I have not looked at your code, but isn't it true that the *whole* saturnian 
system is tilted? I am almost sure the problem comes from the order in which 
you do the transformations. What I mean is that when applying the tilt, this 
should be done to a union of Saturn + rings + satellite. So, you have first 
to make your satellite orbit around  the planet without the tilt (and at the 
origin), and only at the end tilt the complete saturnian system (and 
translate it where it has to go). That way you are sure the satellite 
remains in its correct orbit.

Thomas

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