I am searching for a math-accurate book on this subject, in particular for this topics:
$n$-body problem, getting more detailed when $n=2$.
Efeméride calculation.
Orbit determination.
- Perturbation theory.
I am a math student and this is the only physics-related course in my career so I need to read something really basic.
If you are just starting I recommend checking out Pollard's mathematical introduction to celestial mechanics and Szebehely's adventures in celestial mechanics.
Szebeheley's also has a detailed list of references. Also for Szebeheley's I think the first edition is better and the second edition got too long.