The Copernican Revolution

CONTENTS
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Astronomy, ancient cultures, constellations
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Geocentric model, Aristotle, Ptolemy
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Copernican Revolution
●
Birth of modern science, scientific method
●
Galileo
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Kepler's Laws
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Newton's Laws of Motions

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Astronomy: study of the universe (all space-time-energy-
matter)

Ancient cultures dealt with astronomy for practical purposes

(navigation, planting …)

Ancient Egypt and Mesopotamia are the first places that gave
birth to science.

B.C. 3000 - Development of calendar based on 365 day-system

in ancient Egypt.

B.C. 2400 - Sumerians developed a time and angle

measurement system similar to the present system.

B.C. 2679 - Records of novae and supernovae by ancient

Chinese.
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 Stonehenge
The inset shows sunrise at Stonehenge at the summer solstice. As
seen from the center of the stone circle, the Sun rose directly over the
“heel stone” on the longest day of the year. (English Heritage)

Construction: 2800 – 1100 B.C.

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The Big Horn Medicine
Wheel, in Wyoming
was built by the Plains
Indians

Caracol temple in
5 Mexico
 Constellations

Group of stars that form an apparent shape

on the sky (Orion, Virgo, Aries, Ursa major,
Gemini…).

Knowledge of ancient cultures was based on

continuous observations of the constellations and
some bright stars.

How does the sky change over a year?

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 THE GEOCENTRİC MODEL
Aristotle (384 – 322 B.C.)
Everything was moving on circular orbits around
Earth (PERFECT FORM).
All the other stars were thought to be attached to a
“celestial sphere” rotating around Earth.
Earth, the Sun, the Moon and the five planets were
known (Mercury, Venus, Mars, Jupiter and Saturn).
 Planets' motions were not regular!!!

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 How to explain the properties of the planets?

• Always near the ecliptic (apparent circular path of

the Sun on the sky).
• Speed up and slow down.
• Brightness variations.
• Prograde and retrograde motions.

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Apparent motion of Mars on the sky.
2007-8, by Tunç Tezel
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 PTOLEMY (Batlamyus)

• constructed the best geocentric model (140 A.D.) of the

planets: Syntaxis (Almagest, “the greatest”) consists
of more than 80 circles.
• very complicated model!
• cannot explain the brightness variations of the planets.
• Some other flaws of the model were also noticed later.
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Geocentric Model

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Ptolemy’s Geocentric Model

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 Aristarcus (310 – 210 B.C.):

• “All the planets and Earth revolve around the Sun.

Earth also rotates around its axis once each day”

• Not accepted due to strong influence of Aristotle’s

teaching at that time.

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• More than ~1400 years, Ptolemaic model
was accepted as the correct representation of
the Universe in many different cultures.

• Religious authorities also supported this

model and prohibited the expression of ideas
against the geocentric model.

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 COPERNICAN REVOLUTION:

“EARTH IS NOT AT THE CENTER”

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Nicolas Copernicus (1473–1543)
• Earth rotates around its spin axis
once a day.
• Apparent daily motions of the stars
are due to this rotation of Earth.
• All the planets including Earth
revolve around the Sun.
• Only the Moon revolves around
Earth.
• Stars are at very large distances,
therefore we do not observe parallax
effect.
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The model was simple and beautiful, but put Earth
to an ordinary position. This was against religious
teaching.

His ideas were published in Latin (1543), and had

little impact.

The model accounts for the retrograde motions and

the varying brightness of the planets as well.

But, it was prohibited in 1616, and remained

prohibited until the end of the 18th century.

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 Galileo Galilei (1564–1642)
Italian mathmatician and philosopher

First steps toward

experimental
science!

(Modern science!)

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Galileo Galilei (1564–1642)

Galilei Galileo built his own

telescope and observed the
sky (1609) .
These were the first scientific
observations of the sky made
by a telescope.
Galileo’s observations changed
the old ideas about the
planetary system.
2009 was celebrated as
International Year of
Astronomy

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 Galileo Galilei (1564–1642)

Galileo observed:
the surface of the moon,
the Sun spots and variations of their positions
(They were rotating once per month),

4 moons of Jupiter (evidence against Aristotelian

picture!),

Phases of Venus! (This was important to compare the

models)

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4 Moons of Jupiter

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Surface of the Moon

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Galileo’s Sun spot observations. June 1612.

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Galileo’s sketch of “the Copernican model of the Universe.
Dialog…, 1632. (4 moons of Jupiter are also seen in the picture).

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Starry Messenger (Sidereus Nuncius, 1610)
includes the conclusions of his observations in
Italian. This was translated into Chinese and
published in China in 1615 .
“Dialog Concerning the Two Chief World
Systems” (1632)
House arrest (1633)

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• “Two New Sciences” (1638) – On mechanics, inertia, and
pendulums; includes a discussion of scientific method as
well. This could be considered as the first scientific book.
“...Universe is governed by laws which can be understood
by the human mind and is driven by forces whose affects
can be calculated using mathematics.”
Galileo Galilei
• Two New Sciences had a great impact on development
of science in Europe and all over the world.
• The Church finally, “publicly” forgave Galileo, in 1992.

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Direct evidence for the orbital motion of Earth came with the
observations of :
• Aberration of star light (James Bradly, 1728)
• Stellar parallax (Friedrich Bessel, 1838)

“ Copernican principle” is now used to express that we

are not at a special position in the universe!
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 Tycho Brahe
(1546-1601)

•High accuracy position

measurements of stars by naked
eye, in his observatory in
Denmark.
•Moved to Prague, as Imperial
mathematician of the Holy
Roman Empire (1597).
•Kepler came to Prague (1600)
to work with Brahe.

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• Takiyüddin built up one of the best observatories in
Tophane (1575, in the period of Murat III).
• Observational devices were similar to (or even better
than) those used by Tycho Brahe.
• A comet appeared in 1577, outbreak of a plague
epidemic in1578.
• These were seen as direful events caused by the new
observatory.
• The observatory was completely destroyed in 1580.

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Johannes Kepler (1571–1630)
-supported the heliocentric model,
-worked on the Brahe’s valuable
data of the planets (for about 30
years),
-determined the distances and speeds
of the planets using triangulation
taking the Earth's orbit as the
baseline.
-This work ended up with three
important laws.
(A good example of scientific
method in obtaining the scientific
knowledge.)
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Ellipse

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 KEPLER’S LAWS:

1. Planets revolve around the Sun in elliptical orbits with the

Sun at one focus.

2. A line connecting any of the planets to the Sun sweeps out

equal areas in equal time intervals.

3. Square of the orbital period is proportional to the qube of

the semi-major axis, (P2 α a3).

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Some Properties of Planetary Orbits

a: Semi-major axis
e: eccentricity (a measure of
the flatness of the ellipse)
e = 0 for a circle
0 < e < 1 (ellipse, E < 0),
e = 1 (parabola, E = 0),
e > 1 (hyperbola, E > 0).
a& e are sufficient to describe
an ellipse

Total Energy: E = potential energy + kinetic energy

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Kepler’s Second Law

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 What are the actual distances between the planets?
• Kepler’s laws give the distances in the Solar system
in terms of astronomical unit (mean Earth – Sun
distance)
• But, what is one astronomical unit in meters?
- Parallax method for Mercury and Venus during
their transits of the Sun (Distance measurement using the
parallax method is to be described later).

- Modern method: RADAR (RAdio Detection And

Ranging) technique.

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θ

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Some Solar System Properties

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Solar Transit

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Astronomical Unit

1 AU = 1.5 x 1011 m
= 1.5 x 108 km
= 150 million km

Now, all the distances in the

solar system can be
converted into meters.

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• Kepler’s laws are empirical (derived directly
from the observations).
• What are the physical laws that can account
for the observed behaviors of the planets
around the Sun?
 Newton’s Laws

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Isaac Newton (1642–1727)

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Recall:

Newton’s Laws:
(1) If the net force acting on an object is zero then
the object’s velocity does not change.

(2) F = m a

(3) Action–reaction (F12 = - F21)

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Gravitational Force

F: Force (Newton, N)

G = 6.67 x 10-11 N m2 kg-2

(Gravitational constant)

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Solar Gravity

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Orbits

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Escape Speed

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 Planetary Orbits

The planetary orbits are elliptical, but very

close to circle (except Mercury; Pluto is not a planet
anymore).

In our calculations, we will assume that the planets have

circular orbits with the Sun at the center of the orbit.

How to estimate the mass of a planet?

Why is P2 proportional to r3 ?
→ White board notes.

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