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History and Philosophy of Western Astronomy
Tags: philosophy, science, scienceliteracy, western on 2008-04-10 -All Annotations (0) -About
in list: History of Western Thought
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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.
- The celestial objects are bright points of light while the Earth is an
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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. -

History and Philosophy of Western Astronomy
Tags: astronomy, philosophy, western on 2008-02-25 -All Annotations (0) -About
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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.'' -
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!
- Major axis---the length of the longest dimension of an ellipse.
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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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- 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?
- What two basic kinds of models have been proposed to explain the
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- 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?
- In what ways was the Ptolemaic model a good scientific model and in
History and Philosophy of Western Astronomy
Tags: astronomy, science, western on 2008-02-25 -All Annotations (0) -About
in list: History of Western Thought
more fromwww.astronomynotes.com
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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). -
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.
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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!
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