General equation of motion with gravitational field

[Jhenrique]

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)?

* Illustration:

 

[Matterwave]

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).

See here: http://en.wikipedia.org/wiki/Kepler_problem