MAE 161A
Due Thursday, Oct. 12 (at the beginning of class)
D. R. Boone, UCLA
1
Homework # 1
Use this page as your coversheet
Instructions:
Show all steps for credit.
All homework submissions must be
neat and legible. Please staple multiple sheets of paper and write your name
on the first page. Show all your work and circle the final answer. Points will
be deducted if the final answer has missing or incorrect units.
Name:
SID:
1.
Center of Mass.
a)
Assume the average distance between Pluto and its binary moon Charon is
19,600 km, and use
P
=870 km
3
/sec
2
,
C
=106 km
3
/sec
2
, R
P
=1190 km. Show that
the center of mass of the Pluto-Charon system lies outside the surface of Pluto.
b)
Would the two-body assumptions made in class hold for this system? Why or why
not?
2.
Two-body problem.
a)
Prove that for the two-body problem, the eccentricity vector
𝒆
is constant.
b)
Curtis Problem 2.19
3.
Super moon.
The period of the moon is 27.32 days and the eccentricity of its orbit is
e
= 0.0549.
Its diameter is 3,474 km.
a)
Find the distances to apogee and perigee.
b)
For an observed located at the center of the Earth (assume the Earth is
transparent), determine the angle subtended by the moon at apogee and perigee.
What percentage bigger does the moon look at perigee?
4.
Parabolic orbit.
Assume the Earth’s orbit is circular (
e
= 0) with period of 365 days.
The initial mass of the Sun is
M
s
= 1.99 × 10
30
kg, but then it is instantaneously
decreased.
How small must the S
un’s new mass be in order for the Earth’s orbit to
become parabolic?
5.
Orbit Quantities.
Compute the orbit quantities in Curtis Problem 2.21.
6.
Trajectory planning.
Using Matlab (or your programing language of choice) and the
orbit equation, plot the trajectories for the following cases:
a)
Geocentric orbit with
𝑣
𝑝
= 8 km/s
,
𝑟
𝑝
= 7000 km
b)
Heliocentric circular orbit with
𝑎 = 1.5 × 10
8
km
c)
A parabolic orbit around Mars with
𝑟
𝑝
= 5000 km
Please turn in your code along with your plots for each orbit.
