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Physics 231
General University
Physics
Lecture 30
Lecture 9
1
Last Meeting
±
Gravitation
²
Newton’s Universal Law of Gravitation
Lecture 9
2
Today
±
Gravity and Planetary Motion
²
Kepler’s Laws
Lecture 9
3
Lecture 9
4
Lecture 9
5
Kepler’s Laws, Introduction
±
Johannes Kepler was a German
astronomer
±
He was Tycho Brahe’s assistant
²
Brahe was the last of the “naked eye”
astronomers
±
Kepler analyzed Brahe’s data and
formulated three laws of planetary motion
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Lecture 9
6
Kepler’s Laws
±
Kepler’s First Law
²
All planets move in
elliptical orbits
with the Sun at
one focus
a
b
Lecture 9
7
Kepler’s Laws (cont.)
±
Kepler’s Second Law
²
The radius vector
drawn from the Sun to
a planet sweeps out
equal areas in equal
time
intervals
²
Consequence of
conservation of
angular momentum
±
Consequence of central
force
Lecture 9
8
Kepler’s Laws (cont.)
³
Kepler’s Third Law
²
The
square of the orbital period
of
any planet is proportional to the
cube
of the semimajor axis
of the
elliptical orbit
3
2
a
T
∝
Lecture 9
9
Notes About Ellipses
±
F
1
and
F
2
are each a
focus
of the ellipse
²
They are located a
distance
c
from the center
±
The longest distance
through the center is the
major axis
²
a
is the
semimajor axis
Lecture 9
10
Notes About Ellipses (cont.)
±
The shortest distance
through the center is
the
minor axis
²
b
is the
semiminor axis
±
The
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 Spring '08
 ELLIS
 Physics, Gravity, Planet, Kepler's laws of planetary motion, Celestial mechanics, Johannes Kepler

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