R.G. Melton
AERSP 309
HW #12
Fall 2005
(Practice Problems only – not to hand in)
1.
A satellite in low Earth orbit is oriented as shown.
The s/c is oriented such that its
2
1
ˆ
ˆ
b
b
−
plane
coincides with the orbital (
θ
i
i
r
ˆ
ˆ
−
) plane.
a.
Develop an expression for the gravity gradient torques in terms of the angle
.
b.
For the case of small librations (oscillations) about only the 3axis and
I
3
>I
2
>I
1
, and
assuming that
remains small, show that
0
2
3
=
+
k
I
±
±
, where
k
is a constant.
c.
The equation above describes simple harmonic motion about the 3axis.
Find an
expression for the period of this librational motion, and evaluate it for the case of
R
= 7000
km,
I
1
=
3000,
I
2
= 5000,
I
3
= 7500 kg
⋅
m
2
.
d.
Suppose that this satellite were placed into an elliptical orbit with period equal to that of
the librational motion.
What is the consequence?
(Hint:
don’t ever do this)
2.
If the specific impulse of a given propellant combination is
I
sp
= 450 s. and the s/c has initial mass
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 MELTON
 Planet, Spacecraft propulsion, propellant combination, radiator fin

Click to edit the document details