May 2010

Ancient Greek Astronomers- Ptolemy Application: Students Sophia Berberidou Katerina Micheli Giannis Matzoukis Teachers Panagiotis Ioannidis George Mystax Theodoros Mitsiakis

“Πληθὺν Ἠελίοιο βοῶν, ὦ ξεῖνε, μέτρησον φροντίδ᾽ ἐπιστήσας, εἰ μετέχεις σοφίης, πόσση ἄρ᾽ ἐν πεδίοις Σικελῆς ποτ᾽ ἐβόσκετο νήσου Θρινακίης τετραχῇ στίφεα δασσαμένη χροίην ἀλλάσσοντα …”

Calcola, o amico, il numero dei buoi del Sole, operando con cura, tu che possiedi molta scienza; calcola in quale numero pascolavano un giorno sulle pianure dell'isola sicula Trinacria, distribuiti in quattro gruppi di vario colore distribuiti in quattro gruppi di vario colore:

The previous verses, of which the translation is given in both English and Italian is the start of the famous Archimedes’ cattle problem. Archimedes is an ancient Greek mathematician and astronomer who lived here in Sicily during the 3 rd century B.C. He sent that problem to his friend, Eratosthenes from Cyrene.

We can see that the Mediterranean Sea, although it is considered as an inland sea, it is an open sea that always connected its people, not only with trade, but also with their common interest in Mathematics and Science in general. Although our presentation of today concerns mostly Ptolemaeus, it would be a great omission on our side not to mention some of the greatest Greek astronomers.

ERATOSTHENES OF CYRENE Eratosthenes of Cyrene (276 BC – 194 BC) was a Greek mathematician, geographer and astronomer. He was the first person to calculate the circumference of the Earth and also made a system of latitude and longitude.

He also created a map of the world. Around 255 BC he invented the armillary sphere. He calculated the Earth's circumference around 240 BC, using the knowledge of the angle of the elevation of the sun at noon, on the summer solstice in Alexandria and on Elephantine Island near Syene (now Aswan, Egypt).

Eratosthenes's map

Eratosthenes calculated the region of Earth in stages. We don’t know however the precision of measurement, as we don’t know what kind of stage he used. If he used the Attic stage (184,98 meters) then he calculated the region in kilometers. If he used the walking stage (157,50 meters) then he calculated in kilometers which is a precise enough calculation, taking into consideration that today the region of the earth is calculated in , 86 kilometers, while during the French Revolution it was calculated in kilometers.

Eratosthenes also devised the system of geographic parallel. He stated that it is possible to travel at the length of one geographic parallel. If one starts their travel from Iberia, sailing the Atlantic Ocean, they can reach India. He also invented a way of calculation of “prime” numbers known as the Sieve of Eratosthenes. The term Geography is attributed to Eratosthenes too.

Archytas of Tarentum Archytas (428–347 BC) was an Ancient Greek philosopher, mathematician, astronomer and statesman. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato.

Eudoxus of Cnidus One of the best mathematicians and astronomers of the Plato era, Eudoxus of Cnidus (Cnidus, Asia Minor) around 400 B.C. devised the system of concentric spheres and gave the first systematic explanation of the movements of the sun, the moon and the planets, emphasizing once again the ancient Greeks’ insistence in the spherical perfection.

Hipparchus Hipparchus from Rhodes or Hipparchus from Nicaea (190 B.C B.C.) was a Greek astronomer, geographer, cartographer and mathematician who is considered to be the “father of Astronomy”, the “prince of observation” and the “founder of trigonometry”. His patience, his wit but also his passion in everything he did, are absolutely very impressive.

In the 2nd century B.C. he calculated that the solar or tropical year is 365,242 days, when today the methods confirm his calculation in 365, days! The discovery of precession of equators is attributed to Hipparchus. He also calculated the diameter of the Moon and its variable distance from the Earth.

The globe is kept on the shoulders of a Roman statue of Atlas bearing a carved map of the sky, which was probably based on the missing stellar map of Hipparchus, states an American expert on the history of astronomy. The diameter of the statue of the mythical Titan, who was forced by Zeus to hold the sky on his shoulders, is known as "Atlas Farnese" and it is part of the Farnese Collection in the National Archaeological Museum of Naples

Since the Antiquity two theories have been developed about the movement of the planets: the geocentric and the heliocentric theory.

The geocentric model (also known as "geocentrism”, "geocentricism," or the Ptolemaic view of the universe), is the theory, now superseded, that the Earth is the center of the universe and other objects go around it. Belief in this system was common in Ancient Greece. Aristotle and Ptolemaeus, as well as most, but not all, Ancient Greek philosophers, adopted the view that the Sun, the Moon, the stars, and other planets which were visible by naked eye, circle the Earth.

Heliocentrism, or heliocentricism, is the astronomical theory that the Earth and the planets revolve around the Sun and that the Sun is stationary and in the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth in the center. The notion that the Earth revolves around the Sun was first proposed in the 3rd century BC by Aristarchus of Samos. However, the fully geocentrical model was brought to completion by the mathematician and astronomer Nicolaus Copernicus in the following centuries.

Aristarchus of Samos Aristarchus of Samos (310 B.C. - about 230 B.C.) was a Greek astronomer and mathematician, who was born in Samos. He is the first recorded person who proposed the heliocentrical model of the Solar System, and who placed the Sun and not the Earth in the center of the known Universe (for this reason he is known as “The Greek Copernicus”).

Initially his ideas about Astronomy were not accepted and they were considered inferior to those of Aristotle and Ptolemaeus, until the same ideas were developed by Copernicus about 2000 years afterwards.

Claudius Ptolemaeus was a famous Greek philosopher who was born in Roman Egypt and lived in Alexandria (about 100 to 170 A.D.). Claudius Ptolemaeus or Ptolemy

His most important work, “Biggest” or “Mathematic Syntax”, (Greek Μεγίστη) was preserved in Arabic as “Almagest” and was supported by the observations of various previous astronomers and mostly by Hipparchus. His work gave the spark to the Arabs to develop Astronomy. Also, Ptolemaeus dealt with music, optics, divinatory astrology and geography.

Manuscript of Al-magest (Η Μεγίστη)

Ptolemaeus considered the Earth spherical and motionless, and bigger than the all the other celestial objects. In order to explain the retrograde movement of the planets, he introduced the geocentric model of cam circles and epicycles that had already been proposed by Apollonius from Pergaio and Hipparchus. Furthermore, he laid emphasis on the significance of “equalizing point” or “exisotes” (equant). By placing the observer in the equalizing point, one can see all the objects turn around him in an epicycle, covering in equal time equal angles (something that refers to the law of equal areas of Kepler). This model gave satisfactory results, with a fault of only few degrees. This is the reason why this theory was applied for 14 centuries.

In “Biggest Syntax” Ptolemaeus records the geocentric system of Hipparchus and at the same time he systematizes and combines it with his own observations. The result was a complete astronomical composition which included a list of stars and constellations. This was a predictive model for the future places of the celestial bodies and the future eclipse of the Sun and the Moon. In addition, it was a perception of the Universe as a total of concentric spheres, where the planets, the Sun and the Moon moved in the surface of their own cosmic spheres, while the fixed stars are placed en masse in an exterior sphere.

BIBLIOGRAPHY Wikipedia STUDY-GUIDE/ rlando_ jpg

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