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1. Jul 22, 2016

### Matter_Matters

Hey guys, looking to get some advice on satellite navigation. Can anyone recommend a nice text book covering Newton, Kepler, Lagrange etc and their contributions to orbital motion. Also any textbooks on MATLAB or Maple examples of orbits - relativistic or Newtonian it doesn't matter. Not put off with Tensor's or any differential geometry so graduate level would be ideal.

2. Jul 23, 2016

### Staff: Mentor

I'm going to guess that you haven't received any responses yet because your question is a bit confusing. When I see "Satellite Navigation" I think "GPS", but then you talk about orbital motion, which doesn't seem to have much to do with that. Can you clarify? I don't think I'd be much more help than google, so I'll also just ask: have you looked for an introductory Newtonian physics textbook? Or an astronomy textbook?

3. Jul 23, 2016

### Matter_Matters

Thanks for the reply. I agree it is confusing. The end result is definitely to understand satellite motion ie the GPS and the relativistic effects. However, what I was after was a book that dealt solely with celestial/artificial satellites mechanics and presented the entire subject. I've taken plenty of Mechanics classes etc so I'm not after an introductory mechanics book. I want a book that goes beyond the simple central force problem and also attempts some programming of the results. Celestial mechanics is obviously a dying subject due to people being more interested in curved space times and the deepest secrets of black holes but it is extremely important for people trying to understand satellite motion and it's hard to find a proper treatment of the subject that is mathematically sophisticated. The books I've found are terrible to say the least. Anyways all help is appreciated.

4. Jul 23, 2016

### mpresic

Colorado -Boulder has at least two courses devoted to satellite motion. Many other schools courses with titles such as: Orbital dynamics, or satellite orbit determination. I think for example George Born has a textbook on it. Or maybe you can look at class notes for such courses. I have friends that took courses and are currently expert in satellite orbit determination, and if as you say the books are terrible, perhaps they did learn from class notes. I cannot say.
The books that treat satellite orbit determination are heavy on optimal estimation, least squares and kalman filtering. This is unavoidable.

I do not think celestial dynamics is dead, just because we have the general theory of relativity. I believe (although I have not looked myself) that you can find recent journal articles in celestial mechanics without reference to curved space time.

5. Jul 24, 2016

If you want a good, practical, yet remarkably inexpensive book on the topic, pick up a copy of Fundamentals of Astrodynamics by Bate, Mueller and White. It's a softcover priced around $17.00. It covers the classical theory and methods. 6. Jul 24, 2016 ### D H Staff Emeritus And if you want a very good (not great), extremely practical, but definitely more expensive (in some cases, a whole lot more expensive) pick up a copy of Fundamentals of Astrodynamics and Applications by David Vallado et al. The softcover price for the third edition is well over$200 (used). The fourth edition is much more affordable, only \$77 or so (new). Vallado is a much better and much more thorough reference than is Bate, Mueller and White. But you pay the price.

7. Jul 25, 2016

### Matter_Matters

That's great, thank you I'll check if the university has them. Would you know which direction to point me if I wanted to consider particle orbits using Keplers laws and then a comparison for Schwarzschild geometry using MATLAB?

8. Jul 25, 2016

### Staff: Mentor

Amazon will have the BMW book.

I'm not terribly familiar with MATLAB myself; I tend to use MathCAD when tinkering. But it seems to me that you'll want to search for information regarding solving differential equations, and in particular, numerical integration methods. There are numerous integrators that can be used to integrate orbits. You may find that MATLAB has a built-in library of suitable functions. Look at the literature to see what's what.

In the past I've implemented simple Verlet integrators for orbit simulations, and an RKF7 (Runge-Kutta-Fehlberg) for precision work simulating a spacecraft gravity assist maneuver. I've done these using MathCAD, a basic programming language, and even Excel macros.