History of Western Thought

A paradigm is a general consensus of belief of how the world works. It is
a mental framework we use to interpret what happens around us. It is what could
be called ``common sense''.
The Pythagorean Paradigm had three key points about the movements
of celestial objects:

1. The planets, Sun, Moon and stars move in perfectly circular orbits;
   
2. The speed of the planets, Sun, Moon and stars in their circular orbits is
   perfectly uniform;
   
3. The Earth is at the exact center of the motion of the celestial bodies.

Retrograde motion is the projected position of a planet on the
background stars as the Earth overtakes it (or is passed by, in the case of the
inner planets). The figure below illustrates this. Retrograde motion is just an
optical illusion! You see the
same sort of effect when you pass a slower-moving truck on the highway. As you
pass the truck, it appears to move backward with respect to the background
trees and mountains. If you continue observing the truck, you will eventually see
that the truck is moving forward with respect to the background scenery. The
relative geometry of you and the other object determines what you see projected
against some background.

• In what ways was the Ptolemaic model a good scientific model and in
  what ways was it not?
  
• What is the Copernican model and how did it explain retrograde motion?

• What two basic kinds of models have been proposed to explain the
  motions of the planets?
  
• What is the Ptolemaic model? What new things did Ptolemy add to his
  model?
  
• Why are epicycles needed in Ptolemy's model?

Galileo Galilei (1564--1642 C.E.) was
the first person we know of that used the telescope for astronomical
observations (starting in 1609). The telescope was originally used as a naval
tool to assess the strength
of the opponent's fleet from a great distance. He found many new things when
he looked through his telescope:

1. The superior light-gathering power of his telescope over the naked eye
   enabled him to see many,
   many new fainter stars that were never seen before. This made Bruno's argument more
   plausible.
   
2. The superior resolution and magnification over the naked eye enabled him to
   see pits and craters on the Moon and spots on the Sun. This meant that the
   Earth is not only place of change and decay!
   
   
   
   

• With his superior ``eye'' he discovered four moons orbiting Jupiter. These
  four moons (Io, Europa, Ganymede, and
  Callisto) are called the Galilean satellites in his honor. In this system
  Galileo saw a mini-model of the heliocentric system. The moons are not
  moving around the Earth but are centered on Jupiter. Perhaps other objects,
  including the planets, do not move around the Earth.
  
• He also made the important discovery that Venus goes through a complete set
  of phases. The gibbous and full phases
  of Venus are impossible in the Ptolemaic model but possible in Copernican model
  (and Tychonic model too!). In the Ptolemaic model Venus was always
  approximately between us and the Sun and was never found further away from the
  Earth than the Sun. Because of this geometry, Venus should always be in a
  crescent, new, or quarter phase. The only way to arrange Venus to make a
  gibbous or full phase is to have it orbiting the Sun so that, with respect
  to our viewpoint, Venus could get on the other side of, or behind, the Sun
  further away from us than the Sun. This was
  possible only if Venus orbited the Sun (see the figure at the end of the
  planetary motions section
  of the previous chapter).

• Major axis---the length of the longest dimension of an ellipse.
  
• Semi-major axis---one half of the major axis and equal to the distance
  from the center of the ellipse to one end of the ellipse. It is also the average
  distance of a planet from the Sun at one focus.
  
• Minor axis---the length of the shortest dimension of an ellipse.
  
• Perihelion---point on a planet's orbit that is closest to the Sun. It
  is on the major axis.
  
• Aphelion---point on a planet orbit that is farthest from the Sun. It
  is on the major axis directly opposite the perihelion point. The aphelion +
  perihelion = the major axis.
  
• Focus---one of two special points along the major axis such that the
  distance
  between it and any point on the ellipse + the distance between the other focus
  and the same point on the ellipse is always the same value. The Sun is at one of
  the two foci (nothing is at the other one). The Sun is NOT at the center of the
  orbit!

• The celestial objects are bright points of light while the Earth is an
  immense, nonluminous sphere of mud and rock. Modern astronomers now know that the stars are
  objects like our Sun but very far away and the planets are just reflecting
  sunlight.
  
• The Greeks saw little change in the heavens---the stars are the same night after night.
  In contrast to this, they saw the Earth as the home of birth, change, and destruction. They
  believed that the celestial bodies have an immutable
  regularity that is never achieved on the corruptible Earth. Today astronomers know that
  stars are born and eventually die (some quite spectacularly!)---the length of
  their lifetimes are much more than a human lifetime so they appear unchanging.
  Also, modern astronomers know that the stars do change positions with respect to each other
  over, but without a telescope, it takes hundreds of years to notice the
  slow changes.
  
• Finally, our senses show that the Earth appears to be stationary!
  Air, clouds, birds, and other things unattached to the ground are not left
  behind as they would be if the Earth was moving. There should be a strong wind
  if the Earth were spinning as suggested by some radicals. There is no strong wind.
  If the Earth were moving, then anyone jumping from a high point would
  hit the Earth far behind from the point where the leap began. Furthermore, they knew
  that things can be flung off an object that is spinning rapidly. The observation that
  rocks, trees, and people are not hurled off the Earth proved to them that the Earth was
  not moving. Today we have the
  understanding of inertia and forces that explains why this does not happen even
  though the Earth is spinning and orbiting the Sun. That understanding, though, developed
  about 2000 years after Plato.

The model he chose was one
developed by another follower of Plato, Eudoxus. The planets and stars were on concentric
crystalline spheres centered on the Earth. Each planet, the Sun, and the Moon were on
their own sphere. The stars were placed on the largest sphere surrounding all of the rest.

Aristotle chose this model because most popular and observational evidence supported it
and his physics and theory of motion necessitated a geocentric
(Earth-centered) universe. In his theory of motion, things naturally move to the
center of the Earth and
the only way to deviate from that is to have a force applied to the object.
So a ball
thrown parallel to the ground must have a force continually pushing it along.
This idea was unchallenged for almost two thousand years until Galileo showed
experimentally that things will not move or change their motion unless a force
is applied. Also, the crystalline spheres model agreed with the Pythagorean paradigm of
uniform, circular motion (see the previous
section).