I was studying the equations of free fall and of launch when I realize that those equations are spetial case of a object in motion through of a gravitational field. So exist some general equation that describe the motion (the trajetory*) of the object through of the field (using initial values like moment, velocity, position, direction, mass, gravity, distance, etc)?
There certainly are...this is just the central force problem (actually it's the Kepler problem) in Newtonian mechanics. You need 12 initial value data, 2 initial positions, and 2 initial velocities (each of which have 3 components).
