14th Greek Australian Legal and Medical Conference
Cape Sounion, Greece 2013

Cosmology of Classical Greece

Dr Peter Champness RFD, MBBS, BMed Sci, M Med, FRANZCR

The title of my presentation is Cosmology of Classical Greece. It is not actually my intention to talk much about cosmology, but rather some insights and advances made by Greek philosophers in the field of Astronomy. I will take the liberty of considering instances where I think that the Greek Philosophers made correct deductions based on their observations, and leave out parts where they seem confused by modern standards.

We may however briefly consider the Cosmology of Ancient and Present times.

Cosmology may be thought of as speculation about the nature of our universe, including its origin and the eventual end

According to our current cosmology, which is greatly influenced by the invention of the telescope, the universe burst into existence about 13.7 billion years ago in an event called the big bang.

Before the Big Bang there was Nothing, neither space nor time nor mass nor energy. At the very moment of creation the universe existed as a singularity, a mathematical abstraction defining a point with no dimension. Initially there was only energy at infinite temperature. During a period of initial inflation the proto universe expanded and cooled.

When sufficiently cooled the energy condensed into matter, firstly protons and electrons, then hydrogen and helium gas. The gases collected themselves into gas clouds. Thermonuclear reactions commenced spontaneously when the gas clouds became dense due to gravitational contraction and the clouds became stars.

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The stars are all gathered together into galaxies, of which there are a very great number. In this image, which covers just 1 degree arc in the sky we can see dozens of galaxies. Each galaxy contains hundreds of millions of stars.

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Our sun is part of the Milky way galaxy and all the stars which we can see with the unaided eye are within the Milky way. The Milky way is a spiral galaxy, which is the most common type, with curved spiral arms. The sun is located at the edge of one of the spiral arms called the Orion arm, about 2/3rds of the way from the centre, in a fairly empty part of the galaxy. That is probably just as well for us as we are less likely to be disturbed here by passing comets and stars or intense cosmic radiation which might cause massive destruction.

By comparison the cosmology in classical Greece was based on ordinary experience and observations obtained with the naked eye. Our earth was at the centre of things and the sun, moon, planets and stars went around it. According to Aristotle all earthly substances were composed of four elements; namely earth, water, fire and air. Earthly things were imperfect because they were subject to change and decay. The heavens however were perfect and were composed of quintessence, the fifth element, which was weightless and incorruptible. The heavens were also immutable (unchanging) , in contradistinction to our modern evolving universe.

In the 5th century BC, Astronomy in Greece, as in other cultures, was a practical matter, chiefly used to predict appropriate times in the agricultural calendar. An exception was Babylonia, where astronomical observations were an important part of Astrology. Hence the Babylonians had a history of detailed astronomical observations going back to at least 1600 BC, particularly involving eclipses, the motions of the planets and the appearances of comets.

A poem by Hesiod (8th century BC) on Works and Days contains the following passage: “When the Pleiades, daughters of Atlas rise, begin reaping and when they set, begin ploughing”. By rising the heliacal rising is implied. The heliacal rising of the Pleiades means that they become visible just above the eastern horizon before the onset of the morning twilight and are then extinguished by the gradually brightening sky. This occurs after the star group has been invisible for about 40 days because it is too close to the sun to be observed.

Likewise the heliacal rising of the star Sirius was noted in Egypt because it is the brightest star in the sky and was associated with the onset of the annual flood of the Nile.

Meton

Meton of Athens is regarded as the earliest scientific astronomer in Greece because he made actual observations using equipment. He established his observatory in Athens at the Pnyx, a meeting place near the Acropolis,

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Pnyx, Athens showing the speakers platform. Metons observatory is said to be above the steps.

Meton established the date of the summer solstice in 432 BC, hence measuring the length of the year.

From his observatory at the Pnyx, the sun (and the moon) rise over this long ridge. Meton described the summer solstice as a turning of the Sun, because the Sun would rise, each day a little further north of its previous position, until the day of the summer solstice, also known as mid summer day and the longest day of the year. After that the sun turns about and starts to move south again.

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Moon Rise over the ridge in Athens

Meton is credited with the discovery of the Metonic Cycle, which relates the regular cycles of the moon, giving us the Months, with the cycles of the sun, that is, a Year.

The civil calendars in Greece at the time were a disorderly process. Each year had 12 named months, each beginning with the new moon, but it is necessary to intercalate an additional month every now and then to keep the year in concert with the seasons. However there was no consistency between the calendars of the various city states, either internally or between states.

Meton was concerned with creating an ideal civil calendar. He noted that a period of 19 years is equal to 235 lunar months (6940 days). The lunar month is 29 ½ days in length, hence alternating months need to be 29 and 30 days to be consistent with the new moon, Since the year of 365 ¼ day is about 11 days longer than 12 lunar months an additional intercalary month is required every third or second year and in the Metonic cycle the intercalary months are introduced in years 3,6,8,11,14, 17 and 19. After 19 years the cycle repeats.

The translation of Babylonian astronomical cuneiform texts have established that the Metonic cycle was known in Babylon long before Meton’s time, hence it is not known if he adopted the Babylonian cycle or discovered it independently.

Despite Meton’s efforts ,it seems that no Greek city state adopted the Metonic calendar. However the Metonic cycle is still in use to this day in the Jewish calendar. Consequently the dates of the Jewish feast days vary from year to year in the Western calendar.

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This slide shows the Jewish Calendar and it is seen that the months alternate in length , 29 and 30 days. The intercalary month is Adar Biet, which is an extra month of Adar, occurring in years 3,6,8,11,14,17 and 19. The normal month of Adar is called Adar 1 in a leap year. The Jewish calendar is said to have been introduced by Ezra, corresponding with the time of the Jewish exile in Babylon in 500 BC and celebrated in Psalm 137, which was set to Music in a well known song by Boney M, “By the Rivers of Babylon”.

Note: The process of an intercalary period is quite familiar to us, since our own calendar requires the addition of an extra day, once every 4 years on the 29 February. This adjustment came into use in the calendar of Julius Caesar in 46 BC, known as the Julian Calendar. What is less well known is that the Julian Calendar has 3 days too many in each 400 years. Consequently the calendar introduced by Pope Gregory in 1582 had to delete 10 days which had accumulated since 64 BC and changed the rule on leap years. Subsequently the century years, are no longer leap years unless divisible by 400. Hence the year 2000 was a leap year but the years 1900 and 2100 are not.

Pythagoras

One of the important insights is credited to Pythagorus and that is that the earth is a sphere. The Greeks were happy to believe that the earth is a sphere, since they held that the circle and the sphere are perfect shapes, but Pythagorus also noted that the shadow of the earth, when it falls on the moon during an eclipse of the moon is circular. Some people think that the prevailing view in the middle ages, before Columbus, was that the earth was flat. That view however is wrong since all educated people, including Columbus knew that the earth was a sphere. Moreover the size of the earth was known due to a calculation by Erastosthenes of Alexandria, who estimated that the circumference of the earth was 250,000 stadia (42,000km).

Eudoxus

Eudoxus, a student of Plato, proposed that system of celestial spheres, that become the central feature of Greek astronomy and persisted until overturned by Galileo. In Eudoxus system, the fixed stars are all imbedded in the outer sphere, which rotates about the earth once a day, from east to west. The sun, moon and planets all have their own spheres, which are carried around by the outer sphere of fixed stars but rotate in the opposite direction. It was axiomatic to the Greek Philosophers that the celestial movements of the heavenly bodies should be described by uniform circular motion. The system works quite well for the sun and the moon but does a poor job of explaining the motions of the planets. That lead on to ever more complicated mechanical arrangements involving epicycles, deferents, equants etc. Despite all the refinements, the system of spheres could never accurately explain the retrograde motion of the planets when they are at their closest approach. The change in brightness of the planets is even more problematic. Venus and Mars in particular become much brighter, during their closest approach to earth

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In this image of the Greek Cosmology, earth (being the heaviest element falls to the centre and forms a sphere. The water floats on top surrounded by air, then fire. The sun, moon and planets each have their own spheres, which are driven by the outermost, firmament of fixed stars, but rotate gradually in the opposite direction. The celestial sphere (firmament) rotates from east to west, once every 24 hours. The other spheres rotate from west to east against the background of the fixed stars at rates varying from 1 month (Moon) to 29 years (Saturn).

Note: The moon and the inner planets (Mercury and Venus) are shown closer than the sun. Regular observation shows that Mercury and Venus never move far from the sun. Hence the scheme, depicted here, which shows both Venus and Mercury orbiting the Earth cannot be correct and needed to be modified to somehow attach the spheres of Mercury and Venus to the Sun sphere.

Aristarchus

Aristarchus of Samos was the first person to advance the Hypothesis that the sun lies at the centre of the Universe, that the daily risings and settings are due to the rotation of the earth on its own axis and that the earth rotates about the sun. His original work has now been lost. It is mentioned by Archimedes in his book the Sand Reckoner, where he says of Aristarchus; “His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the sun on the circumference of a circle, 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’s Theory predates Copernicus by 2000 years but was not accepted at the time. The objections to the heliocentric theory were that the fixed stars would show parallax, unless they were an impossibly great distance away and that it did not accord with Aristotelean Physics which said that, due to their nature, heavy objects (eg the Earth) remained fixed

Aristarchus’ heliocentric universe was not accepted at the time and at least one philosopher called for him to be charged with impiety.

Anaxagoras

Such ideas could be indeed be dangerous, Anaxagoras, who anticipated the atomic theory of matter declared that the “sun is a red hot stone, larger than the Peloponnese.” A very reasonable idea one would think. For that impetiety he was sentenced to death, but later died in exile.

Distance to the Sun. Aristarchus did leave one book, titled “On sizes and Distances”, versions of which are extant in which he set out to measure the distance to the moon and to the sun. According to Aristarchus the distance to the moon was about 30 earth diameters, which is a good estimate, and the distance to the Sun was 19 times the distance to the moon, which is about 20 times too small. He did however demonstrate that the sun is lot further away than the moon, which was a very useful discovery and set conditions which assisted Erasthosthenes to measure the size of the earth.

Aristarchus” measurement of the relative distance of the sun and the moon was based on the observation that when the moon is exactly half illuminated, the angle between the sun, moon and earth is a right angle. If the angle between the sun, earth and moon is measured at the same time, the relative lengths of the sides of the triangle are defined.

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A few months ago, when I went to put out the rubbish bin for collection I noticed that the line of the shadow on the moon, known as the terminator, seemed to be a straight line, perfect for performing my own measurement. It is not safe to look directly at the sun, hence my simple apparatus consisting of a styrofoam box lid and three nails. Steadying the lid on the fence post I sighted the moon with two nails, then made a mark where the shadow of the third nail intersected the line to the moon. Back inside the house with the aid of a protractor I measured the sun, earth, moon angle. As you can see I made two marks corresponding to 89 and 90 degrees. Fudging my results in the best scientific tradition to match the expected result I took the average ie 89.5 degrees. My measurement is better the Aristarchus who obtained 87 degrees, hence my estimate of the distance to the sun is 114 times the distance to the moon, still too short by a factor of about 3.5.

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Note: Aristarchus did not measure the angle with a protractor in the way that I did, Instead he measured the time interval from one half moon to the next. The time from the the half moon to the next half moon via the new moon, is slightly less than the time from the half moon to the next half moon via a full moon. Comparing the two time intervals he derived 87 degrees. His accuracy problem was the same as mine. That is because it is very difficult to judge the moment when the terminator (shadow line on the moon) is an exact straight line.

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Distance to the Moon: he estimate of the distance to the moon is obtained by estimating the size of the earth’s shadow, during an eclipse of the moon. Lunar eclipses occur at least twice per year when the sun earth and moon are in exact alignment. Unlike the solar eclipse they can be seen anywhere on the night side of the earth. In this time lapse image of a lunar eclipse we can estimate the size of the earth’s shadow as about 4 times the size of the moon. Since the angular size of the moon is about 0.5 degrees it follows that the angular size of the earth’s shadow, at the same distance as the moon, is 2 degrees. Hence we obtain the result that the distance to the moon is about 29 earth diameters.

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Alexander the Great

Alexander was the greatest military commander of all time. He is mentioned here because his conquests of the whole of the classical world opened up the already extended Greek world to include Mesopotamia, Persia and Egypt. Hence all of the extensive and carefully recorded observations of the Babylonians become available to the Greeks. Aspects o Egyptian learning and culture were also assimilated\\..

Although Alexander died as a young man at the age of 36, he did not lack the best education available at the time. His Tutor was Aristotle, who in turn was a student of Plato.

Erastosthenes

To my mind Erastosthenes measurement of the size of the earth stands, along with Aristarchus’s measurement of the lunar and solar distances, as the greatest achievements of ancient astronomy.

According to the accounts Erastosthenes knew that “On a certain day of the year in Syene the sun illuminates the bottom of a deep well.” The accounts then explain that by setting up a shadow stick in Alexandria and measuring the angle of the sun, Erastosthenes could determine the angular distance, as measured from the centre of the earth, between Syene and Alexandria. When the distance between the two places is known the circumference of the earth is a simple calculation in Geometry.

When I first read the account, and for many years after, I was unable to understand his method. Since the earth is rotating at the rate of 360 degrees every 24 hours, or as the Greeks thought, the sun was going around the earth at the same rate, it seemed to me that Erastosthenes would have had to take his measurement in Alexandria at the same moment that the sun shone down the well in Syene, and this is in fact correct. For each hour difference in time between the measurements the angular measurement changes by 15 degrees. In the absence of radio communication, or a telephone, how could Erastosthenes know when to measure the sun’s angle?

The answer is that Erastosthenes was cleverer that I am and also that I had not read the text carefully. It says; “On a certain day”. Which day? Well it does not say days but DAY. As noted earlier by Meton, the Sun seems to move North and South during the year between the limits of the Tropic of Cancer and the Tropic of Capricorn. With some thought it is apparent that if Syene was located between the tropics the sun would shine down to the bottom of the well on two days every year. If North of the Tropic of Cancer, the sun could never shine to the bottom of the well. Once it is known that Syene was the site of the present day Aswan, it turns out that Syene was indeed located on the Tropic of Cancer!

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That has important consequences. The only day that the sun can shine down to the bottom of the well in Syene is the day of the Summer Solstice ie 21 June. And the time is local noon when the sun is directly over head. Even better Syene is located almost due South of Alexandria. That means that local noon in Syene and Alexandria occur at about the same time. Therefore all Erastosthenes had to do was take his shadow stick measurement at local noon on the day of the Summer Solstice. Accordingly he found that the sun is 7 degrees South of the Zenith, in Alexandria, at local noon, on the day of the summer solstice.

One of my sources claimed that Erastosthenes took his holiday in Syene and observed the sun shining down the well for himself. I think that is very unlikely for two reasons. Firstly Erastosthenes was the chief librarian at the famous library of Alexandria, the greatest repository of knowledge in the ancient world. He could have found the account of the well among the library’s many documents. Secondly, according to the historian Herodotus, the journey from Syene to Alexandria took fifty days by caravan. I doubt that Erastosthenes would have wanted to take 100 days of holiday just to travel to Syene and look down a well.

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Now Erastosthenes had all the information required. Estimating that a caravan of laden camels travels about 100 stadia/day, the distance from Syene to Alexandria is 50*100 stadia=5000 stadia (about 830 kilometres). If an arc on the surface of the earth of 7 degrees measures 5000 stadia, then the total circumference is 360/7*5000=257,000 stadia (42,900km). The modern day value is 40,000km.

Hipparchus of Rhodes

Hipparchus is perhaps the most accomplished of all he classical Greek philosopher astronomers. He is remembered because he made the first star atlas ever compiled, consisting of 850 stars, each carefully cataloged by position and brightness, using a scale similar to that used today. He positioned the stars on the celestial sphere or globe, including a system of constellations, which are the same as we use today.

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The star Atlas of Hipparchus is said to be represented here in a Statue known as the Farnese Atlas, in the Museum of Milan. Atlas carries on his shoulders the celestial sphere instead of the earth. The Farnese atlas does not show any stars, but it does have the Constellations in their correct positions. Because the celestial sphere is seen from the outside the positions of the constellations are reversed compared to a star atlas.

Two constellations shown in the picture are the Centaur and the Ship Argo, which are of interest to us because they are southern hemisphere costellations.

The Centaur contains the two bright stars known as the pointers to the Southern Cross and is also the symbol of the Melbourne Medical School.

The ship Argo was the ship of Jason and his Argonauts in which he sought the Golden Fleece. In a modern star atlas the constellation Argo has been subdivided in to Vella, (The Sails), Carina (The Keel), Puppis (The Poop deck) and Pyxis (The Compass)

Hipparchus also made extensive studies of the occurrences of eclipses ,solstices and heliacal risings, comparing his own observations with those of Meton and earlier Babylonian texts, to which he had direct access thanks to the military conquests of Alexander the Great. Hipparchus claimed that he had records of all the eclipses since 600BC. His purpose in this study was to improve the measurement of the cycles of the sun and the moon. This was no easy task, because as I have noted before the Greeks had no agreed calendar and intercalated months and days in a haphazard way at the decision of the civil magistrate in each state or province. To make the cyclical repetition of these events more understandable he converted all the recorded Dates to the Egyptian calendar which used an unvarying year of 365 days. As a result he discovered that the Tropical year, which is the time from one summer solstice to the next, differs from the sidereal year by about 20 minutes. The Sidereal year is the time for the sun to return to the same position against the background of fixed stars, which can be measured from the heliacal risings of the stars. He called this the Precession of the Equinoxes.

The reference point for the positions of stars on the celestial sphere is measured from the Vernal Equinox, which is the point on the celestial sphere where the plane of the sun’s path (ecliptic), crosses the celestial equator. As a result of the Precession the Vernal Equinox moves gradually from one zodiacal constellation to the next with a period of 24,000 years

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The Babylonians must have known about the vernal equinox, because they began their zodiacal calendar from the first point of Aries, which is where the Vernal Equinox was in their time. By the time of Hipparchus it had moved into Pisces, and as we know from the song from the musical “Hair”, we are now at the ”Dawning of the Age of Aquarius”.

A consequence of the Precession of the Equinoxes is that after a long period of time the heliacal rising of the Pleiades no longer tells the Greek farmers when to plant their crops and the rising of Sirius does not predict the onset of the annual flood of the Nile. The Classical view that the heavens are unchanging thus gradually gave way to the modern concept of constant change and no stability.

Note: The turning points of the Sun (Solstices) are easier to understand from a classical point of view, but are difficult to judge precisely. The summer solstice could only be judged by the rising of the sun and might be determined to an accuracy of about a day by interpolation.

The Prime meridian of the celestial sphere should be judged to greater accuracy, but there are no lines in the sky. How then can the equinoctial point be established? The sun is moving quite a lot from day to day at the time of the equinox, and this would allow greater accuracy in the determination if there was some way to measure it!

The answer had been established by the time of Hipparchus. It was known as an Equatorial Ring.

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Image if a ring is located at the equator in a vertical position When the sun is South of the equator the shadow of the upper part of the ring is always to one side of the bottom of the ring. When the sun is to the North the shadow is on the other side. On the day of the equinox the shadow of the upper part falls exactly on the lower part. Because the rays of the sun are slightly convergent the shadow is very slightly narrower than the lower part o the ring and the equinoctial point can be established with an accuracy of a few hours (much better than the solstice).

The ring can be placed at any point of the Earth so long as it is parallel to the equator. One of these rings (with a diameter of 2 cubits) was positioned in Alexandria, near the Library, and another on Rhodes (the island of Hipparchus).

Conclusion:

The Greek Philosophers made extra ordinary deductions about the size and nature of the universe. They did this by speculating about the causes of things and by careful observation, to which they applied their mathematical discoveries of Geometry.

Sometimes correct ideas, such as the Heliocentric theory of Aristarchus were rejected or ignored. Other times incorrect ideas such as the Geocentric theory took hold and persisted for several thousand years. The work of Claudius Ptolemy, known as the Almagest (the Greatest), in 13 volumes was so comprehensive that it helped to cause the loss of earlier works because it contained everything that was known, or needed to be known in the field.

All of the observations needed to replicate or confirm the discoveries I have described here can be made by any individual, using nothing more than naked eye, and perhaps the taking of some notes, which is for me much of the fascination of amateur astronomy.

Note: At the time of the Conference at Cape Sounion (2-8 June 2013), both Mercury and Venus had just become visible in the early evening sky. Some people asked me how to see them. We were not always successful in making the observation because both were very low above the western horizon and only visible for a short time before the sky became dark.

Mercury is no longer visible. Venus however has become a much more spectacular object, becoming ever brighter and because of its greater elongation from the sun, is visible for longer after sun set in a fully dark sky. Good viewing until the end of November 2013.

Mercury will be visible again in the early evening sky from mid September to mid October 2013 . Saturn and Mercury will be very close together for about a week each side of 08 October, which should make both easy to recognize.