Physics 140 –
Fall 2007
15 November:
lecture #21
Approximating the earth as a sphere of uniform
density, at what radius
inside
the earth is the
gravitational acceleration equal to the value that
would be felt a height of 3
R
E
above Earth
’
s
surface
?
1.
R
E
/ 2
2.
R
E
/ 3
3.
R
E
/ 4
4.
R
E
/ 9
5.
R
E
/ 16
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View Full Document1) Planets move in
ellipses of
semimajor axis
a
with the sun
at a focus.
An ellipse has
eccentricity
e,
where
ea
is the distance from
the center to a focus.
perihelion 
R
p
=
a
(1–
e
)
closest point
in sunplanet
orbit
aphelion 
R
a
=
a
(1+
e
)
farthest point
in sunplanet
orbit
Kepler’s laws of planetary motion
2) Planetary orbits sweep out
equal areas in equal times
.
This law reflects the fact that gravity is a
central force
.
Since
gravity acts along the radial direction connecting two bodies,
it produces no torque on either.
For a planet of mass
m
, the
angular momentum of the orbit is conserved
and determines
the rate of area
A
swept out by its orbit
3) The
square of the orbital period
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 Fall '07
 Evrard
 Acceleration, Mass, General Relativity, Kepler's laws of planetary motion, Celestial mechanics

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