Ptolemaic System


Ptolemaic system geocentric theory of the Universe as presented in Ptolemy's Almagest of ad 140. The Earth is taken to be the centre of the Universe, with the Moon, Mercury, Venus, the Sun, Mars, Jupiter and Saturn revolving around it. Outside lies the sphere of the fixed stars.

The orbit of a planet as described by eudoxus was such that it moves around in a small circle, called the epicycle. The centre of the epicycle itself revolves about the Earth on a larger circle called the deferent. Ptolemy added two further points, the eccentric and the equant, to each orbit. The eccentric is at the centre of a line joining the Earth and the equant; the deferent is centred on the eccentric point rather than on the Earth itself. The centre of the epicycle thus moves around the deferent with a variable velocity that makes it appear to be moving with uniform angular velocity when viewed from the equant point - in direct conflict with the Aristotelian doctrine that the celestial motions had to be perfectly uniform.

The Ptolemaic system allowed the future positions of the planets to be predicted with reasonable accuracy and remained 'state of the art' until ousted by the copernican system.

Ptolemy (Claudius Ptolemaeus) (2nd century ad) Egyptian astronomer and geographer. His chief astronomical work, the Almagest, was largely a compendium of contemporary astronomical knowledge, including a star catalogue, drawing on the work of hipparchus of Nicaea. It described the so-called ptolemaic system, a geocentric universe with the Earth fixed at the centre, and the Moon, Sun and planets revolving about it. Ptolemy's modification of the previous, simpler Greek theory based on epicycles and deferents reproduced the apparent motions of the planets, including retrograde loops, so well that it remained unchallenged until the revival of the heliocentric theory by Nicholas Copernicus in the 16th century.

Little is known about Ptolemy's life. His dates and even his name are uncertain - 'Ptolemy' merely indicates that he had Greek or Greek-naturalized ancestors and lived in Egypt, which was then ruled by the Ptolemaic dynasty. He is sometimes referred to as Claudius, but this probably means simply that Ptolemy's Roman citizenship goes back to the time of the emperor Claudius I. It seems likely, though, that he lived and worked at the famous library and museum in Alexandria.

Ptolemy was a prolific author, but his earliest large work, the Almagest, was not only his greatest, but also the greatest astronomical work of antiquity. It is essentially a basic textbook, expecting its reader to know only the fundamentals of Greek geometry and some familiar astronomical terms; the rest Ptolemy explains.

The first two books form an introduction. They present an outline of the Ptolemaic system - a spherical universe with spheres carrying the planets - and give persuasive arguments that the Earth is stationary at its centre. The basic mathematics, making use of chords (the Greeks did not develop the sines and tangents of modern trigonometry), is described.

Book III discusses the apparent motion of the Sun, using observations mostly by Hipparchus, for whose work Ptolemy shows such reverence that of his own observations he seems to have selected only those that agreed with his predecessor's. A table of the Sun's motion is then constructed. The motion of the Moon according to Hip-parchus is the subject of Book IV. The theory, based on eclipses, accounts for the Moon's motion at conjunction (new moon) and opposition (full moon), but is inadequate for intermediate positions in the orbit.

In Book V, Ptolemy develops his own lunar theory. Based on epicycle and deferent, it is extremely ingenious. His observations showed him that the Moon changed in apparent size, which he accounts for by a kind of crank mechanism operating on the centre of the Moon's epicycle. This theory accounts for the motion of the Moon at all positions of its orbit.

Book VI explains how to calculate every detail of eclipses. Books VII and VIII present tables of positions and pulsar This schematic illustration of a pulsar shows the two beams of radiation directed from the collapsed star along its magnetic poles, which need not coincide with the axis of rotation. If the rotational axis is so aligned that the radiation beams sweep across our line of sight, the rapidly pulsing radio signal characteristic of a pulsar will be detected.

Typically, Ptolemy tackled the problem in a truly scientific way. Using his own observations as well as those of Hipparchus and the Babylonians, he discovered that each planet had two irregularities or 'anomalies'. One depended on the planet's elongation, the other on its position along the ecliptic. Ptolemy had to explain these anomalies by a theory that fitted into the framework of the Greek geocentric universe.

Careful study showed him that the epicycle and deferent would account for the first anomaly. For the second he introduced the ECCENTRIC. Here the centre of the planet's epicycle moved around a point M whose distance from the Earth was determined by the planet's apparent eccentricity. It was another basic condition of Greek planetary motion that each planet should move at an unvarying rate about the centre of the Universe (even though observation showed that not one of them did). Ptolemy satisfied this condition by using another point, the EQUANT, on the opposite side of the Earth to M and an equal distance away. Motion with respect to the equant was uniform. This was an inspired solution, which, with an additional minor modification, explained the motions of all the planets then known.

The Almagest was not Ptolemy's only great text. He wrote the Tetrabiblos on astrology, much of it on 'natural astrology' - the physical effects of the Sun and Moon, for instance. Then he produced Planetary Tables, which were extracted from the Almagest, and a popular abridgement called Planetary Hypotheses, which, however, extends some of his theoretical ideas and in particular his measurements of the distances and sizes of the Sun and Moon. There was also his Phases of the Fixed Stars, which went into more detail about rising and setting of the stars just before dawn and just after sunset, and the Analemma, a book on constructing sundials. He also wrote on geography, music, mechanics, geometry and optics.

Puck Largest of the inner satellites of URANUS, discovered in images returned by VOYAGER 2 as it approached Uranus near the end of 1985. Puck is about 154 km (96 mi) across, roughly spherical in shape, and heavily cratered. It takes 0.762 days to circuit the planet, at a distance of 86,000 km (53,000 mi) from its centre, in a near-circular, near-equatorial orbit.

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Ptolemaic program — Geocentric

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