Post by Senbecc on Apr 27, 2007 22:38:13 GMT -5
About 800 years before the birth of Christ, Greek civilisation began to flourish. What made the ancient Greeks unique at that time was their approach in explaining events in the natural world. Unlike the civilisations that had existed previously [1], the Greeks made a division between what was science and what was religion or superstition. They reasoned that observed phenomena could be explained by detailed theories of nature and are not due to the intervention of a deity or some other mystical being. Despite the fact that not all their observation-based theories proved correct, their approach in attempting to explain nature was a good one. Unfortunately, the prevailing assumption that first rooted itself in the minds of the Greeks was that the universe must not be very large since, compared to the Earth, the heavenly bodies appear so small. Similarly, the Sun and Moon are not very large in the sky. How could the Earth not be the centre of the universe when it appears so massive? In this regard, the Greeks seemed to take observations a little too literally and would not allow for the possibility that the universe could be so vast. Although none of their own writings now survive, Thales of Miletus (624 - 546 BC) and Pythagoras of Samos (ca.580 - ca.500 BC) were two of the earlier Greeks whose ideas were responsible for the shaping of astronomy. Their ideas established two main streams of thought for understanding the nature world. Eventually, these opposing views would leave the Greeks, and later Europe, with a twisted perception of the universe; one which, perhaps, seemed plausible on first thought but would never be able to satisfy the more inquisitive minds.
Thales taught that observable natural processes formed the world. He believed that the world evolved out of water in the same way that dry earth could be reclaimed from the sea. Thales had learned from the Babylonians' methods and there is some debate in literature whether he really predicted an eclipse of the Sun, which took place May 28, 585 BC. In any case, his views had earned great respect among many Greeks.
Pythagoras taught that reality could not be known through sensory observation but only through pure reason. He reasoned that the Earth was a sphere at the centre of the universe and that abstract mathematical forms governed reality. These views came from his real-life discoveries of the laws of musical harmonies and through his study of solid shapes. Later, Plato's (ca.428 - ca.348 BC) philosophy contained the essence of these ideas; namely, the view that the universe we see is based on ideal forms which can be understood through reason alone.
Ironically, despite his beliefs, Pythagoras made some important observations. He was the first person, as far as we know, who seemed to suggest the Earth was spherical and not flat. The reasons for thinking the Earth may not be flat, as summarised later by Aristotle (384 - 322 BC) in about 350 BC, can be derived from observation [2]. The Greeks knew of a star, which appeared after sunset, and a star, which appeared before sunrise [3]. Phythagoras was the first Greek to realise that the two stars were the same object. It was observed that when the evening star was in the sky there was never a morning star and vice versa. Around 500 BC Pythagoras gave this planet the name Aphrodite [4]. Phythagoras also recognised that the plane of the Moon's orbit was tilted with respect to the Earth's equator.
Although Philolaus (5th century BC) was a student of Pythagoras, he did not share his Earth centred view of the universe. Rather, he was the first to suggest that the Earth moved and was not the centre of all things. He believed that the Earth, Sun, Moon and planets all moved around a central fire that was hidden from view by means of an interposed counter-earth. He accounted for the observed daily motion of the heavenly bodies by stated that the Earth revolved around this central fire every 24 hours. Since Philolaus's view seemed to lack rationality, it did not prove to be popular amongst the Greeks.
An early example, which shows the Greeks' devotion to the idea of mathematical purity and to the small-universe assumption, is that of the philosopher Anaxagoras (ca.500 - ca.428 BC). He developed his theories by close observation of natural events. For example, he saw how whirlpools bring order to chaotic water flow. He noticed that mud and wood are draw to the centre of the pool while stones and pebbles are flung outwards. He reasoned that the Sun and stars are pieces of earth that had been flung outwards and heated by friction into their fiery state. He theorised that the stars are like our Sun but are too far away for their heat to reach us. In other words, he believed that the heavens were composed of the same materials as the Earth. His suggestion that the Sun was as large as southern Greece led his peers to accuse him of heresy, take him to trial and exile him from the land.
From the ideas of Thales and other philosophers, Aristotle suggested that the world was composed of four basic elements: earth, water, air and fire. His description of the world began with a ball of earth which is surrounded by a ball of water. In some places, like Greece, the earth protruded through the water resulting in dry land. A ball of air then surrounded the water and finally, a ball of fire. The fire could sometimes be seen as lightning in the sky. The heavenly bodies were not contained in Aristotle's four-element description of the world. They were composed of a fifth element, which he named aether [5]. He believed the heavenly bodies were luminous and moved in endless perfect circles around the Earth. In addition, they were unchanging and incorruptible. Meanwhile, back on the dreary Earth, he proposed the rather pessimistic view that all things are changing and deteriorating from an initial pristine state [6].
The static background of stars in the night sky led Eudoxus of Cnidus (370 BC) to suggest that a large sphere, bearing the stars on its inner surface, moved in a daily rotation with the Earth at its centre. Also within the star sphere there were many interconnecting transparent spheres that revolved in a variety of ways to account for the solar, lunar and planetary motions observed. The model he used was again tied to Plato's philosophy that the universe must be constructed with geometric simplicity. Using 55 concentric transparent spheres, Eudoxus could roughly account for observations of the heavens using simple circular motion. Aristotle wrote a summary of this work.
In Heracleides Ponticus's (ca.390 - after 322 BC) view, the Earth was the immovable centre of the universe. The fact that Mercury and Venus never wandered far from the Sun [7] created an untidy model in the Greeks' Earth-centred view; in which each planet or body circles the Earth independently. Heracleides suggested that the difficulty could be eliminated by assuming that Mercury and Venus circled the Sun and that the Sun circled the Earth. This made him the first to advance the idea of, at least a partial, Sun centred system.
Beginning in about 280 BC, a number of measurement were made by the Greeks combining geometry with observations. Aristarchus of Samos (fl.ca.270 BC) estimated the size of the Earth's shadow on the Moon and used it to determine that the Moon had a diameter about one third that of the Earth; a value which is a little high. He also attempted to find the relative size of the Moon and Sun by using trigonometry. His method relied on the knowledge that the Moon was not a source of light but only reflected the Sun's. If one waited until the Moon was exactly half illuminated then the angle between a line connecting the observer to the Moon and between the Moon and the Sun would be a right angle. One could then measure the angle between the Moon and Sun and use it to solve the last angle within the triangle formed. Using these angles, knowing the Moon's size relative to the Earth and using the fact that both the Sun and Moon have the same apparent size in the sky, Aristarchus calculated that the Sun was 20 times as far from the Earth as the Moon and that the Sun must have a diameter seven times that of Earth. His results were not very close to the real values but this was not the fault of his method. The required angle to be measured differs from 90 degrees by about one-sixth of a degree. This was too small of a difference to measure accurately without the aid of modern equipment.
Aristarchus believed that the Earth turns around on its axis once every 24 hours and revolved around the Sun along with the other planets. Perhaps realising that the Sun was so large led him to consider that the Earth may not be the centre of the universe. He had no evidence for this theology and although the Sun may be large, most considered it to be nothing more than a ball of light which could not be as massive and immovable as the Earth. Most Greek philosophers rejected his proposed model. The main reason for their disbelief was based on the appearance of the background stars. They thought that if the Earth actually revolved around the Sun then the stars should change their positions relative to one another [8]. In defence, Aristarchus stated that if the stars were at such a great distance compared to the width of the Earth's orbit then their positions would still appear as not to change. However, a universe of this magnitude was unthinkable in the minds of the Greeks.
Eratosthenes (ca.276 - ca.194 BC) was the first Greek to come up with a reasonable good measurement for the size of the Earth. It was known to him that on the summer solstice in the city of Syene, modern day Aswan, the Sun was directly overhead [9]. On the same day in Alexandria, he measured the angle of the Sun at midday by using a long vertical stick and measuring the length of its shadow. He found that the Sun was 7.2 degrees from the zenith. He then assumed the Sun's rays were parallel and at right angles to the surface of the Earth at Syene. In a two dimensional diagram, a straight line between the Earth's centre and the city of Alexandria reveals that a 7.2 degrees segment of the Earth has an arc length equal to the distance between the two cities. Eratosthenes estimated the north-south distance between the two cities and then found the circumference of the Earth by calculated how many more segments were required to go around the full 360 degrees. The value found for the circumference was somewhere between 23 300 and 25 000 miles [10].
Hipparchus (fl. 146-127 BC), who some consider to be one of the greatest Greek astronomers, calculated the distance to the Moon by observing the Moon's position in relation to the stars at different positions on Earth. Using the parallax effect and trigonometry, he estimated the Moon was at a distance of 30 times the Earth's diameter. Using Eratosthenes's figure for Earth's diameter, he calculated the distance to be about one quarter of a million miles away. Since the Greeks knew the Moon to be the closest heavenly body, this was the first indication they had that the universe was much larger than they supposed. Without telescopes, the Moon is the only object close enough to utilise the parallax effect in calculation. After revealing the possible vastness of the universe with his calculation, Hipparchus did not extend the Greeks knowledge of the real universe any further but instead engaged in detailed work in describing the mathematics of an Earth-centred model of the solar system.
In the 2nd century AD, the Greeks combined their theories with carefully planned observations. The astronomer Claudius Ptolemaeus (ca.85 - ca.165 AD), usually known as Ptolemy, used Hipparchus's star charts, which contained about 1000 stars, as a background for measuring planetary motion. Instead of Eudoxus's spheres, he modelled the universe using eccentric circles with the Earth near a common centre. This model was able to represent the general eastward motions, at varying speeds, of the Sun, Moon and planets around the zodiac. In order to account for periodic variations in the speed of the Sun and Moon and the retrogression of the planets, he used a second circle, called an epicycle. Each of these bodies revolved uniformly around an epicycle, which had its centre situated on the first circle. Observed motion of each heavenly body could be modelled by correctly choosing the diameters of the two circles and the speed of the circular motion. If this was not possible, as in some cases, a third circle was required.
Ptolemy describes his model and techniques in his earliest work, which has survived, known as the Almagest [11]. According to this work, the Moon and then Mercury and Venus orbit the Earth. The Sun then circled these inner planets followed by Mars, Jupiter and finally Saturn, in that order. As a theoretical model, it is said his work explains the complicated motions of the five planets fairly well; something that can not be said for previous Greek models. However, it does not explain the change in perceived brightness of the planets. For example, in Ptolemy's model, the Moon's orbit contained epicycles, which introduced a relatively large variation in its distance from the Earth. Therefore, if the model correctly represented the universe, the apparent size of the moon should change; which, of course, is not observed. Despite this, it was this geocentric model which prevailed for 1400 years and essentially defined the science of astronomy and the form of our universe during those years.
Written by
David Agar
May 2001
References
A Brief History of Astronomy
w3.restena.lu/al/pub/indivs/wagnjean/astronomy.htm
Asimov, I., Asimov's Chronology of science and discovery.
HarperCollins Published, New York, 1994.
www.phys.virginia.edu/classes/109N/lectures/
Michael Fowler, University of Virginia, 1996.
Aristarchus of Samos by J.J.O'Connor and E.F.Robertson.
www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aristarchus.html
The Concise Oxford Dictionary of English Etymology.
Edited by T. F. Hoad, Clarendon Press, Oxford, 1986.
Reader's Digest Illustrated Encyclopaedic Dictionary.
The Reader's Digest Association, Inc. Pleasantville, New York, 1987.
Lerner, Eric J. The Big Bang Never Happened.
Vintage Books, New York, 1992.
users.jyu.fi/~daagar/index_files/greeks.html
Thales taught that observable natural processes formed the world. He believed that the world evolved out of water in the same way that dry earth could be reclaimed from the sea. Thales had learned from the Babylonians' methods and there is some debate in literature whether he really predicted an eclipse of the Sun, which took place May 28, 585 BC. In any case, his views had earned great respect among many Greeks.
Pythagoras taught that reality could not be known through sensory observation but only through pure reason. He reasoned that the Earth was a sphere at the centre of the universe and that abstract mathematical forms governed reality. These views came from his real-life discoveries of the laws of musical harmonies and through his study of solid shapes. Later, Plato's (ca.428 - ca.348 BC) philosophy contained the essence of these ideas; namely, the view that the universe we see is based on ideal forms which can be understood through reason alone.
Ironically, despite his beliefs, Pythagoras made some important observations. He was the first person, as far as we know, who seemed to suggest the Earth was spherical and not flat. The reasons for thinking the Earth may not be flat, as summarised later by Aristotle (384 - 322 BC) in about 350 BC, can be derived from observation [2]. The Greeks knew of a star, which appeared after sunset, and a star, which appeared before sunrise [3]. Phythagoras was the first Greek to realise that the two stars were the same object. It was observed that when the evening star was in the sky there was never a morning star and vice versa. Around 500 BC Pythagoras gave this planet the name Aphrodite [4]. Phythagoras also recognised that the plane of the Moon's orbit was tilted with respect to the Earth's equator.
Although Philolaus (5th century BC) was a student of Pythagoras, he did not share his Earth centred view of the universe. Rather, he was the first to suggest that the Earth moved and was not the centre of all things. He believed that the Earth, Sun, Moon and planets all moved around a central fire that was hidden from view by means of an interposed counter-earth. He accounted for the observed daily motion of the heavenly bodies by stated that the Earth revolved around this central fire every 24 hours. Since Philolaus's view seemed to lack rationality, it did not prove to be popular amongst the Greeks.
An early example, which shows the Greeks' devotion to the idea of mathematical purity and to the small-universe assumption, is that of the philosopher Anaxagoras (ca.500 - ca.428 BC). He developed his theories by close observation of natural events. For example, he saw how whirlpools bring order to chaotic water flow. He noticed that mud and wood are draw to the centre of the pool while stones and pebbles are flung outwards. He reasoned that the Sun and stars are pieces of earth that had been flung outwards and heated by friction into their fiery state. He theorised that the stars are like our Sun but are too far away for their heat to reach us. In other words, he believed that the heavens were composed of the same materials as the Earth. His suggestion that the Sun was as large as southern Greece led his peers to accuse him of heresy, take him to trial and exile him from the land.
From the ideas of Thales and other philosophers, Aristotle suggested that the world was composed of four basic elements: earth, water, air and fire. His description of the world began with a ball of earth which is surrounded by a ball of water. In some places, like Greece, the earth protruded through the water resulting in dry land. A ball of air then surrounded the water and finally, a ball of fire. The fire could sometimes be seen as lightning in the sky. The heavenly bodies were not contained in Aristotle's four-element description of the world. They were composed of a fifth element, which he named aether [5]. He believed the heavenly bodies were luminous and moved in endless perfect circles around the Earth. In addition, they were unchanging and incorruptible. Meanwhile, back on the dreary Earth, he proposed the rather pessimistic view that all things are changing and deteriorating from an initial pristine state [6].
The static background of stars in the night sky led Eudoxus of Cnidus (370 BC) to suggest that a large sphere, bearing the stars on its inner surface, moved in a daily rotation with the Earth at its centre. Also within the star sphere there were many interconnecting transparent spheres that revolved in a variety of ways to account for the solar, lunar and planetary motions observed. The model he used was again tied to Plato's philosophy that the universe must be constructed with geometric simplicity. Using 55 concentric transparent spheres, Eudoxus could roughly account for observations of the heavens using simple circular motion. Aristotle wrote a summary of this work.
In Heracleides Ponticus's (ca.390 - after 322 BC) view, the Earth was the immovable centre of the universe. The fact that Mercury and Venus never wandered far from the Sun [7] created an untidy model in the Greeks' Earth-centred view; in which each planet or body circles the Earth independently. Heracleides suggested that the difficulty could be eliminated by assuming that Mercury and Venus circled the Sun and that the Sun circled the Earth. This made him the first to advance the idea of, at least a partial, Sun centred system.
Beginning in about 280 BC, a number of measurement were made by the Greeks combining geometry with observations. Aristarchus of Samos (fl.ca.270 BC) estimated the size of the Earth's shadow on the Moon and used it to determine that the Moon had a diameter about one third that of the Earth; a value which is a little high. He also attempted to find the relative size of the Moon and Sun by using trigonometry. His method relied on the knowledge that the Moon was not a source of light but only reflected the Sun's. If one waited until the Moon was exactly half illuminated then the angle between a line connecting the observer to the Moon and between the Moon and the Sun would be a right angle. One could then measure the angle between the Moon and Sun and use it to solve the last angle within the triangle formed. Using these angles, knowing the Moon's size relative to the Earth and using the fact that both the Sun and Moon have the same apparent size in the sky, Aristarchus calculated that the Sun was 20 times as far from the Earth as the Moon and that the Sun must have a diameter seven times that of Earth. His results were not very close to the real values but this was not the fault of his method. The required angle to be measured differs from 90 degrees by about one-sixth of a degree. This was too small of a difference to measure accurately without the aid of modern equipment.
Aristarchus believed that the Earth turns around on its axis once every 24 hours and revolved around the Sun along with the other planets. Perhaps realising that the Sun was so large led him to consider that the Earth may not be the centre of the universe. He had no evidence for this theology and although the Sun may be large, most considered it to be nothing more than a ball of light which could not be as massive and immovable as the Earth. Most Greek philosophers rejected his proposed model. The main reason for their disbelief was based on the appearance of the background stars. They thought that if the Earth actually revolved around the Sun then the stars should change their positions relative to one another [8]. In defence, Aristarchus stated that if the stars were at such a great distance compared to the width of the Earth's orbit then their positions would still appear as not to change. However, a universe of this magnitude was unthinkable in the minds of the Greeks.
Eratosthenes (ca.276 - ca.194 BC) was the first Greek to come up with a reasonable good measurement for the size of the Earth. It was known to him that on the summer solstice in the city of Syene, modern day Aswan, the Sun was directly overhead [9]. On the same day in Alexandria, he measured the angle of the Sun at midday by using a long vertical stick and measuring the length of its shadow. He found that the Sun was 7.2 degrees from the zenith. He then assumed the Sun's rays were parallel and at right angles to the surface of the Earth at Syene. In a two dimensional diagram, a straight line between the Earth's centre and the city of Alexandria reveals that a 7.2 degrees segment of the Earth has an arc length equal to the distance between the two cities. Eratosthenes estimated the north-south distance between the two cities and then found the circumference of the Earth by calculated how many more segments were required to go around the full 360 degrees. The value found for the circumference was somewhere between 23 300 and 25 000 miles [10].
Hipparchus (fl. 146-127 BC), who some consider to be one of the greatest Greek astronomers, calculated the distance to the Moon by observing the Moon's position in relation to the stars at different positions on Earth. Using the parallax effect and trigonometry, he estimated the Moon was at a distance of 30 times the Earth's diameter. Using Eratosthenes's figure for Earth's diameter, he calculated the distance to be about one quarter of a million miles away. Since the Greeks knew the Moon to be the closest heavenly body, this was the first indication they had that the universe was much larger than they supposed. Without telescopes, the Moon is the only object close enough to utilise the parallax effect in calculation. After revealing the possible vastness of the universe with his calculation, Hipparchus did not extend the Greeks knowledge of the real universe any further but instead engaged in detailed work in describing the mathematics of an Earth-centred model of the solar system.
In the 2nd century AD, the Greeks combined their theories with carefully planned observations. The astronomer Claudius Ptolemaeus (ca.85 - ca.165 AD), usually known as Ptolemy, used Hipparchus's star charts, which contained about 1000 stars, as a background for measuring planetary motion. Instead of Eudoxus's spheres, he modelled the universe using eccentric circles with the Earth near a common centre. This model was able to represent the general eastward motions, at varying speeds, of the Sun, Moon and planets around the zodiac. In order to account for periodic variations in the speed of the Sun and Moon and the retrogression of the planets, he used a second circle, called an epicycle. Each of these bodies revolved uniformly around an epicycle, which had its centre situated on the first circle. Observed motion of each heavenly body could be modelled by correctly choosing the diameters of the two circles and the speed of the circular motion. If this was not possible, as in some cases, a third circle was required.
Ptolemy describes his model and techniques in his earliest work, which has survived, known as the Almagest [11]. According to this work, the Moon and then Mercury and Venus orbit the Earth. The Sun then circled these inner planets followed by Mars, Jupiter and finally Saturn, in that order. As a theoretical model, it is said his work explains the complicated motions of the five planets fairly well; something that can not be said for previous Greek models. However, it does not explain the change in perceived brightness of the planets. For example, in Ptolemy's model, the Moon's orbit contained epicycles, which introduced a relatively large variation in its distance from the Earth. Therefore, if the model correctly represented the universe, the apparent size of the moon should change; which, of course, is not observed. Despite this, it was this geocentric model which prevailed for 1400 years and essentially defined the science of astronomy and the form of our universe during those years.
Written by
David Agar
May 2001
References
A Brief History of Astronomy
w3.restena.lu/al/pub/indivs/wagnjean/astronomy.htm
Asimov, I., Asimov's Chronology of science and discovery.
HarperCollins Published, New York, 1994.
www.phys.virginia.edu/classes/109N/lectures/
Michael Fowler, University of Virginia, 1996.
Aristarchus of Samos by J.J.O'Connor and E.F.Robertson.
www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aristarchus.html
The Concise Oxford Dictionary of English Etymology.
Edited by T. F. Hoad, Clarendon Press, Oxford, 1986.
Reader's Digest Illustrated Encyclopaedic Dictionary.
The Reader's Digest Association, Inc. Pleasantville, New York, 1987.
Lerner, Eric J. The Big Bang Never Happened.
Vintage Books, New York, 1992.
users.jyu.fi/~daagar/index_files/greeks.html