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James Linzel's List: Assignment 3: History of Western Astronomical Thought

History and Philosophy of Western Astronomy

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astronomy philosophy science scienceliteracy scientificmethod on 2008-02-25 and saved by 5 people
- The emphasis was on the process of
  learning about the universe rather
  than attaining the goal. But people eventually got tired of learning and wanted
  absolute answers.
- Socrates (lived 470--399 B.C.E.) disagreed with the Sophists,
  teaching that we can attain real truth through
  collaboration with others. By exploring together and being skeptical about ``common
  sense'' notions about the way things are, we can get a correct understanding of
  how our world and society operate. This idea of being skeptical so that a truer understanding
  of nature can be found is still very much a part of modern science.
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- - 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:
    
    The planets, Sun, Moon and stars move in perfectly circular orbits;
    The speed of the planets, Sun, Moon and stars in their circular orbits is
    perfectly uniform;
    The Earth is at the exact center of the motion of the celestial bodies.
History and Philosophy of Western Astronomy

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astronomy science western on 2008-02-25
- Our view of the history of astronomy will now skip almost 1500 years to the next
  major advances in astronomy
- They had preserved and translated the
  Greek writings and adopted the Greek ideals of logic and rational inquiry. Islamic
  astronomers were careful observers of the sky and created accurate star catalogs
  and tables of planet motions. Many of the names of the bright stars in our sky
  have Arabic names (e.g., Deneb, Alberio, Aldebaran, Rigel to name a few).
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- - However,
    advances in the explanations of the motions of the stars and planets were
    made by astronomers in Europe starting in the 16th century.
  - By the 16th century the following paradigm had developed: Man is God's
    special creation of the physical
    universe; the Earth is the center of a mathematically-planned universe and we
    are given the gift of reading this harmony.
  - Scientists use a guiding principle called Occam's Razor to
    choose between two or more models that accurately explain the observations. This
    principle, named after the English philosopher, William
    of Occam, who stated this principle in the mid-1300's, says:
    the best model is the simplest one---the one requiring the fewest
    assumptions and modifications
    in order to fit the observations. Guided by Occam's Razor some scientists
    
    began to have serious doubts about Ptolemy's geocentric model in the early days
    of the Renaissance.
  - During the years between Ptolemy and Copernicus, many small epicycles
    had been added to the main epicycles to make Ptolemy's model agree with the
    observations. By Copernicus' time, the numerous sub-epicycles and offsets had
    made the Ptolemaic model very complicated
  - He
    adopted Aristarchus' heliocentric (Sun-centered) model because he felt that
    God should be at the center of the universe. Copernicus' model had the
    same accuracy as the revised Ptolemaic one but was more elegant.
  - He found that the
    planets farther from the Sun move slower. The different speeds of the planets
    around the Sun provided a very simple explanation for the observed retrograde
    motion.
  - 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.
  - Though Tycho's beliefs of the universe did not have that much of an effect on
    those who followed him, his exquisite observations came to play a key role in
    determining the true motion of the planets by Johannes Kepler. Tycho was
    one of the best observational astronomers who ever lived. Without using a
    telescope, Tycho was able to
    measure the positions of the planets to within a few arc minutes---a
    level of precision and accuracy that was at least ten times better than anyone
    had obtained before!
History and Philosophy of Western Astronomy

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astronomy scienceliteracy western on 2008-02-25
- 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?
- 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?
History and Philosophy of Western Astronomy

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astronomy philosophy science scienceliteracy on 2008-02-25 and saved by 2 people
- Giordano Bruno (lived 1548--1600 C.E.) revived
  Democritus' (a contemporary of Socrates) view that the Sun was
  one of an infinite number of stars.
- 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:
  
  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.
  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!
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- - 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).
  - A scientific model cannot be proven correct, only
    disproven. A model
    that survives repeated tests is one that is consistent with the available
    data.
    His observations were consistent with the heliocentric model, but could also be
    explained with a geocentric model like Tycho's. But for Galileo, the observations
    were enough---he was convinced of the heliocentric system before he used his
    telescope and his observations confirmed his belief.
  - More convincing evidence of the
    Earth's motion around the Sun would have to
    wait until 1729 when James Bradley
    (lived 1693--1762 C.E.) discovered
    that a telescope has to be slightly tilted because of the Earth's motion, just
    as you must tilt an umbrella in front of you when walking quickly in the rain
    to keep the
    rain from hitting your face. The direction the telescope must
    be tilted constantly changes as the Earth orbits the Sun.
    Over a century later, Friedrich W. Bessel
    (lived 1784--1846 C.E.) provided
    further evidence for the Earth's motion by
    measuring the parallax of a nearby star in the late 1830s.
  - Evidence of the Earth's rotation (from west to east) is seen with the
    deflection of objects moving in north-south direction
    caused by the differences in the linear speed of the
    rotation at different
    latitudes. All parts of the Earth take 23 hours 56 minutes to turn once, but
    the
    higher latitudes are closer to the Earth's rotation axis, so they do
    not need to rotate as fast as regions nearer the equator. A moving
    object's west-east speed will stay at the original value it had at the
    start of its motion (unless some force changes it). If the object is
    also changing latitudes, then its west-east speed will be different
    than that for the part of the Earth it is over. Therefore,
    moving objects appear to be deflected to the right in the northern
    hemisphere and to the left in the southern hemisphere. This is called
    the coriolis effect after Gustave-Gaspard Coriolis (lived
    1792--1843 C.E.)
    who deduced the effect in 1835 to
    explain why cannonballs shot long distances kept missing their target
    if the cannon was aimed directly at its target. See
    energy
    flow section for applications (and illustrations) of the
    coriolis effect to planet atmospheres.
  - The coriolis effect and the Foucault pendulum are both based on
    Galileo's discovery that an object's motion (speed and/or direction)
    are changed only if there is a force acting on it.
History and Philosophy of Western Astronomy

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astronomy philosophy western on 2008-02-25
- Johaness Kepler (lived 1571--1630 C.E.) was hired
  by Tycho Brahe to work out the mathematical details of Tycho's version of the
  geocentric universe.
- Kepler was motivated by his
  faith in
  God to try to discover God's plan in the universe---to ``read the mind of God.''
  Kepler shared the Greek view that mathematics was the language of God. He knew that
  all previous models were inaccurate, so he believed that other scientists had not
  yet ``read the mind of God.''
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- - This idea went against the 2,000 year-old Pythagorean
    paradigm of the perfect shape being a circle! Kepler had a hard time convincing
    himself that planet orbits are not circles and his contemporaries, including the
    great scientist Galileo, disagreed with Kepler's conclusion. He discovered
    that planetary orbits
    are ellipses with the Sun at one focus. This is now known as Kepler's
    1st law.
  - An ellipse is a
    squashed circle that can be drawn by punching two thumb tacks into some paper,
    looping a string around the tacks, stretching the string with a pencil, and moving
    the pencil around the tacks while keeping the string taut. The figure traced out
    is an ellipse and the thumb tacks are at the two foci of the ellipse. An oval shape
    (like an egg) is not an ellipse: an oval tapers at one end, but an ellipse is
    tapered at both ends (Kepler had tried oval shapes but he found they did not work).
  - 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!
  - As the foci are moved farther apart from each other, the ellipse becomes more
    eccentric (skinnier). See the figure below.
    A circle is a special form of an ellipse that has the two foci at the same
    point (the center of the ellipse).
  - The eccentricity (e) of an ellipse is a number that
    quantifies how elongated the ellipse is.
  - The figure above illustrates how the shape of an ellipse depends on the
    semi-major axis and the eccentricity. The eccentricity of
    the ellipses increases from top left to bottom left in a counter-clockwise direction
    in the figure but the semi-major axis remains the same. Notice where the Sun
    is for each of the orbits. As the eccentricity increases, the Sun's position is closer
    to one side of the elliptical orbit, but the semi-major axis remains the same.
  - To account for the planets' motion (particularly Mars') among
    the stars,
    Kepler found that the planets must move around the Sun at a variable speed.
    When the planet is close to perihelion, it moves quickly; when
    it is close to aphelion, it moves slowly. This was another break with the
    Pythagorean paradigm of uniform motion! Kepler discovered another rule of
    planet orbits: a line between the planet and the Sun sweeps out equal areas
    in equal times. This is now known as Kepler's 2nd law.
History and Philosophy of Western Astronomy

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astronomy philosophy science scienceliteracy on 2008-02-25
- Every age has its paradigms. Though scientists try to be
  objective, philosophical
  considerations do intrude on the scientific, creative process. That is not a bad
  thing because these beliefs are crucial in providing direction to
  their inquiries and fuel for the creativity mill.
- Experiments are the sole
  judge of scientific truth---nature eventually wins. The ideas are crucial to
  understanding the world but they eventually yield to the facts. Science makes us
  confront the world.
History and Philosophy of Western Astronomy

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philosophy science scienceliteracy western on 2008-04-10 and saved by 2 people
- Plato gave his students a major problem to work on. Their task was to find a
  geometric explanation for the apparent motion of the planets, especially
  the strange retrograde motion. One key observation: as a planet undergoes
  retrograde motion (drifts westward with respect to the stars), it becomes brighter.
  Plato and his students were, of course, also guided by the
  Pythagorean Paradigm. This meant that regardless of the scheme they came up with,
  the Earth should be at the unmoving center of the planet motions. One student named
  Aristarchus violated that rule and developed a model with the Sun at the center.
  His model was not accepted because of the obvious observations against a moving
  Earth.
- 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.
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- - 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).
  - In order to explain the retrograde motion some models used
    epicycles---small circles attached to larger circles centered on the Earth. The
    planet was on the epicycle so it executed a smaller circular motion as it moved around the
    Earth. This meant that the planet's distance from us changed and if the epicyclic motion
    was in the same direction (e.g., counter-clockwise) as the overall motion around the Earth,
    the planet would be closer to the Earth as the epicycle carried the planet backward with
    respect to the usual eastward motion. This explained why planets are brighter as they
    retrogress.
  - Ptolemy
    (lived 85--165 C.E.) set out to
    finally solve the problem of the planets motion.
    He combined the best features of the geocentric models that used epicycles with the most
    accurate observations of the planet positions to create a model that would last for
    nearly 1500 years. He added some refinements to explain the
    details of the observations: an ``eccentric'' for each planet that was the true center
    of its motion (not the Earth!) and an ``equant'' for each planet moved uniformily in
    relation to (not the Earth!). See the figure below for a diagram of this setup.