Course Announcements Wednesday Sept 8

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Course AnnouncementsWednesday Sept 8

• PRS system
• Will send email for registering PRS on web
• Will try (anonymous mode) on Friday
• First quiz on Wednesday Sept 22
• Exam I
• Next Wednesday Sept 15
• Multiple choice, 25 questions
• Covers all lectures up to exam date
• Textbook Chapters 1-5

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Topics for today

• Ptolemys geocentric mode
• Explains retrograde motion
• Based on epicycles
• Renaissance astronomers
• Copernicus (c.1580) heliocentric model
• Tycho Brahe (c.1600) most accruate observational
  data
• Kepler (c.1610)
• 3 laws re. orbits, including elliptical orbits
  confirmed heliocentric model
• Galileo (c1610-1630)
• First telescopic observations
• Four Galilean satellites of Jupiter
• Phases of Venus
• Sunspots
• Isaac Newton
• Law of gravity
• Explains Keplers 3 laws
• Provides theory to understand all planetary
  motions

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Retrograde Motion of planets

• All planets generally move eastward with repsect
  to the background of stars. This is called
  prograde motion
• Near opposition or inferior conjunction, planets
  reverse direction and move westward wr.t. stars
  this is retrograde motion
• Ancient astronomers (since Ptolemy, 150 AD)
  explained retrograde motion as caused by
  epicycles in a geocentric (Earth-centered) model
  of the solar system
• Since Copernicus (1580 CE) and Kepler (c. 1600
  CE), retrograde motion can be explained in
  heliocentric (Sun-centered) model as due to
  varying orbital speeds of planets in nearly
  circular orbits

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Planetary orbits and retrograde motion

• All planets display retrograde motion, including
  inferior planets
• Retrograde motion typically lasts a few months
• For inferior planets (Mercury, Venus),
  retrograde motion occurs near inferior
  conjunction
• For superior planets (Mars, Jupiter, Saturn,
  Neptune, Uranus) retrograde motion occurs near
  opposition
• Web site animation of Mars retrograde motion

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Claudius Ptolemy (c. 85-165 AD)

• Greatest ancient astronomer
• Worked in Alexandria at the great library
• Ptolemy published the Almagest, an encyclopedia
  in which he used centuries of Babylonian
  observations of the motions of the planets to
  justify a geocentric (Earth centered) model of
  the universe.
• The ideas of the Ptolemaic system ruled the
  world of astronomy for 1,500 years, until
  Copernicus and Galileo (c. 1600)

9th cent. Greek MSS of the Almagest (Vatican
Library)
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Footnote The great library at Alexandria, Egypt

• Greatest library in ancient world, containing at
  least 400,000 books
• Aristarchus was librarian c. 150 BCE
• Note Lighthouse at Alexandria harbor was one of
  the 7 wonders of ancient world
• Original collection from Aristotles personal
  collection (c.350 BCE)
• All visitors to Alexandria were required to
  surrender their books for copying (by Royal
  decree)
• Destruction of the library
• Possibly (partly?) destroyed by the army of
  Julius Caesar (47 BCE) who burned the harbor
  during invasion of Egypt
• But there is evidence that library still existed
  in 56 CE (e.g. inscription at right)
• In 391 CE Roman Emporor Theodosuis ordered
  descruction of all pagan temples. This likely
  included the library
• Modern library completed 2002 AD

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Claudius Ptolemy (127-151 AD)

• Worked at library in Alexandria, wrote "Almagest"
  
• Model of planetary motion epicycle carried by a
  deferent. This explains retrograde motion,
  brightness variation.
• Elaboration Earth and motion centers offset
  (equant). This explains the variable angular
  velocity.

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Ptolemys Model of Motion of a Planet (explains
retrograde motion)
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The Complete Geocentric Model of Ptolemy
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Ptolemaic Geocentric Model

• Successes
• First model with predictive power
• In use for 1500 years!
• Shortcomings
• relative sizes of planet orbits arbitrary
• due to the equant, the model was not quite
  geocentric
• likewise it was not quite uniform circular motion
  
• extensions of the model for motion perpendicular
  to the ecliptic was independent of the model for
  motion along the ecliptic.
• The model contains unexplained coincidences

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Ptolemy devised the longest used geocentric model
to explain retrograde loops by putting planets on
epicycles and deferents.
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Epicycles explain retrograde motion in geocentric
models
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Nicolaus Copernicus (c. 1580) devised the first
comprehensive heliocentric (Sun-centered) model

• Copernicus imagined a universe where the Sun was
  at the center instead of Earth.
• He suggested that Earths motion around the Sun
  provided a more natural explanation for
  retrograde loops as Earth passed the other
  planets.

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Heliocentric terminology
Opposition Inferior conjunction Superior
conjunction Greatest eastern elongation (appears
east of the Sun in the sky) Greatest western
elongation (appears west of the Sun in the sky)
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In this heliocentric model, the planets just
appear to move backwards as the faster moving
Earth laps the more distant planet once each
year when it is at opposition.
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Johannes Kepler (1571- 1630)
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Keplers model for the Solar System A Concentric
Series of Crystalline Spheres
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Keplers Three laws

• 1st Law All orbits are Elliptical with Sun at
  one focus (circular orbits are special case of
  elliptical with e 0)
• 2nd Law Planets sweep out equal areas in equal
  time
• 3rd Law P2 a3 (P in yrs, a in AU)

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Keplers 3 laws illustrated
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But why are these laws correct? What physics
causes these motions? A valid scientific model
must be Universal, predicitive, and
falsifiable Kepler didnt have a clue about the
physics
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Sir Isaac Newton (1642 1727) the greatest
physicist who ever lived
As a young faculty member at Cambridge University
(c.1665)
As Warden of the Royal Mint (1705)
Newton was knighted by Queen Anne. However, the
act was "an honor bestowed not for his
contributions to science, nor for his service at
the Mint, but for the greater glory of party
politics in the election of 1705"
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Newtons thought experiment (gedanken) Note
ignores air friction

• Cannonball speed must be 7.9 km/s to achieve
  orbit (17,700 MPH, 26,000 fps). This is much
  higher than muzzle velocities from guns
• Note that cannonball is always in free fall, but
  does not hit Earth if it is in orbit.
• Equation for V

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Newtons law of gravitation
r
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Elliptical Orbits How do they differ from
circular orbits?