ASTR 1210 (O'Connell) Study Guide


"When human life lay groveling in all men's sight, crushed to the earth under the dead weight of superstition...a man of Greece was first to raise mortal eyes in defiance, first to stand erect and brave the challenge...He ventured far out beyond the flaming ramparts of the world and voyaged in mind throughout infinity."
---- Lucretius (ca. 50 BC)

The astronomy practiced by the ancient cultures we have discussed so far does not qualify as an antecedent to modern science because the underlying interpretation was still mythological or supernatural in character.

However, the scientific principles developed by the ancient Greeks (ca. 600 BC - 200 AD) are clear forerunners to modern science. Oddly enough, other highly sophisticated early societies with well-developed technologies, such as the Romans and Chinese, were never able to make strides in mathematics or science comparable to the Greeks. This Guide describes two revolutions in scientific thinking. We are used to hearing the great achievements in science beginning in 17th century Europe described as the "Scientific Revolution." But the leap in thinking that took place two millennia earlier in ancient Greece was also truly revolutionary and deserves to be called the first scientific revolution. Copernicus, in 1540 AD, initiated the second revolution, which required a further two centuries to achieve full momentum.

A. Introduction

Conclusions so far...

Distinction between "historical" and "pre-historical" science: the existence of written records

B. Greek Astronomy (ca. 600 BC - 200 AD)

A Mathematical Perspective

With the Greeks, there is a major shift of emphasis from collecting/recording information to the interpretation of the physical nature of astronomical phenomena, ultimately without religious trappings.

The Greeks had enormous impact, both because they were remarkably innovative and because they left a large, if incomplete, body of written records. They developed the Western versions of: mathematics, science, literature, drama, history, philosophy, and logic. They even developed, based on a cruder version borrowed from the Phoenicians, the basic form of the alphabet we still use today. Not bad work. Theirs was the first (recorded) scientific interpretation of astronomy.

They flourished 600 BC - 200 AD, an 800 year period (over 3 times longer than the United States has existed) during which their best thinkers persistently grappled with the nature of the universe. But Greek science and philosophy were rediscovered during the Renaissance and became the basis of European science until about 1600 AD, so Greek scientific ideas were influential over a span of 2000 years!

Pythagorean Theorm Early discoveries (ca. 525 BC) in fundamental mathematics by Pythagoras and his followers were so surprising and successful that they became the basis of not only the Greek approach to science but also to philosophy. The best known of these is the Pythagorean theorem (illustrated at right). Although the quadratic relation between the sides of a right triangle had been known before for specific cases, the Greeks proved it held for any right triangle. They made tremendous strides in plane and solid geometry.

The Pythagorean theorem led the Greeks directly to the discovery of the existence of numbers like √2 --- now known as "irrational numbers" --- i.e. numbers not expressable as a ratio of whole numbers. This was shocking because the Greek mathematicians knew there is an infinity of rational numbers --- but the irrationals are not to be found among them. This kind of discovery, based on "pure reason," led later Greek thinkers to favor deduction in formulating philosophy and interpretations of natural phenomena.

Pythagoras is quoted as saying "all things are numbers." Writers such as Arthur Koestler and Bertrand Russell argue that Pythagoras was the single greatest influence ever on the human intellect (even when he was wrong).

Extract from Aristarchus' study of the distances to the Moon and Sun

Astronomical Accomplishments

"The purpose of life is the investigation of the Sun, the Moon, and the heavens."
--- Anaxagoras (459 BC)

By 150 BC, thanks to their curiosity, facility with geometry, and persistence in making careful astronomical observations, the Greeks had discovered:

They had measured, using simple geometric arguments:

It's worth emphasizing that the Greeks' unprecedented achivements in observational astronomy were made without the assistance of telescopes or other sophisticated instrumentation.

Scientific Cosmology

The Ultimate Greek Cosmological Model

The Virtues of Greek Cosmology

C. Dark Interlude and Renaissance

The "dark ages" in Europe began with the barbarian influx from the East, 300-400 AD, coinciding with stultifying intellectual control imposed by the powerful Catholic Church. Science & other forms of original thinking fade out. Some new work was done ca. 650-1200 AD by Arab astronomers, who translated some Greek manuscripts and also elaborated and critiqued Ptolemy's models. The manuscripts were preserved by scholars but only taken seriously by most after 1000 AD. They were rediscovered and became the basis of science & philosophy in the early Renaissance. By 1500 AD, astronomy was back to where it had been in 200 AD. We had lost 1300 years!

During 1500 - 1700 AD science reappears, gradually shifting to modern form. The European realization of the existence of the "new" world weakened faith in authorities who had proclaimed it couldn't exist or that the Earth was flat. Older ideas began to be treated skeptically, rather than accepted without question.

A key facilitating technology in spreading new ideas and a flourishing interest in nature: mass-produced printed books.

Within those 200 years, the motion of the planets around the Sun was finally understood, the existence of the force of gravity was recognized, and generalized laws of motion were deduced. These become the basis not just of astronomy and physics, but of technology and engineering, with incalculable effects on civilization.

D. The Copernican Revolution

Copernicus Copernicus (d. 1543) was a Polish cleric with a strong interest in science. He was primarily a mathematician rather than an astronomer. He introduced the modern perspective of the solar system, the one which I used to explain the celestial motions of the Sun, Moon, and planets in earlier lectures. This involved as large a break (in fashionable parlance, a "paradigm shift") with the Greek interpretation of the cosmos as was the Greek break with the supernatural tradition.

Copernicus supplied very little new data. His interpretation was based almost entirely on the Greek observations handed down from 200 AD. But he brought a fresh perspective to the problem of cosmic structure, one that was less influenced by the philosophical prejudices of the Greeks.

Copernicus was a reluctant author, and his famous book De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres) was only published shortly before he died.

Relative Motion

Earth as a Planet

The Origin of Retrograde Motion

Heliocentric Cosmology

"In the middle of all sits Sun enthroned" --- Nicolaus Copernicus (1542)

Copernicus' Heliocentric Model

"Parallax" and the Size of the Universe

The "Copernican Principle"

Reading for this lecture:

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Last modified November 2023 by rwo

Text copyright © 1998-2023 Robert W. O'Connell. All rights reserved. Picture of sunset at Sounion by Bobesh. Pythagorean theorem animation by James Schombert. Eratosthenes' method drawing based on an original at IUCAAP. Epicycle and parallax drawings by Nick Strobel. Parallax animation copyright © by Richard Pogge. Retrograde motion animation from ASTR 161, UTenn at Knoxville. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1210 at the University of Virginia.