We’re working on a battleships/defcon style missile game. I’ve used parabola before to determine a missile trajectory, and I’ve used inverse kinematics to ensure the missile would follow the correct path. Both of these techniques I’ve used in a flat-earth type world, a world with a constant gravity.

I want to ensure that, given a spherical-earth, a missile will begin it’s trajectory at a known vector on the surface of the sphere, and end it’s trajectory at a known destination vector on the surface of the sphere.

I’ve thought about using a polar co-ordinate system, but I’m treading water at the moment.

Has anyone encountered a similar problem? Or can anyone point me in the right direction?