The orbits of planets in this system are similar to epitrochoids, but are not exactly epitrochoids because the angle of the epicycle is not a linear function of the angle of the deferent. Despite the fact that the system is considered geocentric, neither of the circles were centered on the earth, rather each planet's motion was centered at a planet-specific point slightly away from the Earth called the eccentric. Both circles rotate eastward and are roughly parallel to the plane of the Sun's apparent orbit under those systems ( ecliptic). In both Hipparchian and Ptolemaic systems, the planets are assumed to move in a small circle called an epicycle, which in turn moves along a larger circle called a deferent (Ptolemy himself described the point but did not give it a name ). The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant ( However, they fell out of favor with the discovery that planetary motions were largely elliptical from a heliocentric frame of reference, which led to the discovery that gravity obeying a simple inverse square law could better explain all planetary motions. It was developed by Apollonius of Perga and Hipparchus of Rhodes, who used it extensively, during the 2nd century BC, then formalized and extensively used by Ptolemy in his 2nd century AD astronomical treatise the Almagest.Įpicyclical motion is used in the Antikythera mechanism, an ancient Greek astronomical device, for compensating for the elliptical orbit of the Moon, moving faster at perigee and slower at apogee than circular orbits would, using four gears, two of them engaged in an eccentric way that quite closely approximates Kepler's second law.Įpicycles worked very well and were highly accurate, because, as Fourier analysis later showed, any smooth curve can be approximated to arbitrary accuracy with a sufficient number of epicycles. It was first proposed by Apollonius of Perga at the end of the 3rd century BC. Secondarily, it also explained changes in the apparent distances of the planets from the Earth. In particular it explained the apparent retrograde motion of the five planets known at the time. In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος ( epíkuklos) 'upon the circle', meaning "circle moving on another circle") was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. The path-line is the combined motion of the planet's orbit (deferent) around Earth and within the orbit itself (epicycle). Overall, however, his new concept seemed to provide an ultimate demonstration of the perfect harmony of the cosmos, with six planets all continuously revolving in the same direction around the Sun.The epicycles of the planets in orbit around Earth (Earth at the center). He was thus forced to adopt intricate combinations of circles, which made his system technically no less complex than the Ptolemaic system. He also remained faithful to the axiom of the circularity and uniformity of celestial motions. Like his predecessors, Copernicus believed that the planets were embedded in solid crystal spheres. The combination of the two motions generated the celestial body's apparent retrogression. In the Copernican system, instead, both motions are centered on the Sun, but only one is performed by the planet itself the other is the revolution of the Earth. For the ancients, who assumed the Earth to be immobile, each planet moved on a circle called the epicycle, whose center, in turn, moved around the Earth on a larger circle known as the deferent. In fact, it is caused by the Earth's rotation in the opposite direction also apparent is the Sun's annual travel along the ecliptic, actually due to terrestrial rotation the retrograde movement of the planets is apparent as well. The Earth is thus no longer a fixed hub, but revolves around the Sun in one year and on its own axis in twenty-four hours.įor Copernicus, the motion of the heavenly bodies from east to west in the course of a day is only apparent. In the Copernican system, the Sun is immobile at the center of the universe and the planets-including the Earth-rotate around it. He described it in his epoch-making work, De Revolutionibus orbium coelestium. Taking up the hypothesis formulated by Aristarchos of Samos in the third century B.C.E., Nicolaus Copernicus developed the heliocentric theory of celestial motion.
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