4 kepler’s laws why you can get there from here
Post on 21-Dec-2015
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TRANSCRIPT
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Kepler’s LawsKepler’s Laws
Why you can get there from here.
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GoalsGoals
• Kepler: Astrologer turned Astronomer.• Kepler’s Laws.• Proof of Kepler’s 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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Kepler’s Laws
1. Orbits are always ellipses.
2. Sweep out equal areas in equal times.
3. The period of orbit is related to average separation.
32 SeparationPeriod 32 . SeparationconstPeriod
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Concept Test
• Kepler’s 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?a. Planets move fastest when they are moving toward the
Sun.b. Planets move equal distances throughout their orbit of
the Sun.c. Planets move slowest when they are moving away from
the Sun.d. Planets move farther in a given time when they are closer
to the Sun.e. Planets move the same speed at all points during their
orbit of the Sun.
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Gravity is the Force
• Newton’s Law of Gravity:
• So:
• Becomes:
32 . SeparationconstPeriod
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2 4Separation
GMassPeriod
Total
2r
MmGF
TotalMass
SeparationconstPeriod
32 .
)(
)()(
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SunTotal MMass
AUSeparationyearsPeriod
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Concept Test
• You discover a new comet around our Sun:– Average distance from Sun = 4 AU.– What is the period?
a. 1 yearb. 4 yearsc. 8 yearsd. 64 yearse. Don’t have all the necessary information.
)(
)()(
32
SunTotal MMass
AUSeparationyearsPeriod
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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 than it is now. How long will it take the Earth to go around the Sun at this new distance?
a. 1 yearb. 5 yearsc. 11 yearsd. 15 yearse. 125 years
)(
)()(
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SunTotal MMass
AUSeparationyearsPeriod
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Orbital Mechanics
Courtesy David Crisp and WFPC2 Science Team
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Courtesy NASA/JPL/Cornell
Mars
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It Works
Courtesy NASA/JPL/Cornell
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44Spirit: 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:1. Extrasolar Planets2. Black Holes3. The Big Bang4. 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 #4Homework #4
• For Friday 20-Jan: Read Ty7, Ty8, B6.1 – 6.3• Do B6: Problems 2, 7, 15• Imagine the Sun’s surface suddenly became
much hotter (while the Sun’s size remains the same). Compared to the light it now emits, the Sun would emit:a. More ultraviolet light but less visible light.b. More infrared light but less visible light.c. More visible light but less infrared light.d. Less infrared light and less ultraviolet light.e. More ultraviolet light and more visible light.