Geocentric (Earth-centred) Universe
By the early fourth century BC there appears to have been a general agreement among the Greeks that Earth was a stationary sphere centred on a greater sphere of the fixed stars, rotating once daily about Earth from east to west carrying with it the Sun, Moon and the five known planets. Although the Moon and the planets tend to move along the same path as the Sun’s annual motion (the ecliptic), they also deviate from north to south and not infrequently the planets appear to reverse direction (retrograde motion).
Plato (427-347 BC) probably studied under Socrates (c.469-399 BC), after whose execution Plato travelled abroad for the next twelve years and visited Sicily, where he met the tyrant of Syracuse Dionysius-I (c.65; r.405-367 BC) and developed friendships with the tyrant’s son-in-law Dion (c.54; r.357*354 BC) and with Archytas of Tarentum (c.428-c.347 BC). On his return to Athens (388 BC) Plato established the Academy, which he presided over for the rest of his life. When Dionysius-I died, Plato was invited by Dion to train Dionysius II (c.54; r.367*344 BC) to become a philosopher-king. But the new ruler soon tired of his studies, quarrelled with Dion, and Plato had to leave. In 361 BC a further visit to reconcile Dionysius with Dion was unsuccessful and Plato was kept prisoner until Archytas intervened and secured his release.
Plato pictured the Universe as consisting of invisible concentric spheres with a stationary Earth at the centre with the position of each ‘wanderer’ – the Sun, Moon and the five known planets – resulting from a combination of the concentric spheres. Plato is said to have raised the problem of how the apparently irregular motions of the wanderers might be derived from combinations of regular motions of the spheres.
Eudoxus of Cnidus (c.390-c.337 BC) was an astronomer, mathematician, physician, scholar, and student of Plato. According to ancient tradition he studied geometry under Archytas of Tarentum, medicine under Philistion of Locri (c.427-c.347 BC) and philosophy under Plato. In astronomy his description of constellations and their risings and settings was highly influential and he developed a model of planetary motion in which the Sun, Moon and planets were carried around Earth on a series of twenty-seven Earth-centred spheres, with axes rotating at different angles and different speeds.
Callippus of Cyzicus (c.370-c.300 BC) proposed a year of 365¼ days, and subsequently introduced a 76-year cycle of 940 lunar months=(76×12)+28 intercalary months. The first 76-year cycle began in 330-329 BC. He worked with Aristotle to ‘correct and complete the discoveries of Eudoxus’, adding two spheres each for the Sun and Moon and one for each of the planets. Aristotle himself increased the number of spheres to forty-nine to account for the movement of all celestial bodies. The outermost sphere carried the fixed stars, controlled the motion of the others, and was itself controlled by a supernatural agency.
Euclid (c.325-265 BC), who taught mathematics at Alexandria during the reign of Ptolemy-I (c.84; r.305-283 BC), wrote the Elements, which served as the main textbook for teaching mathematics (especially geometry) from the time of it publication until the late nineteenth century AD.
Apollonius of Perge (c.262-c.190 BC) was one of the greatest students of conics in antiquity. He also wrote a text on applied optics and was apparently famous for his astronomical studies. He examined two forms of circular motions. In the first the planet moved around Earth uniformly on a circle, but with Earth to one side of the centre of the circle. Thus in moving in this eccentric circle the planet varied its distance from Earth and therefore varied in its apparent speed across the sky. In the second device, the planet moved uniformly on a small circle or epicycle whose centre moved uniformly on a large carrying circle, or deferent, with Earth at its centre. If the rotation of the planet on the epicycle was sufficiently rapid in relation to the rotation of the epicycle on the deferent, then the planet would appear from time to time to move back-wards, i.e. to retrogress.
Hipparchus (c.190-c.120 BC) was born at Nicaea but spent most of his life at Rhodes. He was the first to construct a theory of the motion of the Sun and Moon firmly based on observational data. The epicycle/eccentric theory had already been worked out by his predecessors, but his contribution was to combine his own observations with Babylonian eclipse records going back to the eighth century BC. He investigated the problem of parallax and improved Aristarchus’ estimates of the diameters and distances of the Sun and Moon from Earth. He discovered the precession of the equinoxes when he compared his own observations with those of Timocharis of Alexandria (c.320-c.260 BC) about 160 years before and found that the longitude of the stars had changed with time.
Claudius Ptolemaeus (c.90-c.168), known as Ptolemy, lived in Alexandria and worked in the museum. His major work, the Almagest (in antiquity it was known as The Greatest Compilation and Arabic translators reduced it to al-Majisti, which became almagestum in medieval Latin) is a complete textbook of Greek astronomy. It provides geometrical tables that allow the movements of the Sun, Moon and the five known planets to be calculated for the indefinite future. It also contains a catalogue of over a thousand stars, arranged in forty-eight constellations, with the longitude, latitude and apparent brightness of each. He later revised the tables and together with an introduction explaining their use published them under the title Handy Tables. His Planetary Hypotheses was a digest of the Almagest, with physical dimensions added to the geometrical models of the Almagest.
In addition to the techniques of the eccentric, epicycle and deferent as used by Apollonius and Hipparchus, to calculate planetary position accurately and conveniently, Ptolemy had to adopt another device, the equant point. Earth is assumed to be located at a point away from the centre of Earth’s ‘circular’ orbit. The equant point is then defined as the mirror image of Earth’s position on the opposite side of the circle. This point is then used to define the motion on the circumference of the small circle (with hindsight it can be seen that the use of the equant point was successful because it has a close relationship with the Keplerian ellipse). Ptolemy first centred the orbits of the Sun, Moon and the five known planets on seven different points near Earth. Then, by manipulating epicycles, deferents, eccentrics and equants he accounted for all the observed movement in the heavens in terms of spheres and circles with a stationary Earth at its unmoving centre.
For a long time astronomers had visualised the movement in the heavens as being restricted to the spaces between invisible concentric spheres centred on Earth. In the Ptolemaic system Earth is surrounded by a sphere within which the Moon moves, both of these are surrounded by a sphere within which Mercury moves, which in turn is surrounded by a sphere within which Venus moves. Surrounding these three spheres is a sphere within which the Sun moves, etc. Between each sphere there is just enough room for that planet’s epicycles.
From the Almagest it is possible to calculate the ratio between a planet’s greatest and least distances from Earth. Ptolemy later insisted that this could be used to calculate absolute distances and gives the distance to the fixed stars (Celestial Sphere) as twenty thousand Earth radii, which is a million times less than today’s measurement to the nearest star.
Leave a Reply