AAE 532 – Orbit Mechanics
Problem Set 4
Due: 9/22/10
Problem 1:
Assume that a system is comprised of two particles that interact only
gravitationally. Define ˆ
e
as a unit vector in the direction of
e
. Define ˆ
p
as a unit vector
90
D
from ˆ
e
such that
ˆ
ˆˆ
×
ep=h
(where
ˆ
h
is a unit vector parallel to orbital angular momentum).
(a)
Demonstrate that the velocity can be written
sin
(
cos
)
e
p
μ
θθ
∗∗
⎡⎤
−+
+
⎣⎦
v=
e
p
(b) In an elliptical orbit, the general expression to relate flight path angle and true anomaly is
tan
sin
re
p
γ
θ
∗
=
Prove that this expression is correct.
Problem 2:
A satellite is in motion about the Earth. Assume that it is reasonable to model the
problem in terms of the relative twobody problem (Earth and satellite). The orbit is
characterized such that
10
aR
=
⊕
and
.6
e
=
. It is currently located (
o
t
) at the point in the orbit
such that
60
o
∗
=
D
.
(a)
Determine the following orbit parameters and satellite state information:
,,
,,,;,, ,
pao o o o
php
e
r
iod
r r r v
E
E
. [List time in hours and all angles in degrees.]
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 Spring '10
 KathleenHowell
 Orbit Mechanics Problem, following orbit parameters

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