trajectory of objects in imperfect conditions.
I am familiar with standard distance-time models for paths of projectiles in perfect conditions, ie, where the curvature doesn't play a role, and where gravity is constant no matter the height. My question is what if you launch a projectile so high that the curvature of earth plays a role, and gravity varies as you increase and decrease height, is there and way to model it's motion, say a distance to surface-time equation? It would probably be similar to basic ones like s(t)=.5at^2+v*t, but since the acceleration changes over time it becomes difficult. It seems the acceleration at any point would be (Fg-Fc)/m (force of gravity minus force centripital, divided my mass), but then you get distance in the equation twice... Also, since (mv^2)/r = Fc how would you know the tangential velocity? Do equations already exist for this?