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Fundamentals of Astrodynamics Bate Mueller&White 1971 .pdf

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Roger R. Bate
Donald D. Mueller
Jerry E. White
When the United States Air Force Academy began teaching astro·
dynamics to undergraduates majoring in astronautics or aerospace
engineering, it found that the traditional approach to the subject

was well over 100 years old. An entirely new text had to be evolved,
geared to the use of high speed digital computers and actual current
practice in industry.

Over the years the new approach was proven

in the classrooms of the Academy; its students entering graduate
engineering schools were found to possess a better understanding of
astrodynamics than others.

So pressing is the need for superior

training in the aerospace sciences that the professor·authors of this
text decided to publish it for other institutions' use. This new Dover
publication is the result.
The text is structured for teaching.

Central emphasis is on use of

the universal variable formulation, although classical methods are

Several original unpublished derivations are included.

A foundation for all that follows is the development of the basic
two-body and nobody equations of motion; orbit determination is
then treated, and the classical orbital elements, coordinate trans­
formations, and differential correction.

Orbital transfer maneuvers

are developed, followed by time-of-flight with emphasis on the uni­
versal variable solution. The Kepler and Gauss problems are treated
in detail. Two-body mechanics are applied to the ballistic missile
problem, including launch error analysis and targeting on a rotating
earth. Some further specialized applications are made to lunar and
interplanetary flight, followed by an introduction to perturbation,
special perturbations, integration schemes and errors, and analytic
formulations of several common perturbations.
Example problems are used frequently, while exercises at the end of
each chapter include derivations and quantitative and qualitative
problems. The authors suggest how to use the text for a first course
in astrodynamics or for a two course sequence.
This new major instructional tool effectively communicates the sub­
ject to engineering students in a manner found in no other textbook.
Its efficiency has been thoroughly demonstrated.

The publishers

feel privileged in joining with the authors to make its concepts and
text matter available to other faculties.
A new work, first published by Dover in 1971. Profusely illustrated
with photographs, diagrams, line drawings, etc.

Four appendices:

"Astrodynamic Constants," "Miscellaneous Constants and Conver­
sions," "Vector Revie,·,," and "Suggested Projects:'


xii +

455pp. 5% x 8y:!. Paperbound.

ISBN 0-486-60061-0

$6.00 in U.S.A.

Fundamentals of

Professor and Head


Assistant Professor of Astronautics


Associate Professor of Astronautics



Copyright © 1971 by Dover Publications, Inc.
All rights reserved under Pan American and In·
ternational Copyright Conventions.

Published in Canada by General Publishing Com­
pany, Ltd., 30 Lesmill Road, Don Mills, Toronto,
Published in the United Kingdom by Constable







WC 2.

Fundalllellials of Astrodynamics is a new work,

first published in 1971 by Dover Publications, Inc.

International Standard Book Nttmber: 0-486-60061-0

LibTary of Congress Catalog Card Number: 73-157430

Manufactured in the United States of America
Dover Publications, Inc.
180 Varick Street
New York, N. Y. 10014

This textb ook is dedicated to the memb ers of
the United States Air F orce who have died in
combat , are missing in action, or are prisoners
of war .


The study of astrodynamics is becoming a common prerequisite for
any engineer or scientist who expects to be involved in the aero space
sciences and their many applications. While manned travel in
Earth-Moon space is becoming more common, we are also
concentrating on sophisticated applications of Earth and interplanetary
satellites in the fields of communications, navigation, and basic
Even the use of satellites simply as transport vehicles or platforihs for
experiments requires a fundamental understanding of astrodynamics.
We also recognize that for some time to come the ballistic missile,
whose mechanics of flight has its foundation in astrodynamics, will be
a front-line weapon in the arsenals of many countries.
Beginning with the first graduating class of 1 95 9 the United States
Air Force Academy has been in the forefront of astrodynamics
education . Much has been learned from this experience concerning both
the structure of the courses and what theoretical approaches are best
for teaching the subject . Consequently, this text is particularly
structured for teaching, rather than as an exhaustive treatment of
The astrodynamic theory is presented with brief historical
digressions. Although many classical methods are discussed, the central
emphasis is on the use of the universal variable formulation. The
theoretical development is rigorous but yet readable and usable . Several
unpublished original derivations are included in the text . Example
problems are used frequently to show the student how the theory can
be applied. Exercises at the end of each chapter include derivations and
quantitative and qualitative problems . Their difficulty ranges from
straightforward to difficult . Difficult problems are marked with an

asterisk ( * ) . In addition to exercises at the end of each chapter,
Appendix D includes several projects which are appropriate for a
second course.
Chapter 1 develop s the foundation for the rest of the book in the
development of the basic two-body and n-b ody equations of motion.
Chapter 2 treat s orbit determination from various types of
observations. It also introduces the classical orbital elements,
coordinate transformations, the non-spherical earth, and differential
correction. Chapter 3 then develops orbital transfer maneuvers such as
the Hohmann t ransfer. Chapters 4 and 5 introduce time -of-flight with
emphasis on the universal variable solution. These chapters treat the
classical Kepler and Gauss problems in detail. Chapter 6 discusses the
application of two-body mechanics to the ballistic missile problem,
including launch error analysis and targeting on a rotating earth.
Chapters 7 and 8 are further specialized applications to lunar and
interplanetary flight. Chapter 9 is a brief introduction to perturb ation
analysis emphasizing special perturb ations. It also includes a discussion
of integration scheme s and errors and analytic formulations of several
common perturbations.
If the text is used for a first course in astrodynamics, the following
sequence is suggested : Chapter 1 , Chapter 2 (sections 2. 1 through 2.7,
2. 1 3 through 2. 1 5), Chapter 3, Chapter 4 (sections 4.1 throu gh 4.5),
Chapter 6 , and Chapter 7 or 8 . A first course could include Project
SITE/TRACK or Proj ect PREDICT in Appendix D. A second course
could be structured as follows : Chapter 2 (sections 2 . 8 through 2 . 1 2),
review the Kepler problem of Chapter 4 and do Project KEPLER,
Chapter 5 including projects GAUSS and INTERCEPT, and Chapter 9.
Contributions to the ideas and methods of this text have been made
by many present and former members of the Department of
Astronautics and Computer Science. Special mention should be made
of the computer applications developed by Colonel Richard G. Rumney
and Lieutenant Colonel Delbert Jacobs . The authors wish to
acknowledge significant contributions by fellow faculty members:
Maj ors Roger C . Brandt , Gilbert F . Kelley, and John C. Swonson, Jr .
and Captains Gordon D. Bredvik , Harvey T. Brock, Thomas J. Eller,
Kenneth D. Kopke , and Leonard R. Kruczynski for composing and
checking example problems and student exercises and for proofreading
portions of the manuscript ; and Maj ors Edward J. Bauman and Walter
J. Rabe for proofreading portions of the manuscript. Special

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