While Newton’s law of gravity suffices for travelling nearby a planetary body, massive objects such as black holes require the more advanced theory of general relativity. To successfully fly a rocket in the vicinity of such an object, a first step is the description of test particle trajectories. In this report, the equations of motion for test particles affected by external forces are derived and used for simulations on a range of examples within the framework of general relativity. An application for these equations is found in the force required to counteract gravity, regardless of any non-radial motion around the black hole. Then, the equations of motion for a rocket test particle, which accelerates by expelling mass, are formulated for radial motion and used to find optimal mass conserving radial trajectories.