Geocentrism vs. Heliocentrism...geocentric model, called the Ptolemaic model. Presented in his book...

© 2007 Jones and Bartlett Publishers

Geocentrism vs. Heliocentrism

Mr. Catt

Courtesy of NASA/JPL-Caltech


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


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.


Parallax


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.


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.


Figure 2.03: The Greek model located the Sun on a sphere that moves

around the stationary Earth inside the celestial sphere of stars.


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.


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.


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.


Epicycles


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.


Epicycles of Venus and Mercury


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.


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.


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.


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.


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)


Eratosthenes


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.


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.


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.


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.


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


Sun’s Motion in Sky


Earth’s Path with Sun Motion


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


Copernicus’ Retrograde Motion


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.


(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.


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.


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.


(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.


Ptolemy vs. Copernicus


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


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


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.


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


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.


Figure 3.05: Venus's motion according to Ptolemy


Phases of Venus


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.


Galileo

Geocentrism vs. Heliocentrism...geocentric model, called the Ptolemaic model. Presented in his book...

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