Ok... the first subject you will have to be competent with is spherical trigonometry, then classical (newtonian) orbits. The classic texts are
Spherical Trigonometry by Smart.
Orbital Mechanics by A.E. Roy
You will have to reach the point where you are able with no more than a scientific calculator to confidently and accurately predict and calculate the circumstances for a solar eclipse and get results in agreement with the methods described in the book by Jan Meeus for calculating ephemerides - without using Meeus' book first (which is cheating).
The next will be thermodynamics, statistical mechanics and requiring a solid foundation in differential equations, a solid basis in vector calculus and tensors if you're going into the physics of stellar interiors.
Then gravitation and relativity theory... the standard text is Gravitation by Misner Thorne and Wheeler
http://www.amazon.com/s/ref=nb_ss_b?...heeler&x=0&y=0
Basically this goes beyond the stuff taught in tertiary applied maths courses, and then some.