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Topic: Deferent and epicycle

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	Deferent and epicycle
		In the Ptolemaic system, the planets are assumed to move in a small circle, called an epicycle, which in turn moves within a larger circle called a deferent.
		The deferent would be considered to be centered on the Earth (as the planet was believed to be in orbit around Earth...
		Most of the time, the eastward motion of the epicycle was in conjunction with the eastward movement of the deference.
	www.ebroadcast.com.au /lookup/encyclopedia/ep/Epicycle.html (142 words)

	Ptolemaic Astronomy in the Middle Ages
		Revolving about the epicycle at a uniform rate determined by the period of conjunction with the sun, each planet moved away from the latter to a fixed limit and then moved toward it again, first to one side, then to the other, in an exaggerated form of retrograde motion.
		The plane of the moon's deferent and epicycle was inclined to that of the ecliptic, and the line of intersection joining the nodes (called the "head and tail of the dragon") was rotated in the ecliptic by a separate motion of the moon's heaven.
		In the planetary models, the deferent was inclined to the ecliptic at a fixed angle, while the epicycle's inclination to the deferent varied from a minimum at the nodes (where the epicycle lay in the plane of the ecliptic) to a maximum at quadrature.
	www.princeton.edu /~hos/mike/texts/ptolemy/ptolemy.html (2606 words)

	Ptolemaic system
		The planets are actually attached to 2 spheres: one sphere which is centered on the earth (the deferent), and another sphere (the epicycle) embedded within the deferent.
		The epicycle rotates within the deferent, causing the planet to move closer to and farther from the earth at different points in its orbit, and even to slow down, stop, and move backward (in retrograde motion.
		The epicycles of Venus and Mercury are always centered on a line between the Earth and the Sun (Mercury being closer to the earth), which explains why they are always near it in the sky.
	www.ebroadcast.com.au /lookup/encyclopedia/pt/Ptolemaic_system.html (595 words)

	Deferent and epicycle - Wikipedia, the free encyclopedia
		The deferent was a circle centered around a point halfway between the equant and the earth.
		Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest.
		The multiplication of epicycles led to a nearly unworkable system by the 16th century.
	en.wikipedia.org /wiki/Epicycle (1085 words)

	Epicycle 26000 Years \| Epicycle And Deferent \| Epicycle And Circle \| Epicycle And Circle (Site not responding. Last check: 2007-11-02)
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	cgcm.info /epicycle-26000-years.htm (355 words)

	Epicycle and Deferent Demo (Site not responding. Last check: 2007-11-02)
		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.
	www.phy.syr.edu /courses/java/demos/kennett/Epicycle/Epicycle.html (274 words)

	Epicycles \| World of Physics
		Epicycles were mathematical modifications added to the geocentric theory to ensure that the model was consistent with astronomical observations.
		Earth is not positioned at the center of the deferent's orbit, but it is instead displaced to one side by a distance called the eccentricity.
		Combining epicycles, deferents, and equants, and sometimes invoking epicycles nested upon epicycles, it becomes possible to fit the observed data regarding a planet's orbit to the geocentric model.
	www.bookrags.com /research/epicycles-wop (447 words)

	Talk Deferent And Epicycle \| Ptolemaic Epicycle \| Epicycle Home Page \| Ptolemy Epicycle (Site not responding. Last check: 2007-11-02)
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	cgcm.info /talk-deferent-and-epicycle.htm (451 words)

	Ptolemy (Site not responding. Last check: 2007-11-02)
		He further supposed that the distance from the Earth to the center of the deferent was equal to the distance from the center of the deferent to the equant.
		The planes of the deferents of the planets were believed to be inclined at small angles to the plane of the ecliptic, while the planes of their epicycles were inclined by equal amounts to those of the deferents, so that the planes of the epicycles would always parallel that of the ecliptic.
		The planes of the deferents of Mercury and Venus were assumed to oscillate above and below the plane of the ecliptic, and likewise the planes of their epicycles were thought to oscillate with respect to the planes of the deferents.
	abyss.uoregon.edu /~js/glossary/ptolemy.html (1349 words)

	Thursday, 7/29 (Site not responding. Last check: 2007-11-02)
		It is the deferent if the center of the circle (point C) is located at the center of the system (in this case it is not, as the earth is the center of the system); it is the eccentric if the center of the circle is not at the center of the system.
		It may also be the center of the system (in which case the larger circle is called the deferent) or it may not be in the center of the system (in which case the larger circle is called the eccentric).
		The epicycle, then, still revolves around the center of the deferent (around the circumference of the deferent) but uniform circular motion around the center of the deferent is replaced by uniform ‘angular’ motion about an equant point.
	www.u.arizona.edu /~jenkinsm/072904.html (489 words)

	Models of Planetary Motion -- McConnell
		By adjusting the size of the epicycle, Ptolemy could fit his model to the size of the retrograde loops observed in the heavens.
		Just as Ptolemy was able to calibrate his model by adjusting the size and speed of the epicycles and deferents, Copernicus was able to calibrate his model by adjusting the size and speed of a planet's orbit.
		Despite his displeasure with the equant model, which he found to be a deviation from the goal of uniform circular motion, Copernicus retained the epicylce on deferent model, which allowed him to make predictions of the future positions of the planets with accuracy comparable to Ptolemy.
	faculty.fullerton.edu /cmcconnell/Planetary_Motion.html (1465 words)

	Comins & Kaufmann, Discovering the Universe (Site not responding. Last check: 2007-11-02)
		At most times the eastward motion of the planet on the epicycle adds to the eastward motion of the epicycle on the deferent.
		When the planet is on the inside of the deferent, its motion along the epicycle is westward.
		Because this motion is faster than the eastward motion of the epicycle on the deferent, the planet appears from Earth to be moving westward in retrograde motion.
	www.physics.uoguelph.ca /phyjlh/Astro/animations/GeogcentricRetro.htm (117 words)

	Ptolemiac Astronomy - Dr Robert A. Hatch
		Briefly, this required that the moon's epicycle be pulled closer to the earth (in order to appear to be traveling faster than would otherwise have been the case) as the moon's epicycle approached quadrature with the mean sun.
		The overall orbit of the center of the moon's epicycle is roughly the inner ovoid curve.
		The line from the epicycle's center to A clearly fluctuates--hence the term 'fluctuating apogee' --since it is constructed through the center of the epicycle from an imaginary point 180° away from the end of the connecting rod on the auxiliary circle.
	web.clas.ufl.edu /users/rhatch/pages/03-Sci-Rev/SCI-REV-Teaching/HIS-SCI-STUDY-GUIDE/0034_summaryPtolemiacAstron.html (2201 words)

	Ptolemy Defferent Epicycle Deferent \| Theoris Des Epicycle Ptolemee \| Ptolemy Deferent Epicycle Deferent \| Epicycle ... (Site not responding. Last check: 2007-11-02)
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	dmnd.info /ptolemy-defferent-epicycle-deferent.htm (301 words)

	Geology 130 Laboratory (Site not responding. Last check: 2007-11-02)
		Theepicycle, the center of the epicycle, and the deferent are all labeled on the diagram.
		One crucial restriction on the movement of Venus is that the center of its epicycle (C) always remains on a line connecting the earth and the sun.
		Figure 5 is drawn in such a way as to fairly accurately reflect the relative sizes of the epicycle of Venus and the radius of the sun's orbit.
	earth.usc.edu /geol130/labmanual/ch3/page14.html (227 words)

	Epicycle On Deferent \| Deferent Exams (Site not responding. Last check: 2007-11-02)
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	ekqz.info /epicycle-on-deferent.htm (381 words)

	Models of the solar system
		The equant was an equal distance on the opposite side of the center of the deferent, with the planet's epicycle moving through equal angles around the equant at equal speeds, and the planet itself moving uniformly around the epicycle.
		The equant--rather than the epicycle, which as a perfect circle was perfectly fine--violated the aesthetic sensibilities of everybody, including Ptolemy himself.
		Epicycles were not a problem to the medievals, because epicycles were perfect circles.
	www.bluffton.edu /~bergerd/NSC_111/science3.html (1501 words)

	[No title]
		Variable parameters in this theory: For each planet: The radii of the deferent and epicycle The rates of revolution of deferent and epicycle The angles of inclination of the planes containing the deferent and epicycle circles.
		Why retrograde motion exists If the revolution of the epicycle is fast enough, then, when the planet's motion along the epicycle is in the opposite direction to the motion of the epicycle-center along the deferent, the net motion will be eastward (relative to the fixed stars), i.e.
		A planet that appears to move faster when near the equinoxes than when near the solstices can be accounted for using a minor epicycle that rotates twice as fast as that planet's deferent.
	www.rci.rutgers.edu /~hgreaves/teaching/phil225/lectures/sep20_kuhn_ch2.doc (953 words)

	Hipparchus (Site not responding. Last check: 2007-11-02)
		The Moon itself would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an epicycle, that itself would move uniformly (with some mean motion in longitude) over the main circular orbit around the Earth, called deferent; see deferent and epicycle.
		* and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122+1/2 : 247+1/2.
		Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+1/2 : 247+1/2), which is too small (60 : 4;45 hexadecimal): Ptolemy established a ratio of 60 : 5+1/4.
	www.theamazingsky.com /Hipparchus.htm (2725 words)

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	cgcm.info /epicycle-and-deferent-auctions.htm (449 words)

	SOME TERMS AND CONCEPTS OF PHYSICAL SCIENCE
		A Deferent is the circle whose center is on or near to the earth in Ptolemy’s geocentric model of the solar system.
		planet or, in some cases, another epicycle moves around the first epicycle.
		A Geocentric Theory is a theory or model of the solar system that places the earth in the center and assumes that the sun, moon, and the other planets revolve around the earth in some manner.
	faculty.eicc.edu /tgibbons/terms.htm (8641 words)

	Geocentrism and Creation (Site not responding. Last check: 2007-11-02)
		By adjusting the sizes of the epicycle and the deferent, and the speeds with which the planet moves on the epicycle and the epicycle moves on the deferent, the planet will occasionally exhibit retrograde motion.
		Furthermore, the epicycle does not move at a uniform rate with respect to the centre of the deferent or the Earth.
		While the epicycle is moving at a uniform rate with respect to the equant, it does not move at a uniform rate with respect to the centre of the deferent or even with respect to the Earth.
	www.answersingenesis.org /tj/v15/i2/geocentrism.asp (9317 words)

	Ptolemy's Models
		A step taken to improve this zero-eccentricity model was to displace the Earth E from the centre of the deferent, C, slightly.
		In Figure 13, planet Z moves uniformly on the epicycle and the centre of the epicycle, K, moves around the deferent at uniform speed.
		However K is now assumed not to move uniform either with respect to the Earth E or the centre of the deferent, C. Instead, uniform motion of K is observed at X which is the mirror image of the Earth E, and is what Ptolemy named as the “equant point”.
	www.math.nus.edu.sg /~mathelmr/projects/heilbron/Ptolemy's_Models.htm (785 words)

	Expt. II-3 Measuring the Size of the Earth
		The planet is attached to the epicycle so as it swings to the outside of the deferent on its journey backwards compared to the stars, it grows fainter due to greater distance.
		But when the epicycle swings the planet inside the deferent, the epicycle's greater speed counteracts the deferent motion so while the planet is close and bright, for a few days it retrogrades, moving faster across the sky than the stars.
		Ptolemy's deferents, epicycles, and equants could explain all motion as well as Eudoxos, but could also explain all observed variations in brightness.
	homepage.mac.com /dtrapp/ePhysics.f/labII_3.html (765 words)

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