APPENDIX
MATLAB Scripts
D
D.1 Introduction
This appendix lists MATLAB scripts that implement all of the numbered algorithms presented
throughout the text. The programs use only the most basic features of MATLAB and are liberally
commented so as to make re

AE402 Orbital Mechanics
Homework 2 - Correction
Problem 2.6
1
= 0. Moreover, the initial time t0 = is taken at the periapsis,
a
r0 .v0
hence, v0 r0 . So, 0 = = Hence, equation (2.39) becomes:
0.
a) For a parabolic orbit, =
(t ) = x3 S(0) + r0 x
=
x3
+ r

AE402 Orbital Mechanics
Homework 3
This homework is due October 1st, homeworks should be turned in to Professor Coverstone at
the beginning of class. For online students, homeworks can be sent to [email protected] before
2:00pm.
Please mention on the

University of Illinois at Urbana-Champaign
Department of Aerospace Engineering
AE 402 Midterm Exam
Open book and open notes
October 22, 2015
Name:
*
Problem 1
1. Give 2 quantities that are conserved throughout the motion for the two-body problem (3rd
quan

AE402 Orbital Mechanics
Homework 1 - Correction
Problem 1.3
See the last 2 pages of this document.
Problem 1.5
1.5.a) With the notations of Fig.1.5 in the book:
. = vcos() = rf
vj
(1)
Moreover, the angular momentums norm is:
| |=| . |= r2 f
h
rr
h
f = 2

AE402 Orbital Mechanics
Homework 4
This homework is due October 13st, homeworks should be turned in to Professor Coverstone at
the beginning of class. For online students, homeworks can be sent to [email protected] before
2:00pm.
Please mention on the

AE402 Orbital Mechanics
Homework 6
This homework is due November 10th, homeworks should be turned in to Professor Coverstone at
the beginning of class. For online students, homeworks can be sent to [email protected] before
2:00pm.
Please mention on th

APPENDIX
B
A Road Map
Figure B.1 is a road map through Chapters 1, 2, and 3. Those who from time to time feel they have lost
their bearings may find it useful to refer to this flowchart, which shows how the various concepts and
results are interrelated. T

AE402 Orbital Mechanics
Homework 5
This homework is due November 3rd, homeworks should be turned in to Professor Coverstone at
the beginning of class. For online students, homeworks can be sent to [email protected] before
2:00pm.
Please mention on the

AE402 Orbital Mechanics
Homework 5 - Solution
Problem 1
1)
a) The payload ratios are the same for the three stages so:
=
m03
mL
m02
=
=
m0 m02
m02 m03
m03 mL
Hence:
m2 = m0 m03
02
m2 = mL m02
03
Thus:
2
1
3
3
m03 = mL m0 = 2466
1
2
3
3
m02 = mL m0 = 6082

AE402 Orbital Mechanics
Homework 7
This homework is due November 19th, homeworks should be turned in to Professor Coverstone at
the beginning of class. For online students, homeworks can be sent to [email protected] before
2:00pm.
Please mention on th

AE402 Orbital Mechanics
Homework 7 - Solution
All students
Continuous-thrust orbit transfer
1. The spacecraft is always on a circular so for any time instant t:
a(t)
a(t) =
v(t)2
v(t)2 =
Taking the derivating with respect to time:
a(t) = 2
v(t)
v(t)3
More

AE402 Orbital Mechanics
10/22/2015
Midterm Solution
Problem 1
1. Angular momentum, specific energy, the rate at which the radius vector sweeps out area.
2. The specific energy is negative for an ellipse (the spacecraft is trapped into the gravitational
fi

APPENDIX
A
Physical Data
The following tables contain information that are commonly available and may be found in the
literature and on the World Wide Web.
Table A.1 Astronomical Data for the Sun, the Planets, and the Moon
Object
Radius
(km)
Mass (kg)
Sid

Preface
The purpose of this book is to provide an introduction to space mechanics for undergraduate engineering students. It is not directed toward graduate students, researchers, and experienced practitioners, who may nevertheless find useful review mate

APPENDIX
Gravitational Potential of a Sphere
E
Figure E.1 shows a point mass m with Cartesian coordinates x; y; z as well a system of N point masses
m1 , m2 , m3 ,. , mN . The ith one of these particles has mass mi and coordinates xi ; yi ; zi . The total

APPENDIX
Computing the Difference
Between Nearly Equal Numbers
F
Let a, b; and c be vectors such that c b a and a < b. Clearly, czb. In order to calculate
Fh1
c3
b3
(F.1)
qh1
c2
b2
(F.2)
we may first define
It follows that
3
2 32
h
i
3
3 1 1 q2
c
1 1 q

APPENDIX
C
Numerical Integration of the
n-Body Equations of Motion
Without loss of generality we shall derive the equations of motion of the three-body system illustrated
in Figure C.1. The equations of motion for n bodies can easily be generalized from t

Index
Note: Page numbers with f denote figures; t tables; b boxes.
A
Apse line rotation
angular momentum, 325
orbit intersection, 322323, 322f
point of intersection, 323
radial velocity, 325
trigonometric identity, 323, 326
Astronomical data, 721
Averagin

AE402 Orbital Mechanics
Homework 2
This homework is due September 17th, homeworks should be turned in to Professor Coverstone
at the beginning of class. For online students, homeworks can be sent to [email protected]
before 2:00pm.
A few rules:
- Late

AE402 Orbital Mechanics
Homework 1
This homework is due September 10th, homeworks should be turned in to Professor Coverstone
at the beginning of class. For online students, homeworks can be sent to [email protected]
before 2:00pm.
A few rules:
- One

AE402 Orbital Mechanics
Homework 3 - Correction
Ground tracking
1)
- Inclination
The inclination corresponds to the highest latitude : i 51 (to be compared with the value
found online for the ISS: 51.6 ).
- Period
The longitude dierence between two patter