Transcript Document

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
• On page 64 Carl says “Kepler stood on the cusp of
history; the last scientific astrologer was the first
astrophysicist.” What’s the difference between these
two and what does it mean to make the transition from
one to the other?
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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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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
units
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Concept Test
• Which of the following orbits is NOT allowed
under Kepler’s First Law?
a.
b.
c.
d.
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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.
b.
c.
d.
e.
Planets move fastest when they are moving toward the Sun.
Planets move farther in a given time when they are closer to 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 the same speed at all points during their orbit of the
Sun.
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Concept Test
Separation( AU )
Period( years) 
MassTotal ( M Sun )
3
2
•
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
•
Saturn takes about 30 years to make one orbit
around the Sun. About how far away from the
Sun is it?
a.
b.
c.
d.
e.
1 AU
5 AU
10 AU
30 AU
900 AU
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Concept Test
Separation( AU )
Period( years) 
MassTotal ( M Sun )
3
2
•
Aliens attack our Sun and reduce it to a tiny cinder only
1/16th its original mass. If the Earth stays at a distance of
1 AU from the Sun, how long will it now take to orbit the
Sun?
a.
b.
c.
d.
e.
1 year
4 years
8 years
16 years
1/16 year
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Kepler’s Laws
• Kepler’s First Law:
– All planets orbit in an ellipse with the Sun at one
focus.
– A circle is a special case of an ellipse where both
focii are at the same point.
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Orbital Mechanics
Courtesy David Crisp and WFPC2 Science Team
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Mars: It Works
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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Cassini at Saturn
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Class Structure
Investigate 3 Key Topics this semester:
1. Extrasolar Planets
2. A warm wet Mars
3. Planetary Perils:
1. Global Warming
2. Impact Hazards
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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 12-Sept: Read B7.1, Do:
1. B3: Problems 33, 54
2. B7: Problem 30
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