Astronomy 217W h a t t h e G r e e k s

K n e w

BabylonWhile many cultures developed often intricate astronomical systems for predicting the seasons and other calendaring purposes, western astronomy (and astrology) traces its roots to Babylonia and their base 60 numbering system.

Clay tablets document an astronomical tradition reaching back to ~3000 BC. They were the first to recognize the periodicity of events like eclipses. In later years, they developed a very empirical and mathematical approach.

Classical Greece 500-323 BC

Greek Astronomy begins to progress beyond calendar-making during the Classical Period. This is the period of the Greek City-States (Athens, Sparta, Thebes, …), the Peloponnesian War and the Persian wars with battles like Marathon, Thermopylae, and Salamis.Greek Culture was limited to Greece and small states along the Aegean shore of Turkey and the Northern Mediterranean.

MuseThe Muses were a set of minor Greek goddesses, the source of inspiration in literature and the arts. Among the 9 was, Urania, the muse of astronomy. She is generally pictured with her globe and compass, with which she could foretell the future by the arrangement of the stars.The other 8 muses are Calliope (Epic poetry), Clio (History), Euterpe (Lyric poetry), Thalia (Comedy), Melpomene (Tragedy), Terpsichore (Dance), Erato (Love poetry), Polyhymnia (Sacred poetry).

Among the greatest of the many Greek scientific discoveries was the realization that the solar system was three dimensional.The finest example of this is the planetary model of Eudoxus of Cnidus (~410-350 BC), which used 27 uniform “spheres” to account for the motions of the solar system.This model was fine tuned by Eudoxus’ student Callippus, who added 7 more spheres to better match observations.

The 3D Universe

Each planet required a sphere to explain each of its apparent periods.

Phases of the MoonWith a 3D geometric realization of the solar system, many previously mysterious phenomena are easily explained.A prime example is the phases of the moon. To the Greeks, this was easily understood as the changing lighting of the Moon by the Sun as the Moon orbited the Earth.

EclipsesAn important observation that contributed to the Greek’s 3D solar system model was observations of eclipses.Observations of solar eclipses led to the conclusion that the Moon was closer to the Earth than the SunThe Greeks also understood why eclipses do not occur every month.

Theoretical TechnologyMany of the Greek’s astronomical advancements relied on the newly formulated theories of planar geometry, trigonometry and spherical geometry that were being developed at the same time.

So strong was this connection that the Greeks regarded astronomy as a branch of mathematics, with noted mathematicians like Autolycus of Pitane and Euclid writing books on astronomy.

The Round EarthThere is evidence that the Greeks knew the Earth was a sphere as early as the 5th Century BC and perhaps as early as Pythagoras (~570-495 BC).Certainly by the time of Aristotle (384–322 BC) it was certain, with Aristotle giving 4 reasons

Every portion of the Earth tends toward the center.Travelers going south see southern constellations rise higher above the horizon.The shadow of Earth on the Moon during a lunar eclipse is round.That elephants lived at the eastern and western extent of his known world.

Spread of HellenismAlexander the Great’s conquests spread Greek ideas and culture through out much of the civilized world.From this point, the Greek language was the language of trade and science, but Greece was not the center of Greek civilization, replaced by Alexandria and other cities.

For Astronomy, this expansion brought prosperity and rich new sources of data, largely Babylonian, allowed a longer perspective to judge change in the Heavens.

The Sizes of the Earth, Moon and Sun

Aristarchus (310 – 230 BC) devised a way to measure the relative sizes of the Earth, Moon and Sun.Unfortunately he wasn’t able to accurately measure θ.

Earth-Sun = Earth-Moon / cos θ = 19 Sun & Moon have similar angular size so RSun = 19 RMoon

By timing lunar eclipse, REarth = 3 RMoon

While he wasn’t able to measure the true value θ = 89.85°, Aristarchus did show that the Sun is much larger.

θ

390390

4

The Radius of the EarthEratosthenes (~276-195 BC) was the third chief librarian of the Great Library of Alexandria and a noted mathematician and geographer. By measuring the sun’s angle on the Solstice at Alexandria and Syene (on the Tropic of Cancer), he calculated the distance from Alexandria to Syrene was 1/50 of the circumference of the Earth.

His estimate of 5000 stadia from Alexandria to Syene gives a circumference of 46,620 km or 39,690 km, using the common Attic or African stadia.

HipparchusThe most noted astronomical observer among the Greeks was Hipparchus of Nicea (~190-120 BC).

Provided accurate measure of Tropical year.Discovered precession of the equinox.Provided more accurate Earth-Moon distance (~70 REarth) via parallax.Produced accurate catalog detailing the position of hundreds of stars.Established the magnitude system for stellar brightness, which is still used today.

Farnes Atlas

ParallaxBinocular vision affords humans and other predators the ability to use Stereopsis to make fine depth discriminations based on parallax, the fact that the line of sight from the left and right eyes are at slight angles to each other.

For the 6 cm separation of human eyes, 1° differenceDistance = 3 cm / tan (0.5°)Distance = 344 cm = 3.44 m

Stellar ParallaxDiurnal or Geocentric Parallax: The Earth’s rotation provides a similar opportunity for distance measurement, with a base line of 6371 km.Distance = 6371 km / tan (0.5°) = 730,044 km = .005 AU

Annual or Heliocentric Parallax: The Earth’s orbit provides a another opportunity for distance measurement, with a base line of 1.5 x 108 km. Distance = 1.5 x 108 km / tan (0.5°) = 1.7 x 1010 km = 114 AU = 1/1800 parsec

First measured by Bessel in 1838.

The Stationary EarthOdd as it may sound today, the Greeks had several reasons they thought the Earth must be stationary and thus the center of the Universe.1)The absence of Stellar Parallax, requiring a Universe

that was too large.2)Lack of perceptible movement of the Earth’s surface3)The (near) constant brightness of Venus along it’s

orbit4)The Aristotelian belief that a heavy object like the

Earth would require to great a force to move. In this the Greeks committed one of the grave errors of deductive logic, equating the absence of evidence as evidence of absence.

HeliocentrismNot all Greeks were fooled by their desire for a compact Universe.Aristarchus (310 – 230 BC), no doubt motivated by his observation that the Sun was larger, proposed a heliocentric system.Aristarchus notion that the larger object should be the center foreshadows the application of Gravity to the Heavens.This was widely discredited and some even suggested charging him the impiety.

Problems with Uniform Spheres

By late in the Hellenistic period, there were an accumulation of observations that the model for the solar system put forth by Eudoxus, Callippus and Aristotle had problems.

Changes in the brightness of the planets Retrograde motion.

Epicycles and DeferentsTo preserve the heavenly “perfection” of uniform circular motion while addressing these problems, Apollonius of Perga (262 BC -190 BC) proposed epicycles, small circles whose centers followed deferents, larger circles centered on the Earth.

Claudius Ptolemaeus (90-168 AD) added equants, about which motions were uniform, to account for the observed variations in the motions of the Sun, Moon and planets. With so many positions, radii and rates of rotation, a wide variety of motions could be accommodated.

Scientific MethodIn these classical Greek explorations of our solar system’s dynamics, one sees the beginnings of the modern scientific method. Greeks like Aristotle, Hipparchus & Aristarchus used observations, to confirm or deny theories.

A cornerstone of the Greek and modern scientific method is empiricism, which asserts that knowledge arises from evidence gathered via sense experience.Despite of their empiricism and deduction, the Greeks were plagued by the believe that the heavens were “perfect” requiring uniform circular motion in spite of evidence to the contrary.

Next TimeCopernicus and Galileo