Using both analytical and computational methods, we modeled an object's orbit around a black hole using Newtonian orbits, using special relativistic orbits and finally using general relativistic orbits. We know that when an object orbits around a black hole, there are certain velocities and radii where the object will no longer orbit and fall into the black hole, in a correct orbit model we should expect to see this feature. This distinctive feature is not captured by our Newtonian model. With special relativity, the feature appears, however, special relativity contains disparities that do not correctly model the effect of gravity. With general relativity, the feature is seen and the disparities from special relativity are no longer apparent. The general relativistic model correctly matches our predictions of the orbit around a black hole, the object either falls into, is bounded by, or is unbounded by the black hole, the model also contains a space where the physics starts to break down, inside the event horizon.