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EAS 4510 Homework #6 Solutions
#1) Problem 3.8, BMW:
1
1
1.1
.290
p
rD
U
e
=
=
2
2
5
.412
p
U
e
=
=
Î
1
1
1.5493
1.99859
a
aD
U
U
=
=
Î
2
2
8.5034
12.0068
a
U
U
=
=
Two possible transfer orbits to analyze are a) going from inner orbit at periapsis to
outer orbit at apoapsis, and b) going from inner orbit at apoapsis to outer orbit at
periapsis.
a)
1
2
1.1
12.0068
pt
p
at
a
rr
D
U
D
U
==
Î
6.5534
.8321
t
t
U
e
=
=
Î
(1
)
1.29058
/
)
)
0.118236
/
)
t
pt
tt
t
at
e
vD
U
T
U
ae
e
U
T
U
µ
+
−
−
+
To go from the inner orbit into this transfer orbit, then from the transfer orbit to
the outer orbit, there are two deltaV’s required.
The total deltaV for the
maneuver is the sum of these two deltaV’s:
__
1
2
()
total
inner to transfer
transfer to outer
pt
p
a
at
VV
V
v
v
v
v
∆=
∆
+
∆
=
−
+−
where
1
p
v
is the periapsis speed of the smallest ellipse, and
2
a
v
is the apoapsis
speed of the largest ellipse.
Î
0.311
/
total
VD
U
T
U
b)
1
2
1.99859
5
pt
a
at
p
D
U
D
U
Î
3.4993
.428859
t
t
U
e
=
=
Î
)
.845537
/
)
)
.337977
/
)
t
pt
t
at
e
U
T
U
e
U
T
U
+
−
−
+
1
2
total
inner to transfer
transfer to outer
pt
a
p
at
V
v
v
v
v
∆
+
∆
=
−
Î
0.443
/
total
U
T
U
Î
Case a) has a smaller
total
V
∆
so that is the best choice as a transfer orbit.
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View Full Document#2) Problem 3.9, BMW:
1
2
3
1
15
rD
U
U
r
=
=
=∞
Î
1
2
1/
1
/
15
cir
cir
vD
U
T
U
U
T
U
=
=
3
0
cir
v
=
Determine the total deltaV required to go from a circle of radius
1
r
to a circle of radius
2
r
a) directly using a Hohmann transfer, and b) by first transferring to a trajectory where
a
r
and then transferring to a circular orbit of radius
2
r
.
a)
There is just one transfer orbit for this scenario:
1
15
pt
at
U
U
=
=
Î
8
.875
t
t
aD
U
e
=
=
Î
1.36931
/
.091287
/
pt
at
U
T
U
U
T
U
=
=
__
1
2
()
total
inner to transfer
transfer to outer
pt
cir
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 Spring '05
 FitzCoy

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