published on 23 July 2013
Astronomy is an area where the Greeks displayed a remarkable talent. Observational astronomy, which was the main form of astronomy elsewhere, was taken a step further in Greece: they attempted to build a model of the universe that could account for the observations. They explored all imaginable alternatives, they considered many different solutions for the various astronomical problems they came across. They not only anticipated many ideas of modern astronomy but also some of their ideas endured for around two millennia. Even at the time of Isaac Newton, some aspects of Aristotelian cosmology were still taught at the University of Cambridge.
Our knowledge of Greek astronomy before the 4th century BCE is very incomplete. We have just a few surviving writings, and most of what we know are references and comments form Aristotle, mostly opinions he is about to criticize. What is clear is that the earth was believed to be a sphere, and that there was an increasing effort to understand nature in purely natural term, without recourse to supernatural explanations.
The Greeks' neighbours, Egyptians and Babylonians, had highly developed astronomies, but the forces driving them were different. Egyptian administration relied on well-established calendars to anticipate the flooding of the Nile; rituals were required to be able to tell the time during the night, and the orientation of monuments in the cardinal directions was also important. Babylonians believed in the reading of omens in the sky as a mean to secure the state. These were all important stimuli to develop a fine astronomy.
Pythagoras is credited as the first Greek to think the earth spherical, but this idea was probably founded on mystic reasons rather than scientific. The Pythagoreans found conclusive evidence in favour of a spherical earth after it was discovered that the moon shines by reflecting light, and the right explanation for eclipses was found. The earth’s shadow on the moon’s surface suggested that the shape of our planet was spherical.
Aristotle's book "On the Heavens" summarizes some astronomical notions before his time. He says, for example, that Xenophanes of Colophon claimed the earth below us is infinite, that it has “pushed its roots to infinity”; others believed the earth rested upon water, a claim whose original author seems to be Thales (according to Aristotle); Anaximenes, Anaxagoras, and Democritus believed the earth was flat which “covers like a lid, the earth beneath it”.
Greek Astronomy after Aristotle
Apart for a few exceptions, the general consensus among Greek astronomers was that the universe was earth-centred. During the 4th century BCE, Plato and Aristotle agreed on a geocentric model but both thinkers did so based on mystical arguments: The stars and planets were carried around the earth on spheres, arranged in a concentric fashion. Plato even described the universe as the Spindle of Necessity, attended by the Sirens and turned by the three Fates. Plato discarded the idea of a universe governed by natural laws, since he rejected any form of determinism. In fact, the unpredictable motions of some planets (especially Mars), were seen by Plato as proof that natural laws could not account for all the changes in nature. Eudoxus, a student of Plato, challenged the views of his teacher by working on a more myth-free mathematical model, but the idea of concentric spheres and circular planetary motion still persisted.
While Aristotle’s justifications for an earth-centred universe lack scientific support, he offers some compelling observational evidence to justify a spherical earth, the most important being the difference in the position of the polar star as one changes latitude, an observation that offered a way to measure the earth’s circumference.
Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent.
(Aristotle: Book 2, Chapter 14, p. 75)
Aristotle, based on the position of the polar star between Greece and Egypt, estimated the size of the planet as 400,000 stadia. We do not know exactly about the conversion of stadia into modern measures, but the general consensus is that 400,000 stadia would be around 64,000 kilometres. This figure is much higher than modern calculations, but what is interesting is that from a theoretical perspective, the calculation is a valid method to calculate the size of our planet; it is the inaccuracy of the figures Aristotle dealt with that prevents him arriving at an acceptable conclusion.
A more accurate figure for the size of our planet would appear later with Eratosthenes (276-195 BCE) who compared the shadows cast by the sun at two different latitudes (Alexandria and Syene) at the exact same time. By simple geometry he then calculated the earth’s circumference to be 250,000 stadia, which is about 40,000 kilometres. Eratosthenes’ calculation is about 15% too high, but the accuracy of his figure would not be equalled until modern times.
The fairly good observations of Aristotelian cosmology coexisted with a number of mystic and aesthetic prejudices. It was believed, for example, that the heavenly bodies were "unregenerate and indestructible" and also "unalterable". All bodies which existed above our planet were considered flawless and eternal, an idea that endured long after Aristotle: even during the Renaissance, when Galileo claimed that the surface of the moon was as imperfect as our planet and filled with mountains and craters, it caused nothing but scandal among Aristotelian scholars who still dominated European thought.
Despite the general consensus on the Earth-centred model, there were a number of reasons that suggested the model was not fully accurate and needed corrections. For example, it was not possible for the geocentric model to explain either the changes in the brightness of the planets or their retrograde motions. Aristarchus of Samos (310 BCE - 290 BCE) was an ancient Greek mathematician and astronomer who came up with an alternative astronomical hypothesis that could address some of these concerns. Anticipating Copernicus and Galileo by almost 20 centuries, he claimed the sun, not the earth, was the fixed centre of the universe, and that the earth, along with the rest of the planets, revolved around the sun. He also said that the stars were distant suns that remained unmoved, and that the size of the universe was much larger than his contemporaries believed. Using careful geometrical analysis based on the size of the earth’s shadow on the moon during a lunar eclipse, Aristarchus knew that the sun was much larger than the earth. It is possible that the idea that tiny objects ought to orbit large ones and not the other way around motivated his revolutionary ideas.
Aristarchus works where the heliocentric model is presented are lost, and we know of them by piecing together later works and references. One of the most important and clear is the one mentioned by Archimedes in his book “The Sand Reckoner”:
[...] But Aristarchus of Samos brought out a book consisting of certain hypotheses, in which the premises lead to the result that the universe is many times greater than that now so called. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.
Aristarchus’ model was a good idea during a bad time, since all Greek astronomers in antiquity took for granted that the orbit of all heavenly bodies had to be circular. The problem was that Aristarchus’ theory could not be reconciled with the supposedly circular movements of the heavenly bodies. In reality planets’ orbits are elliptical, not circular: elliptical orbits or any other non-circular orbit could not be accepted; it was almost a blasphemy from the viewpoint of Greek astronomers.
Hipparchus of Nicea (190 BCE - 120 BCE), the most respected and talented Greek astronomer in antiquity, calculated the length of the lunar month with an error of less than one second and estimated the solar year with an error of six minutes. He made a catalogue of the sky providing the positions of 1080 stars by stating their precise celestial latitude and longitude. Timocharis, 166 years before Hipparchus, had also made a chart. Comparing both charts, Hipparchus calculated that the stars had shifted their apparent position by around two degrees, and thus he discovered and measured the Equinoctial Precession. He calculated the precession to be 36 seconds per year, an estimation a little too short according to modern calculations, which is 50. He also provided most of the calculations that are the backbone of Ptolemy’s work Almagest, a massive astronomical essay completed during the 2nd century CE which remained the standard reference for scholars and unchallenged until the Renaissance.
Hipparchus put an end to Aristarchus’ theory by saying that the geocentric model better explained the observations than did the model of Aristarchus. As a result of this, he is often blamed for bringing astronomical progress backwards by favouring the mistaken earth-centred view. However, this is a risk that surrounds every genius, two sides of the same coin: when they are right they can trigger a revolution of knowledge, and when they are wrong they can freeze knowledge for centuries.
The Aristotelian model was “rescued” by introducing two geometrical tools created by Apollonius of Perga around 200 BCE and perfected by Hipparchus. The conventional circles were replaced by eccentric circles. In an eccentric circle the planets moved as usual in a uniform circular motion around the earth, but our planet was not the centre of the circle, rather, offset the centre. This way, the planet’s speed changes could be accounted for and also the changes in brightness: planets would appear to move faster, and also brighter, when they were nearer the earth, and slower, and also dimmer, when they were away on the far side of their orbit. Apollonius came up with an additional tool, the epicycle, an orbit within an orbit (the moon revolves around the earth and the earth orbits the sun or, in other words, the moon moves around the sun in an epicycle). This device could also account for changes in brightness and speed, and it could also account for the retrograde motions of the planets which had puzzled most Greek astronomers.
Between Hipparchus and Ptolemy’s Almagest we have a three century gap. Some scholars have suggested that this period was some sort of “dark age” for Greek astronomy, while other scholars believe that the Almagest's triumph wiped out all previous astronomical works. This is a superfluous debate since the importance of a scientific work is often measured by the number of previous works it makes redundant.
The Almagest is a colossal work on astronomy. It contains geometrical models linked to tables by which the movements of the celestial bodies could be calculated indefinitely. All Greco-Babylonian astronomical achievements are summarized in this work. It includes a catalogue containing over 1,000 fixed stars. The cosmology of the Almagest would dominate western astronomy for the 14 centuries to come. Although not perfect, it had sufficient accuracy to remain accepted until the Renaissance.
Ironically, Ptolemy was more of an astrologer than astronomer: during his time, there was no sharp distinction between the obscure business of astrology and the science of astronomy. Astronomical observations were merely a side effect of the desire of Ptolemy as an astrologer to be able to tell and anticipate the positions of the planets at all times. Furthermore, Ptolemy was also the author of a work named Tetrabiblos, a classic work on astrology.
The tools devised by Hipparchus and Apollonius allowed sufficient observational accuracy, encouraging the progress of the geocentric model, but total success could never be achieved. Ptolemy added still another device to “save the appearances” of the model: the equant point. The equant was the point symmetrically opposite the eccentric earth, and the planet was required to move in its orbit in such a way that from the perspective of the equant, it would appear to be moving uniformly across the sky. Since the equant was offset from the centre of the orbit, planets had to vary their speed in order to fulfil this requisite. In short, because some basic assumptions of the cosmological model were wrong (the earth centred notion, the perfect circular orbits, etc.), there was the need to add questionable and complicated devices (eccentric circles, epicycles, equants, etc.) to prevent inconsistencies or, at least, try to minimize them. In the end, the Ptolemaic model collapsed not only because of its inaccuracies but mainly because it lacked simplicity. When the sun-centred hypothesis of Copernicus was published in the 16th century CE, it gained popularity not because it was more accurate, but because it was much simpler and it did not have the need of all the overly complex devices that Ptolemy had to use.
The Greek achievements in art, politics, and even in philosophy may be judged according to personal taste, but what they achieved in astronomy is totally beyond question. They not only developed a fine astronomical knowledge, but they also successfully exploited astronomical data that they got from Egyptian, Babylonian, and Chaldean astronomy and managed to merge it with their own knowledge. Even when they made a wrong assumption, they showed a unique creativity to come up with devices to save their mistakes. During the rise of modern science, not until the Renaissance would the world see thinkers with sufficient astronomical competence to challenge the notions of ancient Greek astronomy.
- Bertrand Russell. A History of Western Philosophy. Simon & Schuster/Touchstone, 1967.
- Carl Sagan. Cosmos. Ballantine Books, 1985.
- Daniel J. Boorstin. The Discoverers. Vintage, 1985.
- O Neugebauer. The exact sciences in antiquity. Barnes & Noble, 1993.
- Ptolemy. Ptolemy's Almagest. Princeton University Press, 1998.
- Stephen Hawking. A Brief History of Time. Bantam, 1998.
- Stephen Hawking. On The Shoulders Of Giants. Running Press, 2002.
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