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Pythagoreans (550 BC) |
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Original arguments lost |
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From Aristotle |
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Curvature of Earth |
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Shadow of Earth on Moon during an eclipse |
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View of heavens from N and S hemispheres |
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Path of falling object |
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Different stars seen in north vs. south |
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Objects move toward center of Earth |
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Sphere viewed as a “perfect” shape |
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Earth (solid materials) |
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air (atmosphere) |
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fire (combustion) |
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water (fluids) |
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earth - dense (sinks in water) moves toward the
center of the Earth |
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air - light, moves away from the Earth |
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fire - light also |
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water - denser that air, lighter than earth |
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all elements move is straight lines |
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motion cause by external force |
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removal of force stops motion |
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Earth is corruptible (storms, earthquakes,
decay) |
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Stars are perfect (divine creations) |
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In between are the planets, Sun and Moon |
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These are intermediary in perfection |
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Eternal |
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Main constituent of the heavenly bodies |
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Moves in circular motion |
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Transparent |
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Pure |
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Associated with the stars |
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How big is the Earth? |
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How far away are the Sun and Moon? |
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How big are the Sun and Moon? |
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Assumptions |
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Sun is far away |
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Earth is small compared to everything |
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Result is that the Sun’s rays are parallel |
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Based on shadows cast by objects on Earth |
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Angle at Alexandria is 1/50 of a circle |
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Angle at Syene (Aswan) is 0 |
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Distance between Alexandria and Syene is 5,000
stades |
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Therefore the circumference = 50 x 5000 |
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= 250,000 stades |
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roughly 25,000 miles (27,650 real value) |
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Great agreement |
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Based solely on geometry (algebra, trig.
missing) |
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Angle formed by Sun-Earth-Moon is measured |
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Value was 87 degrees |
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This gives the ratio Earth-Sun/Earth-Moon as
about 18 |
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In other words the Sun is 18 times further away
than is the Moon |
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Real value is 390 |
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Very difficult to tell when the Moon is exactly
half illuminated |
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No trigonometric table yet |
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Needed to use inexact approximations |
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Ratio of Sun diameter to Earth diameter |
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Value was 19/3 or 6.3 |
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With diameter of Earth we get Sun’s radius =
41,457 km |
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Real value is 669,000 km |
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Error is largely in the estimate of distances to
Sun and Moon from Earth |
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Parallax is the apparent displacement of an
object viewed from two different locations a known distance apart |
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Proposed by Hipparchus in ~200 BC based on an
actual solar eclipse of 189 BC |
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Sun - large, always a disc, bright and hot |
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Moon - phases, bright but cold |
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Planets - move against the stars |
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Mercury, Venus - variable brightness, close to
the Sun |
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Mars, Jupiter, Saturn - retrograde motion |
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Stars -
immovable, bright objects |
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Two views |
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At the center of the heavens |
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Not at the center of the heavens |
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Problem – how to test this? |
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Use simple observations |
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views of the stars |
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Use simple arguments |
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Aristarchus - heliocentric system |
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Aristotle (and others) - geocentric system |
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Aristotle won because - |
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idea seemed reasonable |
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simple |
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aim was utility |
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Earth at the center of everything |
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Other objects move in circular orbits |
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The orbits are part of transparent spheres |
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The objects move at constant velocities in their
circular orbits |
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The apparent size of the Sun is roughly constant
- roughly fixed distance from Earth |
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Assumed to move in a circular path centered on
the Earth |
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Therefore, we would expect a constant length to
the four seasons |
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Centered Observed |
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Spring 91 93 |
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Summer 91 93 |
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Autumn 91 90 |
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Winter 91 89 |
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This was observed as early as 330 BC |
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Called the Solar Anomaly |
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Simple motion in a circular orbit centered on
the Earth does not work |
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Example - inferior planets appear to oscillate
back and forth about the Sun |
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Example - superior planets move about the zodiac
but exhibit retrograde motion (the apparent reversal of direction) |
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Simple motion in a circular orbit centered on
the Earth does not work |
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Example - inferior planets appear to oscillate
back and forth about the Sun |
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Example - superior planets move about the zodiac
but exhibit retrograde motion (the apparent reversal of direction) |
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A break with Aristotle, but there was no choice |
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Earth at center |
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Planet moved at constant velocity on a circular
orbit BUT |
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The circular orbit was centered on the circle
centered on the Earth |
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Dates from 2 Cent. BC |
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Model 2 explains retrograde motion |
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Knowing the sizes of the epicycle and deferent
and the velocities the positions of the retrograde motions and their dates
could be calculated |
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This was a good qualitative model for the
superior planets |
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Based on observation alone - size of the Earth |
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Observation plus some assumptions - motion of
the planets |
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Assumptions only - order of the planets (e.g.,
the inferior planets) |
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Mercury and Venus |
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They move close to the Sun |
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There is an apparent oscillating motion of these
planets about the Sun |
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These planets then are either the morning star
or evening star |
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An epicycle ties this together |
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The major difficulty was the accurate prediction
of the motions of Mars |
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Mars is a very powerful force in astrology |
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Necessary to improve the understanding of Mars |
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Enter Ptolemy |
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He was active between 127-145 AD in Alexandria |
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Almost nothing known about his life |
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He was a mathematician, astronomer, geographer |
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His great astronomical work is the Almagest |
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The position and width of the retrograde motion
can be observed |
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The position and width of the retrograde motion
can be predicted from the epicylic model |
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They did not agree! |
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Simple explanation of retrograde motion |
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Simple explanation of the variation of
brightness of the superior planets |
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Predicts that all retrograde events (loops) are
equally spaced around the ecliptic AND these will have the same widths |
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The spacing of the retrograde motions is not
equally spaced |
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The width of the retrograde motions is not
constant but varies from event to event |
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The closer the spacing - the wider the motion |
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Move the Earth away from the center of the
deferent |
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This changes the apparent spacing |
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This changes the apparent width |
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We can change the apparent width and spacing to
the retrograde events by moving the Earth away from the center |
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Cannot however match both the width and spacing |
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Earth is not at the center of the universe (not
a great problem) |
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Aristotle did not mention epicycles |
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The only thing kept is the circular motion |
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There is a non-uniform motion of the epicycle
along the deferent (bothered many including Copernicus) |
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Explained retrograde motion |
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Ordered the Sun, Moon and planets |
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Estimated size of the solar system |
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Mechanism to calculate positions of planets at
any date |
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Lasted roughly 1400 years |
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To improve the agreement between predictions and
observations - needed multiple epicycles. |
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This became too complicated |
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Search began for a new view of the solar system |
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There were no new observations of the positions
of the planets |
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Not really a problem with predictions |
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Switch to the Copernican (heliocentric) system
was equally complex and unfamiliar |
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Copernican system was not accurate - still used
circular orbits |
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More accurate observations |
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New ways of observing |
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New instruments |
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An organization of observing effort |
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“Big science” |
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