How to animate satellite positions with time and velocity dependencies

I am trying to create a program that will model the trajectory of a satellite as it orbits (or not, if the trajectory is a hyperbola) the Earth. I have already written a program using universal variable formulation that takes in initial position and velocity vectors and change in time, and returns the new position and velocity vectors at that time. I've created a program that will plot the trajectory of the satellite. However, I am unsure of how to create an animation of the satellite around the Earth that moves with accurate velocity-and-time-dependencies around the orbit. In other words, an animation that accurately depicts a satellite as it orbits the Earth, not just an animation that depicts the trace of the orbit that the satellite takes each time. Any help would be greatly appreciated.