Goals

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Goals

• Explain how accurate observations led to
  Heliocentric model
• Review contributions of Galileo and Kepler
• Explain Keplers Laws
• Explain Newtons laws of motion and gravity

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Our life has always depended on the stars.
Seafarers needed to navigate and farmers needed
to know when to plant. Our modern calendar was
based on the changing heavens. We have seven
days of the week because there were seven movable
objects in the heavens. We have 12 months in a
year because there are about 12 lunar cycles in a
year. We have 360 degrees in a circle because it
takes about 360 days for the Sun to return to the
same spot among the stars.
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Planetary Motion
Early astronomers were obsessed with perfection
and thought the motions of the heavenly bodies
should be circles. They also thought the Earth
was stationary because they could not feel the
Earth move beneath them. This led to the Earth
centered or Geocentric model of which Ptolemy was
the main supporter. While observations were
crude the model seemed to work, but as
observation improved it became clear that
something was wrong.
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In order to modify his theory, Ptolemy had to add
circles to circles (deferent and Epicycle) to
explain retrograde motion.
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The Heliocentric Model of Nicholas Copernicus

• The earth and all the planets orbit the sun.
• Explains daily motions of stars
• Explains seasonal variations
• Explains brightness changes of planets
• Explains retrograde motion

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Retrograde motion is defined as the brief
westward motion that a planet appears to take
when a slower outer planet is passed by a faster
inner planet.
While the geocentric model required a complicated
set of circles on circles to explain retrograde
motion, the Sun centered (Heliocentric) model
easily explained the observations. Copernicus
was the main supporter for the Heliocentric
model. http//alpha.lasalle.edu/smithsc/Astronomy
/retrograd.html
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While the Copernican theory did explain the
observations better with a simpler model,
civilization at the time resisted the model
partly because the church of the time had
declared the geocentric model as correct with out
regard for scientific observations. What finally
convinced everyone was the observations of
Galileo Galilei.
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• Using his telescope, Galileo discovered
• the Moon had craters and mountains like the
  Earth and was not perfect.
• the Sun was imperfect (sunspots) and rotated on
  its own axis.
• Jupiter had four moons in orbit around it which
  showed things could orbit other things besides
  the Earth.
• Venus showed complete set of phases only
  explainable if it was in orbit around the Sun not
  the Earth.
• Because of his insistence of the Heliocentric
  model based on his observations, Galileo was
  excommunicated from the church and was not
  forgiven until 1992.

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Kepler

• Now that we have the correct heliocentric model
  we need to explain why it is the way it is.
• What causes the planets to orbit the Sun ?
• Why do the different planets have different
  speeds?
• How can we predict their positions in the future?

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Keplers Laws of Motion
First Law The orbits of the planets are in the
shape of an ellipse with the sun at one focus.
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Second Law a vector from the sun to the planet
sweeps out equal areas in equal times
(conservation of angular momentum).
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Third Law the period of a planet and its
semimajor axis are related by. P2 a3
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Newtons Laws
While Kepler discovered certain relationships and
facts concerning how the planets moved about the
Sun he could not explain why. First Law
objects remain in motion at a constant speed and
in a straight line, or at rest, unless acted upon
by an unbalanced force. Second Law F Ma
where F force, M mass, a acceleration Third
Law For every force there is an equal but
opposite force.
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Newtons Law of Universal Gravitation

• Fg GMm
• r2
• where Fg is the force due to gravity, G is a
  constant,
• M and m are the masses of the two
  objects
• r is the distance of their separation.
• Every piece of matter in the universe attracts
  every other piece of matter in the universe.

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Thus gravity provides the force which causes
objects to orbit other objects. Newton invented
calculus to help him solve his problems
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Newtons third law allows us to detect planets
around other stars and determine their mass.
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Resources

• Brecht, Bertolt. Galileo. (N.Y. Grove Press,
  Inc., 1966) There are many editions of this fine
  play about the life and work of Galileo. (also
  called The Life of Galileo)
• Koestler, Arthur. The Sleepwalkers. (N.Y.
  Grosset Dunlap, 1963). An excellent account of
  the lives of the ancient astronomers. The
  chapter The Watershed has been published
  separately and deals specifically with Tycho,
  Kepler, Copernicus and Galileo.
• Hewitt, Paul. Conceptual Physics. 8th ed.
  (Reading, MA Addison-Wesley, 1998) This, and any
  of the previous editions, is one of the most
  understandable explanations of basic physics
  principles that I have found.