Basically, at this point, you are dealing with orbital motion. Kepler's Laws will give you the basic trajectory. From there, you'll have to look into more detailed orbital mechanics for things like time of flight, velocities at each point, and so on.
Of course, in real world, if velocity is high enough for these things to matter, your bigger concern will be drag. It is difficult enough to account for drag with level ground and constant gravity. There are methods, though. Orbital mechanics with drag pretty much have to be solved with numerical methods. If gravity changing with height is a factor, density changing with altitude will certainly be an even bigger factor. That means having a pretty good barometric model on top of which you'll be running your simulation. It gets tricky.