Euler Celestial Analysis: Introduction to Spacecraft Orbit Mechanics

Let me begin with a confession. I read this book months ago and I was stuck on how to write a review. Why? Because this book is really two books in one and I wanted to like both of them. The first book is a tribute to Leonard Euler, perhaps the greatest mathematician ever to live. The second part is an introduction to celestial mechanics, which is a topic Euler pursued with great vigor and success. You might think these two parts would go well together and in the hands of another author that would be true. In this case I am sorry to say that these two parts read as if they were written by two different people.

The first part of the book is, indeed, a lovely tribute to Euler. The author tells us eleven fun facts about him presented before the table of contents. She goes on to discuss the work Euler did in celestial mechanics, which should have been a treat for any reader. Unfortunately, this part of the book is riddled with typing errors, poor editing, and poor writing. While the topic is more than intriguing, this part of the book is difficult to read. If you can tolerate the prose, however, you will find interesting facts and content worthy of a book. For example, the section about tides on Earth due to the gravitation attraction of the moon was lovely. It was, more or less, clear and lucid.

The anecdotes from Euler’s life and struggles were illuminating. I enjoyed learning of how Euler lived and worked. The discussion of the three-body problem is classical material that anyone reading the book would enjoy. The explanation lacked details, however. For example, there is a wonderful picture of Euler’s four body problem but there is no explanation of what it shows.

There is one other (I have to say) irritating aspect of the book that is difficult to accept. The author peppers her work with quotes either from Euler and others. However, she often does not translate the quotes. Some quotes are in French, some Latin, and some German, and many are simply left in their original tongue. It would have been wonderful if the author translated these for the reader. A quick turn to Google translate would have done the trick.

It’s clear the author is infatuated with Euler and wants to show us that, but she should have used a good editor and critic for her work.

The second part of the book (Chapter 9), however, is the almost complete opposite. The prose is clear, lucid, well-written and a joy to read. Anyone who wants an excellent primer on orbital mechanics should read this part. The author takes you through Newton’s laws in three space, and derives the equations of motion. The writing is clear and without errors. She shows you how to work with the equations and even provides worked examples in details and numbers so you can see how to work with the equations. The figures are well drawn and labeled so the reader can easily understand them. I thought the derivations flowed smoothly in a step by step manner that guided the reader to an easy understanding of what would otherwise have been complex. She even provides a section on orbital maneuvers to show the reader how the equations are used for space flight.

This section is excellent.

I cannot whole-heartedly recommend this book but I think if you allow for the poor editing and the other stumbling blocks, if you can see past the rhetorical hurdles, you will enjoy the book and feel a warmth toward the greatest mathematician that this author obviously feels as well.

David S. Mazel is a practicing engineer in Washington, DC. He welcomes your thoughts and feedback. He can be reached at mazeld at gmail dot com.