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Chapter 13
383
Q13.16
Speed is maximum at closest approach. Speed is minimum at farthest distance.
Q13.17
Set the universal description of the gravitational force,
F
GM m
R
g
X
X
=
2
, equal to the local description,
Fm
a
g
=
gravitational
, where
M
X
and
R
X
are the mass and radius of planet
X
, respectively, and
m
is the
mass of a “test particle.” Divide both sides by
m
.
Q13.18
The gravitational force of the Earth on an extra particle at its center must be zero, not infinite as one
interpretation of Equation 13.1 would suggest. All the bits of matter that make up the Earth will pull
in different outward directions on the extra particle.
Q13.19
Cavendish determined
G
. Then from
g
GM
R
=
2
, one may determine the mass of the Earth.
Q13.20
The gravitational force is conservative. An encounter with a stationary mass cannot permanently
speed up a spacecraft. Jupiter is moving. A spacecraft flying across its orbit just behind the planet
will gain kinetic energy as the planet’s gravity does net positive work on it.
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 Fall '11
 Staff
 Physics, Force

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