The Orbits of the Planets

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The Orbits of the Planets
The 2 competing models
Ptolemy 100 AD
Copernicus 1511 AD
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The 16th Century Europe

• Europe rediscovered Greek and Roman learning.
  (Translations of Aristotle into Latin from Arabic
  in the 13th C.

• Explorers sailed to Africa and Asia. Columbus
  discovered America while Copernicus studied at
  the University. Malgalhães (Magellan)
  circumnavigated the globe. All this relied
  heavily on Astronomy.
• Printing was becoming common. A man of modest
  means, like Copernicus, could own books. He had
  2 copies of the Almagest.
• There was an explosion in artistic activity.

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Michelangelos David1501-1504
da Vincis Mona Lisa 1503-1506
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Tycho Brahe (1546 1601)
The discovery of a new star
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Stellar Parallax

• Tycho argued that the new star must be in the
  celestial sphere because it exhibited no
  parallax.
• This discovery showed that the heavens were not
  perfect and unchanging.

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25 Years of Planetary Observations
Tycho caught the attention of King Frederick II
of Denmark With royal funds, he built the
ultimate observatory. He designed, tested
instruments, compiling the most comprehensive and
planetary observations ever, with accuracy of 1,
about 5x better than before.
Uraniborg, Hven complete with wine cellar and
prison
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Johannes Kepler(1571-1630)
Kepler joined Tycho a year before Tychos death
(1600). Assuming Tychos position, Kepler
inherited the records of Tychos
observations. From this Kepler knew that planets
did not travel on circles and devised a new way
to describe planetary motion.
Kepler searched for a single physical explanation
to planetary motion a force between planets and
the Sun.
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Kepler aimed to explain Tychos observations
which showed that planets do not move in
circles He noted that planets closer to the Sun
in Copernicus model moved faster than those
further out. A force must therefore act.
Kepler thought it was magnetic Thus he
believed that a simple set of laws existed by
which all planets move.
Influenced by William Gilberts De Magnete
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Keplers Three Laws

• Planets move about the Sun in elliptical orbits
  with the Sun at one focus.
• The line joining a planet to the Sun sweeps over
  equal areas in equal intervals of time.
• The square of the time of one revolution of a
  planet about the Sun is proportional to the cube
  of the orbits semimajor axis.

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1. Planets move in elliptical orbits with the
Sun at one focus.
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2. The line joining the Sun to the planet sweeps
equal areas in equal intervals of time.
Link to movie
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3. The square of a planets period equals the
cube of its semi-major axis
P2 k a3
P is the period, a is the semi-major axis, k is a
constant which depends on the units of P a.
(For P in years and a in Astronomical Units, k1.)
The farther a planet is from the Sun, the longer
its year
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Simple Example of P2a3

• Consider a hypothetical planet orbiting the sun
  with a semi-major axis of 4 A.U.
• Let a 4 A.U. (Astronomical Units)
• Then a3 43 A.U.3 64 A.U.3
• P2 64 years2
• P SQRT(P2)SQRT(64) years 8 years
• The period of the planet is 8 years.

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Keplers Third Law
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Summary
In the 16th century Europeans began exploring the
planet, navigating by the stars, and renewed
their interest in science and the arts. In
Astronomy this led to the first new theory
describing celestial motions in 1400 years. The
Copernican revolution was a tentative, first step
towards the establishment of the modern
scientific method.