Travel to the Stars with a Book

Saturday was a fun/productive/incredible day. There were mint juleps, a book index that directed me to two pages that were not in the book, and many unanswered questions about fast Fourier transforms (FFT).

Early in the day I was trying to find an idea for my MATLAB class project. After looking through my linear algebra textbooks unsucessifully, I thought of one more book from my collection that might have something inspiring for a project in it.

The book was Fundamentals of Astrodynamics. I originally bought it back in the summer of 2006 at the Barnes & Noble on Bay Street. From the clearance table, this Dover book cost me less than $4. First published in 1971, it is a textbook written by professors Roger R. Bate, Donald D. Mueller, and Jerry E. White at the Air Force Academy to teach about the motion of man-made objects in space.

The book had an appendix with four different programing projects. They were all interesting and I was excited to discover them. Since the projects used the principles discussed in the book, I would have an excellent reference in writing the program. I picked one of the projects and started writing my proposal.

To paraphrase and condense the book's project:

Given the position and velocity of an object in the atmosphere, determine where it will impact the Earth. If the object will not hit, give its point of closest approach. Also determine the time to impact/closest approach, give the type of orbit (circular, rectilinear, elliptical, parabolic, or hyperbolic), and total change in true anomaly from initial observation to impact/closest approach.

Then I started looking through the book to learn what I needed to know to complete the project. The project deadline was a month away, so I started at the beginning of the text. I read carefully and followed all the math from one line to the next. I worked on the examples and did the problems as they came up.

By the time I went to bed I had read all of the first chapter. I had gone through 44 pages of a textbook and understood very nearly every single line, example, and the first few problems at the end. More surprising than that, it all happened in one day.

After my reading I came to a conclusion, astrodynamics is amazing. Starting with Newtons's Laws of Gravity and using them to confirm Kepler's Laws, the book derives how to calculate the orbits of satellites.

Going through the book, I solved a lot of interesting problems and learned some great things. All of the examples used feet and miles. Not just any miles, but nautical miles. In case you are wondering, 1 n.mi.(or NM) = 6076.115 feet (approximate value). For one of the problems, my satellite orbit numbers did not make sense. Then I realized my mistake; I forget about the Earth and the thousands of miles it added to calculations. In case it comes up, the Earth has a mean radius of 3443.92 NM (approx. again).

The book is available directly from Dover Publications. However, the careful searcher will find a preview in Google Books. When I was looking at the preview, I discovered there is a limit to the number of pages of the book that can be viewed, even if almost any page in the book can be chosen for this viewing.

I plan on going through most of the book and doing all of the projects at the end.