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AE 245 Performance of Aircraft and Spacecraft
Homework 1 Solutions
1.
In the development of the standard atmospheric model in Chapter 2, the variation of the acceleration of gravity
with altitude is ignored; that is, the acceleration of gravity is approximated as constant with altitude. Using the
Newtonian gravitational model, compute the acceleration of gravity at sea level, the acceleration of gravity at
50,000 ft altitude, and the acceleration of gravity at 100,000 ft altitude. Based on these computations, describe the
accuracy of this approximation.
Solution:
With the Newtonian gravitational model, the acceleration may be computed as
a
=
GM
E
r
2
,
where
G
=
6
.
673
×
10

20
km
3
kg
·
s
2
,
M
E
=
5
.
974
×
10
24
kg,
R
E
=
6
,
378 km,
h
is the altitude in kilometers, and
r
=
R
E
+
h
.
At sea level,
h
=
0 km, and
a
=
9
.
800
×
10

3
km
/
s
2
=
32
.
15 ft
/
s
2
.
At
h
=
50
,
000 ft
=
15
.
24 km,
a
=
9
.
753
×
10

3
km
/
s
2
=
32
.
00 ft
/
s
2
.
At
h
=
100
,
000 ft
=
30
.
48 km,
a
=
9
.
707
×
10

3
km
/
s
2
=
31
.
85 ft
/
s
2
.
The percent change over 100
,
000 ft is

0
.
9331%. Therefore,
a constant approximation is accurate
.
2.
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This note was uploaded on 12/16/2009 for the course AEROSP 245 taught by Professor Kabamba during the Spring '08 term at University of Michigan.
 Spring '08
 Kabamba

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