Legacy of Aristotle

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Legacy of Aristotle

• Earth at the center of the universe
• Unmoving
• Unchanging
• Corruptible
• All other objects moving in uniform, circular
  motion about the Earth
• Except the stars which were fixed

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Problem

• Given these constraints
• Some planets (for example, Venus) do show a
  simple movement
• Other planets (for example, Mars, Jupiter) do not
  move uniformly across the sky
• How can we explain non-uniform motion given the
  constraints of Aristotle?

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Solutions

• Combine several circular motions
• Nested spheres
• Circular motion centered about a moving point
  (epicycle)
• Or, reorder the structure of the universe
  (heliocentric)
• Historically, epicycles were used

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Simple version of an epicycle
Motion of planet in opposite sense to the
movement of the epicycle
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First version

• Viewed from the Earth, object would appear to
  move at a non-constant velocity
• Would explain the solar anomaly
• But, cannot explain the motion of the superior
  planets retrograde motion
• Need a different version of the epicycle
• Motion around deferent same as motion of the
  epicycle.

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A the bottom, planet is moving left, epicycle is
moving right here we have retrograde motion
Second version motion in the same sense as the
epicycle moves.
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• Important observations
• Width of the retrograde motion (see above)
• Spacing of the ret. Motions
• Planet brightest at retrograde

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Epicycles

• Web site
• http//csep10.phys.utk.edu/astr161/
• lect/retrograde/aristotle.html
• Are reasonable mechanism to explain retrograde
  motion
• Did it work? Mars was the great test

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Inferior planets

• Mercury and Venus
• Show a simple oscillation back and forth about
  the Sun
• A simple epicycle does the job

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Side view of the Sun as seen from Earth with an
inferior planet oscillating about the Sun.
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Epicycle description of the motion of an inferior
planet. Not a unique solution (see later).
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Superior planet motion.
Observed retrograde motions of Mars from AD 109 on
Note the uneven spacing and the variable widths
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Problem with Mars

• Epicycle description gives retrograde events
  evenly distributed around the zodiac
• Epicycle description gives retrograde events of
  equal width.
• Not the observation!

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Departure from the model

• Move the Earth from the center of the deferent
• Moving in one direction changes the apparent
  spacing of the events
• Moving in the other direction changes the
  apparent width of the retrograde events.

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Moving the Earth off center changes the apparent
spacing of the retrograde events
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Moving the Earth off center changes the apparent
width of the retrograde events.
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Here the offset allows the correct spacing. But
not the width.
Here the width of the predicted events is good.
But not the spacing.
The two cannot be accomplished together.
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But the problem still remains

• It is impossible to solve both width and spacing
  by moving the Earth is the same direction
• So we need another degree of freedom to solve the
  problem

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Ptolemy

• 2nd C AD
• Claudius Ptolemeus, Alexandria
• Mathematics
• Trigonometry
• Calculated table of sine values
• Astronomy
• Accurate catalog of stars (best ever)

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Final solution

• Not only move the Earth off center, but -
• Create a fictitious point on the opposite side of
  the center from the Earth (called the equant).
• From the equant, the epicycle appears to move
  uniformly. This means non-uniform motion.
• Huge break with Aristotle.

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Ptolemys description of retrograde motion.
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Apparent motion of an epicycle as seen from Earth
displaced from the center of the epicycle.
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The placement of the equant and the Earth on
opposite sides of the center of the deferent give
an excellent match between calculated and
observed retrograde motions for Mars.
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Still had problems

• One was the size of the Moon as seen from Earth
• The second was the actual placement of the
  inferior planets (structure of the universe).

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But there remained some other problems. For
example, the size of the Moon would vary greatly
due to its epicycle.
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Three different descriptions of the inferior
planets
Traditional view.
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Planets move about the Sun
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Or lie beyond the Sun
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Ptolemy

• Also was interested in the size of the universe.
• He reasoned that the planets could not get closer
  together because of their epicycle motion
• This would give a minimum estimate of the solar
  system (a very modern idea).

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Each color represents the forbidden zone for
other planets. The size of the epicycles gives
the minimum size of the solar system.
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Ptolemys estimate

• Ptolemy got about 19,865 earth radii
• This is about 75 million miles!
• Not very accurate but it did establish that the
  solar system is larger than our comprehension
  allows.
• A tremendous change in the view of the universe