At the end of the lesson, you will be able to compare and contrast contrast the models of the universe by Eudoxus, Aristotle, Aristarchus, Ptolemy, and Copernicus.
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Eudoxus of Cnidus (born c. 395 – 390 B.C.), a Greek astronomer and mathematician, was the first to propose a model of the universe based on geometry. –
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His model composed of 27 concentric spheres with Earth as the center. The Sun, the Moon, the planets, and the fixed stars have spheres . Each sphere is attached to a larger sphere through a pole. The rotation of the spheres on their poles once every 24 hours accounts for the daily rotation of the heavens.
It is unclear whether Eudoxus regarded these spheres as physical entities or just mathematical constructions.
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Aristotle (born c. 384 B.C.), a Greek philosopher and astronomer, considered the model proposed by Eudoxus, but he considered these spheres as physical entities. He thought that these spheres were filled with the divine and eternal “aether ” that caused the spheres to move. He introduced the Prime Mover, as the cause of the movement of the spheres. His model composed of 56 spheres that guided the motion of the Sun, the Moon, and five known planets. As the spheres move, they maintained the same distance from the Earth. Also, they moved at constant speeds.
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Aristarchus of Samos (born c. 310 B.C.), a Greek astronomer and mathematician, was the first to hypothesize that the Sun is the center of the universe. He visualized that the Moon orbits around a spherical Earth which then revolves around the Sun. He believed that the stars are very far away from the Earth as evidenced by the absence of stellar parallax – that is, the stars do not change positions relative to each other as the Earth revolves around the Sun.
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Through geometrical models and mathematical computations, he concluded that –
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the Sun is 20 times farther from the Earth than the Moon is to the Earth; the Earth is about three times larger than the Moon; and the Sun is 20 times larger than the Moon.
He also reasoned out that smaller spheres orbit around larger ones. Thus, the Moon orbits around the Earth, and the Earth orbits around the Sun.
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The Sun, Moon, stars, and planets were believed to move in a uniform circular motion – the “perfect” motion assigned to celestial bodies by the ancient Greeks. However, observations showed otherwise. The paths of the celestial bodies are not circular, and they vary in distances. Babylonians even showed that some planets exhibit a retrograde motion – a motion opposite to that of other planets.
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To explain “imperfect motions” of heavenly bodies, Claudius Ptolemy (born c. 90 A.D.), a Greco-Egyptian astronomer and mathematician, proposed his own geocentric (Earth-centered) model of the universe. He accounted for the apparent motions of the planets around the Earth by assuming that each planet moved around a sphere called an epicycle. The center of the epicycle then moved on a larger sphere called a deferent.
1. A planet moves counterclockwise around the epicycle. 2. The epicycle’s center also moves counterclockwise around the center of the deferent (indicated by the + sign in the image). 3. The center of the epicycle moves around the equant with a uniform speed.
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The Earth is not exactly at the center of the deferent, or it is eccentric (off the center). This explains why, as observed from the Earth, the Sun or a planet moves slowest when it is farthest from the Earth and moves fastest when it is nearest the Earth. The motion of the planet can be described by points 1-7 in the figure below. At point 4, the planet moves in a retrograde (clockwise) motion. The planet is brightest at this point because it is closest to the Earth.
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In 1543, Nicolaus Copernicus, a Renaissance mathematician and astronomer born in Poland, ended the geocentric astronomy era by publishing his work On the Revolutions of the Heavenly Spheres wherein he explained that the Sun, not the Earth, is the center of the universe.
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In his work, he reiterated the ancient Greek concept that the motion of spherical heavenly bodies is uniform, eternal, and circular. He then reasoned that because Earth is spherical, then its motion is circular . He added that the Earth has three different motions: –
daily rotation on its axis,
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yearly motion around the Sun, and the
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precession , or change in orientation, of its axis every 26 000 years.
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He also proposed that the fixed stars are immovable. Their apparent movement is a consequence of the Earth’s rotation. These stars are at immeasurable distances from the Earth, so there is no observable parallax.
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By placing the Sun at the center of the universe and the orbits of Mercury and Venus in between the Sun and the Earth, Copernicus’ model was able to account for the changes in the appearances of these planets and their retrograde motions. The need for epicycles in explaining motions was eliminated.
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Eudoxus’, Aristotle’s, and Ptolemy’s models have the Earth as the center of the universe while Aristarchus’ and Copernicus’ models have the Sun as the center. Eudoxus’ model has 27 concentric spheres for the Sun, Moon, planets, and the stars whose common center is the Earth. Aristotle’s model of the universe is composed of 56 spheres guiding the motion of Sun, Moon and the five known planets.
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Aristarchus said that smaller celestial bodies must orbit the larger ones and since the Sun is much larger than the Earth, then the Earth must orbit around the Sun. Ptolemaic model introduced the concepts of epicycle, deferent, and equant to explain the observed “imperfect” motions of the planets. Copernicus’ model recognized that the Earth rotates on its axis, revolves around the Sun, and undergoes precession.
