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 Greeks (ca. 600
BC - 200 AD) are clear forerunners to modern science. Oddly
enough, other highly sophisticated ancient 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. 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.
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 initiated
the second revolution, which required another 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 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) each year.
In fact, early discoveries (ca. 525 BC) in mathematics
and his followers (e.g. the Pythagorean theorem, irrational numbers, plane 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 wrong).
Extract from Aristarchus' study of the distances
to the Moon and Sun
By 150 BC, the Greeks had discovered:
They had measured, using simple geometric arguments:
- The spherical shape of the Earth. Evidence:
Curvature of ocean horizon seen from good vantage points
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 (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 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
science was largely erroneous.
- 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,
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.
- On philosophical grounds, they favored a highly symmetrical
(spherical), perfect universe.
- Drawing on the atomist interpretation of matter, they attached
special, but arbitrary, characteristics to basic building blocks:
"earth," "air," "water," "ether," etc.
- Although a revolutionary improvement over supernatural
interpretations, this reliance on deduction instead of empirical
investigations ultimately misled Greek astronomers.
"Aristotle maintained that women have fewer teeth than men; although he
was twice married, it never occurred to him to verify this statement
by examining his wives' mouths."
--- Bertrand Russell
- The first attempts at serious cosmological models placed Earth at
the center of the universe (geocentric) and introduced the
notion of "crystalline spheres" concentric with Earth, each carrying a
celestial object and revolving uniformly on an axis. Click on
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 to
the center of the universe.
- The terrestrial region is
regarded as corrupted and changeable, but at larger distances from
Earth the universe becomes ideal, perfect, unchanging.
- 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 allowed 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 how enormous a step forward
this was 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 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:
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 & physics, but of
technology & 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 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 those of 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 true
- 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 C. (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 C's interpretation, the planets, including Earth,
continuously move in the same direction (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 C's system still assumed uniform circular motions for objects and still
required epicycles (because planetary orbits aren't pure circles)
Here is an
animation of C's 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:
this simplifies the Ptolemaic model.
- Copernicus' arguments were based mainly on: (a) simplicity; and (b)
the recognition that motions of the planets 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
"aberration of starlight" caused by the Earth's orbital motion around
the Sun (Bradley, 1729) or the "coriolis effect" caused by its spin (best
demonstrated by the Foucault pendulum--1851).
Copernicus' Heliocentric Model
"Parallax" and the Size of the Universe
- Copernicus 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 change in a nearby star's apparent
location in the sky with respect to more distant stars caused by
viewing them from different positions in Earth's
orbit. See this illustration
and this Java
animation. For more discussion of astronomical parallax,
- The fact that no-one in Copernicus' time could measure a parallactic
shift implied an enormously larger
universe than most astronomers were willing to accept then.
- The first measures of the parallactic shifts for nearby stars
(about 1 arcsecond) were made telescopically by Bessel in 1838,
almost 300 years after Copernicus' death. Using these shifts,
stellar distances can be calculated by simple trigonometry. The
nearest stars are at distances
over 200,000 times the radius of the Earth's orbit. 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. But 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
"Copernican Principle." So far, this assumption has been proven
correct on three entirely different scales: our solar system, our
galaxy, and the extragalactic universe.
Reading for this lecture:
Bennett textbook: Ch. 3.2
Study Guide 6
Optional references: Bertrand Russell, A History of Western
Philosophy; Arthur Koestler, The Sleepwalkers; Timothy
Ferris, Coming of Age in the Milky Way; J. L. E. Dreyer,
A History of Astronomy from Thales to Kepler.
You have two objects, A and B, both of which are the same shape.
B weighs twice as much as A. You drop both simultaneously
from a height of 3 feet. What happens?
You should attempt your own experiments to determine the
answer...don't just take the word of the readings!
Reading for next lecture:
- A (the lighter object) hits the ground first.
- B (the heavier object) hits the ground first.
- They hit at the same time.
Bennett textbook: Ch. 3.3 (Copernicus, Tycho, Kepler, Galileo)
Study Guide 7
February 2014 by rwo
Text copyright © 1998-2014 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. 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.