The Greeks were guided by a paradigm that was first articulated
by Pythagoras , before Socrates' time.
A paradigm is a general consensus of belief of how the world works. It is a
mental framework we use to interpret what happens around us. It is what
could be called ``common sense''.
The Pythagorean Paradigm had three key points about the movements of
celestial objects:
1. The planets, Sun, Moon and stars move in perfectly circular orbits;
2. The speed of the planets, Sun, Moon and stars in their circular orbits
is perfectly uniform;
3. The Earth is at the exact center of the motion of the celestial bodies.
II. Plato gave his students a major problem to work on. Plato and his
students were, of course, also guided by the Pythagorean
Paradigm. This meant that regardless of the scheme they came up
with, the Earth should be at the unmoving center of the planet
motions.
Some of the observations that convinced the Greeks that the Earth
was not moving are
 The Earth is not part of the heavens.
 Today the Earth is known to be just one planet of 8 that orbit an
average star in the outskirts of a large galaxy, but this idea gained
acceptance only recently when telescopes extended our vision.
 The celestial objects are bright points of light while the Earth is an
immense, nonluminous sphere of mud and rock.
 Modern astronomers now know that the stars are objects like our Sun
but very far away and the planets are just reflecting sunlight.
 The Greeks saw little change in the heavens---the stars are the same
night after night. In contrast to this, they saw the Earth as the home of
birth, change, and destruction. They believed that the celestial bodies
have an regularity that is never achieved on the corruptible Earth.
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CHAPTER 2 NOTES (Copernicus, Brahe, Galileo, etc.)
 Today astronomers know that stars are born and eventually die
(some quite spectacularly!)---the length of their lifetimes are much
more than a human lifetime so they appear unchanging. Also,
modern astronomers know that the stars do change positions with
respect to each other over, but without a telescope, it takes hundreds
of years to notice the slow changes.
 Finally, our senses show that the Earth appears to be stationary! Air,
clouds, birds, and other things unattached to the ground are not left
behind as they would be if the Earth was moving. There should be a
strong wind if the Earth were spinning as suggested by some
radicals. There is no strong wind. If the Earth were moving, then
anyone jumping from a high point would hit the Earth far behind from
the point where the leap began. Furthermore, they knew that things
can be flung off an object that is spinning rapidly. The observation
that rocks, trees, and people are not hurled off the Earth proved to
them that the Earth was not moving. Today we have the
understanding of inertia and forces that explains why this does not
happen even though the Earth is spinning and orbiting the Sun. That
understanding, though, developed about 2000 years after Plato.
III. Aristotle (lived 384--322 B.C.E.) was a student of Plato and had
probably the most significant influence on many fields of studies
(science, theology, philosophy, etc.) of any single person in
history. He thought that Plato had gone too far with his
instrumentalist view of theories. Aristotle taught a realist view:
scientific, mathematical tools are not merely tools---they
characterize the way the universe actually
The model he chose was one developed by another follower of
Plato, Eudoxus. The planets and stars were on concentric
crystalline spheres centered on the Earth. Each planet, the Sun,
and the Moon were on their own sphere. The stars were placed on
the largest sphere surrounding all of the rest.
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CHAPTER 2 NOTES (Copernicus, Brahe, Galileo, etc.)
IV. Ptolemy's geocentric universe
 Ptolemy (lived 85--165 C.E.) set out to finally solve the problem of
the planets motion.
 He combined the best features of the geocentric models that used
epicycles with the most accurate observations of the planet positions
to create a model that would last for nearly 1500 years.
 He added some refinements to explain the details of the
observations: an ``eccentric'' for each planet that was the true center
of its motion (not the Earth!) and an ``equant'' for each planet moved
uniformily in relation to (not the Earth!). See the figure below for a
diagram of this setup.
V. COPERNICUS
 One such astronomer, Nicolaus Copernicus (lived 1473--1543 C.E.),
found many deficiencies in the Ptolemaic model.
 He felt that any model of the planet motions must account for the
observations and have circular, uniform motion. The Ptolemaic model
did not do that. Also, the Ptolemaic model was not elegant and,
therefore, ``un-Godlike''.
 During the years between Ptolemy and Copernicus, many small
epicycles had been added to the main epicycles to make Ptolemy's
model agree with the observations.
 By Copernicus' time, the numerous sub-epicycles and offsets had
made the Ptolemaic model very complicated. Surely, God would have
made a cleaner more elegant universe!
VI. BRAHE
 Tycho Brahe (lived 1546--1601 C.E.) revived Heroclides' model that
had the all of the planets, except the stationary Earth, revolving
around the Sun.
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CHAPTER 2 NOTES (Copernicus, Brahe, Galileo, etc.)
 Because Brahe was not a neoplatonist, he believed that the Sun,
Moon, and stars revolved around the Earth.
 Tycho's model was mathematically equivalent to Copernicus' model
but did not violate Scripture and common sense.
VII. GALILEO
 Galileo Galilei (1564--1642 C.E.) was the first person we know of that
used the telescope for astronomical observations (starting in 1609).
 The telescope was originally used as a naval tool to assess the
strength of the opponent's fleet from a great distance. He found many
new things when he looked through his telescope:
o For Galileo the clear observations of a heliocentric universe
was a powerful weapon against the hierarchical structure of the
seventeenth century Church.
o Galileo argued that the heliocentric model is not a mere
instrument but is reality. He stated that his observations
showed that
 Galileo's studies of how forces operate also provide the
foundation to prove that Earth spins on its axis.
 Although the stars and Sun appear to rise and set every
night or day, they are actually stationary.
 Evidence of the Earth's rotation (from west to east) is
seen with the deflection of objects moving in north-south
direction caused by the differences in the linear speed of
the rotation at different latitudes.
 All parts of the Earth take 23 hours 56 minutes to turn
once, but the higher latitudes are closer to the Earth's
rotation axis, so they do not need to rotate as fast as
regions nearer the equator.
 A moving object's west-east speed will stay at the original
value it had at the start of its motion (unless some force
changes it).
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CHAPTER 2 NOTES (Copernicus, Brahe, Galileo, etc.)
o Galileo is often considered the father of modern science because his
ideas were not derived from thought and reason alone.
o He used the guidance of nature (experiments). This marked a
revolutionary change in science---observational experience became
the key method for discovering nature's rules.
o His arguments for the heliocentric model and the critical role of
objective observation of nature in science got him into trouble with the
Church.
o The struggle between Galileo and the Church was not a battle
between science and religion but was part of a larger battle over
different conceptions of the proper routes to knowledge, God, and
world view.
VIII. Kepler
 Johaness Kepler (lived 1571--1630 C.E.) was hired by Tycho Brahe
to work out the mathematical details of Tycho's version of the
geocentric universe.
 Kepler was a religious individualist. He did not go along with the
Roman Catholic Church or the Lutherans.
 He had an ardent mystical neoplatonic faith. He wanted to work with
the best observational data available because he felt that even the
most elegant, mathematically-harmonious theories must match
reality.
 Kepler was motivated by his faith in God to try to discover God's plan
in the universe---to ``read the mind of God.'' Kepler shared the Greek
view that mathematics was the language of God.
He knew that all previous models were inaccurate, so he believed
that other scientists had not yet ``read the mind of God.''