978-0073398242 Chapter 12 Solution Manual Part 16

subject Type Homework Help
subject Pages 9
subject Words 1506
subject Authors Brian Self, David Mazurek, E. Johnston, Ferdinand Beer, Phillip Cornwell

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PROBLEM 12.101
It was observed that as the Voyager I spacecraft reached the point of its trajectory closest to the planet Saturn,
it was at a distance of 3
185 10km from the center of the planet and had a velocity of 21.0 km/s. Knowing
that Tethys, one of Saturn’s moons, describes a circular orbit of radius 3
295 10km at a speed of 11.35 km/s,
determine the eccentricity of the trajectory of Voyager I on its approach to Saturn.
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PROBLEM 12.102
A satellite describes an elliptic orbit about a planet of mass M.
Denoting by 0
r and 1,r respectively, the minimum and maximum
values of the distance r from the satellite to the center of the planet,
derive the relation
2
01
112GM
rr h

where h is the angular momentum per unit mass of the satellite.
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PROBLEM 12.103
A space probe is describing a circular orbit about a planet of radius
R
. The altitude of the probe above the
surface of the planet is
R
and its speed is
v
0
. To place the probe in an elliptic orbit which will bring it closer
to the planet, its speed is reduced from
v
0
to
0
,v
where 1,
by firing its engine for a short interval of
time. Determine the smallest permissible value of
if the probe is not to crash on the surface of the planet.
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PROBLEM 12.104
A satellite describes a circular orbit at an altitude of 19 110 km above
the surface of the earth. Determine (a) the increase in speed required at
point A for the satellite to achieve the escape velocity and enter a
parabolic orbit, (b) the decrease in speed required at point A for the
satellite to enter an elliptic orbit of minimum altitude 6370 km, (c) the
eccentricity
of the elliptic orbit.
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PROBLEM 12.104 (Continued)
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PROBLEM 12.105
A space probe is to be placed in a circular orbit of 5600 mi radius
about the planet Venus in a specified plane. As the probe reaches
A, the point of its original trajectory closest to Venus, it is inserted
in a first elliptic transfer orbit by reducing its speed by Δ.
A
v This
orbit brings it to Point B with a much reduced velocity. There the
probe is inserted in a second transfer orbit located in the specified
plane by changing the direction of its velocity and further reducing
its speed by Δ.
B
v Finally, as the probe reaches Point C, it is
inserted in the desired circular orbit by reducing its speed by Δ.
C
v
Knowing that the mass of Venus is 0.82 times the mass of the earth,
that 3
9.3 10 mi
A
r and 3
190 10
B
rmi, and that the probe
approaches A on a parabolic trajectory, determine by how much the
velocity of the probe should be reduced (a) at A, (b) at B, (c) at C.
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PROBLEM 12.105 (Continued)
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PROBLEM 12.106
For the space probe of Problem 12.105, it is known that rA3
9.3 10 mi and that the velocity of the probe is
reduced to 20,000 ft/s as it passes through A. Determine (a) the distance from the center of Venus to Point B,
(b) the amounts by which the velocity of the probe should be reduced at B and C, respectively.
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PROBLEM 12.106 (Continued)
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PROBLEM 12.107
As it describes an elliptic orbit about the sun, a spacecraft
reaches a maximum distance of 6
202 10 mi from the center
of the sun at Point A (called the aphelion) and a minimum
distance of 6
92 10mi at Point B (called the perihelion). To
place the spacecraft in a smaller elliptic orbit with aphelion at
A
and perihelion at ,
B
where
A
and
B
are located
6
164.5 10mi and 6
85.5 10mi, respectively, from the center
of the sun, the speed of the spacecraft is first reduced as it
passes through A and then is further reduced as it passes
through .B
Knowing that the mass of the sun is 332.8 3
10
times the mass of the earth, determine (a) the speed of the
spacecraft at A, (b) the amounts by which the speed of the
spacecraft should be reduced at A and
B
to insert it into the
desired elliptic orbit.

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