Satelite Tracking: Solving My Career Advancment Puzzle

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jstrz13phys
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I am completely lost. I am taking a course in Space Systems Engineering for Career Advancment. I have been asked to predict (without a program/software) when I will be able to see a satelite from a given lat, long from earth. I know the altitude is 350KM and I also know the inclination angle. It is in a circular orbit so I know what the average speed is. What I don't know is where to go next. Everytime I start I get lost - how do I handle spinnig earth, the woble the Earth has from moon, etc. I am not looking for the solution to be given to me but hopefully some websites, books etc that I can read and learn to understand the procedure. Thanks
 
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Amsat is the amateur satelite spotters organistation http://www.amsat.org/ has a lot of useful articles and formulae.

Most of the secondary effects you mention have a very small contribution to the apparent position of the satelite - I wouldn't worry about them yet.
The important thing is to get a good intuitive picture of what inclination / declination / right ascension / alt-az mean. A small toy globe can really help!