geocentrism vs. heliocentrism...geocentric model, called the ptolemaic model. presented in his book...
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Geocentrism vs. Heliocentrism
Mr. Catt
Courtesy of NASA/JPL-Caltech
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The Greek Geocentric Model
1. There is a fundamental difference between the
contributions to astronomy made by the ancient
Greeks and those made by other ancient civilizations.
The Greeks were interested in astronomy because of a pure
philosophical desire to understand how the universe works.
They believed in, and looked for, a sense of symmetry, order,
and unity in the cosmos.
They took the first steps in creating a unified model of the
universe
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Parallax is the
apparent shifting of
nearby objects with
respect to distant ones
as the position of the
observer changes.
2. Aristotle argued that the absence of parallax for the
stars in the sky implied that the Earth must be at the
center of the solar system.
– This is a valid scientific argument.
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Parallax
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4. Stellar parallax was not observed until 1838; the
greatest annual shift observed for any star is only 1.5
arcseconds.
5. Even though Aristotle used a correct logical
argument, the conclusion was wrong because it was
based on incomplete data.
– Parallax is hard to observe because stars are at great
distances from us.
6. Aristotle used very good arguments to conclude that:
– the Moon and Earth are spherical,
– the Sun is farther away from earth than the Moon is.
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7. Aristotle saw a difference in the ―natural‖ behavior of
Earthly objects compared to heavenly objects. He
believed that two different sets of rules existed, one
for Earthly objects and one for celestial objects.
8. The Greeks’ love of geometry led them to construct a
model of the heavens based on spheres, with the
Earth at the center.
– To account for the Sun’s apparent motion in the sky, the Sun
was located on a sphere around the Earth, inside the celestial
sphere of the stars. The axes of the two spheres were tilted
with respect to one another.
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Figure 2.03: The Greek model located the Sun on a sphere that moves
around the stationary Earth inside the celestial sphere of stars.
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9. Ptolemy (150 AD) presented the most comprehensive
geocentric model, called the Ptolemaic model.
Presented in his book called the Almagest, it held
sway for more than 1,300 years.
10. Because the heavens were viewed as perfect, the use
in the Ptolemaic model of the symmetrical circle to
model the motions of celestial objects was thought to
be the most reasonable choice.
11. Five planets are visible to the naked eye:
– Mercury,
– Venus,
– Mars,
– Jupiter,
– Saturn.
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12. The Ptolemiac model fit the fact that the planets
– Sometimes stop their eastward motion among the stars and
move westward for a while.
– This is called retrograde motion.
13. The planets always stay near the ecliptic.
– In addition, Mercury and Venus never appear very far from
the position of the Sun in the sky. Thus their elongation (the
angle in the sky from an object to the Sun) is small.
14. Any model for the planets must explain these
observations.
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A Model of Planetary
Motion: Epicycles
1. Ptolemy’s geocentric
model was able to
explain the planetary
motions using epicycles.
An epicycle is the circular
orbit of a planet, the center
of which revolves around
the Earth in another circle.
Fig. 2-5
Figure 2.05: Mars's motion on its epicycle results in a looping path.
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Epicycles
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2. The model retained the idea of perfect heavenly
circles and uniform speeds.
– The model explained why the planets never move far from the
ecliptic, but treated Mercury and Venus as special cases in
order to explain their small elongations.
Figure 2.06: In the
Ptolemaic model, the
centers of Mercury's and
Venus's epicycles stay
between the Earth and the
Sun.
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Epicycles of Venus and Mercury
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3. Ptolemy’s model meets the first two criteria of a
good scientific model fairly well.
• The model must fit the data.
• The model must make predictions that can be tested and be
of such nature that it would be possible to disprove it.
but it is much less successful with the third.
• The model should be aesthetically pleasing— simple, neat,
and elegant.
4. Ptolemaic model did fit the data, so we must judge it
as an acceptable model even though it lacked that
certain neatness we would like.
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Aristarchus's Heliocentric Model
1. 400 years before Ptolemy, around 280 BC, the Greek
philosopher Aristarchus proposed a moving-Earth
solution to explain celestial motions.
– He introduced the concept of a spinning Earth and the first
heliocentric model, 1800 years before Copernicus
2. Even though Aristarchus could not explain the lack of
observable parallax at his time (Aristotle’s argument),
he believed that the Sun was at the center of the solar
system because it was much bigger in size than the
Earth.
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3. With powerful and simple arguments based on
observations he concluded:
– The Sun was about 20 times farther from the Earth than the Moon
is.
– He showed that the Earth is 3 times larger than the Moon in
diameter, and the Sun is about 20 times larger than the Moon in
diameter.
– This implies the Sun is about 7 times larger than the Earth in
diameter.
4. Aristarchus was the first to create a map of the solar
system. He simply did not have the scale for it.
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2. By comparing shadows at noon during summer solstice at two different locations he understood that the Sun must be directly overhead (at the zenith) in Syene but that the Sun’s direction was off the vertical by 7 in Alexandria.
Measuring the Size
of the Earth
1. Eratosthenes (276--195 BC)
was the first person to clearly
understand the Earth’s shape
and approximate size.
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3. He realized that the 7 difference was due to the
Earth’s curvature.
Therefore the Earth’s circumference was about 360/7 50 times the
distance between the two cities.
Knowing this distance he was able to find the Earth’s
diameter.
His calculation was very close to the correct value.
Linear distance between Syene and Alexandria: ~ 574 miles
Earth Radius ~ 4,597 miles (~ 14 % too large) – better than any
previous radius estimate. (Actual radius is 3,963 miles)
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Eratosthenes
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4. Combining the calculations of Aristarchus and
Eratosthenes, the ancient Greeks had for the first time
measurements of the radii of Earth, Moon, and Sun
and their relative distances.
We had to wait until 1769 AD to observe the actual value of the
astronomical unit and thus the true dimensions of the solar system.
5. The important point here is not the accuracy of the
measurements but the power of simple logical
arguments that allowed the ancient Greeks to have a
very good sense of the solar system more than 2000
years ago.
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The Marriage of Aristotle and Christianity
1. In the 13th century St. Thomas Aquinas blended the
natural philosophy of Aristotle and Ptolemy’s work
with Christian beliefs.
2. A central, unmoving Earth fit perfectly with Christian
thinking and a literal interpretation of the Bible.
3. People during the Middle Ages placed a great reliance
on authority, especially authorities of the past.
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Nicolaus Copernicus and the Heliocentric
Model
1. Copernicus, a contemporary of Columbus, worked for
40 years on a heliocentric—Sun-centered—model for
two reasons.
– Ptolemy’s predicted positions for celestial objects had
become less accurate over time.
– The Ptolemaic model was not aesthetically pleasing enough.
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The Copernican System
1. Copernicus’ system revived many of the ideas of
Aristarchus.
– An Earth that rotates from west to east under a stationary sky
produces the same observations as a rotating celestial
sphere from east to west around a stationary Earth.
2. Copernicus’ system is heliocentric with the Earth
being just another one of the planets, all of them
revolving around the Sun.
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3. As seen from high above the Earth’s North Pole, all
planets move in a counterclockwise direction, with the
planets closer to the Sun moving faster than those
farther away.
4. To explain the apparent motion of the Sun in the sky,
Copernicus’ model had the plane of the Earth’s
equator tilted with respect to the plane of its orbit
around the Sun.
Fig. 2-15
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Sun’s Motion in Sky
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Earth’s Path with Sun Motion
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5. Copernicus’ model explains the
generally west to east motion of
the planets, as does Ptolemy’s.
However, the observed
retrograde motion of planets
such as Mars is explained more
simply in the Copernican
system. Retrograde motion is a
natural result in a heliocentric
system.
6. Copernicus had the Moon
revolving around the Earth and
all the planets circling the Sun.Figure 2.19c: Copernicus’s Sun-
centered theory of the layout of the
universe
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Copernicus’ Retrograde Motion
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Comparing the Two Models
1. Accuracy in Fitting the Data
(a) Copernicus’ model was not accurate enough to
account for all observed planetary motions.
Copernicus’ assumption of uniform motion (like
Ptolemy) forced him to add small epicycles of his
own to improve accuracy.
(b) Copernicus did not abandon the circle as the
preferred planetary orbit. He considered circles the
best representative of the heavens’ repetitive
motions.
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(c) Once parallax was observed
(in 1838), it provided obvious
evidence that the heliocentric
model is the better one.
Stellar parallaxes prove the
Earth moves.
Parallax also provided
evidence that stars are not all
at the same distance from
Earth, which was assumed in
both the Copernican model
and the Ptolemaic model.
(d) Using the evidence available
in the 1500s, both models
had about the same errors.
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2. Predictive Power
(a) A good theory (or model) must make testable
predictions that might allow the theory (or model)
to be disproved.
(b) Both the Copernican and Ptolemaic models made
predictions about parallax. When parallax was
finally observed, it proved that the Ptolemaic
model was wrong.
(c) The Copernican model also made predictions
about relative distances of the then known
planets from the Sun; these predictions were
(much) later confirmed.
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3. Simplicity: Mercury and Venus
(a) Copernicus liked his model because it was
aesthetically more pleasing than the Ptolemaic
model.
A good model is nearly always simple and elegant in its power
to explain and predict.
(b) The Copernican model could explain the motions of
Mercury and Venus without resorting to special rules
needed by the Ptolemaic model.
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(c) Copernicus offered a simpler explanation for
retrograde motion that required no use of epicycles.
He did use epicycles, however, in order to make his
model fit as accurate as possible.
(d) Copernicus, who died in 1543 just as his book De
Revolutionibus was published, started such an
upheaval in people’s thinking that the word
―revolution‖ took on a second meaning that is so
familiar to us today.
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Ptolemy vs. Copernicus
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3. Models of the universe have changed over the past
4000 years, with most of the changes coming in the
last 500 years.
Fig. 2-24
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Galileo Galilei and the Telescope
1. Galileo was born in 1564 and was a contemporary of
Kepler. He built his first telescope in 1609.
2. Galileo was the first to use a telescope to study the
sky. He made five important observations that
affected the comparison between the geocentric and
heliocentric theories.
(a) Mountains and valleys on the Moon
(b) Sunspots
(c) More stars than can be observed with the naked eye
(d) Four moons of Jupiter
(e) Complete cycle of phases of Venus
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Observing the Moon, the Sun, and the Stars
1. Though Galileo’s first three observations do not
disprove the geocentric model, they cast doubt
on its basic assumption of perfection in the
heavens.
2. The existence of stars too dim to be seen with
the naked eye also cast doubt on the literal
interpretation of some Biblical passages.
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Jupiter’s Moons
1. In 1610 Galileo discovered that Jupiter had four satellites of its own, now known as the Galilean moons of Jupiter.
2. The motion of Jupiter and its orbiting moons contradicted the Ptolemaic notions that the Earth is the center of all things and that if the Earth moved through space it would leave behind the Moon.
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Figure 3.03c: Io and Europa in front of Jupiter
Courtesy of NASA, Voyager 2 photo/JPL
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The Phases of Venus
1. Galileo observed that Venus goes through a full
set of phases: full, gibbous, quarter, crescent.
2. Venus’s full set of phases cannot be explained by
the Ptolemaic model but can be explained by the
heliocentric model.
3. The Ptolemaic model predicts that Venus will
always appear in a crescent phase, which is not
borne out by the observations.
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Figure 3.05: Venus's motion according to Ptolemy
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Phases of Venus
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Phases of Venus
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4. Also, the heliocentric model explains the correlation between Venus’ phases and its corresponding observed sizes.
5. Galileo is credited with setting the standard for studying nature through reliance on observation and experimentation to test hypotheses.
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Galileo