Keplers Laws

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Keplers Laws
Why you can get there from here.
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Goals

• Kepler Astrologer turned Astronomer.
• Keplers Laws.
• Proof of Keplers Laws.

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Astrology to Astronomy

• Kepler was an astrologer.
• Looked for Perfect Solids
• Wants did not match with Observations (tests).
• Followed the facts where they led.
• The result works.

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Keplers Laws

• Orbits are always ellipses.
• Sweep out equal areas in equal times.
• The period of orbit is related to average
  separation.

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Concept Test

• Keplers second law says a line joining a planet
  and the Sun sweeps out equal areas in equal
  amounts of time. Which of the following
  statements means nearly the same thing?
• Planets move fastest when they are moving toward
  the Sun.
• Planets move equal distances throughout their
  orbit of the Sun.
• Planets move slowest when they are moving away
  from the Sun.
• Planets move farther in a given time when they
  are closer to the Sun.
• Planets move the same speed at all points during
  their orbit of the Sun.

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Gravity is the Force

• Newtons Law of Gravity
• So
• Becomes

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Concept Test

• You want to launch a satellite into geostationary
  orbit (i.e., it always stays over the same spot
  on Earth as the Earth turns), what is the only
  thing you need to know in order to determine how
  far from the Earth the satellite needs to orbit?
• The mass of the satellite.
• The period of the satellites orbit.
• The mass of the Earth.
• The mass of the Sun.
• The average distance to the Sun.

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Concept Test

• You discover a new comet around our Sun
• Average distance from Sun 4 AU.
• What is the period?
• 1 year
• 4 years
• 8 years
• 64 years
• Dont have all the necessary information.

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Concept Test

• In a few billion years the sun will expand. In
  order to avoid the destruction of the Earth,
  humanity moves the Earth 5 times farther away
  from the Sun that it now is. How long will it
  take the Earth to go around the Sun at this new
  distance
• 1 year
• 5 years
• 11 years
• 15 years
• 125 years

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Orbital Mechanics
Courtesy David Crisp and WFPC2 Science Team
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Mars
Courtesy NASA/JPL/Cornell
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It Works
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Spirit View of Columbia Hills from floor of
Gusev Crater
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Spirit In the Columbia Hills.
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Opportunity Eagle Crater in Meridiani Planum
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Opportunity View of Endurance Crater
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Opportunity View of sand Dunes in floor of
Endurance Crater
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Class Structure

• Investigate 4 Key Topics this semester
• Extrasolar Planets
• Black Holes
• The Big Bang
• SETI

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Class Structure

• During each topic
• Pieces in a puzzle.
• Many pieces in several topics
• At the end of each topic
• See how pieces fit.
• See how the scientific method is applied
• What is the evidence
• Have a test.

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Homework 4

• For Friday 17-Sept Read Ty7, Ty8, B6.1 6.3
• Do B6 Problems 2, 7, 15
• Imagine the Suns surface suddenly became much
  hotter (while the Suns size remains the same).
  Compared to the light it now emits, the Sun
  would emit
• More ultraviolet light but less visible light.
• More infrared light but less visible light.
• More visible light but less infrared light.
• Less infrared light and less ultraviolet light.
• More ultraviolet light and more visible light.