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An Introduction to the Mathematics and Methods of Astrodynamics ...
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The all-inclusive treatise on "Astrodynamics" by Richard H. Battin clearly must be counted among the great classics in scientific literature. This text documents the fundamental theoretical developments in astrodynamics and space navigation that eventually led to man's ventures into space. It includes all the essential elements of celestial mechanics, spacecraft trajectories, and space navigation as well as the his- tory of the underlying mathematical developments over the past three centuries culminating finally with the 20th century space exploration.
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An
Introduction to the
Mathematics and Methods
of
Astrodynamics, Revised Edition
Richard H. Battin, Ph.D.
Senior Lecturer in Aeronautics and Astronautics
Massachusetts Institute
of
Technology
EDUCATION
SERIES
1.
s.
przemieniecki
Series Editor-in-Chief
Air Force Institute
of
Technology
Wright-Patterson Air Force Base,
Ohio
Published
by
American Institute
of
Aeronautics
and
Astronautics,
Inc.
1801
Alexander Bell Drive, Reston,
VA
20191
American Institute
of
Aeronautics and Astronautics, Inc., Reston, Virginia
Library
of
Congress Cataloging-in-Publication Data
Battin, Richard
H.
An
introduction to the mathematics and methods
of
astrodynamics I Richard
H.
Battin.-
Rev.
ed.
p.
cm.-(AIAA
education series)
Includes bibliographical references and index.
I. Astrodynamics-Mathematics.
I. Title. II. Series.
TL1050.B35 1999
629.4'II-dc21
99-13266
ISBN 1-56347-342-9 (alk. paper)
4 5
Copyright © 1999 by the American Institute
of
Aeronautics and Astronautics, Inc. All
rights reserved. Printed in the United States
of
America. No part
of
this publication may
be
reproduced, distributed,
or
transmitted, in any form
or
by any means, or stored in a data
base
or
retrieval system, without the prior written permission
of
the publisher.
Data and information appearing in this book are for informational purposes only. AIAA
is not responsible for any injury or damage resulting from use or reliance, nor does AIAA
warrant that use
or
reliance will be free from privately owned rights.
To Martha and
Les
Margery, Thomas, Pamela, and Jeffrey
Foreword
The all-inclusive treatise on "Astrodynamics" by Richard
H.
Battin clearly must be
counted among the great classics
in
scientific literature. This text documents the
fundamental theoretical developments
in
astrodynamics and space navigation that
eventually led to man's ventures into space. It includes all the essential elements
of
celestial mechanics, spacecraft trajectories, and space navigation as well as the his-
tory
of
the underlying mathematical developments over the past three centuries
culminating finally with the
20th century space exploration. The author has now
updated this text as the revised edition by including new materials
in
Chapters
1,
3,6,
and
11.
The first half
of
his text deals with the necessary mathematical preliminaries
of
hypergeometric functions, analytical dynamics, the two-body problem leading to
the solution
of
two-body orbits, Kepler's equation, and Lambert's problem. The sec-
ond
half
includes non-Keplerian motion, patched-conic orbits and perturbation
methods, variation
of
parameters, two-body orbital transfer, numerical integration
of
the equations
of
motion in orbital mechanics, the celestial position fix for space-
craft, and space navigation. All the mathematical concepts are fully explained so
that there is no need for additional reference materials. The most abstruse mathe-
matical derivations are made simple through clarity
of
style, logical exposition, and
attention to details.
Dr. Battin has produced a textbook that will be used by the present and future
generations
of
aerospace engineers as they venture beyond the Apollo program to
conquer the
"high frontier." This text is a great testimony
of
Dr.
Battin's exception-
al pioneering work as a scientist and engineer and his outstanding personal contri-
butions to the
U.S. space program.
The Education Series
of
textbooks and monographs published by the American
Institute
of
Aeronautics and Astronautics embraces a broad spectrum
of
theory and
application
of
different disciplines in aeronautics and astronautics, including aero-
space design practice. The series includes also texts on defense science, engineer-
ing, and management. The series serves as teaching texts as well as reference mate-
rials for practicing engineers, scientists, and managers. The complete list
of
text-
books published in the series (over sixty titles) can be found on the end pages
of
this
volume.
J.S. Przemieniecki
Editor-in-Chief
AIAA Education Series
Prologue
This article appeared
in
the
New
York
Times
on
the eve of
the Apollo 8 mission.
It
was
reprinted
in
a special
Look
magazine issue titled: Apollo 8-Voyage to the Moon.
The
Apollo voyage
to
the
moon represents a new
and
exciting plateau in
the
ancient
art
of navigation.
By applying principles as old as
the
planetary theories of Kepler
and
technologies as new as
the
high-speed electronic digital computer,
an
astro-
naut
can
determine
the
position
and
course of his craft in
the
vastness of
outer
space
with
an
accuracy
that
Columbus or Prince Henry
the
Navigator
would have deemed impossible in their time.
Ever since
man
first went
to
sea, the need to navigate accurately has
been a
constant
challenge. For many centuries only
the
brave
or
foolhardy
dared
to
venture
out
of sight of land except for short distances. Progress
in navigation was extremely slow,
and
not until
just
200 years ago could a
ship's location
at
sea be determined with anything approaching precision.
The
ability
to
determine
latitude-the
distance
north
or
south
of the
Equator-by
observing
the
angle
that
the North
Star
makes
with
the
horizon was known in early times.
The
instrument used for this purpose,
the
astrolabe, was invented by
the
Greeks more
than
2,000 years ago
and
well may
be
the
oldest scientific instrument in
the
world.
The
mariner's compass was introduced much later, in
the
12th
or
13
th
century.
With
it, a seaman could set a course and, by estimating
the
speed of
the
ship,
obtain
a crude approximation of his position. However,
only
the
ship'S
latitude
could be verified by direct observation.
It
was
not
until
the
18
th
century
that
east-west distances, called lon-
gitude, could
be
measured accurately.
In
fact,
it
was quite recently in
history before
it
was even recognized
that
the
essential element required
to
obtain longitude was a reliable
and
transportable clock.
During
the
16
th
and
17th centuries,
the
longitude problem assumed
enormous proportions
to
each of
the
maritime powers. Fantastic rewards
were offered for
the
solution as each nation vied
to
become
the
first
to
develop
the
important
capability of accurate navigation
at
sea.
The
world's leading scientists devoted their attention
to
the
problem.
Economic, political,
and
military considerations were
at
stake,
and
the
vii
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