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Ph 111.01
October 31, 2008
PS 9c (24)
Problem 1.
Practice with proportions.
Two masses a distance R apart attract each other with a
gravitational force F. For each of the cases below, give the factor by which F is changed, if:
a.) if R is multiplied by
3
, then F
new
=
· F
old
b.) if R is multiplied by
3.9
, then F
new
=
· F
old
c.) if R is divided by
2
, then F
new
=
· F
old
Solution.
The equation that we are analyzing is
12
2
Gm m
F
R
=
We can see that it is proportional to 1/r
2
 that is to say, the equation divides by the square of
R.
So, if
R
is multiplied by a certain factor, the force is divided by the square of that factor.
Or, equivalently, the force is multiplied by (1/(the factor))^2.
(a)
The factor is 3. So
()
2
new
old
old
1
* 0.111111
3
FF
F
⎛⎞
==
⎜⎟
⎝⎠
(b)
The factor is 3.9. So
2
new
old
old
1
* 0.0657
3.9
F
(c)
The factor is 0.5. So
2
new
old
old
1
*4
0.5
F
Problem 2 = Walker P. 1229.
A typical GPS (Global
Positioning System) satellite orbits at an altitude of
3.1
10
7
m. (Astronomical data needed for this problem can be found
on the inside back cover of the text.)
h
R
earth
GPS
r=R+h
(a) Find the orbital period of such a satellite.
hours
(b) Find the orbital speed of such a satellite.
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 Fall '08
 Staff
 Force, Mass

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