From Ptolemy to the Renaissance Years 200 to 1500

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From Ptolemy to the RenaissanceYears 200 to 1500
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Start thinking about your essay
Press report on a scientific study
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Arguments for a Geocentric Universe

• If the Earth were moving, we would have a sense
  of motion. There is no sensation of motion
  therefore, the Earth is not moving.
• We dont fall off as the Earth speeds ahead.
• The apparent positions of the stars do not
  change, i.e. we see no parallax.
• The Earth is an important place and it is natural
  that it is at the center of the Universe.

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Ptolemys Own Defense

• Let no one, seeing the difficulty of our
  devices, find troublesome such hypotheses. For
  it is not proper to apply human things to divine
  things from such dissimilar examples.
• Translation What seems complicated to humans
  may seem simple to the gods.

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9th - 13th CenturyBaghdad
Translation of Greek manuscripts Cultivation of
Literature Learning (Abbasid dynasty - from
Persia)
Bayt al-Hikmah (House of Wisdom)
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Occams Razor
William of Ockham (1285-1349) was a Franciscan
monk and philosopher who espoused the virtues of
simplicity and poverty in science and in life.
Suggesting that the Pope conform to the latter
got him excommunicated.
One should not increase, beyond what is
necessary, the number of entities required to
explain anything. If you have two theories that
are equally successful in explaining a
phenomenon, the simpler one is better.
The conviction of simplicity persists.
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The Beginning of the 16th Century

• Europe emerged from the dark ages, rediscovered
  Greek and Roman learning and explored the world.

• Ventures to Africa and Asia. Columbus discovered
  America while Copernicus studied at the
  University. Malgalhães (Magellan)
  circumnavigated the globe.
• Printing became common. A man of modest means,
  like Copernicus, could own books. He had 2
  copies of the Almagest.
• There was an explosion in artistic activity.

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Michelangelos David1501-1504
da Vincis Mona Lisa 1503-1506
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Finally we shall place the Sun himself at the
center of the Universe. All this is suggested
by the systematic procession of events and the
harmony of the whole Universe, if only we face
the facts, as they say, with both eyes open
- Nicolaus Copernicus De Revolutionibus
orbium coelestium
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Copernicus (1473-1543) Son of a successful
merchant in central Poland. Studied to be a
physician, which, at the time included
astronomy, because doctors used astrology to
decide on treatments. Worked as a deacon.
He wrote the first draft of De Revoluitonibus in
1513, but, worried about how it would be
received, he delayed publication until 1543, when
he was on his death bed.
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Copernicus Solar System

• The Sun is at the center
• Simpler than Ptolemys Model (No need for
  epicycles)
• Circular Orbits are assumed. This will be proved
  wrong.
• More accurate? No, it had about the same
  accuracy.

From De Revolutionibus

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Summary

• We can determine the architecture of the solar
  system from planetary stellar paths across the
  sky.
• If we add epicycles and several other fixes it
  is possible to predict the motion of the planets.
• Ptolemys geocentric model provided the most
  accurate predictions of celestial motion. It
  allowed people to navigate across oceans.
• The geocentric model is cumbersome.
• 1400 years later Copernicus proposed a
  Solar-centric model, but is no better than
  Ptolemys in accuracy.

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The seasons are caused by the tilt of the Earth.
Earth is tilted 23.5º from the plane of the solar
system
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Movies

• Earth around the Sun
• NASA movie of Earth

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Summary
The lunar phase is the appearance of the
illuminated part of the moon as seen from Earth.
The phase of the moon changes as the moon
revolves about the Earth. Seasons on Earth are
caused by the tilt of the Earth w.r.t. its
rotation plane about the Sun. The motion of
stars across the sky results from the Earths
spin. Note that, as seen from the equator, stars
rise in the east and set in the west. As seen
from the North Pole, stars appear to revolve
around the polar star.
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Tycho Brahe (1546 1601)
The discovery of a new star
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Stellar Parallax

• Tycho argued that the new star must be in the
  celestial sphere because it exhibited no
  parallax.
• This discovery showed that the heavens were not
  perfect and unchanging.

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25 Years of Planetary Observations
Tycho appealed to King Frederick II of
Denmark With royal funds, he built the ultimate
observatory. He designed, tested instruments,
compiling the most comprehensive and planetary
observations ever, with accuracy of 1, about 5x
better than before.
Uraniborg, Hven complete with wine cellar and
prison
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Andromeda Galaxy
Orion
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Orion Nebula
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Andromeda Galaxy
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Johannes Kepler(1571-1630)
Kepler joined Tycho a year before Tychos death
(1600). Assuming Tychos position, Kepler
inherited the records of Tychos
observations. From this Kepler knew that planets
did not travel on circles and devised a new way
to describe planetary motion.
Kepler searched for a single physical explanation
to planetary motion a force between planets and
the Sun.
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Tychos observations showed that planets do not
move in circles Planets closer to the Sun in
Copernicus model moved faster than those further
out. A force must therefore act. Kepler
thought it was magnetic He postulated that a
simple set of laws explains planetary motion.
Influenced by William Gilberts De Magnete
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Keplers Three Laws

• Planets move about the Sun in elliptical orbits
  with the Sun at one focus.
• The line joining a planet to the Sun sweeps over
  equal areas in equal intervals of time.
• The square of the time of one revolution of a
  planet about the Sun is proportional to the cube
  of the orbits semimajor axis.

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1. Planets move in elliptical orbits with the
Sun at one focus.
focus
focus
x
x
?
Eccentricity e c/a a semi-major axis c
center to focus distance (along major
axis)
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2. The line joining the Sun to the planet sweeps
equal areas in equal intervals of time.
Link to movie
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3. The square of a planets period is
proportional to the cube of its semi-major axis
P2 k a3
P is the period, a is the semi-major axis, k is a
constant which depends on the units of P a.
(For P in years and a in Astronomical Units, k1.)
The farther a planet is from the Sun, the longer
its year
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Simple Example of P2a3

• Consider a hypothetical planet orbiting the sun
  with a semi-major axis of 4 A.U.
• Let a 4 A.U. (Astronomical Units)
• Then a3 43 A.U.3 64 A.U.3
• P2 64 years2
• P SQRT(P2)SQRT(64) years 8 years
• The period of the planet is 8 years.

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Keplers Third Law
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Summary
In the 16th century, Europeans began exploring
Earth, navigating by the stars, and renewed their
interest in science and the arts. In Astronomy
this led to the first new theory describing
celestial motions in 1400 years. The Copernican
revolution was a tentative, first step towards
the establishment of the modern scientific
method.