To develop terminology and understanding of the physical/mathematical problems you could look into the books of Jean Meeus. "Astronomical Algorithms" contains, ...well, exactly that: small recipes to solve problems in positional astronomy or calculate ephemerides. Check Willman Bell publishers for the english version of his books.

I liked "Celestial Mechanics" by Laurence Taff, but it's calculus-heavy which is nice if you're interested in the mathematical background and want to see some practical calculation examples.

Somewhere in the middle between these books is "Astronomical Methods and Calculations" by Acker and Jaschek. The exercises and solutions in this book come very close to the example you give.

Apologies for not putting links to the books but just google for author/title. Or check your local library.