You see the green dot next to the timestep? If it goes red you're bound to get flying things.
Alot of the moons take <5 days to orbit, so if you're running 30 fps, and it's taking 1 day to orbit, you're getting 30 calculations for the circle running 1 second = 1 day, that's not even a circle, that's a polygon. And you're getting a decagon for 1 sec = 3 days. I'm afraid you can't do the simulations you want to do.
There is a program I know that will allow you to go faster and it will work (it does all the calculations but doesn't show the frames until it's gotten far enough), and it has a 15 day trial... But it's over $60.