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PROBLEM 12.101
It was observed that during its second flyby of the earth, the Galileo
spacecraft had a velocity of 14.1 km/s as it reached its minimum altitude
of 303 km above the surface of the earth. Determine the eccentricity of
the trajectory of the spacecraft during this portion of its flight.
SOLUTION
For earth,
6
6.37
10 m
R
=×
63
6
0
6.37
10
303.
10
6.673
r
+×
=
×
()
( )
9
2
00
6.673
10
14.1 10
94.09
10 m /s
hr
v
==
×
×=
×
2
26
1
2
3
2
9.81 6.37
10
398.06
GM
gR
×
=
×
2
0
1
1
GM
r
h
ε
=
+
( )
(
)
2
9
2
61
2
0
94.09
10
13
.
3
3
6.673
10
398.06
10
h
rGM
×
+=
=
=
××
3.33
1
=
−
2.33
=
W
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View Full DocumentPROBLEM 12.112
It was observed that during its first flyby of the earth, the Galileo
spacecraft had a velocity of
10
.
5
km
/s as it reached its minimum distance
of
730
0
km
from the center of the earth. Assuming that the trajectory of
the spacecraft was parabolic, determine the time needed for the spacecraft
to travel from
B
to
C
on its trajectory.
SOLUTION
For earth,
6
2
6370
km
6
.
37
10
m
,
9
.
81
m
/s
Rg
=
=
×
=
()
(
)
2
2
6
14
3
2
9
.
81
6
.
37
10
3
.
9806
10
m
/s
GM
gR
=
=
×=
×
At point
A
,
6
730
0
km
7
.
3
10
m
A
r
=
=
×
10
.
5
km
/s
10500
m
/s
A
v
= =
from which
92
76
.
65
m
/s
AA
h
r
v
== ×
For trajectory
BAC
,
2
1
1
cos
with
1
GM
r
h
εθ
ε
=+
=
At point
A
,
0
while at
and
,
90
BC
θ
==
±
°
2
2
11
or
2
B
CA
GM
h
rr
r
G
M
h
=
As the spacecraft travels from
B
to
C
, the area swept out is a parabolic area
A
.
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 Spring '10
 Prof.V.H.Chu

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