Ok I am not exactly sure what subject this goes under as I can't find a good way of calculating it in my calc book and racked my brain for other methods, but I am stumped. Ok basically here is the problem.

I know my position in space, any coordinate system will do. I am inside of a sphere that has radius r. Knowing my position and a vector pointing at a known angle, I need to figure out where the vector and the sphere intersect.

That seems a little convoluted, so I will try to explain the practical application.

I know my position on earth (latitude, longitude, altitude).

I know exactly where the sun is with respect to me (Zenith angle, Azimuth angle)

If I look directly at the sun (DO NOT ATTEMPT), where does the vector I am looking at intersect with a sphere that has a radius of 1000 meters greater than my current altitude.

Keep in mind that the earth curves, so a simple trig calculation doesn't do the trick.

It seems so simple, but I just can not figure out how to solve it.

If anyone could point me toward a theorem or technique or law I would appreciate it.