MAE146: Astronautics – Homework
Assigned: Friday, February 5
th
,
2010
Due date: Wednesday , February 10
th
,
2010,
(at the beginning of the lecture)
Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget
to write your name on your copy to receive credit.
Problem 1 (10pts): On derivatives
Compute the following derivatives:
1.
∂
∂vector
r
1

vector
r

3
2.
∂
∂vector
r
1

vector
r

n
, n
≥
1
3.
∂
∂θ
1
(1+
e
cos
θ
)
where
e
is a constant.
4.
∂
∂θ
1
(1+
e
cos
θ
)
3
where
e
is a constant.
Problem 2 (10pts): On numerical integration
Solve problem 2.5 of the textbook (p. 146 of current edition). In addition, please plot the resulting orbit segment of
the 24
hr
period.
The problem consists of numerically integrating the R2BP equations for a time span of 24
hr
, starting from the
following initial conditions (given in an ECI frame):
•
Position: (6600
.
0
km,
0
.
0
km,
0
.
0
km
).
•
Velocity: (0
km/s,
12
.
0
km/s,
0
.
0
km/s
).
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 Winter '10
 Villac
 Derivative, Force, ECI frame

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