Here it is, in all its glory, which I finally got working with the helpful feedback of this forum. :-) Now the orbit trajectories seem more legitimate and give circles, ellipses, etc. It took a bit of figuring out but got there in the end.

http://files.kiwiheretic.com/science/orbits2.html
Of course, nothing is drawn to scale in this simulation, but it does now give a real world example, namely the moon and earth, of orbit trajectories.

I used the Euler method in the end any errors it produces seem to be less than a few pixels wide for any reasonable step size as the orbits now close back on themselves after a complete circuit.

You can alter the angular velocity, the radial velocity and earth moon distance and watch the trajectory path change.

My interest in all of this was inspired by the Juno mission as I noticed that as Juno entered Jupiter's orbit it had to fire its rockets for half an hour during insertion. This computer model doesn't quite go that far but hopefully gives me a basis for working out one in that direction. I'm basically trying to understand how critical that lengthy rocket burn was to the whole insertion endeavour.

Anyway, if you spot any errors in my computer model let me know. I will probably need to replace Euler method something more like the Leap frog integrator if its going to project forward in time very far, especially if I start to look at more complex three or four body systems.