /~lattis/clavius/CLAVIUS.HTM (334 words)

	Footnotes on Epicycles
		It has been about a year since I launched Footnotes on Epicycles; the one year mark is Wednesday.
		I have been migrating between servers and, in the course of doing so, made the decision not to renew fecundity.info after the next year of registration runs out.
		The old one should forward for the next thirteen months or so, so you may change over bookmarks at your convenience.
	laser.fontmonkey.com /foe/index.php (1946 words)

	Epicycles Explain Retrograde Motion (Site not responding. Last check: 2007-10-11)
		As a planet moves around on its epicycle, the center of the epicycle (called the ``deferent'') moves around the Earth.
		When its motion brings it inside the deferent circle, the planet undergoes retrograde motion.
		Is this page a copy of Strobel's Astronomy Notes?
	www.astronomynotes.com /history/epicycle.htm (43 words)

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