Transcript Kepler`s Laws

Kepler’s Laws
September 21, 2009
Taking Care of Business (TCB)
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Read textbook Unit 12
Take Moon observations
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6 Observations due September 28
Test #1 – September 18 to September 21
Sept 16 class – last day of test material
 Reserve your test date/time ASAP
 InQsit instructions on Blackboard
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Discussion Review
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How were Tycho Brahe’s observations critical to
the development of astronomy?
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He brought up the idea of the planets positions
again, and tried to improve them
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Made a new model
Kepler’s First Law
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The orbit of each planet about the Sun is an
ellipse with the Sun at one focus
Kepler’s Second Law
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As a planet moves
around its orbit, it
sweeps out equal areas in
equal times
To do this, a planet must
move slower at aphelion
than it does at perihelion
Kepler’s Third Law
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More distant planets
orbit the Sun at slower
average speeds, obeying
the mathematical
relationship of p2=a3
(p2=ka3) where p is the
planet’s orbital period in
years and a is the average
distance from the Sun in
AU
Example
 What about comets? Assume a comet has a high
eccentricity of 0.95(e) with a semi-major axis of
40(a)AU. How long will it take this comet to orbit
the Sun? Where at in its orbit will it spend most of
its time? Near the Sun at perihelion? Far from the
Sun at aphelion? Or maybe somewhere in between?
p2 = ka3
P=253 years, at the aphelion when it is furthest away
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If p is measured in years and a is measured in AU,
then k = 1.
Post Tutorial Question
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If a small weather satellite and the large
International Space Station are orbiting Earth at
the same altitude above Earth’s surface, which
object takes longer to orbit once around Earth?
a) the large space station
b) the small weather satellite
c) They would take the same amount of time.
Post Tutorial Question
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Consider a planet orbiting the Sun. If the mass of
the planet doubled but the planet stayed at the same
orbital distance, then the planet would take
a) more than twice as long to orbit the Sun.
b) exactly twice as long to orbit the Sun.
c) the same amount of time to orbit the Sun.
d) exactly half as long to orbit the Sun.
e) less than half as long to orbit the Sun.