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5.5 Satellites in circular orbits
here are many different satellites and other objects currently orbiting the
There are many different satellites and other objects currently orbiting the
earth.
How did they get there???
et’s start shooting projectiles horizontally
ach time with increasing speed:
Let’s start shooting projectiles horizontally – each time with increasing speed:
But, if I shoot the projectiles fast enough, so that they cover a large distance,
the ground beneath does not stay flat, since the earth is curved.
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View Full Document Let’s say the elephant’s trunk
1 m above the ground.
is 1 m above the ground.
The last projectile he fired is
moving very fast, so it covers
a lot of ground as it falls due
to gravity.
By the time it falls a distance
of 1 m, the earth’s surface has
curved away by 1 m, so the
projectile is still 1 m above the
surface.
The projectile always stays 1
m above the surface.
Thus, the projectile is in a 1m
igh orbit!
high orbit!
When a satellite is launched, a rocket takes it above the atmosphere, and then
we give it enough horizontal speed such that it falls toward the earth at the same
rate as which the earth curves away beneath it.
Thus,
satellite motion is circular motion
, and we should be able to identify a
centripetal force:
The only force we have is the gravitational force.
F
G
F
G
is also a radial force, and the only one, thus:
C
G
F
F
=
r
v
v
m
m
m
s
s
e
2
r
r
G
2
Now I can solve for
r
, the radius of the satellite’s circular orbit.
2
v
m
G
r
e
=
Notice, the radius of the orbit does not
depend on the mass of the satellite, but
only on its speed.
Thus, for each orbital speed,
v
, there is one and only one (unique) radius of orbit.
Note:
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This note was uploaded on 09/25/2011 for the course PHYS 2002 taught by Professor Blackmon during the Spring '08 term at LSU.
 Spring '08
 BLACKMON
 Physics, Current, Orbits

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