ASTR 1210 (O'Connell) Study Guide
6. TWO REVOLUTIONS: THE BEGINNINGS OF
"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
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
So, only one of the hundreds of ancient cultures of which
we are aware made real progress toward scientific understanding. This
is a remarkable and sobering circumstance.
In fact, some writers argue that, far from being historically
inevitable, the development of proto-scientific thought in ancient
Greece was so fortuitous that we might still be in the "dark ages"
today without the Greeks.
Students could profitably spend some time contemplating the dominant
effects of historical contingency in shaping the familiar world
they see around them and how strange (and possibly awful) things might
be if our global or personal histories had been just a bit
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.
Conclusions so far...
Distinction between "historical" and "pre-historical" science:
- Sky phenomena and motions were important to most human
- Astronomical time cycles were recognized and studied by
- Tracking astronomical cycles encouraged development of certain
- Systematic, persistent observations
- Multi-generational methods of record-keeping (often no traces
- Skilled design of simple observing "instruments"---e.g. special
alignments in buildings
- Basic types of geometry and counting/arithmetic
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
In earlier (and many later) cultures, cosmologies were
mythological or supernatural. They had a strong "projective"
tendency: human characteristics, inflated to divine proportions,
were imposed outwards on the cosmos. Direct, persistent, supernatural
control of sky phenomena was assumed.
Starting with the philosopher/scientist Thales of Miletus (ca. 600
BC), these elements were discarded by the Greeks. Thales insisted
that natural phenomena should be explained within nature without
appeal to supernatural beings or forces.
The Greeks had enormous impact, both because they were remarkably
innovative and because they left a large, coherent body of
written records. They developed the Western versions of: mathematics,
science, literature, history, philosophy, and logic. Not bad work.
Theirs was the first (recorded) scientific interpretation of
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 was rediscovered during the Renaissance
and became the basis of European thinking until about 1600 AD, so
Greek scientific ideas were influential over a span of 2000
Greek geometry (e.g. Euclid) is, of course, still the foundation
of mathematics and is taught to millions of people (however reluctant
they may be) each year.
In fact, early discoveries (ca. 525 BC) in mathematics
and his followers (e.g. the Pythagorean
numbers, plane and solid geometry) became the basis of not only the Greek
approach to science but also to philosophy. 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
One important impetus for the Greek interest in both astronomy and
geometry was the need for accurate navigation around their
convoluted coastline and across their island provinces (click on the map
Extract from Aristarchus' study of the distances
to the Moon and Sun
By 150 BC, thanks to their curiosity, facility with geometry, and
persistence in making careful astronomical observations, the Greeks
"The purpose of life is the
investigation of the Sun, the Moon, and the heavens." |
---- Anaxagoras (459 BC)
They had measured, using simple geometric arguments:
- The spherical shape of the Earth (ca. 500 BC).
Curvature of ocean horizon seen from good vantage points
The recognition that the Earth was not an enormous flat plane, which
was the obvious "common sense" inference made by all cultures before
the Greeks, was the first link in the chain of reasoning that led
to the discovery that Earth is a planet.
Different stars visible from different latitudes
Length of day changes at different latitudes
Circular shape of Earth's shadow on Moon during lunar eclipses
Shadow lengths at different latitudes at same time of day (Eratosthenes, see
- The spherical shape of the Moon, the fact that it shines by
reflected Sunlight, and the origin of lunar phases (see
Study Guide 5)
- The origin of eclipses (shadow effects on a sphere,
see Study Guide 5). Thales was
the first to predict a solar eclipse, in 585 BC.
- The existence of precession of the equinoxes (Hipparchus,
see Study Guide 5).
- The approximate distance to the Moon & Sun (Aristarchus, ca. 250
BC, see extract above)
- The diameter of Earth to an accuracy of about 150 miles
(Eratosthenes, ca. 200 BC). Eratosthenes' method uses simple
measurement of shadow lengths at noon at different latitudes on
a given day. It then applies the geometric concept of the
congruence of triangles, as shown in the diagram below.
If the Earth had been flat, the shadow lengths at the
two latitudes would have been the same.
Eratosthenes estimated the diameter of the Earth to be 8050 miles; the
true value is 7900 miles. An amazing feat, particularly if you
consider the fact that most "educated" people today, 2200 years later,
would have trouble figuring out how to do this (or how to explain
eclipses or the phases of the Moon).
- The Greeks explored a wide variety of interpretations of the
physical universe. Early on (ca. 400 BC),
the Atomists, followers of Democritus and Epicurus,
arrived at an astonishingly modern interpretation in which all matter
is composed of indivisible particles called "atoms," which interact
according to natural laws. Gods or other supernatural influences were
assumed to be unimportant in controlling nature. The universe was
thought to be enormous, even infinite, and filled with worlds like
Earth, many of them inhabited by similar lifeforms. The atomists
influenced a number of thinkers, through the time of the Roman poet
Lucretius (ca. 50 BC), but they were overshadowed by the philosophy of
Plato and Aristotle, whose physical science was largely
It is remarkable that a concept as strange and completely unintuitive
as an infinite universe
arose so early in the history of scientific thinking. It was probably
the Greeks' work in mathematics and the realization of the existence
of arbitrarily large numbers that led them in this direction.
- The Greeks developed the first scientific cosmological models
- Greek models were intended to be consistent with their
large and accurate collection of observations of the Sun, Moon,
planets, and stars.
- They treated the Sun, Moon, planets, stars as inanimate physical
objects, not living beings with supernatural volition and
- Influenced by the
philosophical idealism of Plato &
Aristotle, who became the most important philosphers in history, they
attempted to deduce the character of nature from abstract
postulates (like mathematical axioms), with little appeal to empirical
tests and with explicit dismissal of experiments. Plato argued
that astronomers should not observe the sky but instead explore it by
pure thought (luckily, most Greek astronomers ignored this
- The first attempts at serious cosmological models placed the
Earth at the center of the universe and
introduced the notion of "crystalline spheres" concentric with
Earth, each carrying a celestial object and revolving uniformly on an
axis. Click on the thumbnail at right for a larger view.
- Aristarchus (ca. 250 BC) proposed instead a heliocentric
(sun-centered) cosmos, based on his realization
that the Sun was probably larger than Earth, but this was not favored.
The Ultimate Greek Cosmological Model
- Developed by Ptolemy, ca. 130 AD
- The model is geocentric, with a spherical Earth
sitting stationary at the center of a spherical universe.
- In this picture:
- The Earth is fundamentally distinct from the planets. It
occupies a special location and has special properties.
Objects fall downward toward the Earth not because its gravity
attracts them (as in our modern view) but because they tend to move
toward the center of the universe.
- The terrestrial region is regarded as corrupted and changeable,
but at larger distances from Earth the universe becomes ideal,
- All celestial objects move in (perfect) uniform, circular
motions around Earth
- Earth does not spin on its axis; rather, the universe revolves about
Earth once a day.
Note that as long as you do not admit it is possible for the Earth to
spin on its axis, the observed diurnal motion of the sky requires
that the Earth be at the center of the Universe.
- But in the real solar system, the Earth moves
around the Sun, and the planetary orbits are not perfectly
- Therefore, Ptolemy had to add a number of complicated geometric features
in order to reproduce the observed planetary motions.
- Viewed from Earth, the planets all appear to undergo occasional
"retrograde motion"---a brief, loop-like reversal in their
general eastward motion with respect to the stars. This was readily
visible in the computer planetarium simulations I showed in class. For an example,
- To reproduce such motions, Ptolemy's model
used "epicycles" (a compound system of wheels moving
on wheels). See the illustration below. The epicycles were purely
geometrical constructs, without any presumed physical reality to
- Here is an animation showing
how epicycles generate retrograde motion.
- Ptolomy's complex model was a success it that it produced
accurate predictions of the locations of the planets for
several centuries into the future. But because of its inherent flaws,
errors accumulated over time.
- Here is an animation
of a Ptolemy-like model.
The Virtues of Greek Cosmology
Ptolemy's work is often treated dismissively because it "got the solar
system wrong" and was discarded by the "Copernican Revolution."
However, it is important to appreciate that this was an enormous
step forward over all the other modes of thinking at the time and,
in fact, over any other framework for understanding the universe for
more than a millennium(!)
Science is a cumulative and pan-cultural enterprise. It
discards wrong ideas that are found to be unsupported empirically but
retains useful ones. Statistically, most scientific
ideas have been wrong. Wrong ideas are just as important as "right"
ideas if they are credible in their time and establish empirical tests
that push the envelope of scientific understanding outward.
Despite their many misconceptions, the Greeks laid the groundwork for
all later science. Many features of the cosmology of the Greeks
propagated through to modern science, including these:
Ptolemy's model reproduced the angular motions of the planets on the
sky reasonably well. Despite flaws, this is a scientific
model which makes predictions that can be tested: e.g.
concerning the brightnesses of the planets and their distances from
the Earth as they move around their complex orbits. Although the
Greeks apparently did not test the models this way, later observers
like Tycho could easily do so.
- They attempted to incorporate all of the extant
- They insisted that theoretical models reproduce the observations.
- They regarded the planets, Moon, and Sun as inanimate, physical
objects moving through space without supernatural
interference. This was a tremendous break with the interpretations of
almost all other cultures of the time.
- Their models were based on mathematics. All later science likewise
used mathematics (of an ever-increasing sophistication). The modern
view is that although all things may not BE numbers (as the Pythagoreans
claimed), all things can be measured by numbers.
- The models emphasized geometrical symmetry. In modern
science, symmetry emerged as a central concept in simplifying
mathematical descriptions of nature. Symmetry
was found to be the conceptual key to understanding subatomic particles,
crystalline solids, DNA molecules, and a wealth of other phenomena.
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 by Arab
astronomers after 600. Greek manuscripts were preserved by scholars
but only taken seriously after 1000 AD. They were rediscovered &
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: mass-produced printed
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 (d. 1543), who was primarily a mathematician, 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 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
- Copernicus introduces the concept of relative
motion: namely that apparent motions in the sky could be
produced by motions of the
Earth as well as by motions of the cosmic bodies and that it
was difficult to tell these cases apart.
- For instance, the apparent revolution of the sky around the Earth
once a day, which was traditionally interpreted as a rotating universe
surrounding a central, stationary Earth, could equally well be
produced by a spinning Earth in a stationary universe. But in
that case, the Earth would not have to reside at the center of
the universe---it could be anywhere, and we would still see the same
Earth as a Planet
- Copernicus recognizes Earth to be a planet with two
independent kinds of motion. It spins on its rotational axis
once a day, and it orbits the Sun once a year.
- Identifying Earth as a planet was a much greater leap than might
be supposed. Remember that Copernicus did not have access to
telescopes, so he could not know that the planets were spherical or
not self-luminous (like the Earth). Until the time of
Galileo (1609, 66 years after Copernicus died), no one saw the planets
as anything other than glowing points of light.
The recognition that Earth was a planet also eliminated the
distinction that the Greeks had assumed between the physical
properties of the Earth and the objects in the celestial realm. It
was now possible that matter had universally common properties,
just as the Atomists like Democritus had proposed (and we know to be
- A wrenching change in perspective: Earth is now merely one among
the (six) known planets. It has been "dethroned" from its special
situation at the center of the universe and has lost the unique
properties associated with that location attributed to it by Aristotle
and the Greek philosophers. The Sun becomes the most important object
in the solar system.
- Removing the Earth from its imagined special cosmic location was
the first step toward the modern theory of gravity. Aristotle believed
that objects fell Earthward because it was at the center of attraction.
But if the Earth is not at the center of the universe, then some other
influence must be attracting matter to it. Newton (120 years later)
realized that each object with mass exerts an attractive force
(gravity) on all other objects with mass.
- The extent to which conditions on the other planets
resemble those on Earth was not known to Copernicus (without telescopes), but
there was no evidence then that they were very different. A
"multiplicity of worlds" therefore emerges,
possibly inhabited worlds.
The Origin of Retrograde Motion
- In Copernicus' interpretation, the planets, including Earth,
continuously move in the same direction in their orbits
(counterclockwise around the Sun as seen from above Earth's north
pole). Planets nearer the Sun move around faster. Retrograde
loops in the celestial paths of the planets are naturally explained as
the reflex of the Earth's orbital motion (i.e. the
fact that we observe the other planets from a moving platform). For
instance, Mars appears to move backwards in our sky as the
Earth "catches up to and passes" it in its orbit. See the animation
- But Copernicus' system still assumed uniform circular
motions for objects and therefore still required epicycles (because
planetary orbits aren't pure circles)
Here is an
animation of his model.
"In the middle of all sits Sun enthroned"
--- Nicolaus Copernicus (1542)
- Copernicus hence develops the heliocentric model, with
the Sun in the center of the universe surrounded by 6 orbiting planets.
- Copernicus' arguments were based mainly on: (a) simplicity; and (b)
the recognition that some features of the planets' motion in Ptolemy's model (e.g.
retrograde loops) were synchronized with the motion of the Sun, which
implied the Sun was the key object.
- Three examples of simplification in the Copernican picture: the
epicycles responsible for the retrograde motion of the planets were
eliminated; the alignment of the centers of the epicycles for Mercury
and Venus with the Sun was explained without arbitrary assumptions;
and the fact that the relative sizes of the retrograde loops of the
planets decreased with distance from the Earth had a natural, not
- But Copernicus had no conclusive observational evidence of
Earth's motion, either its spin or revolution around Sun.
- Such evidence became available only much later, with telescopes
and other instruments which could measure, for instance, the
of starlight" caused by the Earth's orbital motion around the Sun
(Bradley, 1729) or
effect" caused by its spin (best demonstrated by the Foucault
Copernicus' Heliocentric Model
"Parallax" and the Size of the Universe
- Copernicus' model assumed the stars resided in a fixed shell
at the edge of the spherical universe, but unlike most earlier models
there was a finite thickness to this shell, so the stars were
distributed in depth.
- He was forced to assume that the stars were very
distant in order that the "parallactic shift" would be too
small to measure.
- The parallactic shift is a simple geometric effect. The
apparent location on the sky of a nearby star with respect to
more distant stars changes when it is viewed from different
positions in Earth's orbit. See this
illustration and this
QuickTime animation. There would be no parallactic shift in the
geocentric model for the universe. For more discussion of
- The parallactic shift decreases in direct proportion to the
distance of a star. The fact that no one in Copernicus' time could
measure a parallactic shift implied either that the Earth did not move
around the Sun, contrary to Copernicus' interpretaion, or that the
distance to the nearest stars, and hence the universe,
is enormously larger than most astronomers were willing to
Naked eye observers cannot determine the angular separations between
stars to much better than one minute of arc. The absence of
parallactic shifts larger than this implies, in the heliocentric
model, that the stars must be at least 3000 Astronomical Units away.
(One AU is the radius of the Earth's orbit.) This is over 300
times the distance of Saturn and is a radical increase in the
scale of the universe surrounding the Earth by pre-Copernican
After their invention in 1609, telescopes could, in principle, have
provided much better parallax determinations. But the quality of
their lenses or mirrors was so poor that they were not up to this task
until over 200 years later.
- The first measure of the parallactic shift for a nearby
star (about 1 arcsecond) was made by Friedrich Bessel using a special
in 1838, almost 300 years after Copernicus' death.
Using these shifts, stellar distances can be calculated by simple
trigonometry (the same method known as triangulation). The
nearest stars are at distances of over 200,000 AU's. Even
Copernicus himself would have been flabbergasted by the scale of our
- In Ptolemy's model, the universe must rotate around the Earth once a
day. It therefore cannot be very large, although there was no
definitive evidence concerning its size. In Copernicus' model, this
diurnal motion is caused by the Earth's spin. The universe is
stationary. This permits it, in principle, to be infinite in
The "Copernican Principle"
Copernicus' system had profound philosophical, religious, and scientific
implications because it removes the Earth (and by inference, the human
race) from a privileged location. The idea that scientific arguments
should assume that human beings have a typical, rather than
special, perspective on the universe became known as the
So far, this assumption has been proven correct on three
entirely different scales: our solar system, our galaxy, and the
extragalactic universe. Even the solar system itself is not
special: we now have identified thousands of
Reading for this lecture:
Reading for next lecture:
Bennett textbook: Ch. 3.3 (Copernicus, Tycho, Kepler, Galileo)
Study Guide 7
June 2017 by rwo
Text copyright © 1998-2017 Robert W. O'Connell. All
rights reserved. Picture of sunset at Sounion by
Eratosthenes' method drawing based on 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