Fundamentals of Astrodynamics (Dover Books on Aeronautical Engineering) 1st Edition by Roger R. Bate (PDF)

Description

When the United States Air Force Academy began teaching astrodynamics 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 the 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 Dover edition is the result.The text is structured for teaching. Central emphasis is on use of the universal variable formulation, although classical methods are discussed. Several original unpublished derivations are included. A foundation for all that follows is the development of the basic two-body and n-body equations of motion; orbit determination is then treated, and the classical orbital elements, coordinate transformations, and differential correction. Orbital transfer maneuvers are developed, followed by time-of-flight with emphasis on the universal 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 formulation 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 major instructional tool effectively communicates the subject to engineering students in a manner found in no other textbook. Its efficiency has been thoroughly demonstrated. Dover feels privileged in joining with the authors to make its concepts and text matter available to other faculties.

User’s Reviews

Editorial Reviews: From the Back Cover When the United States Air Force Academy began teaching astrodynamics 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 the 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 Dover edition is the result.The text is structured for teaching. Central emphasis is on use of the universal variable formulation, although classical methods are discussed. Several original unpublished derivations are included. A foundation for all that follows is the development of the basic two-body and n-body equations of motion; orbit determination is then treated, and the classical orbital elements, coordinate transformations, and differential correction. Orbital transfer maneuvers are developed, followed by time-of-flight with emphasis on the universal 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 formulation 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 major instructional tool effectively communicates the subject to engineering students in a manner found in no other textbook. Its efficiency has been thoroughly demonstrated. Dover feels 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A whole new crop of astrodynamics books appeared shortly after sputnik. This book by Bate, et al., is a fine specimen of this genre. It carries a copyright and publication date of 1971. No revisions are mentioned, but Appendix A contains the date 1975 in a footnote. However, the book must have been written some years prior, as it makes no mention of Apollo (even though the cover shows a photo of the Apollo Lunar Lander).The introduction tells us the book was specifically written for astrodynamics classes at the Air force Academy. This suggests a dry, terse, and highly focused book. Focused it is, but it is also contains significant and interesting historical material; and surprisingly, quite a bit of droll humor. (Examples: page 155 shows a spent booster dropping into the ocean with a gigantic splash. P. 321: “Which is more useful, the Sun or the Moon? … The Moon … since it gives us light during the night … whereas the sun shines only in the daytime, when it is light anyway.”)Chapter 1 states the basic equations of motion, leading to the conic sections. The derivation is well paced. Chapter 2 provides an introduction to orbit determination, showing how the orbital elements can be computed from observations. Chapter 3 covers types of orbital maneuvers. Chapter 4 deals with the time-of-flight, Kepler’s equation, and universal variables. Chapter 5 provides a more extensive treatment of orbit determination. Chapter 6 reflects the books origin and purpose in its thorough discussion of ballistic missile trajectories. (It might not be too far afield to suggest this might have been the primary purpose of this course.) Three more chapters cover perturbation theory and other topics.Compared to its peers: 1) compared to Herrick’s “Astrodynamics” (vol. 1 & 2) Bate is faster paced and has a more modern feel; 2) Thomson’s “Introduction to Space Dynamics” is faster paced, covers more ground, and more forward looking; and 3) Battin’s “An Introduction to the Mathematics and Methods of Astrodynamics” — well this book is in a class by itself; no other astrodynamics book has such rich excursion into applied mathematics and Apollo history.In general, I am impressed with the derivations and explanations. Occasionally there is a weakness. One example appears on p. 114, and relates to the Gibbsian method of orbit determination. This method relies on three radius vectors and no time data. The authors point out that three vectors have nine independent components, but since these must lie in the same plane there are only eight. So far, so good. But in general only six independent data points are required to determine the orbit … so it would appear that we have two too many. The resolution is that in general each observation (data point) must carry a time stamp. Since in this case we don’t have these, we are missing three pieces of information, and the actual number of independent data points is (effectively) five. Therefore, although the trajectory can be determined, the location of the satellite on the trajectory cannot.All in all, one of the very best books to learn the subject from.

⭐I’m a chip design engineer by trade (BSEE ’84), and I was in middle school during the Apollo years. The MSL mission to Mars re-inspired me to self-study how the folks at JPL do their work.Also, I’ve used programming languages throughout my engineering career, and recently decided I need to learn Python.So I decided to read this book as if I’m a student, and use Python to solve the problems. (I’m using Pythonista, an iOS app with useful Python 3.5 packages built in. Version 3.5 allows use of Greek characters in the code, so I can match those in the text.)I initially researched, then decided to avoid certain astrodynamics packages available for the language; because they basically have all the problems solved.What I have used though is the NumPy and SymPy packages, that give units and symbolic functions, such as finding the algebraic form of derivative of an algebraic expression.The best part of this experience has been that the book uses units that I can program in the same fashion. When checking answers, the units print out along with the numbers, so if there’s an error, I can see from the wrong units where the bug in my code might be.The book has a handful of errors, as others have pointed out.But one other issue has been that the time frame of the book (I was a sophomore in high school when the first edition was published) is such that precision problems encountered and discussed therein just don’t exist.For example, in Section 9.5, page 413, there is a discussion and examples of loss of precision because ‘the machine’ can only represent 6 significant digits. My Pythonista result for the same example problem shows 16 decimal digits; giving a correct answer where the book predicts a roundoff error in the 5th decimal digit. In all, there are many problems where the answer is different, and I have to just decide that it’s a round off problem of the old computer, but not my code.One intuitive connection pleasure has been due to my having been in a US Air Force radar surveillance career field in the late 70s, and the authors spend a bit of time on tidbits like determination of ICBM trajectory from 2 radar sitings (BMEWS), satellite tracking, other things where now I understand what my old radar computers were doing under the covers while I watched and tracked from my scope. (Side note: it was my exposure to computers during my radar days that influenced me to study and get my Bachelors in EE, focused on computers.)Overall, it’s been a useful book for learning the basic of the subject, as well as learning a new programming language.

⭐This was my first foray into the field of astrodynamics, and I’m glad I started with this.It covers the basics of orbital mechanics such as the 2-body and n-body problems, dealing with perturbations and changing orbits. The book isn’t just technical information, and includes a significant amount of context for the equations and theory, with the author giving relevant names, dates and history which keeps it from feeling dry.It refers to itself as a resource for teachers, but I’ve found using it as a self-learning tool works just fine.In fact, unless I knew otherwise I would think that it was written specifically for this purpose.When you eventually get around to the equations each chapter, it feels like you’ve been building up to it for the last couple of minutes of reading which is quite encouraging considering the difficulty of many of them.The diagrams are generally high-quality and easy to read but the typesetting for the maths is not perfect, and many variables look weird and distracting.The book also mostly uses Imperial units as it was initially published in the US in the 70’s, which is a real shame as everyone uses SI units nowadays.Overall, I’d recommend this text because of its low price and reasonable clarity, despite the problems I’ve outlined.

⭐Good book, useful information and interesting to read but the imperial units are a bit annoying. It is unusual for scientifici books these days to use imperial units, SI units are used in most places, but as this boook is quite old and by american authors it’s not so surprising to find it using imperial units. Fortunately the mathematics is the same in SI, metric or imperial, only the constants change.

⭐I’m only a chapter into the book, but the authors certainly have a way with words and making the content interesting and understandable — both highly important qualities in a book. Aesthetically, though, the book leaves a little bit to be desired. This complaint is actually what has caused me to write a (brief) review so early into my reading it.The big problem is the typesetting of the mathematics. If ever you’ve seen a modern maths text, or a historic classic, you’ll know that the layout of the maths is a huge issue, and that it’s usually very well done: they’ll use LaTeX mostly, and even if they don’t, the typesetting isn’t a distracting. In this book, though, for me, it is. There are very misaligned equations, messed up fractions, text that should be on a separate line below the equation actual is before the equation or immediately after it on the same line.These grievances may be for only a small subset of people that care about the design of a book, but I think they’re worth noting.That said, it’s not going to stop me from reading the book, but it will be in the back of my mind that this could’ve been done much better with only little effort.

⭐A great book, very informative and covers quite a lot. Unfortunately though it uses imperial measurements, which makes the calculations much more awkward to do if you aren’t very familiar with the imperial system.

⭐The are not too many books that cover this subject matter – and none at this low price. This book was first published many years ago and appears to be a reprint. One downside of this is the layout and font of the formulas is a little confusing – aside from that first rate book.

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