Transcript Kepler`s Laws

Kepler’s Laws
Why you can get there from here.
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Goals
• Kepler: Astrologer turned Astronomer.
• Kepler’s Laws.
• Proof of Kepler’s Laws.
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Astrology to Astronomy
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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.
Period  Separation
2
3
Period  const.  Separation
2
3
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Concept Test
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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.
b.
c.
d.
e.
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
• Newton’s Law of Gravity:
• So:
Mm
F G 2
r
Period  const.  Separation
2
3
• Becomes:
Separation
( AU
42 Separation
3 )
Period
 const
Period
Period
( years
)  .  Separation
GMassTotalMass
Mass
( M Sun )
TotalTotal
2
3
3
22
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Concept Test
Separation( AU )
Period ( years ) 
MassTotal ( M Sun )
3
2
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You discover a new comet around our Sun:
– Average distance from Sun = 4 AU.
– What is the period?
a.
b.
c.
d.
e.
1 year
4 years
8 years
64 years
Don’t have all the necessary information.
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Concept Test
Separation( AU )
Period ( years ) 
MassTotal ( M Sun )
3
2
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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:
a.
b.
c.
d.
e.
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
Courtesy NASA/JPL/Cornell
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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:
1. Extrasolar Planets
2. Black Holes
3. The Big Bang
4. 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:
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See how pieces fit.
See how the scientific method is applied
What is the evidence
Have a test.
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Homework #4
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For Friday 17-Sept: 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.
b.
c.
d.
e.
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.
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