Reddit reviews Fundamentals of Astrodynamics and Applications

https://www.amazon.com/Fundamentals-Astrodynamics-Applications-David-Vallado/dp/1881883140

The most thorough astrodynamics book I've found.

This book is very good at explaining most everything, from the basics to n-body motion to control theory. It is written from the perspective of numerical analysis but also has analytical formulae.

I don't know if you're affiliated with a university, but see if you can get a hold of this book: https://www.amazon.com/Fundamentals-Astrodynamics-Applications-David-Vallado/dp/1881883140 . There's a section on angles only orbital determination using methods developed by Gauss and Laplace including the actual algorithms.

The 6 elements you mentioned are the Keplarian orbital elements. The reason you need six is that in order to describe an orbit fully, you need a position and a velocity. Since we live in 3D space, position and velocity vectors have three elements. Making for a total of six. The Keplarian elements are just a different way of expressing a position and a velocity.

I'm still a little confused on what exactly you are doing. Is this for a story? In reality, the way this would work is that if you found a comet you believed to be headed for Earth, you would share its position in the sky with other astronomers. The only information you would need to share is the Ra and Dec on the sky. Then other astronomers would verify its orbital elements independent of your calculations. This way your results could be replicated and corroborated and thus make them more likely to be true. You actually wouldn't want to share your specific orbit calculations as that might prime the other scientists to come to the same conclusions as you.

David Vallado's book is a great resource and a good start!

http://www.amazon.com/Fundamentals-Astrodynamics-Applications-David-Vallado/dp/1881883140

I love SMAD for spacecraft design! My go-to for orbits stuff (my professional specialty) is "orbital mechanics for engineering students" (http://www.amazon.com/gp/aw/d/0080977472?pc_redir=1396560153&robot_redir=1$ and the next one is "fundamentals of astrodynamics and applications" (http://www.amazon.com/gp/aw/d/1881883140?pc_redir=1396676486&robot_redir=1).