FLSpacecraft

The FLSpacecraft application uses physical laws (classical mechanics) to simulate a spacecraft entering and interacting with the Earth-Moon system. The craft is roughly the size and mass of the Apollo Command and Service modules combined, with the ability to fire the Service Module's main engine in short bursts to accelerate and decelerate along the direction of travel.

Note that the simulation takes a lot of computing power, however since the app is free you can just download it and see how it goes on your iPhone or iPad. Chances are you will be fine, however if it bogs down you can try moving the speed slider at the top of the window to the "Faster" setting (which will reduce the number of recalculations for a given orbit).